[{"_1":2,"_22936":-5,"_22937":-5},"loaderData",{"_3":4,"_12":13},"root",{"_5":6,"_7":-5,"_8":9},"isAuthenticated",false,"user","features",{"_10":11},"billing",true,"routes/functions.$functionId",{"_14":15,"_33":34,"_2194":2195},"function",{"_16":17,"_18":19,"_20":21,"_22":21,"_23":24,"_29":30,"_31":32},"name","eigen.dense.destroy","signature","eigen.dense.destroy(A)","summary","Free the memory associated with a matrix.","description","params",[25],{"_16":26,"_22":27,"_28":6},"A","- Matrix handle to destroy","optional","returns","void","examples",[],"package",{"_35":36,"_16":37,"_22":38,"_39":40,"_41":42,"_43":44,"_45":46},"id","eigen-generated","Linear Algebra (Eigen)","Eigen linear algebra library for matrix operations.","tier","free","icon","📐","namespace","eigen","functions",[47,57,64,71,79,86,97,105,111,127,139,149,157,165,173,182,193,203,211,218,227,235,246,255,263,271,278,285,292,301,308,317,326,335,345,352,363,372,380,387,395,15,402,415,423,433,441,448,460,468,475,482,489,497,508,518,527,537,545,555,565,572,581,589,597,606,614,623,632,640,650,665,675,683,691,699,706,713,720,727,734,741,748,755,762,769,776,783,790,800,807,815,824,831,839,847,855,863,871,879,887,895,903,911,918,924,932,939,948,956,964,975,986,999,1006,1016,1032,1039,1048,1056,1065,1075,1083,1090,1099,1107,1116,1124,1135,1145,1155,1163,1175,1186,1194,1203,1212,1221,1230,1240,1247,1256,1264,1272,1288,1299,1310,1319,1328,1335,1342,1354,1367,1378,1388,1396,1404,1414,1426,1438,1445,1452,1469,1479,1499,1508,1516,1525,1535,1543,1556,1564,1574,1583,1595,1607,1617,1627,1634,1640,1647,1654,1665,1674,1683,1691,1699,1706,1715,1727,1736,1746,1755,1764,1772,1781,1789,1796,1805,1814,1823,1831,1839,1846,1855,1862,1871,1878,1889,1896,1903,1915,1925,1933,1942,1951,1958,1965,1973,1982,1989,2000,2008,2018,2026,2035,2043,2051,2058,2065,2072,2079,2087,2095,2102,2109,2116,2125,2133,2140,2147,2153,2159,2165,2171,2178,2186],{"_16":48,"_18":49,"_20":50,"_22":51,"_23":52,"_29":30,"_31":56},"eigen.core.configureEigen","eigen.core.configureEigen(config)","Configure the Eigen WASM module loader.\r","Configure the Eigen WASM module loader.\r\n\r\nMust be called before loadEigenModule() if custom configuration is needed.",[53],{"_16":54,"_22":55,"_28":6},"config","- Configuration options",[],{"_16":58,"_18":59,"_20":60,"_22":60,"_23":61,"_29":62,"_31":63},"eigen.core.getEigenModule","eigen.core.getEigenModule()","Get the loaded Eigen WASM module.",[],"EigenModule",[],{"_16":65,"_18":66,"_20":67,"_22":67,"_23":68,"_29":69,"_31":70},"eigen.core.isEigenLoaded","eigen.core.isEigenLoaded()","Check if the Eigen WASM module has been loaded.",[],"boolean",[],{"_16":72,"_18":73,"_20":74,"_22":75,"_23":76,"_29":77,"_31":78},"eigen.core.loadEigenModule","eigen.core.loadEigenModule()","Load and initialize the Eigen WASM module.\r","Load and initialize the Eigen WASM module.\r\n\r\nThis function is safe to call multiple times - the module is only loaded once\r\nand subsequent calls return the cached module.",[],"Promise",[],{"_16":80,"_18":81,"_20":82,"_22":83,"_23":84,"_29":30,"_31":85},"eigen.core.resetEigenModule","eigen.core.resetEigenModule()","Reset the Eigen WASM module state.\r","Reset the Eigen WASM module state.\r\n\r\nThis clears the cached module and allows reconfiguration.\r\nUseful for testing or when module needs to be reloaded.",[],[],{"_16":87,"_18":88,"_20":89,"_22":90,"_23":91,"_29":95,"_31":96},"eigen.core.allocateFloat64Array","eigen.core.allocateFloat64Array(size)","Eigen WASM Memory Management Utilities\r","Eigen WASM Memory Management Utilities\r\n\r\nHelper functions for managing memory transfers between JavaScript and WASM.\r\nEigen uses column-major storage order (Fortran-style), same as LAPACK.",[92],{"_16":93,"_22":94,"_28":6},"size","- Number of float64 elements to allocate","number",[],{"_16":98,"_18":99,"_20":100,"_22":100,"_23":101,"_29":95,"_31":104},"eigen.core.allocateInt32Array","eigen.core.allocateInt32Array(size)","Allocate memory for an Int32Array on the WASM heap.",[102],{"_16":93,"_22":103,"_28":6},"- Number of int32 elements to allocate",[],{"_16":106,"_18":107,"_20":108,"_22":108,"_23":109,"_29":95,"_31":110},"eigen.core.allocatePointer","eigen.core.allocatePointer()","Allocate memory for a pointer (used for output parameters).",[],[],{"_16":112,"_18":113,"_20":114,"_22":114,"_23":115,"_29":125,"_31":126},"eigen.core.columnMajorToRowMajor","eigen.core.columnMajorToRowMajor(data, rows, cols)","Convert a column-major Float64Array to 2D row-major array.",[116,119,122],{"_16":117,"_22":118,"_28":6},"data","- Column-major data",{"_16":120,"_22":121,"_28":6},"rows","- Number of rows",{"_16":123,"_22":124,"_28":6},"cols","- Number of columns","number[][]",[],{"_16":128,"_18":129,"_20":130,"_22":130,"_23":131,"_29":137,"_31":138},"eigen.core.copyFromWasm","eigen.core.copyFromWasm(ptr, size)","Copy data from WASM heap memory to a new Float64Array.",[132,135],{"_16":133,"_22":134,"_28":6},"ptr","- Pointer to source data in WASM memory",{"_16":93,"_22":136,"_28":6},"- Number of float64 elements to copy","Float64Array",[],{"_16":140,"_18":141,"_20":142,"_22":142,"_23":143,"_29":147,"_31":148},"eigen.core.copyInt32FromWasm","eigen.core.copyInt32FromWasm(ptr, size)","Copy Int32 data from WASM heap memory to a new Int32Array.",[144,145],{"_16":133,"_22":134,"_28":6},{"_16":93,"_22":146,"_28":6},"- Number of int32 elements to copy","Int32Array",[],{"_16":150,"_18":151,"_20":152,"_22":152,"_23":153,"_29":95,"_31":156},"eigen.core.copyInt32ToWasm","eigen.core.copyInt32ToWasm(data)","Copy Int32 data to WASM heap memory.",[154],{"_16":117,"_22":155,"_28":6},"- Source data (Int32Array or number[])",[],{"_16":158,"_18":159,"_20":160,"_22":160,"_23":161,"_29":95,"_31":164},"eigen.core.copyToWasm","eigen.core.copyToWasm(data)","Copy a JavaScript array to WASM heap memory.",[162],{"_16":117,"_22":163,"_28":6},"- Source data (Float64Array or number[])",[],{"_16":166,"_18":167,"_20":168,"_22":168,"_23":169,"_29":30,"_31":172},"eigen.core.freeMemory","eigen.core.freeMemory(ptr)","Free memory on the WASM heap.",[170],{"_16":133,"_22":171,"_28":6},"- Pointer to free (obtained from allocate* functions or _malloc)",[],{"_16":174,"_18":175,"_20":176,"_22":176,"_23":177,"_29":95,"_31":181},"eigen.core.readPointer","eigen.core.readPointer(ptrPtr)","Read a pointer value from WASM memory.",[178],{"_16":179,"_22":180,"_28":6},"ptrPtr","- Pointer to the pointer to read",[],{"_16":183,"_18":184,"_20":185,"_22":186,"_23":187,"_29":191,"_31":192},"eigen.core.rowMajorToColumnMajor","eigen.core.rowMajorToColumnMajor(arr2d)","Convert a 2D row-major array to column-major Float64Array.\r","Convert a 2D row-major array to column-major Float64Array.\r\n\r\nEigen uses column-major storage (like Fortran/MATLAB), while JavaScript\r\ntypically uses row-major ordering. This function converts between them.",[188],{"_16":189,"_22":190,"_28":6},"arr2d","- 2D array in row-major order (arr[row][col])","{\r\n data: Float64Array;\r\n rows: number;\r\n cols: number;\r\n}",[],{"_16":194,"_18":195,"_20":196,"_22":196,"_23":197,"_29":137,"_31":202},"eigen.core.viewWasmMemory","eigen.core.viewWasmMemory(ptr, size)","Create a view into WASM heap memory without copying.",[198,200],{"_16":133,"_22":199,"_28":6},"- Pointer to data in WASM memory",{"_16":93,"_22":201,"_28":6},"- Number of float64 elements",[],{"_16":204,"_18":205,"_20":206,"_22":207,"_23":208,"_29":209,"_31":210},"eigen.core.getEigenWrappers","eigen.core.getEigenWrappers()","Get type-safe wrapped functions for all Eigen WASM operations.\r","Get type-safe wrapped functions for all Eigen WASM operations.\r\n\r\nThe wrappers are cached after first creation for performance.",[],"EigenWrappers",[],{"_16":212,"_18":213,"_20":214,"_22":215,"_23":216,"_29":30,"_31":217},"eigen.core.resetWrappers","eigen.core.resetWrappers()","Reset the cached wrappers.\r","Reset the cached wrappers.\r\n\r\nCalled internally when the module is reset.",[],[],{"_16":219,"_18":220,"_20":221,"_22":221,"_23":222,"_29":225,"_31":226},"eigen.decompositions.cholesky","eigen.decompositions.cholesky(A)","Compute Cholesky decomposition: A = LL^T",[223],{"_16":26,"_22":224,"_28":6},"- Symmetric positive-definite matrix","CholeskyResult",[],{"_16":228,"_18":229,"_20":230,"_22":230,"_23":231,"_29":69,"_31":234},"eigen.decompositions.isPositiveDefinite","eigen.decompositions.isPositiveDefinite(A)","Check if a matrix is positive-definite by attempting Cholesky decomposition.",[232],{"_16":26,"_22":233,"_28":6},"- Symmetric matrix",[],{"_16":236,"_18":237,"_20":238,"_22":238,"_23":239,"_29":69,"_31":245},"eigen.decompositions.isSymmetric","eigen.decompositions.isSymmetric(A, tol?)","Check if a matrix is symmetric within a tolerance.",[240,242],{"_16":26,"_22":241,"_28":6},"- Matrix to check",{"_16":243,"_22":244,"_28":11},"tol","- Tolerance for element comparison (default: 1e-10)",[],{"_16":247,"_18":248,"_20":249,"_22":249,"_23":250,"_29":253,"_31":254},"eigen.decompositions.eig","eigen.decompositions.eig(A)","Compute eigenvalue decomposition for general (non-symmetric) matrices.",[251],{"_16":26,"_22":252,"_28":6},"- Square matrix","EigResult",[],{"_16":256,"_18":257,"_20":258,"_22":258,"_23":259,"_29":261,"_31":262},"eigen.decompositions.eigSymmetric","eigen.decompositions.eigSymmetric(A)","Compute eigenvalue decomposition for symmetric matrices: A = V * D * V^T",[260],{"_16":26,"_22":233,"_28":6},"EigSymmetricResult",[],{"_16":264,"_18":265,"_20":266,"_22":266,"_23":267,"_29":269,"_31":270},"eigen.decompositions.eigvals","eigen.decompositions.eigvals(A)","Compute eigenvalues only for general matrices.",[268],{"_16":26,"_22":252,"_28":6},"{\r\n real: Float64Array;\r\n imag: Float64Array;\r\n}",[],{"_16":272,"_18":273,"_20":274,"_22":274,"_23":275,"_29":137,"_31":277},"eigen.decompositions.eigvalsSymmetric","eigen.decompositions.eigvalsSymmetric(A)","Compute eigenvalues only for symmetric matrices.",[276],{"_16":26,"_22":233,"_28":6},[],{"_16":279,"_18":280,"_20":281,"_22":281,"_23":282,"_29":69,"_31":284},"eigen.decompositions.hasNegativeEigenvalues","eigen.decompositions.hasNegativeEigenvalues(A)","Check if all eigenvalues have negative real parts.",[283],{"_16":26,"_22":252,"_28":6},[],{"_16":286,"_18":287,"_20":288,"_22":288,"_23":289,"_29":69,"_31":291},"eigen.decompositions.hasPositiveEigenvalues","eigen.decompositions.hasPositiveEigenvalues(A)","Check if all eigenvalues have positive real parts.",[290],{"_16":26,"_22":252,"_28":6},[],{"_16":293,"_18":294,"_20":295,"_22":295,"_23":296,"_29":69,"_31":300},"eigen.decompositions.hasRealEigenvalues","eigen.decompositions.hasRealEigenvalues(A, tol?)","Check if all eigenvalues are real (within tolerance).",[297,298],{"_16":26,"_22":252,"_28":6},{"_16":243,"_22":299,"_28":11},"- Tolerance for imaginary parts (default: 1e-10)",[],{"_16":302,"_18":303,"_20":304,"_22":304,"_23":305,"_29":95,"_31":307},"eigen.decompositions.spectralRadius","eigen.decompositions.spectralRadius(A)","Compute the spectral radius of a matrix.",[306],{"_16":26,"_22":252,"_28":6},[],{"_16":309,"_18":310,"_20":311,"_22":311,"_23":312,"_29":69,"_31":316},"eigen.decompositions.isSingular","eigen.decompositions.isSingular(A, tol?)","Check if a matrix is singular (has zero or near-zero determinant).",[313,314],{"_16":26,"_22":252,"_28":6},{"_16":243,"_22":315,"_28":11},"- Tolerance for zero comparison (default: 1e-14)",[],{"_16":318,"_18":319,"_20":320,"_22":320,"_23":321,"_29":324,"_31":325},"eigen.decompositions.lu","eigen.decompositions.lu(A)","Compute LU decomposition with partial pivoting: PA = LU",[322],{"_16":26,"_22":323,"_28":6},"- Square matrix to decompose","LUResult",[],{"_16":327,"_18":328,"_20":329,"_22":329,"_23":330,"_29":333,"_31":334},"eigen.decompositions.qr","eigen.decompositions.qr(A)","Compute QR decomposition: A = QR",[331],{"_16":26,"_22":332,"_28":6},"- Matrix to decompose (m × n)","QRResult",[],{"_16":336,"_18":337,"_20":338,"_22":338,"_23":339,"_29":95,"_31":344},"eigen.decompositions.rankQR","eigen.decompositions.rankQR(A, tol?)","Compute the numerical rank of a matrix using QR decomposition.",[340,342],{"_16":26,"_22":341,"_28":6},"- Matrix",{"_16":243,"_22":343,"_28":11},"- Tolerance for zero diagonal elements (default: 1e-10)",[],{"_16":346,"_18":347,"_20":348,"_22":348,"_23":349,"_29":95,"_31":351},"eigen.decompositions.condSVD","eigen.decompositions.condSVD(A)","Compute the condition number of a matrix using SVD.",[350],{"_16":26,"_22":341,"_28":6},[],{"_16":353,"_18":354,"_20":355,"_22":355,"_23":356,"_29":361,"_31":362},"eigen.decompositions.pinv","eigen.decompositions.pinv(A, tol?)","Compute the Moore-Penrose pseudoinverse using SVD.",[357,359],{"_16":26,"_22":358,"_28":6},"- Matrix (m × n)",{"_16":243,"_22":360,"_28":11},"- Tolerance for zero singular values","MatrixHandle",[],{"_16":364,"_18":365,"_20":366,"_22":366,"_23":367,"_29":95,"_31":371},"eigen.decompositions.rankSVD","eigen.decompositions.rankSVD(A, tol?)","Compute the numerical rank of a matrix using SVD.",[368,369],{"_16":26,"_22":341,"_28":6},{"_16":243,"_22":370,"_28":11},"- Tolerance for zero singular values (default: max(m,n) * eps * s[0])",[],{"_16":373,"_18":374,"_20":375,"_22":375,"_23":376,"_29":378,"_31":379},"eigen.decompositions.svd","eigen.decompositions.svd(A)","Compute the Singular Value Decomposition: A = U * diag(S) * V^T",[377],{"_16":26,"_22":332,"_28":6},"SVDResult",[],{"_16":381,"_18":382,"_20":383,"_22":383,"_23":384,"_29":137,"_31":386},"eigen.decompositions.svdvals","eigen.decompositions.svdvals(A)","Compute only the singular values of a matrix.",[385],{"_16":26,"_22":358,"_28":6},[],{"_16":388,"_18":389,"_20":390,"_22":390,"_23":391,"_29":95,"_31":394},"eigen.dense.cols","eigen.dense.cols(A)","Get the number of columns in a matrix.",[392],{"_16":26,"_22":393,"_28":6},"- Matrix handle",[],{"_16":396,"_18":397,"_20":398,"_22":398,"_23":399,"_29":95,"_31":401},"eigen.dense.dataPtr","eigen.dense.dataPtr(A)","Get the raw data pointer for a matrix.",[400],{"_16":26,"_22":393,"_28":6},[],{"_16":403,"_18":404,"_20":405,"_22":405,"_23":406,"_29":95,"_31":414},"eigen.dense.get","eigen.dense.get(A, i, j)","Get a single element from a matrix.",[407,408,411],{"_16":26,"_22":393,"_28":6},{"_16":409,"_22":410,"_28":6},"i","- Row index (0-based)",{"_16":412,"_22":413,"_28":6},"j","- Column index (0-based)",[],{"_16":416,"_18":417,"_20":418,"_22":418,"_23":419,"_29":137,"_31":422},"eigen.dense.getCol","eigen.dense.getCol(A, j)","Get a column from a matrix as a Float64Array.",[420,421],{"_16":26,"_22":393,"_28":6},{"_16":412,"_22":413,"_28":6},[],{"_16":424,"_18":425,"_20":426,"_22":426,"_23":427,"_29":137,"_31":432},"eigen.dense.getDiag","eigen.dense.getDiag(A, k?)","Get the diagonal of a matrix as a Float64Array.",[428,429],{"_16":26,"_22":393,"_28":6},{"_16":430,"_22":431,"_28":11},"k","- Diagonal offset (0 = main diagonal, >0 = above, <0 = below)",[],{"_16":434,"_18":435,"_20":436,"_22":436,"_23":437,"_29":137,"_31":440},"eigen.dense.getRow","eigen.dense.getRow(A, i)","Get a row from a matrix as a Float64Array.",[438,439],{"_16":26,"_22":393,"_28":6},{"_16":409,"_22":410,"_28":6},[],{"_16":442,"_18":443,"_20":444,"_22":444,"_23":445,"_29":95,"_31":447},"eigen.dense.rows","eigen.dense.rows(A)","Get the number of rows in a matrix.",[446],{"_16":26,"_22":393,"_28":6},[],{"_16":449,"_18":450,"_20":451,"_22":451,"_23":452,"_29":30,"_31":459},"eigen.dense.set","eigen.dense.set(A, i, j, value)","Set a single element in a matrix.",[453,454,455,456],{"_16":26,"_22":393,"_28":6},{"_16":409,"_22":410,"_28":6},{"_16":412,"_22":413,"_28":6},{"_16":457,"_22":458,"_28":6},"value","- Value to set",[],{"_16":461,"_18":462,"_20":463,"_22":463,"_23":464,"_29":466,"_31":467},"eigen.dense.shape","eigen.dense.shape(A)","Get the shape of a matrix as [rows, cols].",[465],{"_16":26,"_22":393,"_28":6},"[number, number]",[],{"_16":469,"_18":470,"_20":471,"_22":471,"_23":472,"_29":95,"_31":474},"eigen.dense.size","eigen.dense.size(A)","Get the total number of elements in a matrix.",[473],{"_16":26,"_22":393,"_28":6},[],{"_16":476,"_18":477,"_20":478,"_22":478,"_23":479,"_29":137,"_31":481},"eigen.dense.toArray","eigen.dense.toArray(A)","Convert a matrix to a Float64Array (column-major order).",[480],{"_16":26,"_22":393,"_28":6},[],{"_16":483,"_18":484,"_20":485,"_22":485,"_23":486,"_29":125,"_31":488},"eigen.dense.toArray2D","eigen.dense.toArray2D(A)","Convert a matrix to a 2D JavaScript array (row-major order).",[487],{"_16":26,"_22":393,"_28":6},[],{"_16":490,"_18":491,"_20":492,"_22":493,"_23":494,"_29":361,"_31":496},"eigen.dense.abs","eigen.dense.abs(A)","Eigenwasm - High-level TypeScript API for Eigen Linear Algebra Library\r","Eigenwasm - High-level TypeScript API for Eigen Linear Algebra Library\r\n\r\nThis package provides TypeScript bindings for the Eigen C++ linear algebra library\r\ncompiled to WebAssembly. It offers both functional and object-oriented APIs for\r\ndense matrices, vectors, sparse matrices, decompositions, and linear solvers.",[495],{"_16":26,"_22":341,"_28":6},[],{"_16":498,"_18":499,"_20":500,"_22":500,"_23":501,"_29":361,"_31":507},"eigen.dense.add","eigen.dense.add(A, B)","Add two matrices: C = A + B",[502,504],{"_16":26,"_22":503,"_28":6},"- First matrix",{"_16":505,"_22":506,"_28":6},"B","- Second matrix (must have same dimensions as A)",[],{"_16":509,"_18":510,"_20":511,"_22":511,"_23":512,"_29":361,"_31":517},"eigen.dense.addScalar","eigen.dense.addScalar(A, scalar)","Add a scalar to all elements: C = A + scalar",[513,514],{"_16":26,"_22":341,"_28":6},{"_16":515,"_22":516,"_28":6},"scalar","- Scalar value to add",[],{"_16":519,"_18":520,"_20":521,"_22":521,"_23":522,"_29":361,"_31":526},"eigen.dense.divScalar","eigen.dense.divScalar(A, scalar)","Divide all elements by a scalar: C = A / scalar",[523,524],{"_16":26,"_22":341,"_28":6},{"_16":515,"_22":525,"_28":6},"- Scalar divisor",[],{"_16":528,"_18":529,"_20":530,"_22":530,"_23":531,"_29":361,"_31":536},"eigen.dense.elementDiv","eigen.dense.elementDiv(A, B)","Element-wise division: C = A ./ B",[532,534],{"_16":26,"_22":533,"_28":6},"- First matrix (numerator)",{"_16":505,"_22":535,"_28":6},"- Second matrix (denominator, must have same dimensions as A)",[],{"_16":538,"_18":539,"_20":540,"_22":540,"_23":541,"_29":361,"_31":544},"eigen.dense.elementMul","eigen.dense.elementMul(A, B)","Element-wise multiplication: C = A .* B",[542,543],{"_16":26,"_22":503,"_28":6},{"_16":505,"_22":506,"_28":6},[],{"_16":546,"_18":547,"_20":548,"_22":548,"_23":549,"_29":361,"_31":554},"eigen.dense.elementPow","eigen.dense.elementPow(A, p)","Compute the power of each element: C = A .^ p",[550,551],{"_16":26,"_22":341,"_28":6},{"_16":552,"_22":553,"_28":6},"p","- Power exponent",[],{"_16":556,"_18":557,"_20":558,"_22":558,"_23":559,"_29":361,"_31":564},"eigen.dense.mul","eigen.dense.mul(A, B)","Multiply two matrices: C = A * B",[560,562],{"_16":26,"_22":561,"_28":6},"- First matrix (m × k)",{"_16":505,"_22":563,"_28":6},"- Second matrix (k × n)",[],{"_16":566,"_18":567,"_20":568,"_22":568,"_23":569,"_29":361,"_31":571},"eigen.dense.neg","eigen.dense.neg(A)","Negate a matrix: C = -A",[570],{"_16":26,"_22":341,"_28":6},[],{"_16":573,"_18":574,"_20":575,"_22":575,"_23":576,"_29":361,"_31":580},"eigen.dense.scale","eigen.dense.scale(A, scalar)","Multiply a matrix by a scalar: C = A * scalar",[577,578],{"_16":26,"_22":341,"_28":6},{"_16":515,"_22":579,"_28":6},"- Scalar value",[],{"_16":582,"_18":583,"_20":584,"_22":584,"_23":585,"_29":361,"_31":588},"eigen.dense.sqrt","eigen.dense.sqrt(A)","Compute element-wise square root: C = sqrt(A)",[586],{"_16":26,"_22":587,"_28":6},"- Matrix (elements should be non-negative)",[],{"_16":590,"_18":591,"_20":592,"_22":592,"_23":593,"_29":361,"_31":596},"eigen.dense.sub","eigen.dense.sub(A, B)","Subtract two matrices: C = A - B",[594,595],{"_16":26,"_22":503,"_28":6},{"_16":505,"_22":506,"_28":6},[],{"_16":598,"_18":599,"_20":600,"_22":600,"_23":601,"_29":361,"_31":605},"eigen.dense.subScalar","eigen.dense.subScalar(A, scalar)","Subtract a scalar from all elements: C = A - scalar",[602,603],{"_16":26,"_22":341,"_28":6},{"_16":515,"_22":604,"_28":6},"- Scalar value to subtract",[],{"_16":607,"_18":608,"_20":609,"_22":609,"_23":610,"_29":361,"_31":613},"eigen.dense.clone","eigen.dense.clone(A)","Create a deep copy of a matrix.",[611],{"_16":26,"_22":612,"_28":6},"- Matrix handle to copy",[],{"_16":615,"_18":616,"_20":617,"_22":617,"_23":618,"_29":361,"_31":622},"eigen.dense.diag","eigen.dense.diag(values)","Create a diagonal matrix from a vector of diagonal values.",[619],{"_16":620,"_22":621,"_28":6},"values","- Values to place on the diagonal",[],{"_16":624,"_18":625,"_20":626,"_22":626,"_23":627,"_29":361,"_31":631},"eigen.dense.eye","eigen.dense.eye(n)","Create an identity matrix.",[628],{"_16":629,"_22":630,"_28":6},"n","- Size of the square matrix",[],{"_16":633,"_18":634,"_20":635,"_22":635,"_23":636,"_29":361,"_31":639},"eigen.dense.fromArray2D","eigen.dense.fromArray2D(arr2d)","Create a matrix from a 2D JavaScript array (row-major order).",[637],{"_16":189,"_22":638,"_28":6},"- 2D array where arr2d[i][j] is element at row i, column j",[],{"_16":641,"_18":642,"_20":643,"_22":643,"_23":644,"_29":361,"_31":649},"eigen.dense.full","eigen.dense.full(rows, cols, value)","Create a matrix filled with a constant value.",[645,646,647],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},{"_16":457,"_22":648,"_28":6},"- Value to fill the matrix with",[],{"_16":651,"_18":652,"_20":653,"_22":654,"_23":655,"_29":361,"_31":664},"eigen.dense.linspace","eigen.dense.linspace(start, end, n)","Create a matrix with linearly spaced values.\r","Create a matrix with linearly spaced values.\r\n\r\nCreates a row vector with `n` values linearly spaced between `start` and `end`.",[656,659,662],{"_16":657,"_22":658,"_28":6},"start","- Starting value",{"_16":660,"_22":661,"_28":6},"end","- Ending value (inclusive)",{"_16":629,"_22":663,"_28":6},"- Number of values",[],{"_16":666,"_18":667,"_20":668,"_22":668,"_23":669,"_29":361,"_31":674},"eigen.dense.matrix","eigen.dense.matrix(data, rows, cols)","Create a matrix from a Float64Array (column-major order).",[670,672,673],{"_16":117,"_22":671,"_28":6},"- Matrix data in column-major order",{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},[],{"_16":676,"_18":677,"_20":678,"_22":678,"_23":679,"_29":361,"_31":682},"eigen.dense.ones","eigen.dense.ones(rows, cols)","Create a matrix filled with ones.",[680,681],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},[],{"_16":684,"_18":685,"_20":686,"_22":686,"_23":687,"_29":361,"_31":690},"eigen.dense.random","eigen.dense.random(rows, cols)","Create a matrix with random values in the range [-1, 1].",[688,689],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},[],{"_16":692,"_18":693,"_20":694,"_22":694,"_23":695,"_29":361,"_31":698},"eigen.dense.zeros","eigen.dense.zeros(rows, cols)","Create a matrix filled with zeros.",[696,697],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},[],{"_16":700,"_18":701,"_20":702,"_22":702,"_23":703,"_29":69,"_31":705},"eigen.dense.allFinite","eigen.dense.allFinite(A)","Check if all matrix elements are finite (not NaN or Infinity).",[704],{"_16":26,"_22":341,"_28":6},[],{"_16":707,"_18":708,"_20":709,"_22":709,"_23":710,"_29":95,"_31":712},"eigen.dense.det","eigen.dense.det(A)","Compute the determinant of a square matrix.",[711],{"_16":26,"_22":252,"_28":6},[],{"_16":714,"_18":715,"_20":716,"_22":716,"_23":717,"_29":69,"_31":719},"eigen.dense.hasInf","eigen.dense.hasInf(A)","Check if a matrix contains any infinite values.",[718],{"_16":26,"_22":341,"_28":6},[],{"_16":721,"_18":722,"_20":723,"_22":723,"_23":724,"_29":69,"_31":726},"eigen.dense.hasNaN","eigen.dense.hasNaN(A)","Check if a matrix contains any NaN values.",[725],{"_16":26,"_22":341,"_28":6},[],{"_16":728,"_18":729,"_20":730,"_22":730,"_23":731,"_29":95,"_31":733},"eigen.dense.max","eigen.dense.max(A)","Find the maximum element in a matrix.",[732],{"_16":26,"_22":341,"_28":6},[],{"_16":735,"_18":736,"_20":737,"_22":737,"_23":738,"_29":95,"_31":740},"eigen.dense.mean","eigen.dense.mean(A)","Compute the mean of all elements in a matrix.",[739],{"_16":26,"_22":341,"_28":6},[],{"_16":742,"_18":743,"_20":744,"_22":744,"_23":745,"_29":95,"_31":747},"eigen.dense.min","eigen.dense.min(A)","Find the minimum element in a matrix.",[746],{"_16":26,"_22":341,"_28":6},[],{"_16":749,"_18":750,"_20":751,"_22":751,"_23":752,"_29":95,"_31":754},"eigen.dense.norm","eigen.dense.norm(A)","Compute the Frobenius norm of a matrix: ||A||_F = sqrt(sum(a_ij^2))",[753],{"_16":26,"_22":341,"_28":6},[],{"_16":756,"_18":757,"_20":758,"_22":758,"_23":759,"_29":95,"_31":761},"eigen.dense.norm1","eigen.dense.norm1(A)","Compute the 1-norm (maximum absolute column sum).",[760],{"_16":26,"_22":341,"_28":6},[],{"_16":763,"_18":764,"_20":765,"_22":765,"_23":766,"_29":95,"_31":768},"eigen.dense.normInf","eigen.dense.normInf(A)","Compute the infinity-norm (maximum absolute row sum).",[767],{"_16":26,"_22":341,"_28":6},[],{"_16":770,"_18":771,"_20":772,"_22":772,"_23":773,"_29":95,"_31":775},"eigen.dense.normMax","eigen.dense.normMax(A)","Compute the max norm (maximum absolute element).",[774],{"_16":26,"_22":341,"_28":6},[],{"_16":777,"_18":778,"_20":779,"_22":779,"_23":780,"_29":95,"_31":782},"eigen.dense.normSquared","eigen.dense.normSquared(A)","Compute the squared Frobenius norm: ||A||_F^2 = sum(a_ij^2)",[781],{"_16":26,"_22":341,"_28":6},[],{"_16":784,"_18":785,"_20":786,"_22":786,"_23":787,"_29":95,"_31":789},"eigen.dense.prod","eigen.dense.prod(A)","Compute the product of all elements in a matrix.",[788],{"_16":26,"_22":341,"_28":6},[],{"_16":791,"_18":792,"_20":793,"_22":793,"_23":794,"_29":95,"_31":799},"eigen.dense.std","eigen.dense.std(A, ddof?)","Compute the standard deviation of all elements in a matrix.",[795,796],{"_16":26,"_22":341,"_28":6},{"_16":797,"_22":798,"_28":11},"ddof","- Delta degrees of freedom (0 for population, 1 for sample std)",[],{"_16":801,"_18":802,"_20":803,"_22":803,"_23":804,"_29":95,"_31":806},"eigen.dense.sum","eigen.dense.sum(A)","Compute the sum of all elements in a matrix.",[805],{"_16":26,"_22":341,"_28":6},[],{"_16":808,"_18":809,"_20":810,"_22":810,"_23":811,"_29":95,"_31":814},"eigen.dense.trace","eigen.dense.trace(A)","Compute the trace of a matrix (sum of diagonal elements).",[812],{"_16":26,"_22":813,"_28":6},"- Matrix (typically square)",[],{"_16":816,"_18":817,"_20":818,"_22":818,"_23":819,"_29":95,"_31":823},"eigen.dense.variance","eigen.dense.variance(A, ddof?)","Compute the variance of all elements in a matrix.",[820,821],{"_16":26,"_22":341,"_28":6},{"_16":797,"_22":822,"_28":11},"- Delta degrees of freedom (0 for population, 1 for sample variance)",[],{"_16":825,"_18":826,"_20":827,"_22":827,"_23":828,"_29":361,"_31":830},"eigen.dense.adjoint","eigen.dense.adjoint(A)","Compute the adjoint (conjugate transpose) of a matrix: B = A^H",[829],{"_16":26,"_22":341,"_28":6},[],{"_16":832,"_18":833,"_20":834,"_22":834,"_23":835,"_29":361,"_31":838},"eigen.dense.conjugate","eigen.dense.conjugate(A)","Compute the complex conjugate of a matrix.",[836],{"_16":26,"_22":837,"_28":6},"- Matrix to conjugate",[],{"_16":840,"_18":841,"_20":842,"_22":842,"_23":843,"_29":361,"_31":846},"eigen.dense.inverse","eigen.dense.inverse(A)","Compute the inverse of a square matrix: B = A^(-1)",[844],{"_16":26,"_22":845,"_28":6},"- Square matrix to invert",[],{"_16":848,"_18":849,"_20":850,"_22":850,"_23":851,"_29":361,"_31":854},"eigen.dense.normalize","eigen.dense.normalize(A)","Compute the normalized matrix (divide by Frobenius norm).",[852],{"_16":26,"_22":853,"_28":6},"- Matrix to normalize",[],{"_16":856,"_18":857,"_20":858,"_22":858,"_23":859,"_29":30,"_31":862},"eigen.dense.normalizeInPlace","eigen.dense.normalizeInPlace(A)","Normalize a matrix in-place (divide by Frobenius norm).",[860],{"_16":26,"_22":861,"_28":6},"- Matrix to normalize (modified in-place)",[],{"_16":864,"_18":865,"_20":866,"_22":866,"_23":867,"_29":30,"_31":870},"eigen.dense.setIdentity","eigen.dense.setIdentity(A)","Set a matrix to identity in-place.",[868],{"_16":26,"_22":869,"_28":6},"- Square matrix to set to identity (modified in-place)",[],{"_16":872,"_18":873,"_20":874,"_22":874,"_23":875,"_29":30,"_31":878},"eigen.dense.setOnes","eigen.dense.setOnes(A)","Set all matrix elements to one in-place.",[876],{"_16":26,"_22":877,"_28":6},"- Matrix to fill with ones (modified in-place)",[],{"_16":880,"_18":881,"_20":882,"_22":882,"_23":883,"_29":30,"_31":886},"eigen.dense.setRandom","eigen.dense.setRandom(A)","Set all matrix elements to random values in [-1, 1] in-place.",[884],{"_16":26,"_22":885,"_28":6},"- Matrix to randomize (modified in-place)",[],{"_16":888,"_18":889,"_20":890,"_22":890,"_23":891,"_29":30,"_31":894},"eigen.dense.setZero","eigen.dense.setZero(A)","Set all matrix elements to zero in-place.",[892],{"_16":26,"_22":893,"_28":6},"- Matrix to zero (modified in-place)",[],{"_16":896,"_18":897,"_20":898,"_22":898,"_23":899,"_29":361,"_31":902},"eigen.dense.transpose","eigen.dense.transpose(A)","Compute the transpose of a matrix: B = A^T",[900],{"_16":26,"_22":901,"_28":6},"- Matrix to transpose",[],{"_16":904,"_18":905,"_20":694,"_22":694,"_23":906,"_29":909,"_31":910},"eigen.dense.Matrix.zeros","eigen.dense.Matrix.zeros(rows, cols)",[907,908],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},"Matrix",[],{"_16":912,"_18":913,"_20":678,"_22":678,"_23":914,"_29":909,"_31":917},"eigen.dense.Matrix.ones","eigen.dense.Matrix.ones(rows, cols)",[915,916],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},[],{"_16":919,"_18":920,"_20":626,"_22":626,"_23":921,"_29":909,"_31":923},"eigen.dense.Matrix.eye","eigen.dense.Matrix.eye(n)",[922],{"_16":629,"_22":95,"_28":6},[],{"_16":925,"_18":926,"_20":927,"_22":927,"_23":928,"_29":909,"_31":931},"eigen.dense.Matrix.random","eigen.dense.Matrix.random(rows, cols)","Create a matrix with random values in [-1, 1].",[929,930],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},[],{"_16":933,"_18":934,"_20":935,"_22":935,"_23":936,"_29":909,"_31":938},"eigen.dense.Matrix.from","eigen.dense.Matrix.from(arr2d)","Create a matrix from a 2D array.",[937],{"_16":189,"_22":125,"_28":6},[],{"_16":940,"_18":941,"_20":942,"_22":942,"_23":943,"_29":909,"_31":947},"eigen.dense.Matrix.fromData","eigen.dense.Matrix.fromData(data, rows, cols)","Create a matrix from a Float64Array (column-major).",[944,945,946],{"_16":117,"_22":137,"_28":6},{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},[],{"_16":949,"_18":950,"_20":951,"_22":951,"_23":952,"_29":909,"_31":955},"eigen.dense.Matrix.diag","eigen.dense.Matrix.diag(values)","Create a diagonal matrix.",[953],{"_16":620,"_22":954,"_28":6},"number[]",[],{"_16":957,"_18":958,"_20":643,"_22":643,"_23":959,"_29":909,"_31":963},"eigen.dense.Matrix.full","eigen.dense.Matrix.full(rows, cols, value)",[960,961,962],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},{"_16":457,"_22":95,"_28":6},[],{"_16":965,"_18":966,"_20":967,"_22":967,"_23":968,"_29":973,"_31":974},"eigen.operators.addOp","eigen.operators.addOp(A, B)","Add two linear operators: (A + B) * x = A * x + B * x",[969,971],{"_16":26,"_22":970,"_28":6},"- First linear operator",{"_16":505,"_22":972,"_28":6},"- Second linear operator","LinearOperator",[],{"_16":976,"_18":977,"_20":978,"_22":978,"_23":979,"_29":973,"_31":985},"eigen.operators.affineOp","eigen.operators.affineOp(A, b)","Create an operator that applies A and then adds a constant vector.",[980,982],{"_16":26,"_22":981,"_28":6},"- Linear operator",{"_16":983,"_22":984,"_28":6},"b","- Constant vector to add",[],{"_16":987,"_18":988,"_20":989,"_22":989,"_23":990,"_29":973,"_31":998},"eigen.operators.blockDiagonalOp","eigen.operators.blockDiagonalOp(operators, inputDims, outputDims)","Create a block diagonal operator from multiple operators.",[991,994,996],{"_16":992,"_22":993,"_28":6},"operators","- Array of linear operators for each block",{"_16":995,"_22":954,"_28":6},"inputDims",{"_16":997,"_22":954,"_28":6},"outputDims",[],{"_16":1000,"_18":1001,"_20":1002,"_22":1002,"_23":1003,"_29":973,"_31":1005},"eigen.operators.cacheOp","eigen.operators.cacheOp(A)","Wrap an operator to cache its result for repeated calls with the same input.",[1004],{"_16":26,"_22":981,"_28":6},[],{"_16":1007,"_18":1008,"_20":1009,"_22":1009,"_23":1010,"_29":973,"_31":1015},"eigen.operators.composeOp","eigen.operators.composeOp(A, B)","Compose two linear operators: (A * B) * x = A(B(x))",[1011,1013],{"_16":26,"_22":1012,"_28":6},"- Outer operator (applied second)",{"_16":505,"_22":1014,"_28":6},"- Inner operator (applied first)",[],{"_16":1017,"_18":1018,"_20":1019,"_22":1019,"_23":1020,"_29":973,"_31":1031},"eigen.operators.linearCombinationOp","eigen.operators.linearCombinationOp(alpha, A, beta, B)","Create a linear combination of operators: (alpha*A + beta*B) * x",[1021,1024,1026,1029],{"_16":1022,"_22":1023,"_28":6},"alpha","- Coefficient for A",{"_16":26,"_22":1025,"_28":6},"- First operator",{"_16":1027,"_22":1028,"_28":6},"beta","- Coefficient for B",{"_16":505,"_22":1030,"_28":6},"- Second operator",[],{"_16":1033,"_18":1034,"_20":1035,"_22":1035,"_23":1036,"_29":973,"_31":1038},"eigen.operators.negOp","eigen.operators.negOp(A)","Negate a linear operator: (-A) * x = -(A * x)",[1037],{"_16":26,"_22":981,"_28":6},[],{"_16":1040,"_18":1041,"_20":1042,"_22":1042,"_23":1043,"_29":973,"_31":1047},"eigen.operators.scaleOp","eigen.operators.scaleOp(A, alpha)","Scale a linear operator: (alpha * A) * x = alpha * (A * x)",[1044,1045],{"_16":26,"_22":981,"_28":6},{"_16":1022,"_22":1046,"_28":6},"- Scalar multiplier",[],{"_16":1049,"_18":1050,"_20":1051,"_22":1051,"_23":1052,"_29":973,"_31":1055},"eigen.operators.stackOp","eigen.operators.stackOp(operators)","Create an operator that applies multiple operators and returns the concatenated result.",[1053],{"_16":992,"_22":1054,"_28":6},"- Array of linear operators",[],{"_16":1057,"_18":1058,"_20":1059,"_22":1059,"_23":1060,"_29":973,"_31":1064},"eigen.operators.subOp","eigen.operators.subOp(A, B)","Subtract two linear operators: (A - B) * x = A * x - B * x",[1061,1062],{"_16":26,"_22":970,"_28":6},{"_16":505,"_22":1063,"_28":6},"- Second linear operator (subtracted)",[],{"_16":1066,"_18":1067,"_20":1068,"_22":1068,"_23":1069,"_29":973,"_31":1074},"eigen.operators.transposeOp","eigen.operators.transposeOp(_A, transposeOperator)","Create the transpose operator: A^T where A^T(y) = A^*(y) in the dual sense.",[1070,1072],{"_16":1071,"_22":973,"_28":6},"_A",{"_16":1073,"_22":973,"_28":6},"transposeOperator",[],{"_16":1076,"_18":1077,"_20":1078,"_22":1078,"_23":1079,"_29":973,"_31":1082},"eigen.operators.denseMatvec","eigen.operators.denseMatvec(A)","Create a matrix-vector multiplication operator from a dense matrix.",[1080],{"_16":26,"_22":1081,"_28":6},"- Dense matrix handle",[],{"_16":1084,"_18":1085,"_20":1086,"_22":1086,"_23":1087,"_29":973,"_31":1089},"eigen.operators.denseMatvecTranspose","eigen.operators.denseMatvecTranspose(A)","Create a transpose matrix-vector operator: x -> A^T * x",[1088],{"_16":26,"_22":1081,"_28":6},[],{"_16":1091,"_18":1092,"_20":1093,"_22":1093,"_23":1094,"_29":973,"_31":1098},"eigen.operators.diagMatvec","eigen.operators.diagMatvec(d)","Create a diagonal matrix-vector operator from a vector of diagonal elements.",[1095],{"_16":1096,"_22":1097,"_28":6},"d","- Vector of diagonal elements",[],{"_16":1100,"_18":1101,"_20":1102,"_22":1102,"_23":1103,"_29":973,"_31":1106},"eigen.operators.identityOp","eigen.operators.identityOp(n)","Create an identity operator: x -> x (copy)",[1104],{"_16":629,"_22":1105,"_28":6},"- Vector dimension",[],{"_16":1108,"_18":1109,"_20":1110,"_22":1110,"_23":1111,"_29":973,"_31":1115},"eigen.operators.sparseMatvec","eigen.operators.sparseMatvec(S)","Create a matrix-vector multiplication operator from a sparse matrix.",[1112],{"_16":1113,"_22":1114,"_28":6},"S","- Sparse matrix handle",[],{"_16":1117,"_18":1118,"_20":1119,"_22":1119,"_23":1120,"_29":973,"_31":1123},"eigen.operators.symmetricMatvec","eigen.operators.symmetricMatvec(A)","Create a symmetric matrix-vector operator with only lower triangular storage.",[1121],{"_16":26,"_22":1122,"_28":6},"- Lower triangular part of a symmetric matrix",[],{"_16":1125,"_18":1126,"_20":1127,"_22":1127,"_23":1128,"_29":973,"_31":1134},"eigen.operators.zeroOp","eigen.operators.zeroOp(m, n?)","Create a zero operator: x -> 0",[1129,1132],{"_16":1130,"_22":1131,"_28":6},"m","- Output dimension",{"_16":629,"_22":1133,"_28":11},"- Input dimension (optional, defaults to m)",[],{"_16":1136,"_18":1137,"_20":1138,"_22":1138,"_23":1139,"_29":361,"_31":1144},"eigen.solvers.solveCholesky","eigen.solvers.solveCholesky(A, b)","Solve the linear system Ax = b using Cholesky decomposition.",[1140,1142],{"_16":26,"_22":1141,"_28":6},"- Symmetric positive-definite coefficient matrix (n × n)",{"_16":983,"_22":1143,"_28":6},"- Right-hand side (n × 1 or n × k for multiple RHS)",[],{"_16":1146,"_18":1147,"_20":1148,"_22":1148,"_23":1149,"_29":361,"_31":1154},"eigen.solvers.solveNormalEquations","eigen.solvers.solveNormalEquations(A, b)","Solve the normal equations A^T A x = A^T b using Cholesky decomposition.",[1150,1152],{"_16":26,"_22":1151,"_28":6},"- Coefficient matrix (m × n)",{"_16":983,"_22":1153,"_28":6},"- Right-hand side (m × 1)",[],{"_16":1156,"_18":1157,"_20":1158,"_22":1158,"_23":1159,"_29":361,"_31":1162},"eigen.solvers.lstsq","eigen.solvers.lstsq(A, b)","Solve the least squares problem: minimize ||Ax - b||_2",[1160,1161],{"_16":26,"_22":1151,"_28":6},{"_16":983,"_22":1153,"_28":6},[],{"_16":1164,"_18":1165,"_20":1166,"_22":1166,"_23":1167,"_29":1173,"_31":1174},"eigen.solvers.lstsqFull","eigen.solvers.lstsqFull(A, b, rcond?)","Solve least squares with full diagnostic output.",[1168,1169,1170],{"_16":26,"_22":1151,"_28":6},{"_16":983,"_22":1153,"_28":6},{"_16":1171,"_22":1172,"_28":11},"rcond","- Cutoff for small singular values (default: machine epsilon * max(m,n))","LeastSquaresResult",[],{"_16":1176,"_18":1177,"_20":1178,"_22":1178,"_23":1179,"_29":361,"_31":1185},"eigen.solvers.lstsqWeighted","eigen.solvers.lstsqWeighted(A, b, weights)","Solve weighted least squares: minimize ||W^(1/2)(Ax - b)||_2",[1180,1181,1182],{"_16":26,"_22":1151,"_28":6},{"_16":983,"_22":1153,"_28":6},{"_16":1183,"_22":1184,"_28":6},"weights","- Weights vector (m × 1), non-negative",[],{"_16":1187,"_18":1188,"_20":1189,"_22":1189,"_23":1190,"_29":361,"_31":1193},"eigen.solvers.inverseLU","eigen.solvers.inverseLU(A)","Compute the inverse of a matrix using LU decomposition.",[1191],{"_16":26,"_22":1192,"_28":6},"- Square matrix (n × n)",[],{"_16":1195,"_18":1196,"_20":1197,"_22":1197,"_23":1198,"_29":361,"_31":1202},"eigen.solvers.solveLU","eigen.solvers.solveLU(A, b)","Solve the linear system Ax = b using LU decomposition.",[1199,1201],{"_16":26,"_22":1200,"_28":6},"- Square coefficient matrix (n × n)",{"_16":983,"_22":1143,"_28":6},[],{"_16":1204,"_18":1205,"_20":1206,"_22":1206,"_23":1207,"_29":361,"_31":1211},"eigen.solvers.leastSquaresQR","eigen.solvers.leastSquaresQR(A, b)","Solve a least squares problem: minimize ||Ax - b||_2",[1208,1210],{"_16":26,"_22":1209,"_28":6},"- Coefficient matrix (m × n, typically m ≥ n)",{"_16":983,"_22":1153,"_28":6},[],{"_16":1213,"_18":1214,"_20":1215,"_22":1215,"_23":1216,"_29":361,"_31":1220},"eigen.solvers.solveQR","eigen.solvers.solveQR(A, b)","Solve the linear system Ax = b using QR decomposition.",[1217,1219],{"_16":26,"_22":1218,"_28":6},"- Coefficient matrix (m × n, m ≥ n)",{"_16":983,"_22":1153,"_28":6},[],{"_16":1222,"_18":1223,"_20":1224,"_22":1224,"_23":1225,"_29":361,"_31":1229},"eigen.solvers.solve","eigen.solvers.solve(A, b)","Solve the linear system Ax = b.",[1226,1228],{"_16":26,"_22":1227,"_28":6},"- Coefficient matrix (n × n for square, m × n for least squares)",{"_16":983,"_22":1143,"_28":6},[],{"_16":1231,"_18":1232,"_20":1233,"_22":1233,"_23":1234,"_29":361,"_31":1239},"eigen.solvers.solveMultiple","eigen.solvers.solveMultiple(A, B)","Solve multiple linear systems with the same coefficient matrix.",[1235,1237],{"_16":26,"_22":1236,"_28":6},"- Coefficient matrix (n × n)",{"_16":505,"_22":1238,"_28":6},"- Right-hand sides matrix (n × k)",[],{"_16":1241,"_18":1242,"_20":1243,"_22":1243,"_23":1244,"_29":30,"_31":1246},"eigen.sparse.destroySparse","eigen.sparse.destroySparse(S)","Destroy a sparse matrix and free its memory.",[1245],{"_16":1113,"_22":1114,"_28":6},[],{"_16":1248,"_18":1249,"_20":1250,"_22":1250,"_23":1251,"_29":1254,"_31":1255},"eigen.sparse.sparse","eigen.sparse.sparse(rows, cols)","Create an empty sparse matrix with given dimensions.",[1252,1253],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},"SparseMatrixHandle",[],{"_16":1257,"_18":1258,"_20":1259,"_22":1259,"_23":1260,"_29":1254,"_31":1263},"eigen.sparse.sparseDiag","eigen.sparse.sparseDiag(diagonal)","Create a sparse diagonal matrix.",[1261],{"_16":1262,"_22":621,"_28":6},"diagonal",[],{"_16":1265,"_18":1266,"_20":1267,"_22":1267,"_23":1268,"_29":1254,"_31":1271},"eigen.sparse.sparseEye","eigen.sparse.sparseEye(n)","Create a sparse identity matrix.",[1269],{"_16":629,"_22":1270,"_28":6},"- Size of the matrix",[],{"_16":1273,"_18":1274,"_20":1275,"_22":1275,"_23":1276,"_29":1254,"_31":1287},"eigen.sparse.sparseFromCOO","eigen.sparse.sparseFromCOO(rows, cols, rowIndices, colIndices, values)","Create a sparse matrix from COO (Coordinate) format arrays.",[1277,1278,1279,1282,1285],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},{"_16":1280,"_22":1281,"_28":6},"rowIndices","- Array of row indices",{"_16":1283,"_22":1284,"_28":6},"colIndices","- Array of column indices",{"_16":620,"_22":1286,"_28":6},"- Array of values",[],{"_16":1289,"_18":1290,"_20":1291,"_22":1291,"_23":1292,"_29":1254,"_31":1298},"eigen.sparse.sparseFromDense","eigen.sparse.sparseFromDense(denseHandle, tol?)","Create a sparse matrix from a dense matrix, keeping only non-zero elements.",[1293,1296],{"_16":1294,"_22":1295,"_28":6},"denseHandle","- Handle to dense matrix",{"_16":243,"_22":1297,"_28":11},"- Tolerance for considering values as zero (default: 0)",[],{"_16":1300,"_18":1301,"_20":1302,"_22":1302,"_23":1303,"_29":1254,"_31":1309},"eigen.sparse.sparseFromTriplets","eigen.sparse.sparseFromTriplets(rows, cols, triplets)","Create a sparse matrix from a list of triplets (COO format).",[1304,1305,1306],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},{"_16":1307,"_22":1308,"_28":6},"triplets","- Array of {row, col, value} objects",[],{"_16":1311,"_18":1312,"_20":1313,"_22":1313,"_23":1314,"_29":1317,"_31":1318},"eigen.sparse.createMatvec","eigen.sparse.createMatvec(S)","Create a sparse matrix-vector product function (closure).",[1315],{"_16":1113,"_22":1316,"_28":6},"- Sparse matrix","(x: VectorHandle) => VectorHandle",[],{"_16":1320,"_18":1321,"_20":1322,"_22":1322,"_23":1323,"_29":95,"_31":1327},"eigen.sparse.density","eigen.sparse.density(S, rows, cols)","Get the density of a sparse matrix (nnz / total elements).",[1324,1325,1326],{"_16":1113,"_22":1114,"_28":6},{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},[],{"_16":1329,"_18":1330,"_20":1331,"_22":1331,"_23":1332,"_29":69,"_31":1334},"eigen.sparse.isEmpty","eigen.sparse.isEmpty(S)","Check if a sparse matrix is empty (has no non-zeros).",[1333],{"_16":1113,"_22":1114,"_28":6},[],{"_16":1336,"_18":1337,"_20":1338,"_22":1338,"_23":1339,"_29":95,"_31":1341},"eigen.sparse.nnz","eigen.sparse.nnz(S)","Get the number of non-zero elements in a sparse matrix.",[1340],{"_16":1113,"_22":1114,"_28":6},[],{"_16":1343,"_18":1344,"_20":1345,"_22":1345,"_23":1346,"_29":1352,"_31":1353},"eigen.sparse.sparseMV","eigen.sparse.sparseMV(S, x)","Compute sparse matrix-vector product: y = S * x",[1347,1349],{"_16":1113,"_22":1348,"_28":6},"- Sparse matrix (m × n)",{"_16":1350,"_22":1351,"_28":6},"x","- Input vector (n × 1)","VectorHandle",[],{"_16":1355,"_18":1356,"_20":1357,"_22":1357,"_23":1358,"_29":1352,"_31":1366},"eigen.sparse.sparseSolve","eigen.sparse.sparseSolve(S, b, method?)","Solve sparse linear system with automatic method selection.",[1359,1361,1363],{"_16":1113,"_22":1360,"_28":6},"- Sparse coefficient matrix (n × n)",{"_16":983,"_22":1362,"_28":6},"- Right-hand side vector (n × 1)",{"_16":1364,"_22":1365,"_28":11},"method","- Solver method: 'auto', 'lu', 'cg', 'bicgstab'",[],{"_16":1368,"_18":1369,"_20":1370,"_22":1370,"_23":1371,"_29":1352,"_31":1377},"eigen.sparse.sparseSolveBiCGSTAB","eigen.sparse.sparseSolveBiCGSTAB(S, b, _options?)","Solve sparse linear system Ax = b using BiCGSTAB method.",[1372,1373,1374],{"_16":1113,"_22":1360,"_28":6},{"_16":983,"_22":1362,"_28":6},{"_16":1375,"_22":1376,"_28":11},"_options","IterativeSolverOptions",[],{"_16":1379,"_18":1380,"_20":1381,"_22":1381,"_23":1382,"_29":1352,"_31":1387},"eigen.sparse.sparseSolveCG","eigen.sparse.sparseSolveCG(S, b, _options?)","Solve sparse linear system Ax = b using Conjugate Gradient method.",[1383,1385,1386],{"_16":1113,"_22":1384,"_28":6},"- Sparse coefficient matrix (n × n), must be symmetric positive-definite",{"_16":983,"_22":1362,"_28":6},{"_16":1375,"_22":1376,"_28":11},[],{"_16":1389,"_18":1390,"_20":1391,"_22":1391,"_23":1392,"_29":1352,"_31":1395},"eigen.sparse.sparseSolveLU","eigen.sparse.sparseSolveLU(S, b)","Solve sparse linear system Ax = b using SparseLU (direct method).",[1393,1394],{"_16":1113,"_22":1360,"_28":6},{"_16":983,"_22":1362,"_28":6},[],{"_16":1397,"_18":1398,"_20":1250,"_22":1250,"_23":1399,"_29":1402,"_31":1403},"eigen.sparse.SparseMatrix.create","eigen.sparse.SparseMatrix.create(rows, cols)",[1400,1401],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},"SparseMatrix",[],{"_16":1405,"_18":1406,"_20":1407,"_22":1407,"_23":1408,"_29":1402,"_31":1413},"eigen.sparse.SparseMatrix.fromTriplets","eigen.sparse.SparseMatrix.fromTriplets(rows, cols, triplets)","Create a sparse matrix from triplets (COO format).",[1409,1410,1411],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},{"_16":1307,"_22":1412,"_28":6},"- Array of {row, col, value} triplets",[],{"_16":1415,"_18":1416,"_20":1417,"_22":1417,"_23":1418,"_29":1402,"_31":1425},"eigen.sparse.SparseMatrix.fromCOO","eigen.sparse.SparseMatrix.fromCOO(rows, cols, rowIndices, colIndices, values)","Create a sparse matrix from separate COO arrays.",[1419,1420,1421,1422,1423],{"_16":120,"_22":121,"_28":6},{"_16":123,"_22":124,"_28":6},{"_16":1280,"_22":1281,"_28":6},{"_16":1283,"_22":1284,"_28":6},{"_16":620,"_22":1424,"_28":6},"- Array of non-zero values",[],{"_16":1427,"_18":1428,"_20":1429,"_22":1430,"_23":1431,"_29":1402,"_31":1437},"eigen.sparse.SparseMatrix.fromDense","eigen.sparse.SparseMatrix.fromDense(data, tolerance?)","Create a sparse matrix from a dense 2D array.\r","Create a sparse matrix from a dense 2D array.\r\nOnly non-zero values are stored.",[1432,1434],{"_16":117,"_22":1433,"_28":6},"- 2D array in row-major order",{"_16":1435,"_22":1436,"_28":11},"tolerance","- Values with |value| < tolerance are treated as zero",[],{"_16":1439,"_18":1440,"_20":1267,"_22":1267,"_23":1441,"_29":1402,"_31":1444},"eigen.sparse.SparseMatrix.eye","eigen.sparse.SparseMatrix.eye(n)",[1442],{"_16":629,"_22":1443,"_28":6},"- Matrix dimension (n × n)",[],{"_16":1446,"_18":1447,"_20":1259,"_22":1259,"_23":1448,"_29":1402,"_31":1451},"eigen.sparse.SparseMatrix.diag","eigen.sparse.SparseMatrix.diag(diagonal)",[1449],{"_16":1262,"_22":1450,"_28":6},"- Diagonal values",[],{"_16":1453,"_18":1454,"_20":1455,"_22":1455,"_23":1456,"_29":1402,"_31":1468},"eigen.sparse.SparseMatrix.tridiag","eigen.sparse.SparseMatrix.tridiag(n, lower, main, upper)","Create a sparse tridiagonal matrix.",[1457,1459,1462,1465],{"_16":629,"_22":1458,"_28":6},"- Matrix dimension",{"_16":1460,"_22":1461,"_28":6},"lower","- Value on sub-diagonal",{"_16":1463,"_22":1464,"_28":6},"main","- Value on main diagonal",{"_16":1466,"_22":1467,"_28":6},"upper","- Value on super-diagonal",[],{"_16":1470,"_18":1471,"_20":1472,"_22":1472,"_23":1473,"_29":1402,"_31":1478},"eigen.sparse.SparseMatrix.banded","eigen.sparse.SparseMatrix.banded(n, bands)","Create a sparse matrix from a banded structure.",[1474,1475],{"_16":629,"_22":1458,"_28":6},{"_16":1476,"_22":1477,"_28":6},"bands","- Array of {offset, values} where offset is band position",[],{"_16":1480,"_18":1481,"_20":1482,"_22":1482,"_23":1483,"_29":361,"_31":1498},"eigen.utilities.block","eigen.utilities.block(A, startRow, startCol, numRows, numCols)","Extract a submatrix (block) from a matrix.",[1484,1486,1489,1492,1495],{"_16":26,"_22":1485,"_28":6},"- Source matrix handle",{"_16":1487,"_22":1488,"_28":6},"startRow","- Starting row index (0-based)",{"_16":1490,"_22":1491,"_28":6},"startCol","- Starting column index (0-based)",{"_16":1493,"_22":1494,"_28":6},"numRows","- Number of rows in the block",{"_16":1496,"_22":1497,"_28":6},"numCols","- Number of columns in the block",[],{"_16":1500,"_18":1501,"_20":1502,"_22":1502,"_23":1503,"_29":361,"_31":1507},"eigen.utilities.blockDiag","eigen.utilities.blockDiag(matrices)","Create a block diagonal matrix from multiple matrices.",[1504],{"_16":1505,"_22":1506,"_28":6},"matrices","- Array of matrix handles to place on the diagonal",[],{"_16":1509,"_18":1510,"_20":1511,"_22":1511,"_23":1512,"_29":1352,"_31":1515},"eigen.utilities.col","eigen.utilities.col(A, j)","Extract a column from a matrix as a vector.",[1513,1514],{"_16":26,"_22":393,"_28":6},{"_16":412,"_22":413,"_28":6},[],{"_16":1517,"_18":1518,"_20":1519,"_22":1519,"_23":1520,"_29":1352,"_31":1524},"eigen.utilities.diagonal","eigen.utilities.diagonal(A, k?)","Extract the diagonal of a matrix as a vector.",[1521,1522],{"_16":26,"_22":393,"_28":6},{"_16":430,"_22":1523,"_28":11},"- Diagonal offset (0 = main, positive = above, negative = below)",[],{"_16":1526,"_18":1527,"_20":1528,"_22":1528,"_23":1529,"_29":1352,"_31":1534},"eigen.utilities.flatten","eigen.utilities.flatten(A, order?)","Flatten a matrix to a vector.",[1530,1531],{"_16":26,"_22":393,"_28":6},{"_16":1532,"_22":1533,"_28":11},"order","- 'F' for column-major (default), 'C' for row-major",[],{"_16":1536,"_18":1537,"_20":1538,"_22":1538,"_23":1539,"_29":361,"_31":1542},"eigen.utilities.hstack","eigen.utilities.hstack(matrices)","Horizontally concatenate matrices: [A, B, C, ...]",[1540],{"_16":1505,"_22":1541,"_28":6},"- Array of matrix handles to concatenate",[],{"_16":1544,"_18":1545,"_20":1546,"_22":1546,"_23":1547,"_29":361,"_31":1555},"eigen.utilities.reshape","eigen.utilities.reshape(A, newRows, newCols)","Reshape a matrix to new dimensions.",[1548,1549,1552],{"_16":26,"_22":393,"_28":6},{"_16":1550,"_22":1551,"_28":6},"newRows","- New number of rows",{"_16":1553,"_22":1554,"_28":6},"newCols","- New number of columns",[],{"_16":1557,"_18":1558,"_20":1559,"_22":1559,"_23":1560,"_29":1352,"_31":1563},"eigen.utilities.row","eigen.utilities.row(A, i)","Extract a row from a matrix as a vector.",[1561,1562],{"_16":26,"_22":393,"_28":6},{"_16":409,"_22":410,"_28":6},[],{"_16":1565,"_18":1566,"_20":1567,"_22":1567,"_23":1568,"_29":361,"_31":1573},"eigen.utilities.selectCols","eigen.utilities.selectCols(A, indices)","Extract columns from a matrix.",[1569,1570],{"_16":26,"_22":393,"_28":6},{"_16":1571,"_22":1572,"_28":6},"indices","- Array of column indices to extract",[],{"_16":1575,"_18":1576,"_20":1577,"_22":1577,"_23":1578,"_29":361,"_31":1582},"eigen.utilities.selectRows","eigen.utilities.selectRows(A, indices)","Extract rows from a matrix.",[1579,1580],{"_16":26,"_22":393,"_28":6},{"_16":1571,"_22":1581,"_28":6},"- Array of row indices to extract",[],{"_16":1584,"_18":1585,"_20":1586,"_22":1586,"_23":1587,"_29":30,"_31":1594},"eigen.utilities.setBlock","eigen.utilities.setBlock(A, startRow, startCol, B)","Set a block of a matrix to values from another matrix.",[1588,1590,1591,1592],{"_16":26,"_22":1589,"_28":6},"- Target matrix handle (modified in place)",{"_16":1487,"_22":1488,"_28":6},{"_16":1490,"_22":1491,"_28":6},{"_16":505,"_22":1593,"_28":6},"- Source matrix containing values to set",[],{"_16":1596,"_18":1597,"_20":1598,"_22":1598,"_23":1599,"_29":30,"_31":1606},"eigen.utilities.setCol","eigen.utilities.setCol(A, j, v)","Set a column of a matrix from a vector.",[1600,1602,1603],{"_16":26,"_22":1601,"_28":6},"- Matrix handle (modified in place)",{"_16":412,"_22":413,"_28":6},{"_16":1604,"_22":1605,"_28":6},"v","- Vector containing new column values",[],{"_16":1608,"_18":1609,"_20":1610,"_22":1610,"_23":1611,"_29":30,"_31":1616},"eigen.utilities.setDiagonal","eigen.utilities.setDiagonal(A, v, k?)","Set the diagonal of a matrix from a vector.",[1612,1613,1615],{"_16":26,"_22":1601,"_28":6},{"_16":1604,"_22":1614,"_28":6},"- Vector containing diagonal values",{"_16":430,"_22":1523,"_28":11},[],{"_16":1618,"_18":1619,"_20":1620,"_22":1620,"_23":1621,"_29":30,"_31":1626},"eigen.utilities.setRow","eigen.utilities.setRow(A, i, v)","Set a row of a matrix from a vector.",[1622,1623,1624],{"_16":26,"_22":1601,"_28":6},{"_16":409,"_22":410,"_28":6},{"_16":1604,"_22":1625,"_28":6},"- Vector containing new row values",[],{"_16":1628,"_18":1629,"_20":1630,"_22":1630,"_23":1631,"_29":361,"_31":1633},"eigen.utilities.vstack","eigen.utilities.vstack(matrices)","Vertically concatenate matrices: [A; B; C; ...]",[1632],{"_16":1505,"_22":1541,"_28":6},[],{"_16":1635,"_18":1636,"_20":348,"_22":348,"_23":1637,"_29":95,"_31":1639},"eigen.utilities.cond","eigen.utilities.cond(A)",[1638],{"_16":26,"_22":393,"_28":6},[],{"_16":1641,"_18":1642,"_20":1643,"_22":1643,"_23":1644,"_29":95,"_31":1646},"eigen.utilities.frobeniusNorm","eigen.utilities.frobeniusNorm(A)","Compute the Frobenius norm of a matrix.",[1645],{"_16":26,"_22":393,"_28":6},[],{"_16":1648,"_18":1649,"_20":1650,"_22":1650,"_23":1651,"_29":95,"_31":1653},"eigen.utilities.nuclearNorm","eigen.utilities.nuclearNorm(A)","Compute the nuclear norm (trace norm) of a matrix.",[1652],{"_16":26,"_22":393,"_28":6},[],{"_16":1655,"_18":1656,"_20":1657,"_22":1657,"_23":1658,"_29":1663,"_31":1664},"eigen.utilities.nullspace","eigen.utilities.nullspace(A, tolerance?)","Compute an orthonormal basis for the null space of A.",[1659,1661],{"_16":26,"_22":1660,"_28":6},"- Matrix handle (m × n)",{"_16":1435,"_22":1662,"_28":11},"- Singular values below this define the null space","VectorHandle[]",[],{"_16":1666,"_18":1667,"_20":1668,"_22":1668,"_23":1669,"_29":95,"_31":1673},"eigen.utilities.numericalRank","eigen.utilities.numericalRank(A, tolerance?)","Compute the numerical rank using a tolerance.",[1670,1671],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1672,"_28":11},"- Absolute tolerance for considering a singular value as zero",[],{"_16":1675,"_18":1676,"_20":1677,"_22":1677,"_23":1678,"_29":361,"_31":1682},"eigen.utilities.pinv","eigen.utilities.pinv(A, tolerance?)","Compute the Moore-Penrose pseudoinverse of a matrix.",[1679,1680],{"_16":26,"_22":1660,"_28":6},{"_16":1435,"_22":1681,"_28":11},"- Singular values below this are treated as zero",[],{"_16":1684,"_18":1685,"_20":1686,"_22":1686,"_23":1687,"_29":1663,"_31":1690},"eigen.utilities.range","eigen.utilities.range(A, tolerance?)","Compute an orthonormal basis for the column space (range) of A.",[1688,1689],{"_16":26,"_22":1660,"_28":6},{"_16":1435,"_22":1681,"_28":11},[],{"_16":1692,"_18":1693,"_20":1694,"_22":1694,"_23":1695,"_29":95,"_31":1698},"eigen.utilities.rank","eigen.utilities.rank(A, tolerance?)","Compute the matrix rank using SVD.",[1696,1697],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1681,"_28":11},[],{"_16":1700,"_18":1701,"_20":1702,"_22":1702,"_23":1703,"_29":95,"_31":1705},"eigen.utilities.spectralNorm","eigen.utilities.spectralNorm(A)","Compute the spectral norm (2-norm) of a matrix.",[1704],{"_16":26,"_22":393,"_28":6},[],{"_16":1707,"_18":1708,"_20":1709,"_22":1709,"_23":1710,"_29":69,"_31":1714},"eigen.utilities.isDiagonal","eigen.utilities.isDiagonal(A, tolerance?)","Check if a matrix is diagonal.",[1711,1712],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1713,"_28":11},"- Maximum allowed off-diagonal value",[],{"_16":1716,"_18":1717,"_20":1718,"_22":1718,"_23":1719,"_29":69,"_31":1726},"eigen.utilities.isEqual","eigen.utilities.isEqual(A, B, tolerance?)","Check if two matrices are equal within a tolerance.",[1720,1722,1724],{"_16":26,"_22":1721,"_28":6},"- First matrix handle",{"_16":505,"_22":1723,"_28":6},"- Second matrix handle",{"_16":1435,"_22":1725,"_28":11},"- Maximum allowed element-wise difference",[],{"_16":1728,"_18":1729,"_20":1730,"_22":1730,"_23":1731,"_29":69,"_31":1735},"eigen.utilities.isIdentity","eigen.utilities.isIdentity(A, tolerance?)","Check if a matrix is the identity matrix.",[1732,1733],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1734,"_28":11},"- Maximum allowed deviation",[],{"_16":1737,"_18":1738,"_20":1739,"_22":1739,"_23":1740,"_29":69,"_31":1745},"eigen.utilities.isInvertible","eigen.utilities.isInvertible(A, tolerance?)","Check if a matrix is invertible (non-singular).",[1741,1743],{"_16":26,"_22":1742,"_28":6},"- Matrix handle (must be square)",{"_16":1435,"_22":1744,"_28":11},"- Tolerance for determinant check",[],{"_16":1747,"_18":1748,"_20":1749,"_22":1749,"_23":1750,"_29":69,"_31":1754},"eigen.utilities.isLowerTriangular","eigen.utilities.isLowerTriangular(A, tolerance?)","Check if a matrix is lower triangular.",[1751,1752],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1753,"_28":11},"- Maximum allowed above-diagonal value",[],{"_16":1756,"_18":1757,"_20":1758,"_22":1758,"_23":1759,"_29":69,"_31":1763},"eigen.utilities.isOrthogonal","eigen.utilities.isOrthogonal(A, tolerance?)","Check if a matrix is orthogonal (A^T * A = I).",[1760,1761],{"_16":26,"_22":1742,"_28":6},{"_16":1435,"_22":1762,"_28":11},"- Maximum allowed deviation from identity",[],{"_16":1765,"_18":1766,"_20":1767,"_22":1767,"_23":1768,"_29":69,"_31":1771},"eigen.utilities.isPositiveDefinite","eigen.utilities.isPositiveDefinite(A)","Check if a matrix is positive definite.",[1769],{"_16":26,"_22":1770,"_28":6},"- Matrix handle (must be square and symmetric)",[],{"_16":1773,"_18":1774,"_20":1775,"_22":1775,"_23":1776,"_29":69,"_31":1780},"eigen.utilities.isPositiveSemiDefinite","eigen.utilities.isPositiveSemiDefinite(A, tolerance?)","Check if a matrix is positive semi-definite.",[1777,1778],{"_16":26,"_22":1742,"_28":6},{"_16":1435,"_22":1779,"_28":11},"- Tolerance for eigenvalue check",[],{"_16":1782,"_18":1783,"_20":1784,"_22":1784,"_23":1785,"_29":69,"_31":1788},"eigen.utilities.isSingular","eigen.utilities.isSingular(A, tolerance?)","Check if a matrix is singular (determinant is zero).",[1786,1787],{"_16":26,"_22":1742,"_28":6},{"_16":1435,"_22":1744,"_28":11},[],{"_16":1790,"_18":1791,"_20":1792,"_22":1792,"_23":1793,"_29":69,"_31":1795},"eigen.utilities.isSquare","eigen.utilities.isSquare(A)","Check if a matrix is square (rows == cols).",[1794],{"_16":26,"_22":393,"_28":6},[],{"_16":1797,"_18":1798,"_20":1799,"_22":1799,"_23":1800,"_29":69,"_31":1804},"eigen.utilities.isSymmetric","eigen.utilities.isSymmetric(A, tolerance?)","Check if a matrix is symmetric (A == A^T) within a tolerance.",[1801,1802],{"_16":26,"_22":1742,"_28":6},{"_16":1435,"_22":1803,"_28":11},"- Maximum allowed difference between A[i,j] and A[j,i]",[],{"_16":1806,"_18":1807,"_20":1808,"_22":1808,"_23":1809,"_29":69,"_31":1813},"eigen.utilities.isUpperTriangular","eigen.utilities.isUpperTriangular(A, tolerance?)","Check if a matrix is upper triangular.",[1810,1811],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1812,"_28":11},"- Maximum allowed below-diagonal value",[],{"_16":1815,"_18":1816,"_20":1817,"_22":1817,"_23":1818,"_29":69,"_31":1822},"eigen.utilities.isZero","eigen.utilities.isZero(A, tolerance?)","Check if a matrix is the zero matrix.",[1819,1820],{"_16":26,"_22":393,"_28":6},{"_16":1435,"_22":1821,"_28":11},"- Maximum allowed value",[],{"_16":1824,"_18":1825,"_20":1826,"_22":1826,"_23":1827,"_29":95,"_31":1830},"eigen.vector.dataPtrVec","eigen.vector.dataPtrVec(v)","Get the raw data pointer for a vector.",[1828],{"_16":1604,"_22":1829,"_28":6},"- Vector handle",[],{"_16":1832,"_18":1833,"_20":1834,"_22":1834,"_23":1835,"_29":30,"_31":1838},"eigen.vector.destroyVec","eigen.vector.destroyVec(v)","Free the memory associated with a vector.",[1836],{"_16":1604,"_22":1837,"_28":6},"- Vector handle to destroy",[],{"_16":1840,"_18":1841,"_20":1842,"_22":1842,"_23":1843,"_29":95,"_31":1845},"eigen.vector.firstVec","eigen.vector.firstVec(v)","Get the first element of a vector.",[1844],{"_16":1604,"_22":1829,"_28":6},[],{"_16":1847,"_18":1848,"_20":1849,"_22":1849,"_23":1850,"_29":95,"_31":1854},"eigen.vector.getVec","eigen.vector.getVec(v, i)","Get a single element from a vector.",[1851,1852],{"_16":1604,"_22":1829,"_28":6},{"_16":409,"_22":1853,"_28":6},"- Index (0-based)",[],{"_16":1856,"_18":1857,"_20":1858,"_22":1858,"_23":1859,"_29":95,"_31":1861},"eigen.vector.lastVec","eigen.vector.lastVec(v)","Get the last element of a vector.",[1860],{"_16":1604,"_22":1829,"_28":6},[],{"_16":1863,"_18":1864,"_20":1865,"_22":1865,"_23":1866,"_29":30,"_31":1870},"eigen.vector.setVec","eigen.vector.setVec(v, i, value)","Set a single element in a vector.",[1867,1868,1869],{"_16":1604,"_22":1829,"_28":6},{"_16":409,"_22":1853,"_28":6},{"_16":457,"_22":458,"_28":6},[],{"_16":1872,"_18":1873,"_20":1874,"_22":1874,"_23":1875,"_29":95,"_31":1877},"eigen.vector.sizeVec","eigen.vector.sizeVec(v)","Get the size (length) of a vector.",[1876],{"_16":1604,"_22":1829,"_28":6},[],{"_16":1879,"_18":1880,"_20":1881,"_22":1881,"_23":1882,"_29":137,"_31":1888},"eigen.vector.sliceVec","eigen.vector.sliceVec(v, start, end)","Get a slice of a vector as a new Float64Array.",[1883,1884,1886],{"_16":1604,"_22":1829,"_28":6},{"_16":657,"_22":1885,"_28":6},"- Start index (inclusive, 0-based)",{"_16":660,"_22":1887,"_28":6},"- End index (exclusive)",[],{"_16":1890,"_18":1891,"_20":1892,"_22":1892,"_23":1893,"_29":137,"_31":1895},"eigen.vector.toArrayVec","eigen.vector.toArrayVec(v)","Convert a vector to a Float64Array.",[1894],{"_16":1604,"_22":1829,"_28":6},[],{"_16":1897,"_18":1898,"_20":1899,"_22":1899,"_23":1900,"_29":954,"_31":1902},"eigen.vector.toJSArrayVec","eigen.vector.toJSArrayVec(v)","Convert a vector to a JavaScript array.",[1901],{"_16":1604,"_22":1829,"_28":6},[],{"_16":1904,"_18":1905,"_20":1906,"_22":1906,"_23":1907,"_29":1352,"_31":1914},"eigen.vector.arangeVec","eigen.vector.arangeVec(start, end, step?)","Create a vector with values from start to end with given step.",[1908,1909,1911],{"_16":657,"_22":658,"_28":6},{"_16":660,"_22":1910,"_28":6},"- Ending value (exclusive)",{"_16":1912,"_22":1913,"_28":11},"step","- Step size (default: 1)",[],{"_16":1916,"_18":1917,"_20":1918,"_22":1918,"_23":1919,"_29":1352,"_31":1924},"eigen.vector.basisVec","eigen.vector.basisVec(n, i)","Create a standard basis vector (one-hot vector).",[1920,1922],{"_16":629,"_22":1921,"_28":6},"- Vector length",{"_16":409,"_22":1923,"_28":6},"- Index of the 1 element (0-based)",[],{"_16":1926,"_18":1927,"_20":1928,"_22":1928,"_23":1929,"_29":1352,"_31":1932},"eigen.vector.cloneVec","eigen.vector.cloneVec(v)","Create a copy of a vector.",[1930],{"_16":1604,"_22":1931,"_28":6},"- Vector to copy",[],{"_16":1934,"_18":1935,"_20":1936,"_22":1936,"_23":1937,"_29":1352,"_31":1941},"eigen.vector.fullVec","eigen.vector.fullVec(n, value)","Create a vector filled with a constant value.",[1938,1939],{"_16":629,"_22":1921,"_28":6},{"_16":457,"_22":1940,"_28":6},"- Fill value",[],{"_16":1943,"_18":1944,"_20":1945,"_22":1945,"_23":1946,"_29":1352,"_31":1950},"eigen.vector.linspaceVec","eigen.vector.linspaceVec(start, end, n)","Create a vector with linearly spaced values.",[1947,1948,1949],{"_16":657,"_22":658,"_28":6},{"_16":660,"_22":661,"_28":6},{"_16":629,"_22":663,"_28":6},[],{"_16":1952,"_18":1953,"_20":1954,"_22":1954,"_23":1955,"_29":1352,"_31":1957},"eigen.vector.onesVec","eigen.vector.onesVec(n)","Create a vector filled with ones.",[1956],{"_16":629,"_22":1921,"_28":6},[],{"_16":1959,"_18":1960,"_20":1961,"_22":1961,"_23":1962,"_29":1352,"_31":1964},"eigen.vector.randomVec","eigen.vector.randomVec(n)","Create a vector with random values in [-1, 1].",[1963],{"_16":629,"_22":1921,"_28":6},[],{"_16":1966,"_18":1967,"_20":1968,"_22":1968,"_23":1969,"_29":1352,"_31":1972},"eigen.vector.vector","eigen.vector.vector(data)","Create a vector from a Float64Array.",[1970],{"_16":117,"_22":1971,"_28":6},"- Vector data",[],{"_16":1974,"_18":1975,"_20":1976,"_22":1976,"_23":1977,"_29":1352,"_31":1981},"eigen.vector.vectorFromArray","eigen.vector.vectorFromArray(arr)","Create a vector from a JavaScript array.",[1978],{"_16":1979,"_22":1980,"_28":6},"arr","- Array of numbers",[],{"_16":1983,"_18":1984,"_20":1985,"_22":1985,"_23":1986,"_29":1352,"_31":1988},"eigen.vector.zerosVec","eigen.vector.zerosVec(n)","Create a vector filled with zeros.",[1987],{"_16":629,"_22":1921,"_28":6},[],{"_16":1990,"_18":1991,"_20":1992,"_22":1992,"_23":1993,"_29":1352,"_31":1999},"eigen.vector.addVec","eigen.vector.addVec(u, v)","Add two vectors: w = u + v",[1994,1997],{"_16":1995,"_22":1996,"_28":6},"u","- First vector",{"_16":1604,"_22":1998,"_28":6},"- Second vector (must have same length)",[],{"_16":2001,"_18":2002,"_20":2003,"_22":2003,"_23":2004,"_29":95,"_31":2007},"eigen.vector.angleVec","eigen.vector.angleVec(u, v)","Compute the angle between two vectors in radians.",[2005,2006],{"_16":1995,"_22":1996,"_28":6},{"_16":1604,"_22":1998,"_28":6},[],{"_16":2009,"_18":2010,"_20":2011,"_22":2011,"_23":2012,"_29":1352,"_31":2017},"eigen.vector.cross","eigen.vector.cross(u, v)","Compute the cross product of two 3D vectors: u × v",[2013,2015],{"_16":1995,"_22":2014,"_28":6},"- First 3D vector",{"_16":1604,"_22":2016,"_28":6},"- Second 3D vector",[],{"_16":2019,"_18":2020,"_20":2021,"_22":2021,"_23":2022,"_29":95,"_31":2025},"eigen.vector.distanceVec","eigen.vector.distanceVec(u, v)","Compute the distance between two vectors: ||u - v||_2",[2023,2024],{"_16":1995,"_22":1996,"_28":6},{"_16":1604,"_22":1998,"_28":6},[],{"_16":2027,"_18":2028,"_20":2029,"_22":2029,"_23":2030,"_29":95,"_31":2034},"eigen.vector.dot","eigen.vector.dot(u, v)","Compute the dot product of two vectors: u · v",[2031,2032],{"_16":1995,"_22":1996,"_28":6},{"_16":1604,"_22":2033,"_28":6},"- Second vector (must have same length as u)",[],{"_16":2036,"_18":2037,"_20":2038,"_22":2038,"_23":2039,"_29":1352,"_31":2042},"eigen.vector.elementMulVec","eigen.vector.elementMulVec(u, v)","Compute element-wise product: w_i = u_i * v_i",[2040,2041],{"_16":1995,"_22":1996,"_28":6},{"_16":1604,"_22":1998,"_28":6},[],{"_16":2044,"_18":2045,"_20":2046,"_22":2046,"_23":2047,"_29":95,"_31":2050},"eigen.vector.maxVec","eigen.vector.maxVec(v)","Find the maximum element.",[2048],{"_16":1604,"_22":2049,"_28":6},"- Vector",[],{"_16":2052,"_18":2053,"_20":2054,"_22":2054,"_23":2055,"_29":95,"_31":2057},"eigen.vector.meanVec","eigen.vector.meanVec(v)","Compute the mean of all elements.",[2056],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2059,"_18":2060,"_20":2061,"_22":2061,"_23":2062,"_29":95,"_31":2064},"eigen.vector.minVec","eigen.vector.minVec(v)","Find the minimum element.",[2063],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2066,"_18":2067,"_20":2068,"_22":2068,"_23":2069,"_29":1352,"_31":2071},"eigen.vector.negVec","eigen.vector.negVec(v)","Negate a vector: w = -v",[2070],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2073,"_18":2074,"_20":2075,"_22":2075,"_23":2076,"_29":95,"_31":2078},"eigen.vector.norm1Vec","eigen.vector.norm1Vec(v)","Compute the L1 norm (Manhattan norm): ||v||_1 = sum(|v_i|)",[2077],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2080,"_18":2081,"_20":2082,"_22":2082,"_23":2083,"_29":1352,"_31":2086},"eigen.vector.normalizeVec","eigen.vector.normalizeVec(v)","Return a normalized copy of a vector.",[2084],{"_16":1604,"_22":2085,"_28":6},"- Vector to normalize",[],{"_16":2088,"_18":2089,"_20":2090,"_22":2090,"_23":2091,"_29":30,"_31":2094},"eigen.vector.normalizeVecInPlace","eigen.vector.normalizeVecInPlace(v)","Normalize a vector in-place (divide by its norm).",[2092],{"_16":1604,"_22":2093,"_28":6},"- Vector to normalize (modified in-place)",[],{"_16":2096,"_18":2097,"_20":2098,"_22":2098,"_23":2099,"_29":95,"_31":2101},"eigen.vector.normInfVec","eigen.vector.normInfVec(v)","Compute the infinity norm (max norm): ||v||_∞ = max(|v_i|)",[2100],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2103,"_18":2104,"_20":2105,"_22":2105,"_23":2106,"_29":95,"_31":2108},"eigen.vector.normSquaredVec","eigen.vector.normSquaredVec(v)","Compute the squared Euclidean norm: ||v||_2^2 = sum(v_i^2)",[2107],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2110,"_18":2111,"_20":2112,"_22":2112,"_23":2113,"_29":95,"_31":2115},"eigen.vector.normVec","eigen.vector.normVec(v)","Compute the Euclidean (L2) norm of a vector: ||v||_2 = sqrt(sum(v_i^2))",[2114],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2117,"_18":2118,"_20":2119,"_22":2119,"_23":2120,"_29":1352,"_31":2124},"eigen.vector.scaleVec","eigen.vector.scaleVec(v, scalar)","Scale a vector: w = scalar * v",[2121,2122],{"_16":1604,"_22":2049,"_28":6},{"_16":515,"_22":2123,"_28":6},"- Scale factor",[],{"_16":2126,"_18":2127,"_20":2128,"_22":2128,"_23":2129,"_29":1352,"_31":2132},"eigen.vector.subVec","eigen.vector.subVec(u, v)","Subtract two vectors: w = u - v",[2130,2131],{"_16":1995,"_22":1996,"_28":6},{"_16":1604,"_22":1998,"_28":6},[],{"_16":2134,"_18":2135,"_20":2136,"_22":2136,"_23":2137,"_29":95,"_31":2139},"eigen.vector.sumVec","eigen.vector.sumVec(v)","Compute the sum of all elements.",[2138],{"_16":1604,"_22":2049,"_28":6},[],{"_16":2141,"_18":2142,"_20":1985,"_22":1985,"_23":2143,"_29":2145,"_31":2146},"eigen.vector.Vector.zeros","eigen.vector.Vector.zeros(n)",[2144],{"_16":629,"_22":95,"_28":6},"Vector",[],{"_16":2148,"_18":2149,"_20":1954,"_22":1954,"_23":2150,"_29":2145,"_31":2152},"eigen.vector.Vector.ones","eigen.vector.Vector.ones(n)",[2151],{"_16":629,"_22":95,"_28":6},[],{"_16":2154,"_18":2155,"_20":1961,"_22":1961,"_23":2156,"_29":2145,"_31":2158},"eigen.vector.Vector.random","eigen.vector.Vector.random(n)",[2157],{"_16":629,"_22":95,"_28":6},[],{"_16":2160,"_18":2161,"_20":1976,"_22":1976,"_23":2162,"_29":2145,"_31":2164},"eigen.vector.Vector.from","eigen.vector.Vector.from(arr)",[2163],{"_16":1979,"_22":954,"_28":6},[],{"_16":2166,"_18":2167,"_20":1968,"_22":1968,"_23":2168,"_29":2145,"_31":2170},"eigen.vector.Vector.fromData","eigen.vector.Vector.fromData(data)",[2169],{"_16":117,"_22":137,"_28":6},[],{"_16":2172,"_18":2173,"_20":1936,"_22":1936,"_23":2174,"_29":2145,"_31":2177},"eigen.vector.Vector.full","eigen.vector.Vector.full(n, value)",[2175,2176],{"_16":629,"_22":95,"_28":6},{"_16":457,"_22":95,"_28":6},[],{"_16":2179,"_18":2180,"_20":2181,"_22":2181,"_23":2182,"_29":2145,"_31":2185},"eigen.vector.Vector.basis","eigen.vector.Vector.basis(n, i)","Create a standard basis vector (one-hot).",[2183,2184],{"_16":629,"_22":95,"_28":6},{"_16":409,"_22":95,"_28":6},[],{"_16":2187,"_18":2188,"_20":1945,"_22":1945,"_23":2189,"_29":2145,"_31":2193},"eigen.vector.Vector.linspace","eigen.vector.Vector.linspace(start, end, n)",[2190,2191,2192],{"_16":657,"_22":95,"_28":6},{"_16":660,"_22":95,"_28":6},{"_16":629,"_22":95,"_28":6},[],"allPackages",[2196,3305,3662,3857,4466,5621,5822,6127,6508,10341,11089,16992,17208,34,18639,18901,19947,21021,22266],{"_35":2197,"_16":2198,"_22":2199,"_39":40,"_41":2200,"_45":2201},"core","Core Functions","Essential functions for array creation, mathematics, aggregation, and manipulation. Always available.","🔧",[2202,2227,2240,2255,2276,2296,2315,2328,2340,2366,2387,2421,2439,2451,2463,2476,2486,2499,2513,2528,2539,2550,2568,2581,2593,2605,2619,2633,2645,2656,2666,2689,2705,2718,2730,2742,2754,2775,2791,2818,2837,2848,2860,2871,2887,2901,2915,2932,2943,2954,2968,2982,2994,3006,3026,3038,3058,3077,3090,3104,3118,3131,3153,3171,3192,3205,3219,3237,3252,3265,3276,3287],{"_16":2203,"_18":2204,"_20":2205,"_22":2206,"_23":2207,"_29":2212,"_31":2213,"_2222":2223},"zeros","Z = zeros(n)\nZ = zeros(m, n)","Create array of all zeros","Creates an array of zeros with the specified dimensions. A single argument `n` creates an n×n matrix.",[2208,2210],{"_16":1130,"_22":2209},"Number of rows",{"_16":629,"_22":2211,"_28":11},"Number of columns","NDArray of zeros with the given shape",[2214,2219],{"_2215":2216,"_2217":2218},"code","zeros(3)","output","0 0 0\n0 0 0\n0 0 0",{"_2215":2220,"_2217":2221},"zeros(2, 4)","0 0 0 0\n0 0 0 0","seeAlso",[2224,2225,2226],"ones","eye","rand",{"_16":2224,"_18":2228,"_20":2229,"_22":2230,"_23":2231,"_29":2234,"_31":2235,"_2222":2239},"X = ones(n)\nX = ones(m, n)","Create array of all ones","Creates an array of ones with the specified dimensions. A single argument `n` creates an n×n matrix.",[2232,2233],{"_16":1130,"_22":2209},{"_16":629,"_22":2211,"_28":11},"NDArray of ones with the given shape",[2236],{"_2215":2237,"_2217":2238},"ones(2, 3)","1 1 1\n1 1 1",[2203,2225],{"_16":2225,"_18":2241,"_20":2242,"_22":2243,"_23":2244,"_29":2247,"_31":2248,"_2222":2252},"I = eye(n)","Identity matrix","Creates an n×n identity matrix with ones on the diagonal and zeros elsewhere.",[2245],{"_16":629,"_22":2246},"Size of the square matrix","n×n identity NDArray",[2249],{"_2215":2250,"_2217":2251},"eye(3)","1 0 0\n0 1 0\n0 0 1",[2203,2224,2253,2254],"diag","magic",{"_16":2254,"_18":2256,"_20":2257,"_22":2258,"_23":2259,"_29":2262,"_31":2263,"_2222":2273},"M = magic(n)","Magic square","Creates an n×n magic square matrix where the sum of each row, column, and both main diagonals equals the same magic constant: n(n²+1)/2. For n=1 returns [1], for n=2 there is no magic square so returns [1 3; 4 2] (not a true magic square). Works for all n ≥ 1.",[2260],{"_16":629,"_22":2261},"Size of the magic square (n ≥ 1)","n×n magic square NDArray",[2264,2267,2270],{"_2215":2265,"_2217":2266},"magic(3)","8 1 6\n3 5 7\n4 9 2",{"_2215":2268,"_2217":2269},"magic(4)","16 2 3 13\n 5 11 10 8\n 9 7 6 12\n 4 14 15 1",{"_2215":2271,"_2217":2272},"sum(magic(5))","65 65 65 65 65",[2225,2224,2203,2274,2275],"pascal","hilb",{"_16":2277,"_18":2278,"_20":2279,"_22":2280,"_23":2281,"_29":2289,"_31":2290,"_2222":2294},"linspace","v = linspace(a, b, n)","Generate linearly spaced vector","Returns a row vector of `n` evenly spaced points between `a` and `b` (inclusive).",[2282,2285,2287],{"_16":2283,"_22":2284},"a","Start value",{"_16":983,"_22":2286},"End value",{"_16":629,"_22":2288},"Number of points","1×n NDArray",[2291],{"_2215":2292,"_2217":2293},"linspace(0, 1, 5)","0 0.25 0.5 0.75 1",[2295,2203,2224],"logspace",{"_16":2295,"_18":2297,"_20":2298,"_22":2299,"_23":2300,"_29":2289,"_31":2307,"_2222":2314},"v = logspace(a, b)\nv = logspace(a, b, n)","Generate logarithmically spaced vector","Returns a row vector of `n` logarithmically spaced points between 10^a and 10^b. Default is 50 points.",[2301,2303,2305],{"_16":2283,"_22":2302},"Exponent of start value (10^a)",{"_16":983,"_22":2304},"Exponent of end value (10^b)",{"_16":629,"_22":2306,"_28":11},"Number of points (default: 50)",[2308,2311],{"_2215":2309,"_2217":2310},"logspace(0, 2, 5)","1 3.1623 10 31.623 100",{"_2215":2312,"_2217":2313},"logspace(-2, 0, 3)","0.01 0.1 1",[2277,2203,2224],{"_16":2226,"_18":2316,"_20":2317,"_22":2318,"_23":2319,"_29":2322,"_31":2323,"_2222":2326},"R = rand(n)\nR = rand(m, n)","Uniformly distributed random numbers","Creates an array of uniformly distributed random numbers in the interval (0, 1).",[2320,2321],{"_16":1130,"_22":2209},{"_16":629,"_22":2211,"_28":11},"NDArray of random values in (0, 1)",[2324],{"_2215":2325},"rand(2, 3)",[2327,2203],"randn",{"_16":2327,"_18":2329,"_20":2330,"_22":2331,"_23":2332,"_29":2335,"_31":2336,"_2222":2339},"R = randn(n)\nR = randn(m, n)","Normally distributed random numbers","Creates an array of random numbers drawn from the standard normal distribution (mean 0, variance 1).",[2333,2334],{"_16":1130,"_22":2209},{"_16":629,"_22":2211,"_28":11},"NDArray of normally distributed random values",[2337],{"_2215":2338},"randn(2, 3)",[2226],{"_16":2341,"_18":2342,"_20":2343,"_22":2344,"_23":2345,"_29":2354,"_31":2355,"_2222":2363},"meshgrid","[X, Y] = meshgrid(x, y)\n[X, Y] = meshgrid(v)\n[X, Y] = meshgrid(x, y, 'ij')","Create 2D coordinate matrices","Returns coordinate matrices from coordinate vectors. For vectors x and y, meshgrid returns 2D matrices X and Y where X has x values repeated across rows and Y has y values repeated down columns (MATLAB 'xy' indexing). With a single argument v, uses v for both x and y. An optional 'ij' argument switches to NumPy-style matrix indexing where X varies along the first dimension.",[2346,2348,2351],{"_16":1350,"_22":2347},"X-coordinate vector",{"_16":2349,"_22":2350,"_28":11},"y","Y-coordinate vector (defaults to x if omitted)",{"_16":2352,"_22":2353,"_28":11},"indexing","Indexing mode: 'xy' (default, MATLAB style) or 'ij' (NumPy matrix style)","Two NDArrays [X, Y] of coordinate matrices",[2356,2358,2360],{"_2215":2357},"[X, Y] = meshgrid(1:3, 1:2)",{"_2215":2359},"[X, Y] = meshgrid(-2:0.5:2)",{"_2215":2361,"_2217":2362},"[X, Y] = meshgrid(1:3, 1:5, 'ij')","% X is 3x5, Y is 3x5 (NumPy style)",[2364,2365,2277],"surf","mesh",{"_16":2367,"_18":2368,"_20":2369,"_22":2370,"_23":2371,"_29":2374,"_31":2375,"_2222":2385},"peaks","Z = peaks()\nZ = peaks(n)\n[X, Y, Z] = peaks(...)","Peaks function (test surface)","Generates a test surface with multiple peaks and valleys, commonly used for 3D visualization demos. The function is defined as: Z = 3*(1-X)^2*exp(-X^2-(Y+1)^2) - 10*(X/5-X^3-Y^5)*exp(-X^2-Y^2) - (1/3)*exp(-(X+1)^2-Y^2) evaluated over the range [-3, 3] for both X and Y.",[2372],{"_16":629,"_22":2373,"_28":11},"Grid size (default: 49). Returns an n×n matrix.","n×n NDArray of Z values, or [X, Y, Z] coordinate matrices",[2376,2379,2382],{"_2215":2377,"_2217":2378},"surf(peaks())","% 49×49 surface plot",{"_2215":2380,"_2217":2381},"Z = peaks(30)","% 30×30 matrix",{"_2215":2383,"_2217":2384},"[X, Y, Z] = peaks(25)","% Returns all coordinate matrices",[2364,2365,2341,2386],"gallery",{"_16":2386,"_18":2388,"_20":2389,"_22":2390,"_23":2391,"_29":2400,"_31":2401,"_2222":2417},"A = gallery(matname)\nA = gallery(matname, n)\nA = gallery(matname, n, ...)","Test matrices by name","Generates test matrices useful for testing numerical algorithms. The first argument is a string specifying the matrix type. Available types include: 'hilb' (Hilbert), 'invhilb' (inverse Hilbert), 'pascal', 'magic', 'lehmer', 'minij', 'moler', 'pei', 'kms', 'cauchy', 'circul', 'fiedler', 'tridiag', 'frank', 'grcar', 'hanowa', 'jordbloc', 'clement', 'triw', 'parter'.",[2392,2395,2397],{"_16":2393,"_22":2394},"matname","Name of the test matrix type (string)",{"_16":629,"_22":2396,"_28":11},"Size or first parameter (depends on matrix type)",{"_16":2398,"_22":2399,"_28":11},"...","Additional parameters (depends on matrix type)","Test matrix of the specified type",[2402,2405,2408,2411,2414],{"_2215":2403,"_2217":2404},"gallery('hilb', 4)","4×4 Hilbert matrix",{"_2215":2406,"_2217":2407},"gallery('pascal', 5)","5×5 Pascal matrix",{"_2215":2409,"_2217":2410},"gallery('lehmer', 3)","1.0000 0.5000 0.3333\n0.5000 1.0000 0.6667\n0.3333 0.6667 1.0000",{"_2215":2412,"_2217":2413},"gallery('pei', 3, 2)","3×3 Pei matrix with alpha=2",{"_2215":2415,"_2217":2416},"gallery('kms', 4, 0.5)","4×4 KMS Toeplitz matrix with rho=0.5",[2275,2418,2274,2254,2419,2420],"invhilb","toeplitz","hankel",{"_16":2422,"_18":2423,"_20":2424,"_22":2425,"_23":2426,"_29":2430,"_31":2431,"_2222":2435},"sin","Y = sin(X)","Sine of argument in radians","Computes the sine of each element. Operates element-wise on arrays.",[2427],{"_16":2428,"_22":2429},"X","Input angle in radians (scalar or NDArray)","Sine values (same shape as input)",[2432],{"_2215":2433,"_2217":2434},"sin(pi/2)","1",[2436,2437,2438],"cos","tan","asin",{"_16":2436,"_18":2440,"_20":2441,"_22":2442,"_23":2443,"_29":2445,"_31":2446,"_2222":2449},"Y = cos(X)","Cosine of argument in radians","Computes the cosine of each element. Operates element-wise on arrays.",[2444],{"_16":2428,"_22":2429},"Cosine values (same shape as input)",[2447],{"_2215":2448,"_2217":2434},"cos(0)",[2422,2437,2450],"acos",{"_16":2437,"_18":2452,"_20":2453,"_22":2454,"_23":2455,"_29":2457,"_31":2458,"_2222":2461},"Y = tan(X)","Tangent of argument in radians","Computes the tangent of each element. Operates element-wise on arrays.",[2456],{"_16":2428,"_22":2429},"Tangent values (same shape as input)",[2459],{"_2215":2460,"_2217":2434},"tan(pi/4)",[2422,2436,2462],"atan",{"_16":2438,"_18":2464,"_20":2465,"_22":2466,"_23":2467,"_29":2470,"_31":2471,"_2222":2475},"Y = asin(X)","Inverse sine (arcsine)","Computes the inverse sine of each element. Result is in radians in the range [-pi/2, pi/2].",[2468],{"_16":2428,"_22":2469},"Input values in [-1, 1] (scalar or NDArray)","Angle in radians",[2472],{"_2215":2473,"_2217":2474},"asin(1)","1.5708",[2422,2450,2462],{"_16":2450,"_18":2477,"_20":2478,"_22":2479,"_23":2480,"_29":2470,"_31":2482,"_2222":2485},"Y = acos(X)","Inverse cosine (arccosine)","Computes the inverse cosine of each element. Result is in radians in the range [0, pi].",[2481],{"_16":2428,"_22":2469},[2483],{"_2215":2484,"_2217":2474},"acos(0)",[2436,2438,2462],{"_16":2462,"_18":2487,"_20":2488,"_22":2489,"_23":2490,"_29":2470,"_31":2493,"_2222":2497},"Y = atan(X)","Inverse tangent (arctangent)","Computes the inverse tangent of each element. Result is in radians in the range (-pi/2, pi/2).",[2491],{"_16":2428,"_22":2492},"Input value (scalar or NDArray)",[2494],{"_2215":2495,"_2217":2496},"atan(1)","0.7854",[2437,2498,2438],"atan2",{"_16":2498,"_18":2500,"_20":2501,"_22":2502,"_23":2503,"_29":2508,"_31":2509,"_2222":2512},"Y = atan2(B, A)","Four-quadrant inverse tangent","Computes the four-quadrant inverse tangent of B/A, using the signs of both arguments to determine the quadrant.",[2504,2506],{"_16":505,"_22":2505},"Y-coordinates (scalar or NDArray)",{"_16":26,"_22":2507},"X-coordinates (scalar or NDArray)","Angle in radians in (-pi, pi]",[2510],{"_2215":2511,"_2217":2496},"atan2(1, 1)",[2462,2422,2436],{"_16":2514,"_18":2515,"_20":2516,"_22":2517,"_23":2518,"_29":2520,"_31":2521,"_2222":2525},"sinh","Y = sinh(X)","Hyperbolic sine","Computes the hyperbolic sine of each element.",[2519],{"_16":2428,"_22":2492},"Hyperbolic sine values",[2522],{"_2215":2523,"_2217":2524},"sinh(0)","0",[2526,2527,2422],"cosh","tanh",{"_16":2526,"_18":2529,"_20":2530,"_22":2531,"_23":2532,"_29":2534,"_31":2535,"_2222":2538},"Y = cosh(X)","Hyperbolic cosine","Computes the hyperbolic cosine of each element.",[2533],{"_16":2428,"_22":2492},"Hyperbolic cosine values",[2536],{"_2215":2537,"_2217":2434},"cosh(0)",[2514,2527,2436],{"_16":2527,"_18":2540,"_20":2541,"_22":2542,"_23":2543,"_29":2545,"_31":2546,"_2222":2549},"Y = tanh(X)","Hyperbolic tangent","Computes the hyperbolic tangent of each element.",[2544],{"_16":2428,"_22":2492},"Hyperbolic tangent values",[2547],{"_2215":2548,"_2217":2524},"tanh(0)",[2514,2526,2437],{"_16":2551,"_18":2552,"_20":2553,"_22":2554,"_23":2555,"_29":2558,"_31":2559,"_2222":2565},"exp","Y = exp(X)","Exponential (e^x)","Computes e raised to the power of each element.",[2556],{"_16":2428,"_22":2557},"Exponent values (scalar or NDArray)","Exponential values",[2560,2562],{"_2215":2561,"_2217":2434},"exp(0)",{"_2215":2563,"_2217":2564},"exp(1)","2.7183",[2566,2567],"log","log10",{"_16":2566,"_18":2569,"_20":2570,"_22":2571,"_23":2572,"_29":2575,"_31":2576,"_2222":2579},"Y = log(X)","Natural logarithm","Computes the natural logarithm (base e) of each element.",[2573],{"_16":2428,"_22":2574},"Input values > 0 (scalar or NDArray)","Natural log values",[2577],{"_2215":2578,"_2217":2434},"log(exp(1))",[2551,2567,2580],"log2",{"_16":2567,"_18":2582,"_20":2583,"_22":2584,"_23":2585,"_29":2587,"_31":2588,"_2222":2592},"Y = log10(X)","Common logarithm (base 10)","Computes the base-10 logarithm of each element.",[2586],{"_16":2428,"_22":2574},"Base-10 log values",[2589],{"_2215":2590,"_2217":2591},"log10(100)","2",[2566,2580,2551],{"_16":2580,"_18":2594,"_20":2595,"_22":2596,"_23":2597,"_29":2599,"_31":2600,"_2222":2604},"Y = log2(X)","Base-2 logarithm","Computes the base-2 logarithm of each element.",[2598],{"_16":2428,"_22":2574},"Base-2 log values",[2601],{"_2215":2602,"_2217":2603},"log2(8)","3",[2566,2567,2551],{"_16":2606,"_18":2607,"_20":2608,"_22":2609,"_23":2610,"_29":2613,"_31":2614,"_2222":2617},"sqrt","Y = sqrt(X)","Square root","Computes the square root of each element.",[2611],{"_16":2428,"_22":2612},"Input values >= 0 (scalar or NDArray)","Square root values",[2615],{"_2215":2616,"_2217":2603},"sqrt(9)",[2618,2551],"abs",{"_16":2618,"_18":2620,"_20":2621,"_22":2622,"_23":2623,"_29":2625,"_31":2626,"_2222":2630},"Y = abs(X)","Absolute value","Computes the absolute value of each element.",[2624],{"_16":2428,"_22":2492},"Absolute values",[2627],{"_2215":2628,"_2217":2629},"abs(-5)","5",[2606,2631,2632],"floor","ceil",{"_16":2631,"_18":2634,"_20":2635,"_22":2636,"_23":2637,"_29":2639,"_31":2640,"_2222":2643},"Y = floor(X)","Round toward negative infinity","Rounds each element to the nearest integer toward negative infinity.",[2638],{"_16":2428,"_22":2492},"Rounded values",[2641],{"_2215":2642,"_2217":2603},"floor(3.7)",[2632,2644,2618],"round",{"_16":2632,"_18":2646,"_20":2647,"_22":2648,"_23":2649,"_29":2639,"_31":2651,"_2222":2655},"Y = ceil(X)","Round toward positive infinity","Rounds each element to the nearest integer toward positive infinity.",[2650],{"_16":2428,"_22":2492},[2652],{"_2215":2653,"_2217":2654},"ceil(3.2)","4",[2631,2644,2618],{"_16":2644,"_18":2657,"_20":2658,"_22":2659,"_23":2660,"_29":2639,"_31":2662,"_2222":2665},"Y = round(X)","Round to nearest integer","Rounds each element to the nearest integer.",[2661],{"_16":2428,"_22":2492},[2663],{"_2215":2664,"_2217":2654},"round(3.5)",[2631,2632],{"_16":2667,"_18":2668,"_20":2669,"_22":2670,"_23":2671,"_29":2677,"_31":2678,"_2222":2685},"sum","S = sum(A)\nS = sum(A, dim)","Sum of array elements","Returns the sum of the elements. With a dimension argument, sums along that dimension (1-indexed).",[2672,2674],{"_16":26,"_22":2673},"Input array (scalar or NDArray)",{"_16":2675,"_22":2676,"_28":11},"dim","Dimension to sum along (1-indexed)","Sum value (scalar or NDArray)",[2679,2682],{"_2215":2680,"_2217":2681},"sum([1 2 3])","6",{"_2215":2683,"_2217":2684},"A = [1 2; 3 4]; sum(A, 1)","4 6",[2686,2687,2688],"mean","min","max",{"_16":2686,"_18":2690,"_20":2691,"_22":2692,"_23":2693,"_29":2697,"_31":2698,"_2222":2702},"M = mean(A)\nM = mean(A, dim)","Average of array elements","Returns the arithmetic mean. With a dimension argument, computes the mean along that dimension.",[2694,2695],{"_16":26,"_22":2673},{"_16":2675,"_22":2696,"_28":11},"Dimension to average along (1-indexed)","Mean value (scalar or NDArray)",[2699],{"_2215":2700,"_2217":2701},"mean([1 2 3 4])","2.5",[2667,2703,2704],"std","var",{"_16":2703,"_18":2706,"_20":2707,"_22":2708,"_23":2709,"_29":2713,"_31":2714,"_2222":2717},"S = std(A)\nS = std(A, dim)","Standard deviation","Returns the standard deviation of the elements. With a dimension argument, computes along that dimension.",[2710,2711],{"_16":26,"_22":2673},{"_16":2675,"_22":2712,"_28":11},"Dimension (1-indexed)","Standard deviation (scalar or NDArray)",[2715],{"_2215":2716,"_2217":2591},"std([2 4 4 4 5 5 7 9])",[2704,2686],{"_16":2704,"_18":2719,"_20":2720,"_22":2721,"_23":2722,"_29":2725,"_31":2726,"_2222":2729},"V = var(A)\nV = var(A, dim)","Variance","Returns the variance of the elements. With a dimension argument, computes along that dimension.",[2723,2724],{"_16":26,"_22":2673},{"_16":2675,"_22":2712,"_28":11},"Variance (scalar or NDArray)",[2727],{"_2215":2728,"_2217":2654},"var([2 4 4 4 5 5 7 9])",[2703,2686],{"_16":2687,"_18":2731,"_20":2732,"_22":2733,"_23":2734,"_29":2737,"_31":2738,"_2222":2741},"M = min(A)\nM = min(A, dim)","Minimum value","Returns the smallest element. With a dimension argument, returns the minimum along that dimension.",[2735,2736],{"_16":26,"_22":2673},{"_16":2675,"_22":2712,"_28":11},"Minimum value (scalar or NDArray)",[2739],{"_2215":2740,"_2217":2434},"min([3 1 4 1 5])",[2688,2667],{"_16":2688,"_18":2743,"_20":2744,"_22":2745,"_23":2746,"_29":2749,"_31":2750,"_2222":2753},"M = max(A)\nM = max(A, dim)","Maximum value","Returns the largest element. With a dimension argument, returns the maximum along that dimension.",[2747,2748],{"_16":26,"_22":2673},{"_16":2675,"_22":2712,"_28":11},"Maximum value (scalar or NDArray)",[2751],{"_2215":2752,"_2217":2629},"max([3 1 4 1 5])",[2687,2667],{"_16":2755,"_18":2756,"_20":2757,"_22":2758,"_23":2759,"_29":2763,"_31":2764,"_2222":2772},"any","B = any(A)\nB = any(A, dim)","Test if any elements are nonzero","Returns 1 if any element of A is nonzero, 0 otherwise. With a dimension argument, operates along that dimension.",[2760,2761],{"_16":26,"_22":2673},{"_16":2675,"_22":2762,"_28":11},"Dimension to operate along (1-indexed)","1 if any element is nonzero, 0 otherwise",[2765,2767,2769],{"_2215":2766,"_2217":2434},"any([0 0 1 0])",{"_2215":2768,"_2217":2524},"any([0 0 0])",{"_2215":2770,"_2217":2771},"A = [1 0; 0 0]; any(A, 1)","1 0",[2773,2774],"all","find",{"_16":2773,"_18":2776,"_20":2777,"_22":2778,"_23":2779,"_29":2782,"_31":2783,"_2222":2790},"B = all(A)\nB = all(A, dim)","Test if all elements are nonzero","Returns 1 if all elements of A are nonzero, 0 otherwise. With a dimension argument, operates along that dimension.",[2780,2781],{"_16":26,"_22":2673},{"_16":2675,"_22":2762,"_28":11},"1 if all elements are nonzero, 0 otherwise",[2784,2786,2788],{"_2215":2785,"_2217":2434},"all([1 2 3])",{"_2215":2787,"_2217":2524},"all([1 0 3])",{"_2215":2789,"_2217":2771},"A = [1 1; 1 0]; all(A, 1)",[2755,2774],{"_16":2774,"_18":2792,"_20":2793,"_22":2794,"_23":2795,"_29":2803,"_31":2804,"_2222":2817},"k = find(X)\nk = find(X, n)\nk = find(X, n, direction)","Find indices of nonzero elements","Returns the linear indices of nonzero elements in X. Optionally returns only the first or last n indices.",[2796,2798,2800],{"_16":2428,"_22":2797},"Input array",{"_16":629,"_22":2799,"_28":11},"Number of indices to return",{"_16":2801,"_22":2802,"_28":11},"direction","'first' (default) or 'last' - which indices to return","Vector of indices (1-based)",[2805,2808,2811,2814],{"_2215":2806,"_2217":2807},"find([1 0 3 0 5])","1 3 5",{"_2215":2809,"_2217":2810},"find([1 0 3 0 5], 2)","1 3",{"_2215":2812,"_2217":2813},"find([1 0 3 0 5], 2, 'last')","3 5",{"_2215":2815,"_2217":2816},"A = [1 2 3 4 5]; find(A > 3)","4 5",[2755,2773],{"_16":93,"_18":2819,"_20":2820,"_22":2821,"_23":2822,"_29":2826,"_31":2827,"_2222":2833},"s = size(A)\ns = size(A, dim)","Array dimensions","Returns the size of an array. With a dimension argument, returns the length of that dimension.",[2823,2824],{"_16":26,"_22":2797},{"_16":2675,"_22":2825,"_28":11},"Dimension to query (1-indexed)","Size as NDArray or scalar",[2828,2831],{"_2215":2829,"_2217":2830},"A = zeros(3, 4); size(A)","3 4",{"_2215":2832,"_2217":2654},"size(A, 2)",[2834,2835,2836],"length","numel","ndims",{"_16":2834,"_18":2838,"_20":2839,"_22":2840,"_23":2841,"_29":2843,"_31":2844,"_2222":2847},"n = length(A)","Length of largest array dimension","Returns the length of the largest dimension of the array.",[2842],{"_16":26,"_22":2797},"Scalar length",[2845],{"_2215":2846,"_2217":2629},"length([1 2 3 4 5])",[93,2835],{"_16":2835,"_18":2849,"_20":2850,"_22":2851,"_23":2852,"_29":2854,"_31":2855,"_2222":2859},"n = numel(A)","Number of array elements","Returns the total number of elements in the array.",[2853],{"_16":26,"_22":2797},"Scalar count",[2856],{"_2215":2857,"_2217":2858},"A = zeros(3, 4); numel(A)","12",[93,2834],{"_16":2836,"_18":2861,"_20":2862,"_22":2863,"_23":2864,"_29":2866,"_31":2867,"_2222":2870},"n = ndims(A)","Number of array dimensions","Returns the number of dimensions of the array.",[2865],{"_16":26,"_22":2797},"Scalar dimension count",[2868],{"_2215":2869,"_2217":2591},"A = zeros(3, 4); ndims(A)",[93,2834],{"_16":2872,"_18":2873,"_20":2874,"_22":2875,"_23":2876,"_29":2880,"_31":2881,"_2222":2885},"reshape","B = reshape(A, m, n)","Reshape array","Reshapes array A into an m-by-n matrix. The number of elements must not change.",[2877,2878,2879],{"_16":26,"_22":2797},{"_16":1130,"_22":2209},{"_16":629,"_22":2211},"Reshaped NDArray",[2882],{"_2215":2883,"_2217":2884},"reshape([1 2 3 4 5 6], 2, 3)","1 3 5\n2 4 6",[93,2886],"transpose",{"_16":2886,"_18":2888,"_20":2889,"_22":2890,"_23":2891,"_29":2894,"_31":2895,"_2222":2899},"B = transpose(A)\nB = A'","Transpose matrix","Transposes a matrix (swaps rows and columns).",[2892],{"_16":26,"_22":2893},"Input matrix","Transposed NDArray",[2896],{"_2215":2897,"_2217":2898},"A = [1 2; 3 4]; A'","1 3\n2 4",[2872,2900],"flip",{"_16":2253,"_18":2902,"_20":2903,"_22":2904,"_23":2905,"_29":2909,"_31":2910,"_2222":2914},"D = diag(v)\nd = diag(A)","Create diagonal matrix or extract diagonal","If the input is a vector, creates a diagonal matrix. If the input is a matrix, extracts the diagonal.",[2906],{"_16":2907,"_22":2908},"v/A","Input vector or matrix","Diagonal matrix or diagonal vector",[2911],{"_2215":2912,"_2217":2913},"diag([1 2 3])","1 0 0\n0 2 0\n0 0 3",[2225,2203],{"_16":2900,"_18":2916,"_20":2917,"_22":2918,"_23":2919,"_29":2923,"_31":2924,"_2222":2928},"B = flip(A)\nB = flip(A, dim)","Flip order of elements","Reverses the order of elements along the specified dimension (default: first non-singleton dimension).",[2920,2921],{"_16":26,"_22":2797},{"_16":2675,"_22":2922,"_28":11},"Dimension to flip along","Flipped NDArray",[2925],{"_2215":2926,"_2217":2927},"flip([1 2 3])","3 2 1",[2929,2930,2931],"fliplr","flipud","rot90",{"_16":2929,"_18":2933,"_20":2934,"_22":2935,"_23":2936,"_29":2923,"_31":2938,"_2222":2942},"B = fliplr(A)","Flip array left to right","Flips a matrix left to right (reverses columns).",[2937],{"_16":26,"_22":2893},[2939],{"_2215":2940,"_2217":2941},"fliplr([1 2 3; 4 5 6])","3 2 1\n6 5 4",[2930,2900,2931],{"_16":2930,"_18":2944,"_20":2945,"_22":2946,"_23":2947,"_29":2923,"_31":2949,"_2222":2953},"B = flipud(A)","Flip array up to down","Flips a matrix up to down (reverses rows).",[2948],{"_16":26,"_22":2893},[2950],{"_2215":2951,"_2217":2952},"flipud([1 2; 3 4])","3 4\n1 2",[2929,2900,2931],{"_16":2931,"_18":2955,"_20":2956,"_22":2957,"_23":2958,"_29":2962,"_31":2963,"_2222":2967},"B = rot90(A)\nB = rot90(A, k)","Rotate array 90 degrees","Rotates the matrix 90 degrees counterclockwise. Optional argument k specifies the number of 90-degree rotations.",[2959,2960],{"_16":26,"_22":2893},{"_16":430,"_22":2961,"_28":11},"Number of 90° rotations (default: 1)","Rotated NDArray",[2964],{"_2215":2965,"_2217":2966},"rot90([1 2; 3 4])","2 4\n1 3",[2900,2886],{"_16":1460,"_18":2969,"_20":2970,"_22":2971,"_23":2972,"_29":2976,"_31":2977,"_2222":2981},"s = lower(str)","Convert string to lowercase","Converts all uppercase characters in the string to lowercase.",[2973],{"_16":2974,"_22":2975},"str","Input string","Lowercase string",[2978],{"_2215":2979,"_2217":2980},"lower(\"Hello World\")","'hello world'",[1466],{"_16":1466,"_18":2983,"_20":2984,"_22":2985,"_23":2986,"_29":2988,"_31":2989,"_2222":2993},"s = upper(str)","Convert string to uppercase","Converts all lowercase characters in the string to uppercase.",[2987],{"_16":2974,"_22":2975},"Uppercase string",[2990],{"_2215":2991,"_2217":2992},"upper(\"Hello World\")","'HELLO WORLD'",[1460],{"_16":2995,"_18":2996,"_20":2997,"_22":2998,"_23":2999,"_29":3001,"_31":3002,"_2222":3005},"strlength","n = strlength(str)","Length of string","Returns the number of characters in the string.",[3000],{"_16":2974,"_22":2975},"Number of characters",[3003],{"_2215":3004,"_2217":2629},"strlength(\"hello\")",[2834],{"_16":3007,"_18":3008,"_20":3009,"_22":3010,"_23":3011,"_29":3018,"_31":3019,"_2222":3024},"strcmp","tf = strcmp(s1, s2)","Compare strings","Returns 1 if the strings are identical, 0 otherwise.",[3012,3015],{"_16":3013,"_22":3014},"s1","First string",{"_16":3016,"_22":3017},"s2","Second string","1 if equal, 0 otherwise",[3020,3022],{"_2215":3021,"_2217":2434},"strcmp(\"abc\", \"abc\")",{"_2215":3023,"_2217":2524},"strcmp(\"abc\", \"def\")",[3025],"strcmpi",{"_16":3025,"_18":3027,"_20":3028,"_22":3029,"_23":3030,"_29":3033,"_31":3034,"_2222":3037},"tf = strcmpi(s1, s2)","Compare strings (case-insensitive)","Returns 1 if the strings are identical ignoring case, 0 otherwise.",[3031,3032],{"_16":3013,"_22":3014},{"_16":3016,"_22":3017},"1 if equal (ignoring case), 0 otherwise",[3035],{"_2215":3036,"_2217":2434},"strcmpi(\"Hello\", \"hello\")",[3007],{"_16":3039,"_18":3040,"_20":3041,"_22":3042,"_23":3043,"_29":3049,"_31":3050,"_2222":3054},"strfind","k = strfind(str, pattern)","Find pattern in string","Returns the starting index of each occurrence of pattern in str. Returns empty array if not found.",[3044,3046],{"_16":2974,"_22":3045},"String to search in",{"_16":3047,"_22":3048},"pattern","Pattern to find","Array of starting indices",[3051],{"_2215":3052,"_2217":3053},"strfind(\"abcabc\", \"bc\")","[2, 5]",[3055,3056,3057],"contains","startsWith","endsWith",{"_16":3059,"_18":3060,"_20":3061,"_22":3062,"_23":3063,"_29":3071,"_31":3072,"_2222":3076},"strrep","s = strrep(str, old, new)","Replace substring","Replaces all occurrences of old with new in str.",[3064,3065,3068],{"_16":2974,"_22":2975},{"_16":3066,"_22":3067},"old","Substring to replace",{"_16":3069,"_22":3070},"new","Replacement string","String with replacements made",[3073],{"_2215":3074,"_2217":3075},"strrep(\"hello world\", \"world\", \"there\")","'hello there'",[3039],{"_16":3078,"_18":3079,"_20":3080,"_22":3081,"_23":3082,"_29":3084,"_31":3085,"_2222":3089},"strip","s = strip(str)","Remove leading and trailing whitespace","Removes leading and trailing whitespace characters from the string.",[3083],{"_16":2974,"_22":2975},"Trimmed string",[3086],{"_2215":3087,"_2217":3088},"strip(\" hello \")","'hello'",[],{"_16":3056,"_18":3091,"_20":3092,"_22":3093,"_23":3094,"_29":3099,"_31":3100,"_2222":3103},"tf = startsWith(str, prefix)","Check if string starts with prefix","Returns 1 if str starts with prefix, 0 otherwise.",[3095,3096],{"_16":2974,"_22":2975},{"_16":3097,"_22":3098},"prefix","Prefix to check","1 if starts with prefix, 0 otherwise",[3101],{"_2215":3102,"_2217":2434},"startsWith(\"hello\", \"hel\")",[3057,3055],{"_16":3057,"_18":3105,"_20":3106,"_22":3107,"_23":3108,"_29":3113,"_31":3114,"_2222":3117},"tf = endsWith(str, suffix)","Check if string ends with suffix","Returns 1 if str ends with suffix, 0 otherwise.",[3109,3110],{"_16":2974,"_22":2975},{"_16":3111,"_22":3112},"suffix","Suffix to check","1 if ends with suffix, 0 otherwise",[3115],{"_2215":3116,"_2217":2434},"endsWith(\"hello\", \"lo\")",[3056,3055],{"_16":3055,"_18":3119,"_20":3120,"_22":3121,"_23":3122,"_29":3126,"_31":3127,"_2222":3130},"tf = contains(str, pattern)","Check if string contains pattern","Returns 1 if str contains pattern, 0 otherwise.",[3123,3124],{"_16":2974,"_22":2975},{"_16":3047,"_22":3125},"Pattern to search for","1 if contains pattern, 0 otherwise",[3128],{"_2215":3129,"_2217":2434},"contains(\"hello world\", \"wor\")",[3056,3057,3039],{"_16":3132,"_18":3133,"_20":3134,"_22":3135,"_23":3136,"_29":3143,"_31":3144,"_2222":3151},"sprintf","s = sprintf(format, A1, A2, ...)","Format data into string","Formats data according to format string. Supports %d (integer), %f (float), %s (string), %e (exponential).",[3137,3140],{"_16":3138,"_22":3139},"format","Format string with conversion specifiers",{"_16":3141,"_22":3142},"A1, A2, ...","Values to format","Formatted string",[3145,3148],{"_2215":3146,"_2217":3147},"sprintf(\"x = %d\", 42)","'x = 42'",{"_2215":3149,"_2217":3150},"sprintf(\"pi = %.4f\", pi)","'pi = 3.1416'",[3152],"disp",{"_16":3154,"_18":3155,"_20":3156,"_22":3157,"_23":3158,"_29":3161,"_31":3162,"_2222":3169},"char","c = char(n)","Convert to character","Converts numeric code to character, or ensures input is a character array.",[3159],{"_16":629,"_22":3160},"Numeric ASCII/Unicode code or string","Character string",[3163,3166],{"_2215":3164,"_2217":3165},"char(65)","'A'",{"_2215":3167,"_2217":3168},"char([72 101 108 108 111])","'Hello'",[3170],"double",{"_16":3172,"_18":3173,"_20":3174,"_22":3175,"_23":3176,"_29":3182,"_31":3183,"_2222":3190},"num2str","s = num2str(A)\ns = num2str(A, precision)","Convert number to string","Converts numeric array to string representation.",[3177,3179],{"_16":26,"_22":3178},"Numeric value or array",{"_16":3180,"_22":3181,"_28":11},"precision","Number of significant digits","String representation of number",[3184,3187],{"_2215":3185,"_2217":3186},"num2str(3.14159)","'3.1416'",{"_2215":3188,"_2217":3189},"num2str(pi, 10)","'3.141592654'",[3191,3132],"str2num",{"_16":3191,"_18":3193,"_20":3194,"_22":3195,"_23":3196,"_29":3199,"_31":3200,"_2222":3204},"n = str2num(str)","Convert string to number","Converts string representation of number to numeric value.",[3197],{"_16":2974,"_22":3198},"String containing numeric value","Numeric value",[3201],{"_2215":3202,"_2217":3203},"str2num(\"3.14\")","3.14",[3172],{"_16":3206,"_18":3207,"_20":3208,"_22":3209,"_23":3210,"_29":3214,"_31":3215,"_2222":3218},"strcat","s = strcat(s1, s2, ...)","Concatenate strings","Concatenates strings horizontally.",[3211],{"_16":3212,"_22":3213},"s1, s2, ...","Strings to concatenate","Concatenated string",[3216],{"_2215":3217,"_2217":2980},"strcat(\"hello\", \" \", \"world\")",[],{"_16":3220,"_18":3221,"_20":3222,"_22":3223,"_23":3224,"_29":3231,"_31":3232,"_2222":3236},"strjoin","s = strjoin(strs, delimiter)","Join strings with delimiter","Joins an array of strings with the specified delimiter.",[3225,3228],{"_16":3226,"_22":3227},"strs","Cell array or string array",{"_16":3229,"_22":3230,"_28":11},"delimiter","Delimiter string (default: space)","Joined string",[3233],{"_2215":3234,"_2217":3235},"strjoin([\"a\", \"b\", \"c\"], \"-\")","'a-b-c'",[3206],{"_16":3238,"_18":3239,"_20":3240,"_22":3241,"_23":3242,"_29":3246,"_31":3247,"_2222":3251},"strsplit","parts = strsplit(str, delimiter)","Split string at delimiter","Splits a string at each occurrence of delimiter.",[3243,3244],{"_16":2974,"_22":2975},{"_16":3229,"_22":3245,"_28":11},"Delimiter string (default: whitespace)","Array of substrings",[3248],{"_2215":3249,"_2217":3250},"strsplit(\"a-b-c\", \"-\")","['a', 'b', 'c']",[3220],{"_16":3152,"_18":3253,"_20":3254,"_22":3255,"_23":3256,"_29":3259,"_31":3260,"_2222":3264},"disp(X)","Display value","Displays the value of a variable or expression without the variable name.",[3257],{"_16":2428,"_22":3258},"Value to display","The input value (also displayed as output)",[3261],{"_2215":3262,"_2217":3263},"disp('hello')","hello",[],{"_16":3266,"_18":3266,"_20":3267,"_22":3268,"_23":3269,"_29":30,"_31":3270,"_2222":3274},"tic","Start stopwatch timer","Starts a stopwatch timer to measure elapsed time. Use with toc to measure execution time of code blocks. Multiple tic calls reset the timer.",[],[3271],{"_2215":3272,"_2217":3273},"tic\nA = rand(100);\ntoc","Elapsed time is 0.012345 seconds.",[3275],"toc",{"_16":3275,"_18":3277,"_20":3278,"_22":3279,"_23":3280,"_29":3281,"_31":3282,"_2222":3286},"t = toc","Read elapsed time from stopwatch","Reads the elapsed time in seconds since the most recent tic call. Prints the elapsed time and returns it as a number. Throws an error if called without a preceding tic.",[],"Elapsed time in seconds (scalar)",[3283],{"_2215":3284,"_2217":3285},"tic\nfor i = 1:100\n rand(10);\nend\nt = toc","Elapsed time is 0.005123 seconds.\nt = 0.005123",[3266],{"_16":3288,"_18":3289,"_20":3290,"_22":3291,"_23":3292,"_29":3296,"_31":3297,"_2222":3304},"eval","eval(expression)\n[output1,...,outputN] = eval(expression)","Evaluate M-Code expression","Evaluates the M-Code contained in the string expression. Variables created or modified in the evaluated code affect the current workspace.",[3293],{"_16":3294,"_22":3295},"expression","String containing M-Code to evaluate","Result of the evaluated expression",[3298,3301],{"_2215":3299,"_2217":3300},"eval('x = 5')","x = 5",{"_2215":3302,"_2217":3303},"Z = eval('magic(3)')","Z = [8 1 6; 3 5 7; 4 9 2]",[],{"_35":3306,"_16":3307,"_22":3308,"_39":40,"_41":42,"_45":3309},"linalg","Linear Algebra","Matrix decompositions, solvers, products, norms, and other linear algebra operations.",[3310,3329,3345,3356,3373,3388,3403,3415,3430,3444,3455,3469,3480,3498,3509,3527,3541,3553,3571,3587,3602,3616,3632,3649],{"_16":3311,"_18":3312,"_20":3313,"_22":3314,"_23":3315,"_29":3318,"_31":3319,"_2222":3325},"eig","D = eig(A)\n[V,D] = eig(A)","Eigenvalues and eigenvectors","With one output, returns a vector of eigenvalues. With two outputs, V contains eigenvectors as columns and D is a diagonal matrix of eigenvalues.",[3316],{"_16":26,"_22":3317},"Square matrix (n×n)","Eigenvalue vector, or [V, D] decomposition",[3320,3323],{"_2215":3321,"_2217":3322},"eig([2 1; 1 2])","3\n1",{"_2215":3324},"[V,D] = eig([2 1; 1 2])",[3326,3327,3328],"svd","det","inv",{"_16":3330,"_18":3331,"_20":3332,"_22":3333,"_23":3334,"_29":3318,"_31":3337,"_2222":3343},"eigh","D = eigh(A)\n[V, D] = eigh(A)","Eigenvalues and eigenvectors of symmetric matrix","Computes eigenvalues and eigenvectors of a symmetric or Hermitian matrix. Eigenvalues are always real and returned in ascending order. More efficient than eig() for symmetric matrices.",[3335],{"_16":26,"_22":3336},"Symmetric/Hermitian matrix (n×n)",[3338,3341],{"_2215":3339,"_2217":3340},"A = [2 1; 1 2];\nD = eigh(A)","1\n3",{"_2215":3342},"[V, D] = eigh([2 1; 1 2])",[3311,3344,3326],"eigvalsh",{"_16":3344,"_18":3346,"_20":3347,"_22":3348,"_23":3349,"_29":3351,"_31":3352,"_2222":3355},"D = eigvalsh(A)","Eigenvalues of symmetric matrix","Computes only the eigenvalues of a symmetric or Hermitian matrix. More efficient than eigh() when eigenvectors are not needed. Eigenvalues are returned in ascending order.",[3350],{"_16":26,"_22":3336},"Vector of eigenvalues in ascending order",[3353],{"_2215":3354,"_2217":3340},"eigvalsh([2 1; 1 2])",[3330,3311],{"_16":3326,"_18":3357,"_20":3358,"_22":3359,"_23":3360,"_29":3363,"_31":3364,"_2222":3370},"S = svd(A)\n[U,S,V] = svd(A)","Singular value decomposition","With one output, returns singular values as a vector. With three outputs, returns the full U*S*V' decomposition where S is a diagonal matrix.",[3361],{"_16":26,"_22":3362},"Input matrix (m×n)","Singular value vector, or [U, S, V] decomposition",[3365,3368],{"_2215":3366,"_2217":3367},"svd([1 0; 0 2])","2\n1",{"_2215":3369},"[U,S,V] = svd([1 0; 0 2])",[3311,3371,3372],"rank","norm",{"_16":3374,"_18":3375,"_20":3376,"_22":3377,"_23":3378,"_29":3380,"_31":3381,"_2222":3386},"qr","R = qr(A)\n[Q,R] = qr(A)","QR decomposition","With one output, returns the upper-triangular R factor. With two outputs, returns Q (orthonormal) and R (upper-triangular).",[3379],{"_16":26,"_22":3362},"R matrix, or [Q, R] decomposition",[3382,3384],{"_2215":3383,"_2217":2251},"qr(eye(3))",{"_2215":3385},"[Q,R] = qr([1 2; 3 4])",[3326,3387,3311],"chol",{"_16":3389,"_18":3390,"_20":3391,"_22":3392,"_23":3393,"_29":3395,"_31":3396,"_2222":3401},"lu","L = lu(A)\n[L,U,P] = lu(A)","LU decomposition with partial pivoting","Factorizes matrix A into lower triangular L (unit diagonal), upper triangular U, and permutation matrix P such that P*A = L*U. With one output, returns the lower triangular factor only.",[3394],{"_16":26,"_22":3362},"Lower triangular factor L, or [L, U, P] decomposition",[3397,3399],{"_2215":3398},"[L,U,P] = lu([2 1; 4 3])",{"_2215":3400},"L = lu([1 2; 3 4])",[3374,3326,3387,3402],"linsolve",{"_16":3387,"_18":3404,"_20":3405,"_22":3406,"_23":3407,"_29":3410,"_31":3411,"_2222":3414},"R = chol(A)","Cholesky factorization","Computes the upper-triangular Cholesky factor R such that R'*R = A. The input must be a symmetric positive-definite matrix.",[3408],{"_16":26,"_22":3409},"Symmetric positive-definite matrix (n×n)","Upper-triangular Cholesky factor R",[3412],{"_2215":3413},"chol([4 2; 2 3])",[3374,3326,3328],{"_16":3327,"_18":3416,"_20":3417,"_22":3418,"_23":3419,"_29":3421,"_31":3422,"_2222":3428},"d = det(A)","Matrix determinant","Computes the determinant of a square matrix.",[3420],{"_16":26,"_22":3317},"Scalar determinant value",[3423,3426],{"_2215":3424,"_2217":3425},"det([1 2; 3 4])","-2",{"_2215":3427,"_2217":2434},"det(eye(3))",[3328,3371,3429],"trace",{"_16":3328,"_18":3431,"_20":3432,"_22":3433,"_23":3434,"_29":3437,"_31":3438,"_2222":3442},"B = inv(A)","Matrix inverse","Computes the multiplicative inverse of a square matrix so that A*B = eye(n). The matrix must be non-singular.",[3435],{"_16":26,"_22":3436},"Non-singular square matrix (n×n)","Inverse matrix (n×n)",[3439],{"_2215":3440,"_2217":3441},"inv([1 2; 3 4])","-2.0000 1.0000\n1.5000 -0.5000",[3327,3443,3402],"pinv",{"_16":3443,"_18":3445,"_20":3446,"_22":3447,"_23":3448,"_29":3450,"_31":3451,"_2222":3454},"B = pinv(A)","Moore-Penrose pseudo-inverse","Computes the pseudo-inverse of a matrix. Works for non-square and singular matrices.",[3449],{"_16":26,"_22":3362},"Pseudo-inverse matrix (n×m)",[3452],{"_2215":3453},"pinv([1 0; 0 0])",[3328,3402,3371],{"_16":3371,"_18":3456,"_20":3457,"_22":3458,"_23":3459,"_29":3461,"_31":3462,"_2222":3467},"r = rank(A)","Matrix rank","Estimates the rank of a matrix using singular value decomposition. The rank is the number of singular values above a tolerance threshold.",[3460],{"_16":26,"_22":2893},"Scalar rank",[3463,3465],{"_2215":3464,"_2217":2603},"rank(eye(3))",{"_2215":3466,"_2217":2434},"rank([1 2; 2 4])",[3326,3327,3468],"cond",{"_16":3429,"_18":3470,"_20":3471,"_22":3472,"_23":3473,"_29":3475,"_31":3476,"_2222":3479},"t = trace(A)","Sum of diagonal elements","Returns the sum of the elements on the main diagonal of a matrix.",[3474],{"_16":26,"_22":2893},"Scalar trace value",[3477],{"_2215":3478,"_2217":2654},"trace(eye(4))",[2253,3327,3311],{"_16":3372,"_18":3481,"_20":3482,"_22":3483,"_23":3484,"_29":3488,"_31":3489,"_2222":3497},"n = norm(A)\nn = norm(A, p)\nn = norm(A, 'fro')","Matrix or vector norm","Computes the norm of a vector or matrix. For vectors, the default is the 2-norm (Euclidean). For matrices, the default is the Frobenius norm. An optional second argument specifies the norm order (1, 2, etc.) or type ('fro' for Frobenius, 'nuc' for nuclear).",[3485,3486],{"_16":26,"_22":2908},{"_16":552,"_22":3487,"_28":11},"Norm order or type: number (1, 2, Inf), or string ('fro', 'nuc')","Scalar norm value",[3490,3492,3495],{"_2215":3491,"_2217":2629},"norm([3 4])",{"_2215":3493,"_2217":3494},"norm([3 4], 1)","7",{"_2215":3496},"norm([1 2; 3 4], 'fro')",[3468,3371,3327],{"_16":3468,"_18":3499,"_20":3500,"_22":3501,"_23":3502,"_29":3504,"_31":3505,"_2222":3508},"c = cond(A)","Condition number","Computes the condition number of a matrix using the ratio of the largest to smallest singular value. A large condition number indicates a nearly singular matrix.",[3503],{"_16":26,"_22":2893},"Scalar condition number",[3506],{"_2215":3507,"_2217":2434},"cond(eye(3))",[3372,3371,3327],{"_16":3510,"_18":3511,"_20":3512,"_22":3513,"_23":3514,"_29":3519,"_31":3520,"_2222":3525},"lstsq","x = lstsq(A, b)\n[x, residuals, rank, s] = lstsq(A, b)","Least-squares solution to linear equation","Computes the least-squares solution to the equation A*x = b. Returns the solution that minimizes ||A*x - b||. With one output, returns the solution vector x. With four outputs, also returns residuals, rank, and singular values.",[3515,3517],{"_16":26,"_22":3516},"Coefficient matrix (m×n)",{"_16":983,"_22":3518},"Ordinate values (m×1) or (m×k)","Solution vector x, or [x, residuals, rank, s]",[3521,3523],{"_2215":3522},"A = [1 0; 1 1; 1 2]; b = [1; 2; 3];\nx = lstsq(A, b)",{"_2215":3524},"[x, res, rnk, s] = lstsq(A, b)",[3526,3443,3374],"mldivide",{"_16":3402,"_18":3528,"_20":3529,"_22":3530,"_23":3531,"_29":3536,"_31":3537,"_2222":3540},"x = linsolve(A, b)","Solve linear system Ax = b","Solves the linear system A*x = b for x, where A is a square matrix and b is a column vector or matrix.",[3532,3534],{"_16":26,"_22":3533},"Coefficient matrix (n×n)",{"_16":983,"_22":3535},"Right-hand side vector or matrix","Solution vector or matrix x",[3538],{"_2215":3539},"A = [1 2; 3 4]; b = [5; 6]; linsolve(A, b)",[3526,3328,3327],{"_16":3526,"_18":3542,"_20":3543,"_22":3544,"_23":3545,"_29":3536,"_31":3549,"_2222":3552},"x = mldivide(A, b)","Matrix left division (A\\b)","Solves the linear system A*x = b. Equivalent to the backslash operator `A\\b`. For square A, this uses direct solving. Prefer this over `inv(A)*b` for numerical stability.",[3546,3548],{"_16":26,"_22":3547},"Coefficient matrix",{"_16":983,"_22":3535},[3550],{"_2215":3551},"A = [1 2; 3 4]; b = [5; 6]; mldivide(A, b)",[3402,3328],{"_16":3554,"_18":3555,"_20":3556,"_22":3557,"_23":3558,"_29":3563,"_31":3564,"_2222":3567},"matmul","C = matmul(A, B)","Matrix multiplication","Matrix multiplication of two arrays. For 2-D arrays, performs standard matrix multiplication. For N-D arrays, broadcasts over batch dimensions and multiplies the last two dimensions.",[3559,3561],{"_16":26,"_22":3560},"First array (..., M, K)",{"_16":505,"_22":3562},"Second array (..., K, N)","Matrix product (..., M, N)",[3565],{"_2215":3566},"matmul([1 2; 3 4], [5 6; 7 8])",[3568,3569,3570],"dot","kron","mpower",{"_16":3568,"_18":3572,"_20":3573,"_22":3574,"_23":3575,"_29":3580,"_31":3581,"_2222":3585},"c = dot(a, b)","Dot product","Computes the dot product of two arrays. For 1-D arrays, returns the inner product. For 2-D arrays, performs matrix multiplication.",[3576,3578],{"_16":2283,"_22":3577},"First input array",{"_16":983,"_22":3579},"Second input array","Dot product result",[3582],{"_2215":3583,"_2217":3584},"dot([1 2 3], [4 5 6])","32",[3586,3569],"cross",{"_16":3586,"_18":3588,"_20":3589,"_22":3590,"_23":3591,"_29":3596,"_31":3597,"_2222":3601},"c = cross(a, b)","Cross product","Computes the cross product of two 3-element vectors.",[3592,3594],{"_16":2283,"_22":3593},"First 3-element vector",{"_16":983,"_22":3595},"Second 3-element vector","3-element cross product vector",[3598],{"_2215":3599,"_2217":3600},"cross([1 0 0], [0 1 0])","0 0 1",[3568,3569],{"_16":3569,"_18":3603,"_20":3604,"_22":3605,"_23":3606,"_29":3611,"_31":3612,"_2222":3615},"K = kron(A, B)","Kronecker tensor product","Computes the Kronecker product of two matrices. Each element of A is multiplied by the entire matrix B.",[3607,3609],{"_16":26,"_22":3608},"First input matrix",{"_16":505,"_22":3610},"Second input matrix","Kronecker product matrix",[3613],{"_2215":3614},"kron([1 0; 0 1], [1 2; 3 4])",[3568,3586],{"_16":3617,"_18":3618,"_20":3619,"_22":3620,"_23":3621,"_29":3626,"_31":3627,"_2222":3631},"outer","C = outer(a, b)","Outer product","Computes the outer product of two vectors, resulting in a matrix where C(i,j) = a(i)*b(j).",[3622,3624],{"_16":2283,"_22":3623},"First vector (m-element)",{"_16":983,"_22":3625},"Second vector (n-element)","Outer product matrix (m x n)",[3628],{"_2215":3629,"_2217":3630},"outer([1 2 3], [4 5])","4 5\n8 10\n12 15",[3568,3586,3569],{"_16":3633,"_18":3634,"_20":3635,"_22":3636,"_23":3637,"_29":3644,"_31":3645,"_2222":3648},"einsum","C = einsum(subscripts, A, B, ...)","Einstein summation convention","Evaluates the Einstein summation convention on the operands. The subscripts string specifies index contractions (e.g., \"ij,jk->ik\" for matrix multiplication).",[3638,3641],{"_16":3639,"_22":3640},"subscripts","Subscript string (e.g., \"ij,jk->ik\")",{"_16":3642,"_22":3643},"A,B,...","Input arrays","Result array according to subscripts",[3646],{"_2215":3647},"einsum('ij,jk->ik', A, B)",[3568,3554],{"_16":3570,"_18":3650,"_20":3651,"_22":3652,"_23":3653,"_29":3657,"_31":3658,"_2222":3661},"B = mpower(A, n)","Matrix power","Raises a square matrix to an integer power. Negative exponents compute the inverse raised to the absolute power.",[3654,3655],{"_16":26,"_22":3317},{"_16":629,"_22":3656},"Integer exponent","Matrix raised to power n",[3659],{"_2215":3660,"_2217":2251},"mpower(eye(3), 2)",[3328,3327],{"_35":3663,"_16":3664,"_22":3665,"_39":40,"_41":3666,"_45":3667},"fft","Fourier Analysis","Fast Fourier Transform, inverse transforms, frequency utilities, and window functions for spectral analysis.","〰️",[3668,3688,3705,3718,3730,3742,3754,3767,3779,3793,3811,3822,3833,3844],{"_16":3663,"_18":3669,"_20":3670,"_22":3671,"_23":3672,"_29":3677,"_31":3678,"_2222":3683},"Y = fft(X)\nY = fft(X, n)","Fast Fourier Transform","Computes the one-dimensional discrete Fourier Transform using the FFT algorithm. If `n` is specified, the input is either truncated or zero-padded to length `n` before transforming.",[3673,3675],{"_16":2428,"_22":3674},"Input signal (vector or array)",{"_16":629,"_22":3676,"_28":11},"Transform length (zero-pads or truncates)","Complex-valued frequency-domain representation",[3679,3681],{"_2215":3680},"fft([1 2 3 4])",{"_2215":3682},"fft([1 0 1 0], 8)",[3684,3685,3686,3687],"ifft","fft2","fftshift","fftfreq",{"_16":3684,"_18":3689,"_20":3690,"_22":3691,"_23":3692,"_29":3698,"_31":3699,"_2222":3702},"x = ifft(Y)\nx = ifft(Y, n)","Inverse Fast Fourier Transform","Computes the one-dimensional inverse discrete Fourier Transform. Recovers the original time-domain signal from its frequency-domain representation.",[3693,3696],{"_16":3694,"_22":3695},"Y","Frequency-domain input",{"_16":629,"_22":3697,"_28":11},"Transform length","Time-domain signal",[3700],{"_2215":3701},"ifft(fft([1 2 3 4]))",[3663,3703,3704],"ifft2","ifftn",{"_16":3685,"_18":3706,"_20":3707,"_22":3708,"_23":3709,"_29":3712,"_31":3713,"_2222":3716},"Y = fft2(X)","2-D Fast Fourier Transform","Computes the two-dimensional discrete Fourier Transform. Useful for image processing and 2-D signal analysis.",[3710],{"_16":2428,"_22":3711},"Input 2-D array","2-D frequency-domain representation",[3714],{"_2215":3715},"fft2(eye(4))",[3703,3663,3717],"fftn",{"_16":3703,"_18":3719,"_20":3720,"_22":3721,"_23":3722,"_29":3725,"_31":3726,"_2222":3729},"x = ifft2(Y)","2-D inverse FFT","Computes the two-dimensional inverse discrete Fourier Transform.",[3723],{"_16":3694,"_22":3724},"Frequency-domain 2-D input","Spatial-domain 2-D signal",[3727],{"_2215":3728},"ifft2(fft2(eye(4)))",[3685,3684,3704],{"_16":3717,"_18":3731,"_20":3732,"_22":3733,"_23":3734,"_29":3737,"_31":3738,"_2222":3741},"Y = fftn(X)","N-dimensional FFT","Computes the N-dimensional discrete Fourier Transform over all axes of the input array.",[3735],{"_16":2428,"_22":3736},"Input N-D array","N-D frequency-domain representation",[3739],{"_2215":3740},"fftn(ones(4, 4))",[3704,3663,3685],{"_16":3704,"_18":3743,"_20":3744,"_22":3745,"_23":3746,"_29":3749,"_31":3750,"_2222":3753},"x = ifftn(Y)","N-dimensional inverse FFT","Computes the N-dimensional inverse discrete Fourier Transform.",[3747],{"_16":3694,"_22":3748},"Frequency-domain N-D input","Spatial-domain N-D signal",[3751],{"_2215":3752},"ifftn(fftn(ones(4, 4)))",[3717,3684,3703],{"_16":3686,"_18":3755,"_20":3756,"_22":3757,"_23":3758,"_29":3761,"_31":3762,"_2222":3765},"Y = fftshift(X)","Shift zero-frequency component to center","Rearranges the output of `fft` by shifting the zero-frequency component to the center of the array. Useful for visualizing the Fourier transform with the DC component in the middle.",[3759],{"_16":2428,"_22":3760},"Input array (typically output of fft)","Shifted array",[3763],{"_2215":3764},"fftshift(fft([1 2 3 4 5 6 7 8]))",[3766,3663,3687],"ifftshift",{"_16":3766,"_18":3768,"_20":3769,"_22":3770,"_23":3771,"_29":3774,"_31":3775,"_2222":3778},"Y = ifftshift(X)","Inverse of fftshift","Undoes the effect of `fftshift`. Shifts the zero-frequency component back to the beginning of the array.",[3772],{"_16":2428,"_22":3773},"Shifted input array","Unshifted array",[3776],{"_2215":3777},"ifftshift(fftshift([1 2 3 4]))",[3686,3663],{"_16":3687,"_18":3780,"_20":3781,"_22":3782,"_23":3783,"_29":3788,"_31":3789,"_2222":3792},"f = fftfreq(n)\nf = fftfreq(n, d)","DFT sample frequencies","Returns the discrete Fourier Transform sample frequencies. For a signal of length `n` with sample spacing `d`, the frequencies are `[0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n)` for even `n`.",[3784,3786],{"_16":629,"_22":3785},"Window length (number of samples)",{"_16":1096,"_22":3787,"_28":11},"Sample spacing (default: 1.0)","Array of sample frequencies",[3790],{"_2215":3791},"fftfreq(8, 0.1)",[3663,3686],{"_16":3794,"_18":3795,"_20":3796,"_22":3797,"_23":3798,"_29":3802,"_31":3803,"_2222":3806},"bartlett","w = bartlett(M)","Bartlett (triangular) window","Returns an M-point Bartlett window. Similar to a triangular window but with zero-valued endpoints. Useful for spectral analysis with reduced spectral leakage.",[3799],{"_16":3800,"_22":3801},"M","Number of points in the window","M-point Bartlett window vector",[3804],{"_2215":3805},"bartlett(8)",[3807,3808,3809,3810],"hamming","hanning","blackman","kaiser",{"_16":3809,"_18":3812,"_20":3813,"_22":3814,"_23":3815,"_29":3817,"_31":3818,"_2222":3821},"w = blackman(M)","Blackman window","Returns an M-point Blackman window. Designed to have close to minimal spectral leakage. Has wider main lobe but lower side lobes than Hamming or Hanning.",[3816],{"_16":3800,"_22":3801},"M-point Blackman window vector",[3819],{"_2215":3820},"blackman(8)",[3807,3808,3794,3810],{"_16":3807,"_18":3823,"_20":3824,"_22":3825,"_23":3826,"_29":3828,"_31":3829,"_2222":3832},"w = hamming(M)","Hamming window","Returns an M-point Hamming window. A raised-cosine window with coefficients optimized to minimize the nearest side lobe. Formula: w(n) = 0.54 - 0.46*cos(2*pi*n/(M-1)).",[3827],{"_16":3800,"_22":3801},"M-point Hamming window vector",[3830],{"_2215":3831},"hamming(8)",[3808,3809,3794,3810],{"_16":3808,"_18":3834,"_20":3835,"_22":3836,"_23":3837,"_29":3839,"_31":3840,"_2222":3843},"w = hanning(M)","Hanning (Hann) window","Returns an M-point Hanning window (also known as Hann window). A raised-cosine window. Formula: w(n) = 0.5*(1 - cos(2*pi*n/(M-1))).",[3838],{"_16":3800,"_22":3801},"M-point Hanning window vector",[3841],{"_2215":3842},"hanning(8)",[3807,3809,3794,3810],{"_16":3810,"_18":3845,"_20":3846,"_22":3847,"_23":3848,"_29":3852,"_31":3853,"_2222":3856},"w = kaiser(M, beta)","Kaiser window","Returns an M-point Kaiser window with shape parameter beta. The Kaiser window approximates the DPSS window and provides a flexible trade-off between main-lobe width and side-lobe level. Common beta values: 0 (rectangular), 5 (similar to Hamming), 6 (similar to Hanning), 8.6 (similar to Blackman).",[3849,3850],{"_16":3800,"_22":3801},{"_16":1027,"_22":3851},"Shape parameter controlling the trade-off","M-point Kaiser window vector",[3854],{"_2215":3855},"kaiser(8, 5)",[3807,3808,3809,3794],{"_35":3858,"_16":3859,"_22":3860,"_39":40,"_41":3861,"_45":3862},"plotting","Data Visualization","M-Code-style plotting functions for inline Chart.js visualizations.","📊",[3863,3883,3897,3908,3919,3934,3948,3971,3997,4035,4049,4060,4076,4087,4097,4109,4123,4139,4152,4165,4175,4189,4199,4212,4224,4235,4245,4254,4263,4275,4291,4304,4321,4341,4354,4364,4385,4410,4430,4451],{"_16":3864,"_18":3865,"_20":3866,"_22":3867,"_23":3868,"_29":3873,"_31":3874,"_2222":3877},"plot","plot(y)\nplot(x, y)","2-D line plot","Creates a line chart. Successive plot() calls add datasets to the same chart; call figure to start a new chart. If one argument is given, it is treated as y-values with x = 1:n. With two arguments, x and y are paired.",[3869,3871],{"_16":1350,"_22":3870,"_28":11},"X-axis data (NDArray or scalar)",{"_16":2349,"_22":3872},"Y-axis data (NDArray or scalar)","null (renders chart inline)",[3875],{"_2215":3876},"x = linspace(0, 2*pi, 50);\nplot(x, sin(x))",[3878,3879,3880,3881,3882],"scatter","bar","loglog","semilogx","semilogy",{"_16":3880,"_18":3884,"_20":3885,"_22":3886,"_23":3887,"_29":3890,"_31":3891,"_2222":3896},"loglog(y)\nloglog(x, y)","Log-log scale plot","Creates a 2-D line plot with logarithmic scales on both the x-axis and y-axis. Useful for visualizing power-law relationships and data spanning multiple orders of magnitude.",[3888,3889],{"_16":1350,"_22":3870,"_28":11},{"_16":2349,"_22":3872},"Line handle",[3892,3894],{"_2215":3893},"x = 1:100;\ny = x.^2;\nloglog(x, y)",{"_2215":3895},"x = logspace(0, 3, 50);\nloglog(x, x.^(-1.5))",[3864,3881,3882],{"_16":3881,"_18":3898,"_20":3899,"_22":3900,"_23":3901,"_29":3890,"_31":3904,"_2222":3907},"semilogx(y)\nsemilogx(x, y)","Semi-logarithmic plot (log x-axis)","Creates a 2-D line plot with a logarithmic scale on the x-axis and a linear scale on the y-axis.",[3902,3903],{"_16":1350,"_22":3870,"_28":11},{"_16":2349,"_22":3872},[3905],{"_2215":3906},"x = logspace(0, 3, 50);\nsemilogx(x, log10(x))",[3864,3880,3882],{"_16":3882,"_18":3909,"_20":3910,"_22":3911,"_23":3912,"_29":3890,"_31":3915,"_2222":3918},"semilogy(y)\nsemilogy(x, y)","Semi-logarithmic plot (log y-axis)","Creates a 2-D line plot with a linear scale on the x-axis and a logarithmic scale on the y-axis. Useful for exponential data.",[3913,3914],{"_16":1350,"_22":3870,"_28":11},{"_16":2349,"_22":3872},[3916],{"_2215":3917},"x = 1:10;\ny = 10.^x;\nsemilogy(x, y)",[3864,3880,3881],{"_16":3879,"_18":3920,"_20":3921,"_22":3922,"_23":3923,"_29":3873,"_31":3928,"_2222":3931},"bar(y)\nbar(x, y)","Bar chart","Creates a vertical bar chart.",[3924,3926],{"_16":1350,"_22":3925,"_28":11},"Category positions or labels (NDArray)",{"_16":2349,"_22":3927},"Bar heights (NDArray)",[3929],{"_2215":3930},"bar([3 7 2 5])",[3864,3932,3933],"histogram","pie",{"_16":3878,"_18":3935,"_20":3936,"_22":3937,"_23":3938,"_29":3873,"_31":3943,"_2222":3946},"scatter(x, y)","Scatter plot","Creates a scatter plot of y versus x.",[3939,3941],{"_16":1350,"_22":3940},"X-coordinates (NDArray)",{"_16":2349,"_22":3942},"Y-coordinates (NDArray)",[3944],{"_2215":3945},"scatter(rand(20, 1), rand(20, 1))",[3864,3879,3947],"spy",{"_16":3947,"_18":3949,"_20":3950,"_22":3951,"_23":3952,"_29":3873,"_31":3961,"_2222":3968},"spy(S)\nspy(S, linespec)\nspy(S, markersize)","Visualize sparsity pattern","Generates a graphical representation of the sparsity pattern of a matrix S. Nonzero values are displayed as markers at their (column, row) positions. The x-axis label shows \"nz = N\" where N is the number of nonzero elements.",[3953,3955,3958],{"_16":1113,"_22":3954},"Input matrix (sparse or full)",{"_16":3956,"_22":3957,"_28":11},"linespec","Line specification for marker style (e.g., 'ro' for red circles)",{"_16":3959,"_22":3960,"_28":11},"markersize","Marker size in points (default: auto-scaled based on matrix size)",[3962,3964,3966],{"_2215":3963},"A = eye(10);\nspy(A)",{"_2215":3965},"B = rand(20, 20) > 0.8;\nspy(B)",{"_2215":3967},"spy(magic(10) > 50, 'ro', 8)",[3878,3969,2774,3970],"imagesc","nnz",{"_16":3972,"_18":3973,"_20":3974,"_22":3975,"_23":3976,"_29":3990,"_31":3991,"_2222":3996},"quiver","quiver(U, V)\nquiver(X, Y, U, V)\nquiver(..., scale)","2-D quiver (velocity) plot","Plots arrows to visualize vector fields. Each arrow starts at position (X, Y) and points in direction (U, V). When only U and V are provided, arrows are placed on an auto-generated grid. The optional scale factor controls arrow length (default: 1, set to 0 to disable auto-scaling).",[3977,3979,3981,3984,3987],{"_16":2428,"_22":3978,"_28":11},"Arrow base X-coordinates (matrix or vector)",{"_16":3694,"_22":3980,"_28":11},"Arrow base Y-coordinates (matrix or vector)",{"_16":3982,"_22":3983},"U","Arrow X-direction components (matrix or vector)",{"_16":3985,"_22":3986},"V","Arrow Y-direction components (matrix or vector)",{"_16":3988,"_22":3989,"_28":11},"scale","Arrow scaling factor (default: 1, 0 disables auto-scaling)","Graphics handle",[3992,3994],{"_2215":3993},"[X, Y] = meshgrid(1:5, 1:5);\nquiver(X, Y, ones(5), ones(5))",{"_2215":3995},"U = cos(linspace(0, 2*pi, 25));\nV = sin(linspace(0, 2*pi, 25));\nquiver(U, V)",[3864,3878,2341],{"_16":3998,"_18":3999,"_20":4000,"_22":4001,"_23":4002,"_29":3990,"_31":4025,"_2222":4032},"fill","fill(X, Y)\nfill(X, Y, C)\nfill(..., Name, Value)","Filled 2-D polygon","Creates a filled polygon with vertices at the coordinates (X, Y). The polygon is automatically closed by connecting the last vertex to the first. Color can be specified as a short name ('r'), long name ('red'), or RGB triplet [r g b] with values in range [0,1].",[4003,4005,4007,4010,4013,4016,4019,4022],{"_16":2428,"_22":4004},"X-coordinates of polygon vertices (vector)",{"_16":3694,"_22":4006},"Y-coordinates of polygon vertices (vector)",{"_16":4008,"_22":4009,"_28":11},"C","Color specification: short name, long name, or RGB triplet",{"_16":4011,"_22":4012,"_28":11},"FaceColor","Fill color (Name-Value pair)",{"_16":4014,"_22":4015,"_28":11},"FaceAlpha","Fill transparency 0-1 (Name-Value pair)",{"_16":4017,"_22":4018,"_28":11},"EdgeColor","Edge color or 'none' (Name-Value pair)",{"_16":4020,"_22":4021,"_28":11},"LineWidth","Edge line width (Name-Value pair)",{"_16":4023,"_22":4024,"_28":11},"LineStyle","Edge line style: '-', '--', ':', '-.', 'none' (Name-Value pair)",[4026,4028,4030],{"_2215":4027},"fill([0 1 0.5], [0 0 1], 'r')",{"_2215":4029},"x = cos(linspace(0, 2*pi, 6));\ny = sin(linspace(0, 2*pi, 6));\nfill(x, y, 'b', 'FaceAlpha', 0.5)",{"_2215":4031},"fill([0 1 1 0], [0 0 1 1], [0.2 0.6 0.8], 'EdgeColor', 'none')",[3864,4033,4034],"patch","area",{"_16":3932,"_18":4036,"_20":4037,"_22":4038,"_23":4039,"_29":3873,"_31":4045,"_2222":4048},"histogram(data)\nhistogram(data, numBins)","Histogram","Creates a histogram of the data, auto-binned into the specified number of bins (default 10).",[4040,4042],{"_16":117,"_22":4041},"Input data (NDArray)",{"_16":4043,"_22":4044,"_28":11},"numBins","Number of bins (default: 10)",[4046],{"_2215":4047},"histogram(randn(100, 1))",[3879,3864],{"_16":3933,"_18":4050,"_20":4051,"_22":4052,"_23":4053,"_29":3873,"_31":4056,"_2222":4059},"pie(data)","Pie chart","Creates a pie chart from the data values.",[4054],{"_16":117,"_22":4055},"Slice values (NDArray)",[4057],{"_2215":4058},"pie([30 20 50])",[3879,3932],{"_16":4061,"_18":4062,"_20":4063,"_22":4064,"_23":4065,"_29":4068,"_31":4069,"_2222":4072},"title","title(str)","Add title to current chart","Sets the title of the most recently created chart.",[4066],{"_16":2974,"_22":4067},"Title string","null",[4070],{"_2215":4071},"plot([1 4 9 16]);\ntitle('Squares')",[4073,4074,4075],"xlabel","ylabel","legend",{"_16":4073,"_18":4077,"_20":4078,"_22":4079,"_23":4080,"_29":4068,"_31":4083,"_2222":4086},"xlabel(str)","Label x-axis","Sets the x-axis label of the most recently created chart.",[4081],{"_16":2974,"_22":4082},"Label string",[4084],{"_2215":4085},"xlabel('Time (s)')",[4074,4061],{"_16":4074,"_18":4088,"_20":4089,"_22":4090,"_23":4091,"_29":4068,"_31":4093,"_2222":4096},"ylabel(str)","Label y-axis","Sets the y-axis label of the most recently created chart.",[4092],{"_16":2974,"_22":4082},[4094],{"_2215":4095},"ylabel('Amplitude')",[4073,4061],{"_16":4075,"_18":4098,"_20":4099,"_22":4100,"_23":4101,"_29":4068,"_31":4105,"_2222":4108},"legend('label1', 'label2', ...)","Add legend to current chart","Adds a legend to the most recently created chart with the given labels.",[4102],{"_16":4103,"_22":4104},"labels","One or more string labels",[4106],{"_2215":4107},"legend('sin', 'cos')",[4061,4073,4074],{"_16":4110,"_18":4111,"_20":4112,"_22":4113,"_23":4114,"_29":4068,"_31":4117,"_2222":4120},"figure","figure\nfigure(n)","Create a new figure","Starts a new figure so the next plotting command creates a fresh chart. Without arguments, creates a new figure with auto-incremented ID. With argument n, switches to figure n.",[4115],{"_16":629,"_22":4116,"_28":11},"Figure number",[4118],{"_2215":4119},"plot([1 2 3]);\nfigure();\nplot([4 5 6])",[3864,3879,3878,4121,4122],"gcf","clf",{"_16":4124,"_18":4125,"_20":4126,"_22":4127,"_23":4128,"_29":4068,"_31":4133,"_2222":4136},"xlim","xlim([min max])","Set x-axis limits","Sets the minimum and maximum values for the x-axis of the current chart.",[4129,4131],{"_16":2687,"_22":4130},"Minimum x value",{"_16":2688,"_22":4132},"Maximum x value",[4134],{"_2215":4135},"plot([1 2 3 4]);\nxlim([0 5])",[4137,4138],"ylim","axis",{"_16":4137,"_18":4140,"_20":4141,"_22":4142,"_23":4143,"_29":4068,"_31":4148,"_2222":4151},"ylim([min max])","Set y-axis limits","Sets the minimum and maximum values for the y-axis of the current chart.",[4144,4146],{"_16":2687,"_22":4145},"Minimum y value",{"_16":2688,"_22":4147},"Maximum y value",[4149],{"_2215":4150},"plot([1 2 3 4]);\nylim([0 5])",[4124,4138],{"_16":4153,"_18":4154,"_20":4155,"_22":4156,"_23":4157,"_29":4068,"_31":4160,"_2222":4163},"xticks","xticks(values)","Set x-axis tick values","Sets custom tick mark positions on the x-axis.",[4158],{"_16":620,"_22":4159},"Vector of tick positions",[4161],{"_2215":4162},"plot([1 2 3 4]);\nxticks([1 2 3 4])",[4164,4124],"yticks",{"_16":4164,"_18":4166,"_20":4167,"_22":4168,"_23":4169,"_29":4068,"_31":4171,"_2222":4174},"yticks(values)","Set y-axis tick values","Sets custom tick mark positions on the y-axis.",[4170],{"_16":620,"_22":4159},[4172],{"_2215":4173},"bar([10 20 30]);\nyticks([0 10 20 30])",[4153,4137],{"_16":4176,"_18":4177,"_20":4178,"_22":4179,"_23":4180,"_29":4068,"_31":4184,"_2222":4187},"xtickangle","xtickangle(angle)","Rotate x-axis tick labels","Sets the rotation angle (in degrees) for x-axis tick labels.",[4181],{"_16":4182,"_22":4183},"angle","Rotation angle in degrees",[4185],{"_2215":4186},"bar([1 2 3]);\nxtickangle(45)",[4188,4153],"ytickangle",{"_16":4188,"_18":4190,"_20":4191,"_22":4192,"_23":4193,"_29":4068,"_31":4195,"_2222":4198},"ytickangle(angle)","Rotate y-axis tick labels","Sets the rotation angle (in degrees) for y-axis tick labels.",[4194],{"_16":4182,"_22":4183},[4196],{"_2215":4197},"bar([1 2 3]);\nytickangle(90)",[4176,4164],{"_16":4200,"_18":4201,"_20":4202,"_22":4203,"_23":4204,"_29":4068,"_31":4208,"_2222":4211},"grid","grid\ngrid('on')\ngrid('off')","Toggle grid lines","Controls the visibility of grid lines on the current chart.",[4205],{"_16":4206,"_22":4207,"_28":11},"state","'on' or 'off' (default: toggle)",[4209],{"_2215":4210},"plot([1 2 3]);\ngrid('on')",[4138,4124,4137],{"_16":4138,"_18":4213,"_20":4214,"_22":4215,"_23":4216,"_29":4068,"_31":4220,"_2222":4223},"axis([xmin xmax ymin ymax])","Set axis limits and scaling","Sets the limits for both x and y axes simultaneously.",[4217],{"_16":4218,"_22":4219},"limits","4-element vector [xmin xmax ymin ymax]",[4221],{"_2215":4222},"plot([1 2 3]);\naxis([0 4 0 4])",[4124,4137,4200],{"_16":4225,"_18":4226,"_20":4227,"_22":4228,"_23":4229,"_29":4068,"_31":4231,"_2222":4234},"hold","hold\nhold('on')\nhold('off')","Hold current plot","Controls whether new plot commands add to or replace the current chart. When hold is on, successive plot commands add datasets to the same chart.",[4230],{"_16":4206,"_22":4207,"_28":11},[4232],{"_2215":4233},"plot([1 2 3]);\nhold('on');\nbar([2 3 4])",[4110,3864],{"_16":4121,"_18":4236,"_20":4237,"_22":4238,"_23":4239,"_29":4240,"_31":4241,"_2222":4243},"f = gcf","Get current figure","Returns the handle (ID) of the current figure.",[],"Figure ID number",[4242],{"_2215":4236},[4110,4244,4122],"gca",{"_16":4244,"_18":4246,"_20":4247,"_22":4248,"_23":4249,"_29":4250,"_31":4251,"_2222":4253},"ax = gca","Get current axes","Returns the handle (ID) of the current axes (same as gcf in this implementation).",[],"Axes ID number",[4252],{"_2215":4246},[4121,4110],{"_16":4122,"_18":4122,"_20":4255,"_22":4256,"_23":4257,"_29":4068,"_31":4258,"_2222":4261},"Clear current figure","Clears all charts from the current figure, resetting its state.",[],[4259],{"_2215":4260},"plot([1 2 3]);\nclf()",[4262,4110],"close",{"_16":4262,"_18":4264,"_20":4265,"_22":4266,"_23":4267,"_29":4068,"_31":4271,"_2222":4274},"close\nclose(fig)","Close figure","Closes the current figure or the specified figure by ID.",[4268],{"_16":4269,"_22":4270,"_28":11},"fig","Figure ID to close",[4272],{"_2215":4273},"close()",[4122,4110],{"_16":4276,"_18":4277,"_20":4278,"_22":4279,"_23":4280,"_29":4068,"_31":4287,"_2222":4290},"text","text(x, y, str)","Add text annotation","Adds a text annotation at the specified (x, y) coordinates in data units.",[4281,4283,4285],{"_16":1350,"_22":4282},"X-coordinate",{"_16":2349,"_22":4284},"Y-coordinate",{"_16":2974,"_22":4286},"Text string",[4288],{"_2215":4289},"plot([1 2 3]);\ntext(2, 2.5, 'Peak')",[4061,4073,4074],{"_16":4292,"_18":4293,"_20":4294,"_22":4295,"_23":4296,"_29":4068,"_31":4300,"_2222":4303},"yyaxis","yyaxis('left')\nyyaxis('right')","Control dual y-axes","Activates either the left or right y-axis for subsequent plotting commands, enabling dual y-axis charts.",[4297],{"_16":4298,"_22":4299},"side","'left' or 'right'",[4301],{"_2215":4302},"plot([1 2 3]);\nyyaxis('right');\nplot([10 20 30])",[4074,4137],{"_16":4305,"_18":4306,"_20":4307,"_22":4308,"_23":4309,"_29":4068,"_31":4317,"_2222":4320},"subplot","subplot(rows, cols, index)","Create subplot grid","Creates a grid of charts with the specified number of rows and columns, and activates the subplot at the given index (1-based).",[4310,4312,4314],{"_16":120,"_22":4311},"Number of rows in grid",{"_16":123,"_22":4313},"Number of columns in grid",{"_16":4315,"_22":4316},"index","1-based position in grid (row-major order)",[4318],{"_2215":4319},"subplot(2, 2, 1);\nplot([1 2 3]);\nsubplot(2, 2, 2);\nbar([4 5 6])",[4110,3864],{"_16":2365,"_18":4322,"_20":4323,"_22":4324,"_23":4325,"_29":4335,"_31":4336,"_2222":4339},"mesh(Z)\nmesh(X, Y, Z)\nmesh(X, Y, Z, C)","3-D wireframe mesh surface","Creates a 3D wireframe mesh surface plot. With one argument, Z provides the heights with X and Y auto-generated as indices. With three arguments, X, Y, and Z define the surface coordinates. The optional C argument provides a color matrix.",[4326,4328,4330,4333],{"_16":2428,"_22":4327,"_28":11},"X-coordinate matrix (auto-generated if omitted)",{"_16":3694,"_22":4329,"_28":11},"Y-coordinate matrix (auto-generated if omitted)",{"_16":4331,"_22":4332},"Z","Height matrix (required)",{"_16":4008,"_22":4334,"_28":11},"Color data matrix (defaults to Z)","null (renders 3D chart inline)",[4337],{"_2215":4338},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X .* exp(-X.^2 - Y.^2);\nmesh(X, Y, Z)",[2364,2341,4340],"zlabel",{"_16":2364,"_18":4342,"_20":4343,"_22":4344,"_23":4345,"_29":4335,"_31":4350,"_2222":4353},"surf(Z)\nsurf(X, Y, Z)\nsurf(X, Y, Z, C)","3-D shaded surface plot","Creates a 3D surface plot with filled faces. With one argument, Z provides the heights with X and Y auto-generated as indices. With three arguments, X, Y, and Z define the surface coordinates. The optional C argument provides a color matrix.",[4346,4347,4348,4349],{"_16":2428,"_22":4327,"_28":11},{"_16":3694,"_22":4329,"_28":11},{"_16":4331,"_22":4332},{"_16":4008,"_22":4334,"_28":11},[4351],{"_2215":4352},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X .* exp(-X.^2 - Y.^2);\nsurf(X, Y, Z)",[2365,2341,4340],{"_16":4340,"_18":4355,"_20":4356,"_22":4357,"_23":4358,"_29":4068,"_31":4360,"_2222":4363},"zlabel(str)","Label z-axis","Sets the z-axis label of the most recently created 3D chart.",[4359],{"_16":2974,"_22":4082},[4361],{"_2215":4362},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X .* exp(-X.^2 - Y.^2);\nsurf(X, Y, Z);\nzlabel('Height')",[4073,4074,4061,2365,2364],{"_16":4365,"_18":4366,"_20":4367,"_22":4368,"_23":4369,"_29":4376,"_31":4377,"_2222":4384},"view","view(az, el)\nview([az el])\nview(2)\nview(3)\n[az, el] = view","Set 3D view angle","Sets the camera viewing angle for 3D plots (mesh, surf). Azimuth is the angle of rotation around the z-axis measured from the negative y-axis (counterclockwise positive). Elevation is the angle from the x-y plane (-90 to 90 degrees). view(2) sets a top-down 2D view (az=0, el=90). view(3) sets the default 3D view (az=-37.5, el=30).",[4370,4373],{"_16":4371,"_22":4372,"_28":11},"az","Azimuth angle in degrees",{"_16":4374,"_22":4375,"_28":11},"el","Elevation angle in degrees","With no arguments, returns [az, el] of current view",[4378,4380,4382],{"_2215":4379},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X .* exp(-X.^2 - Y.^2);\nsurf(X, Y, Z);\nview(45, 30)",{"_2215":4381},"[X, Y] = meshgrid(-2:0.2:2);\nZ = sin(X) .* cos(Y);\nsurf(X, Y, Z);\nview(2) % Top-down view",{"_2215":4383},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X.^2 - Y.^2;\nmesh(X, Y, Z);\nview(3) % Default 3D view",[2365,2364,4340],{"_16":3969,"_18":4386,"_20":4387,"_22":4388,"_23":4389,"_29":4399,"_31":4400,"_2222":4407},"imagesc(C)\nimagesc(x, y, C)\nimagesc(..., clims)","Display matrix as scaled image","Displays a matrix C as an image with scaled colors. Each element of C maps to a color in the colormap, with the minimum value mapping to the first color and maximum to the last. Optional x and y vectors specify the coordinates of the columns and rows.",[4390,4392,4394,4396],{"_16":1350,"_22":4391,"_28":11},"X-axis coordinates for columns (2-element vector or full vector)",{"_16":2349,"_22":4393,"_28":11},"Y-axis coordinates for rows (2-element vector or full vector)",{"_16":4008,"_22":4395},"Data matrix to display",{"_16":4397,"_22":4398,"_28":11},"clims","Color limits [cmin cmax]","null (renders heatmap inline)",[4401,4403,4405],{"_2215":4402},"A = magic(5);\nimagesc(A)",{"_2215":4404},"A = peaks(50);\nimagesc(A)\ncolorbar",{"_2215":4406},"imagesc([0 10], [0 5], rand(10, 20))\ntitle('Random data')",[4408,4409,2365,2364],"colorbar","colormap",{"_16":4408,"_18":4411,"_20":4412,"_22":4413,"_23":4414,"_29":4418,"_31":4419,"_2222":4428},"colorbar\ncolorbar('off')\ncolorbar('location')\nc = colorbar","Add colorbar to current chart","Displays a colorbar showing the color scale for the current heatmap, mesh, or surf plot. Supports location options ('eastoutside', 'westoutside', 'northoutside', 'southoutside') and can return a handle for further property manipulation using set().",[4415],{"_16":4416,"_22":4417,"_28":11},"location","Location string: 'eastoutside' (default), 'westoutside', 'northoutside', 'southoutside', or 'off'","Colorbar handle (when assigned to variable)",[4420,4422,4424,4426],{"_2215":4421},"imagesc(peaks(30));\ncolorbar",{"_2215":4423},"surf(peaks(30));\ncolorbar('southoutside')",{"_2215":4425},"imagesc(rand(20));\nc = colorbar;\nset(c, 'Title', 'Values')",{"_2215":4427},"mesh(peaks);\ncolorbar('off')",[3969,4409,2365,2364,4429],"set",{"_16":4409,"_18":4431,"_20":4432,"_22":4433,"_23":4434,"_29":4440,"_31":4441,"_2222":4450},"colormap(name)\ncolormap(map)\ncmap = colormap","Set or get colormap for current figure","Sets the colormap used for pseudocolor plots like imagesc, mesh, and surf. With no arguments, returns the current colormap as an Mx3 RGB matrix (default 256 rows). With a string argument, sets to a named colormap. With an Mx3 matrix argument, sets a custom colormap where each row is [R G B] with values in range [0,1].",[4435,4437],{"_16":16,"_22":4436,"_28":11},"Colormap name: viridis (default), jet, hot, cool, gray, grayscale, parula, turbo, coolwarm, rainbow, bone, copper, spring, summer, autumn, winter",{"_16":4438,"_22":4439,"_28":11},"map","Mx3 matrix of RGB values (each in [0,1])","Mx3 RGB matrix (query mode) or null (set mode)",[4442,4444,4446,4448],{"_2215":4443},"imagesc(peaks(30));\ncolormap('jet');\ncolorbar",{"_2215":4445},"surf(peaks(25));\ncolormap('hot')",{"_2215":4447},"cmap = colormap % returns 256x3 matrix",{"_2215":4449},"colormap([0 0 1; 1 1 1; 1 0 0]) % custom blue-white-red",[3969,4408,2365,2364],{"_16":4452,"_18":4453,"_20":4454,"_22":4455,"_23":4456,"_29":4068,"_31":4460,"_2222":4465},"shading","shading faceted\nshading flat\nshading interp","Set surface shading mode","Controls the color shading of surface and mesh plots. 'faceted' uses flat coloring with black mesh lines overlaid (default). 'flat' uses flat coloring without mesh lines. 'interp' uses smooth interpolated colors across the surface.",[4457],{"_16":4458,"_22":4459},"mode","Shading mode: 'faceted' (default), 'flat', or 'interp'",[4461,4463],{"_2215":4462},"surf(peaks(30));\nshading interp",{"_2215":4464},"[X, Y] = meshgrid(-2:0.2:2);\nZ = X .* exp(-X.^2 - Y.^2);\nsurf(X, Y, Z);\nshading flat;\ncolorbar",[2364,2365,4409,4408],{"_35":4467,"_16":4468,"_22":4469,"_39":40,"_41":4470,"_45":4471},"poly","Polynomial Functions","Polynomial operations across power, Chebyshev, Legendre, Hermite, HermiteE, and Laguerre bases with fitting, evaluation, calculus, arithmetic, and conversion utilities.","∑",[4472,4492,4510,4525,4540,4556,4577,4591,4604,4617,4632,4646,4657,4668,4684,4699,4713,4725,4741,4756,4772,4783,4794,4807,4822,4832,4843,4852,4864,4877,4887,4895,4907,4919,4933,4948,4960,4970,4983,4992,5001,5010,5020,5031,5039,5047,5057,5067,5078,5093,5103,5113,5125,5134,5144,5153,5163,5174,5182,5190,5200,5210,5221,5234,5244,5254,5266,5275,5285,5294,5304,5315,5323,5331,5341,5351,5362,5377,5387,5397,5409,5418,5428,5437,5447,5458,5466,5474,5484,5494,5505,5515,5523,5531,5539,5547,5563,5576,5592,5608],{"_16":4473,"_18":4474,"_20":4475,"_22":4476,"_23":4477,"_29":4483,"_31":4484,"_2222":4488},"polyval","y = polyval(x, c)","Evaluate power series polynomial","Evaluates a power series polynomial at point x using Horner's method. Coefficients are in ascending order: c(1) + c(2)*x + c(3)*x^2 + ...",[4478,4480],{"_16":1350,"_22":4479},"Point at which to evaluate",{"_16":4481,"_22":4482},"c","Coefficient array in ascending order [c0, c1, c2, ...]","Polynomial value at x",[4485],{"_2215":4486,"_2217":4487},"polyval(2, [1 2 3])","17",[4489,4490,4491],"polyfit","polyder","polyint",{"_16":4493,"_18":4494,"_20":4495,"_22":4496,"_23":4497,"_29":4504,"_31":4505,"_2222":4508},"polyval2d","z = polyval2d(x, y, c)","Evaluate 2-D power series polynomial","Evaluates a 2-D power series polynomial on x-y pairs.",[4498,4500,4502],{"_16":1350,"_22":4499},"x coordinates",{"_16":2349,"_22":4501},"y coordinates",{"_16":4481,"_22":4503},"2-D coefficient array","Polynomial values at (x, y) pairs",[4506],{"_2215":4507},"polyval2d([1 2], [1 2], [1 0; 0 1])",[4473,4509],"polyval3d",{"_16":4509,"_18":4511,"_20":4512,"_22":4513,"_23":4514,"_29":4522,"_31":4523,"_2222":4524},"w = polyval3d(x, y, z, c)","Evaluate 3-D power series polynomial","Evaluates a 3-D power series polynomial on x-y-z triples.",[4515,4516,4517,4520],{"_16":1350,"_22":4499},{"_16":2349,"_22":4501},{"_16":4518,"_22":4519},"z","z coordinates",{"_16":4481,"_22":4521},"3-D coefficient array","Polynomial values at (x, y, z) triples",[],[4473,4493],{"_16":4490,"_18":4526,"_20":4527,"_22":4528,"_23":4529,"_29":4534,"_31":4535,"_2222":4539},"dc = polyder(c)\ndc = polyder(c, m)","Power series derivative","Differentiates a power series polynomial m times. Default m = 1.",[4530,4532],{"_16":4481,"_22":4531},"Coefficient array in ascending order",{"_16":1130,"_22":4533,"_28":11},"Number of derivatives (default: 1)","Differentiated coefficient array",[4536],{"_2215":4537,"_2217":4538},"polyder([1 2 3])","[2 6]",[4491,4473],{"_16":4491,"_18":4541,"_20":4542,"_22":4543,"_23":4544,"_29":4550,"_31":4551,"_2222":4555},"ic = polyint(c)\nic = polyint(c, m)\nic = polyint(c, m, k)","Power series integral","Integrates a power series polynomial m times with integration constants k. Default m = 1, k = [0].",[4545,4546,4548],{"_16":4481,"_22":4531},{"_16":1130,"_22":4547,"_28":11},"Number of integrations (default: 1)",{"_16":430,"_22":4549,"_28":11},"Integration constants (default: all zero)","Integrated coefficient array",[4552],{"_2215":4553,"_2217":4554},"polyint([2 6])","[0 2 3]",[4490,4473],{"_16":4557,"_18":4558,"_20":4559,"_22":4560,"_23":4561,"_29":4568,"_31":4569,"_2222":4573},"polymul","c = polymul(c1, c2)","Multiply two power series polynomials","Multiplies two power series coefficient arrays using convolution.",[4562,4565],{"_16":4563,"_22":4564},"c1","First coefficient array",{"_16":4566,"_22":4567},"c2","Second coefficient array","Product coefficient array",[4570],{"_2215":4571,"_2217":4572},"polymul([1 1], [1 1])","[1 2 1]",[4574,4575,4576],"polydiv","polyadd","polysub",{"_16":4574,"_18":4578,"_20":4579,"_22":4580,"_23":4581,"_29":4586,"_31":4587,"_2222":4590},"[q, r] = polydiv(c1, c2)","Divide two power series polynomials","Divides two power series coefficient arrays. Returns quotient and remainder.",[4582,4584],{"_16":4563,"_22":4583},"Dividend coefficient array",{"_16":4566,"_22":4585},"Divisor coefficient array","Quotient and remainder coefficient arrays",[4588],{"_2215":4589},"polydiv([1 2 1], [1 1])",[4557,4575,4576],{"_16":4575,"_18":4592,"_20":4593,"_22":4594,"_23":4595,"_29":4598,"_31":4599,"_2222":4603},"c = polyadd(c1, c2)","Add two power series polynomials","Adds two power series coefficient arrays.",[4596,4597],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},"Sum coefficient array",[4600],{"_2215":4601,"_2217":4602},"polyadd([1 2], [3 4])","[4 6]",[4576,4557,4574],{"_16":4576,"_18":4605,"_20":4606,"_22":4607,"_23":4608,"_29":4611,"_31":4612,"_2222":4616},"c = polysub(c1, c2)","Subtract two power series polynomials","Subtracts two power series coefficient arrays.",[4609,4610],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},"Difference coefficient array",[4613],{"_2215":4614,"_2217":4615},"polysub([3 4], [1 2])","[2 2]",[4575,4557,4574],{"_16":4618,"_18":4619,"_20":4620,"_22":4621,"_23":4622,"_29":4627,"_31":4628,"_2222":4631},"polypow","c = polypow(c, n)","Raise power series polynomial to a power","Raises a power series polynomial to a non-negative integer power.",[4623,4625],{"_16":4481,"_22":4624},"Coefficient array",{"_16":629,"_22":4626},"Non-negative integer power","Resulting coefficient array",[4629],{"_2215":4630,"_2217":4572},"polypow([1 1], 2)",[4557],{"_16":4633,"_18":4634,"_20":4635,"_22":4636,"_23":4637,"_29":4639,"_31":4640,"_2222":4643},"polyroots","r = polyroots(c)","Find power series polynomial roots","Finds roots of a power series polynomial using companion matrix eigenvalues.",[4638],{"_16":4481,"_22":4531},"Array of roots",[4641],{"_2215":4642},"polyroots([-1 0 1])",[4644,4645],"polyfromroots","polycompanion",{"_16":4644,"_18":4647,"_20":4648,"_22":4649,"_23":4650,"_29":4531,"_31":4653,"_2222":4656},"c = polyfromroots(r)","Construct power series from roots","Constructs a power series polynomial from its roots.",[4651],{"_16":4652,"_22":4639},"r",[4654],{"_2215":4655},"polyfromroots([1 -1])",[4633],{"_16":4645,"_18":4658,"_20":4659,"_22":4660,"_23":4661,"_29":4663,"_31":4664,"_2222":4667},"C = polycompanion(c)","Power series companion matrix","Generates the companion matrix for a power series polynomial.",[4662],{"_16":4481,"_22":4624},"Companion matrix",[4665],{"_2215":4666},"polycompanion([-1 0 1])",[4633],{"_16":4669,"_18":4670,"_20":4671,"_22":4672,"_23":4673,"_29":4679,"_31":4680,"_2222":4683},"polyvander","V = polyvander(x, deg)","Power series Vandermonde matrix","Generates a Vandermonde matrix of the given degree for the given sample points.",[4674,4676],{"_16":1350,"_22":4675},"Sample points",{"_16":4677,"_22":4678},"deg","Degree of polynomial","Vandermonde matrix",[4681],{"_2215":4682},"polyvander([1 2 3], 2)",[4489],{"_16":4489,"_18":4685,"_20":4686,"_22":4687,"_23":4688,"_29":4531,"_31":4695,"_2222":4698},"c = polyfit(x, y, deg)","Least-squares power series fit","Fits a power series polynomial of the given degree to data using least squares.",[4689,4691,4693],{"_16":1350,"_22":4690},"x values",{"_16":2349,"_22":4692},"y values",{"_16":4677,"_22":4694},"Degree of fitting polynomial",[4696],{"_2215":4697},"polyfit([0 1 2 3], [0 1 4 9], 2)",[4473,4669],{"_16":4700,"_18":4701,"_20":4702,"_22":4703,"_23":4704,"_29":4707,"_31":4708,"_2222":4712},"roots","r = roots(p)","Polynomial roots (M-Code convention)","Finds roots of a polynomial specified by descending-order coefficients [a_n, ..., a_1, a_0].",[4705],{"_16":552,"_22":4706},"Coefficient vector in descending order","Column vector of roots",[4709],{"_2215":4710,"_2217":4711},"roots([1 0 -1])","[1; -1]",[4467,4633],{"_16":4467,"_18":4714,"_20":4715,"_22":4716,"_23":4717,"_29":4706,"_31":4720,"_2222":4724},"p = poly(r)","Polynomial from roots (M-Code convention)","Constructs polynomial coefficients in descending order from a vector of roots.",[4718],{"_16":4652,"_22":4719},"Vector of roots",[4721],{"_2215":4722,"_2217":4723},"poly([1 -1])","[1 0 -1]",[4700,4644],{"_16":4726,"_18":4727,"_20":4728,"_22":4729,"_23":4730,"_29":4735,"_31":4736,"_2222":4739},"conv","w = conv(u, v)","Convolution / polynomial multiplication (M-Code convention)","Convolves two vectors, equivalent to polynomial multiplication with descending-order coefficients.",[4731,4733],{"_16":1995,"_22":4732},"First input vector (descending order)",{"_16":1604,"_22":4734},"Second input vector (descending order)","Convolution result (descending order)",[4737],{"_2215":4738,"_2217":4572},"conv([1 1], [1 1])",[4740,4557],"deconv",{"_16":4740,"_18":4742,"_20":4743,"_22":4744,"_23":4745,"_29":4750,"_31":4751,"_2222":4755},"[q, r] = deconv(b, a)","Deconvolution / polynomial division (M-Code convention)","Deconvolves two vectors, equivalent to polynomial long division with descending-order coefficients.",[4746,4748],{"_16":983,"_22":4747},"Dividend vector (descending order)",{"_16":2283,"_22":4749},"Divisor vector (descending order)","Quotient vector (descending order)",[4752],{"_2215":4753,"_2217":4754},"deconv([1 2 1], [1 1])","[1 1]",[4726,4574],{"_16":4757,"_18":4758,"_20":4759,"_22":4760,"_23":4761,"_29":4483,"_31":4765,"_2222":4768},"chebval","y = chebval(x, c)","Evaluate Chebyshev polynomial","Evaluates a Chebyshev polynomial at point x using Clenshaw's algorithm. Coefficients: c(1)*T_0 + c(2)*T_1 + c(3)*T_2 + ...",[4762,4763],{"_16":1350,"_22":4479},{"_16":4481,"_22":4764},"Chebyshev coefficient array",[4766],{"_2215":4767},"chebval(0.5, [1 2 3])",[4769,4770,4771],"chebfit","chebder","chebint",{"_16":4773,"_18":4774,"_20":4775,"_22":4776,"_23":4777,"_29":4504,"_31":4781,"_2222":4782},"chebval2d","z = chebval2d(x, y, c)","Evaluate 2-D Chebyshev polynomial","Evaluates a 2-D Chebyshev polynomial on x-y pairs.",[4778,4779,4780],{"_16":1350,"_22":4499},{"_16":2349,"_22":4501},{"_16":4481,"_22":4503},[],[4757],{"_16":4770,"_18":4784,"_20":4785,"_22":4786,"_23":4787,"_29":4534,"_31":4790,"_2222":4793},"dc = chebder(c)\ndc = chebder(c, m)","Chebyshev derivative","Differentiates a Chebyshev polynomial m times.",[4788,4789],{"_16":4481,"_22":4764},{"_16":1130,"_22":4533,"_28":11},[4791],{"_2215":4792},"chebder([1 2 3])",[4771,4757],{"_16":4771,"_18":4795,"_20":4796,"_22":4797,"_23":4798,"_29":4550,"_31":4803,"_2222":4806},"ic = chebint(c)\nic = chebint(c, m)\nic = chebint(c, m, k)","Chebyshev integral","Integrates a Chebyshev polynomial m times with integration constants k.",[4799,4800,4801],{"_16":4481,"_22":4764},{"_16":1130,"_22":4547,"_28":11},{"_16":430,"_22":4802,"_28":11},"Integration constants",[4804],{"_2215":4805},"chebint([2 6])",[4770,4757],{"_16":4808,"_18":4809,"_20":4810,"_22":4811,"_23":4812,"_29":4568,"_31":4815,"_2222":4818},"chebmul","c = chebmul(c1, c2)","Multiply two Chebyshev polynomials","Multiplies two Chebyshev coefficient arrays.",[4813,4814],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[4816],{"_2215":4817},"chebmul([1 1], [1 1])",[4819,4820,4821],"chebdiv","chebadd","chebsub",{"_16":4819,"_18":4823,"_20":4824,"_22":4825,"_23":4826,"_29":4829,"_31":4830,"_2222":4831},"[q, r] = chebdiv(c1, c2)","Divide two Chebyshev polynomials","Divides two Chebyshev coefficient arrays. Returns quotient and remainder.",[4827,4828],{"_16":4563,"_22":4583},{"_16":4566,"_22":4585},"Quotient and remainder",[],[4808],{"_16":4820,"_18":4833,"_20":4834,"_22":4835,"_23":4836,"_29":4598,"_31":4839,"_2222":4842},"c = chebadd(c1, c2)","Add two Chebyshev polynomials","Adds two Chebyshev coefficient arrays.",[4837,4838],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[4840],{"_2215":4841},"chebadd([1 2], [3 4])",[4821,4808],{"_16":4821,"_18":4844,"_20":4845,"_22":4846,"_23":4847,"_29":4611,"_31":4850,"_2222":4851},"c = chebsub(c1, c2)","Subtract two Chebyshev polynomials","Subtracts two Chebyshev coefficient arrays.",[4848,4849],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[4820,4808],{"_16":4853,"_18":4854,"_20":4855,"_22":4856,"_23":4857,"_29":4627,"_31":4860,"_2222":4863},"chebpow","c = chebpow(c, n)","Raise Chebyshev polynomial to a power","Raises a Chebyshev polynomial to a non-negative integer power.",[4858,4859],{"_16":4481,"_22":4624},{"_16":629,"_22":4626},[4861],{"_2215":4862},"chebpow([1 1], 2)",[4808],{"_16":4865,"_18":4866,"_20":4867,"_22":4868,"_23":4869,"_29":4639,"_31":4871,"_2222":4874},"chebroots","r = chebroots(c)","Find Chebyshev polynomial roots","Finds roots of a Chebyshev polynomial using companion matrix eigenvalues.",[4870],{"_16":4481,"_22":4764},[4872],{"_2215":4873},"chebroots([1 0 -1])",[4875,4876],"chebfromroots","chebcompanion",{"_16":4875,"_18":4878,"_20":4879,"_22":4880,"_23":4881,"_29":4764,"_31":4883,"_2222":4886},"c = chebfromroots(r)","Construct Chebyshev polynomial from roots","Constructs Chebyshev coefficient array from roots.",[4882],{"_16":4652,"_22":4639},[4884],{"_2215":4885},"chebfromroots([1 -1])",[4865],{"_16":4876,"_18":4888,"_20":4889,"_22":4890,"_23":4891,"_29":4663,"_31":4893,"_2222":4894},"C = chebcompanion(c)","Chebyshev companion matrix","Generates the companion matrix for a Chebyshev polynomial.",[4892],{"_16":4481,"_22":4764},[],[4865],{"_16":4896,"_18":4897,"_20":4898,"_22":4899,"_23":4900,"_29":4679,"_31":4903,"_2222":4906},"chebvander","V = chebvander(x, deg)","Chebyshev Vandermonde matrix","Generates a Chebyshev Vandermonde matrix for the given sample points and degree.",[4901,4902],{"_16":1350,"_22":4675},{"_16":4677,"_22":4678},[4904],{"_2215":4905},"chebvander([0 0.5 1], 2)",[4769],{"_16":4769,"_18":4908,"_20":4909,"_22":4910,"_23":4911,"_29":4764,"_31":4915,"_2222":4918},"c = chebfit(x, y, deg)","Least-squares Chebyshev fit","Fits a Chebyshev polynomial of the given degree to data using least squares.",[4912,4913,4914],{"_16":1350,"_22":4690},{"_16":2349,"_22":4692},{"_16":4677,"_22":4694},[4916],{"_2215":4917},"chebfit([0 0.5 1], [1 1.5 2], 1)",[4757,4896],{"_16":4920,"_18":4921,"_20":4922,"_22":4923,"_23":4924,"_29":4927,"_31":4928,"_2222":4931},"cheb2poly","p = cheb2poly(c)","Convert Chebyshev to power series","Converts Chebyshev coefficients to power series coefficients.",[4925],{"_16":4481,"_22":4926},"Chebyshev coefficients","Power series coefficients",[4929],{"_2215":4930},"cheb2poly([1 0 1])",[4932],"poly2cheb",{"_16":4934,"_18":4935,"_20":4936,"_22":4937,"_23":4938,"_29":4483,"_31":4942,"_2222":4945},"legval","y = legval(x, c)","Evaluate Legendre polynomial","Evaluates a Legendre polynomial at point x.",[4939,4940],{"_16":1350,"_22":4479},{"_16":4481,"_22":4941},"Legendre coefficient array",[4943],{"_2215":4944},"legval(0.5, [1 2 3])",[4946,4947],"legfit","legder",{"_16":4947,"_18":4949,"_20":4950,"_22":4951,"_23":4952,"_29":4534,"_31":4955,"_2222":4958},"dc = legder(c)\ndc = legder(c, m)","Legendre derivative","Differentiates a Legendre polynomial m times.",[4953,4954],{"_16":4481,"_22":4941},{"_16":1130,"_22":4533,"_28":11},[4956],{"_2215":4957},"legder([1 2 3])",[4959,4934],"legint",{"_16":4959,"_18":4961,"_20":4962,"_22":4963,"_23":4964,"_29":4550,"_31":4968,"_2222":4969},"ic = legint(c)\nic = legint(c, m)\nic = legint(c, m, k)","Legendre integral","Integrates a Legendre polynomial m times.",[4965,4966,4967],{"_16":4481,"_22":4941},{"_16":1130,"_22":4547,"_28":11},{"_16":430,"_22":4802,"_28":11},[],[4947,4934],{"_16":4971,"_18":4972,"_20":4973,"_22":4974,"_23":4975,"_29":4568,"_31":4978,"_2222":4979},"legmul","c = legmul(c1, c2)","Multiply two Legendre polynomials","Multiplies two Legendre coefficient arrays.",[4976,4977],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[4980,4981,4982],"legdiv","legadd","legsub",{"_16":4980,"_18":4984,"_20":4985,"_22":4986,"_23":4987,"_29":4829,"_31":4990,"_2222":4991},"[q, r] = legdiv(c1, c2)","Divide two Legendre polynomials","Divides two Legendre coefficient arrays.",[4988,4989],{"_16":4563,"_22":4583},{"_16":4566,"_22":4585},[],[4971],{"_16":4981,"_18":4993,"_20":4994,"_22":4995,"_23":4996,"_29":4598,"_31":4999,"_2222":5000},"c = legadd(c1, c2)","Add two Legendre polynomials","Adds two Legendre coefficient arrays.",[4997,4998],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[4982,4971],{"_16":4982,"_18":5002,"_20":5003,"_22":5004,"_23":5005,"_29":4611,"_31":5008,"_2222":5009},"c = legsub(c1, c2)","Subtract two Legendre polynomials","Subtracts two Legendre coefficient arrays.",[5006,5007],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[4981,4971],{"_16":5011,"_18":5012,"_20":5013,"_22":5014,"_23":5015,"_29":4627,"_31":5018,"_2222":5019},"legpow","c = legpow(c, n)","Raise Legendre polynomial to a power","Raises a Legendre polynomial to a non-negative integer power.",[5016,5017],{"_16":4481,"_22":4624},{"_16":629,"_22":4626},[],[4971],{"_16":5021,"_18":5022,"_20":5023,"_22":5024,"_23":5025,"_29":4639,"_31":5027,"_2222":5028},"legroots","r = legroots(c)","Find Legendre polynomial roots","Finds roots of a Legendre polynomial.",[5026],{"_16":4481,"_22":4941},[],[5029,5030],"legfromroots","legcompanion",{"_16":5029,"_18":5032,"_20":5033,"_22":5034,"_23":5035,"_29":4941,"_31":5037,"_2222":5038},"c = legfromroots(r)","Construct Legendre polynomial from roots","Constructs Legendre coefficient array from roots.",[5036],{"_16":4652,"_22":4639},[],[5021],{"_16":5030,"_18":5040,"_20":5041,"_22":5042,"_23":5043,"_29":4663,"_31":5045,"_2222":5046},"C = legcompanion(c)","Legendre companion matrix","Generates the companion matrix for a Legendre polynomial.",[5044],{"_16":4481,"_22":4941},[],[5021],{"_16":5048,"_18":5049,"_20":5050,"_22":5051,"_23":5052,"_29":4679,"_31":5055,"_2222":5056},"legvander","V = legvander(x, deg)","Legendre Vandermonde matrix","Generates a Legendre Vandermonde matrix.",[5053,5054],{"_16":1350,"_22":4675},{"_16":4677,"_22":4678},[],[4946],{"_16":4946,"_18":5058,"_20":5059,"_22":5060,"_23":5061,"_29":4941,"_31":5065,"_2222":5066},"c = legfit(x, y, deg)","Least-squares Legendre fit","Fits a Legendre polynomial of the given degree to data using least squares.",[5062,5063,5064],{"_16":1350,"_22":4690},{"_16":2349,"_22":4692},{"_16":4677,"_22":4694},[],[4934,5048],{"_16":5068,"_18":5069,"_20":5070,"_22":5071,"_23":5072,"_29":4927,"_31":5075,"_2222":5076},"leg2poly","p = leg2poly(c)","Convert Legendre to power series","Converts Legendre coefficients to power series coefficients.",[5073],{"_16":4481,"_22":5074},"Legendre coefficients",[],[5077],"poly2leg",{"_16":5079,"_18":5080,"_20":5081,"_22":5082,"_23":5083,"_29":4483,"_31":5087,"_2222":5090},"hermval","y = hermval(x, c)","Evaluate Hermite polynomial","Evaluates a physicist's Hermite polynomial at point x.",[5084,5085],{"_16":1350,"_22":4479},{"_16":4481,"_22":5086},"Hermite coefficient array",[5088],{"_2215":5089},"hermval(1, [1 2 3])",[5091,5092],"hermfit","hermder",{"_16":5092,"_18":5094,"_20":5095,"_22":5096,"_23":5097,"_29":4534,"_31":5100,"_2222":5101},"dc = hermder(c)\ndc = hermder(c, m)","Hermite derivative","Differentiates a Hermite polynomial m times.",[5098,5099],{"_16":4481,"_22":5086},{"_16":1130,"_22":4533,"_28":11},[],[5102,5079],"hermint",{"_16":5102,"_18":5104,"_20":5105,"_22":5106,"_23":5107,"_29":4550,"_31":5111,"_2222":5112},"ic = hermint(c)\nic = hermint(c, m)\nic = hermint(c, m, k)","Hermite integral","Integrates a Hermite polynomial m times.",[5108,5109,5110],{"_16":4481,"_22":5086},{"_16":1130,"_22":4547,"_28":11},{"_16":430,"_22":4802,"_28":11},[],[5092,5079],{"_16":5114,"_18":5115,"_20":5116,"_22":5117,"_23":5118,"_29":4568,"_31":5121,"_2222":5122},"hermmul","c = hermmul(c1, c2)","Multiply two Hermite polynomials","Multiplies two Hermite coefficient arrays.",[5119,5120],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5123,5124],"hermdiv","hermadd",{"_16":5123,"_18":5126,"_20":5127,"_22":5128,"_23":5129,"_29":4829,"_31":5132,"_2222":5133},"[q, r] = hermdiv(c1, c2)","Divide two Hermite polynomials","Divides two Hermite coefficient arrays.",[5130,5131],{"_16":4563,"_22":4583},{"_16":4566,"_22":4585},[],[5114],{"_16":5124,"_18":5135,"_20":5136,"_22":5137,"_23":5138,"_29":4598,"_31":5141,"_2222":5142},"c = hermadd(c1, c2)","Add two Hermite polynomials","Adds two Hermite coefficient arrays.",[5139,5140],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5143,5114],"hermsub",{"_16":5143,"_18":5145,"_20":5146,"_22":5147,"_23":5148,"_29":4611,"_31":5151,"_2222":5152},"c = hermsub(c1, c2)","Subtract two Hermite polynomials","Subtracts two Hermite coefficient arrays.",[5149,5150],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5124,5114],{"_16":5154,"_18":5155,"_20":5156,"_22":5157,"_23":5158,"_29":4627,"_31":5161,"_2222":5162},"hermpow","c = hermpow(c, n)","Raise Hermite polynomial to a power","Raises a Hermite polynomial to a non-negative integer power.",[5159,5160],{"_16":4481,"_22":4624},{"_16":629,"_22":4626},[],[5114],{"_16":5164,"_18":5165,"_20":5166,"_22":5167,"_23":5168,"_29":4639,"_31":5170,"_2222":5171},"hermroots","r = hermroots(c)","Find Hermite polynomial roots","Finds roots of a Hermite polynomial.",[5169],{"_16":4481,"_22":5086},[],[5172,5173],"hermfromroots","hermcompanion",{"_16":5172,"_18":5175,"_20":5176,"_22":5177,"_23":5178,"_29":5086,"_31":5180,"_2222":5181},"c = hermfromroots(r)","Construct Hermite polynomial from roots","Constructs Hermite coefficient array from roots.",[5179],{"_16":4652,"_22":4639},[],[5164],{"_16":5173,"_18":5183,"_20":5184,"_22":5185,"_23":5186,"_29":4663,"_31":5188,"_2222":5189},"C = hermcompanion(c)","Hermite companion matrix","Generates the companion matrix for a Hermite polynomial.",[5187],{"_16":4481,"_22":5086},[],[5164],{"_16":5191,"_18":5192,"_20":5193,"_22":5194,"_23":5195,"_29":4679,"_31":5198,"_2222":5199},"hermvander","V = hermvander(x, deg)","Hermite Vandermonde matrix","Generates a Hermite Vandermonde matrix.",[5196,5197],{"_16":1350,"_22":4675},{"_16":4677,"_22":4678},[],[5091],{"_16":5091,"_18":5201,"_20":5202,"_22":5203,"_23":5204,"_29":5086,"_31":5208,"_2222":5209},"c = hermfit(x, y, deg)","Least-squares Hermite fit","Fits a Hermite polynomial of the given degree to data using least squares.",[5205,5206,5207],{"_16":1350,"_22":4690},{"_16":2349,"_22":4692},{"_16":4677,"_22":4694},[],[5079,5191],{"_16":5211,"_18":5212,"_20":5213,"_22":5214,"_23":5215,"_29":4927,"_31":5218,"_2222":5219},"herm2poly","p = herm2poly(c)","Convert Hermite to power series","Converts Hermite coefficients to power series coefficients.",[5216],{"_16":4481,"_22":5217},"Hermite coefficients",[],[5220],"poly2herm",{"_16":5222,"_18":5223,"_20":5224,"_22":5225,"_23":5226,"_29":4483,"_31":5230,"_2222":5231},"hermeval","y = hermeval(x, c)","Evaluate probabilist's Hermite polynomial","Evaluates a probabilist's Hermite (HermiteE) polynomial at point x.",[5227,5228],{"_16":1350,"_22":4479},{"_16":4481,"_22":5229},"HermiteE coefficient array",[],[5232,5233],"hermefit","hermeder",{"_16":5233,"_18":5235,"_20":5236,"_22":5237,"_23":5238,"_29":4534,"_31":5241,"_2222":5242},"dc = hermeder(c)\ndc = hermeder(c, m)","HermiteE derivative","Differentiates a HermiteE polynomial m times.",[5239,5240],{"_16":4481,"_22":5229},{"_16":1130,"_22":4533,"_28":11},[],[5243,5222],"hermeint",{"_16":5243,"_18":5245,"_20":5246,"_22":5247,"_23":5248,"_29":4550,"_31":5252,"_2222":5253},"ic = hermeint(c)\nic = hermeint(c, m)\nic = hermeint(c, m, k)","HermiteE integral","Integrates a HermiteE polynomial m times.",[5249,5250,5251],{"_16":4481,"_22":5229},{"_16":1130,"_22":4547,"_28":11},{"_16":430,"_22":4802,"_28":11},[],[5233,5222],{"_16":5255,"_18":5256,"_20":5257,"_22":5258,"_23":5259,"_29":4568,"_31":5262,"_2222":5263},"hermemul","c = hermemul(c1, c2)","Multiply two HermiteE polynomials","Multiplies two HermiteE coefficient arrays.",[5260,5261],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5264,5265],"hermediv","hermeadd",{"_16":5264,"_18":5267,"_20":5268,"_22":5269,"_23":5270,"_29":4829,"_31":5273,"_2222":5274},"[q, r] = hermediv(c1, c2)","Divide two HermiteE polynomials","Divides two HermiteE coefficient arrays.",[5271,5272],{"_16":4563,"_22":4583},{"_16":4566,"_22":4585},[],[5255],{"_16":5265,"_18":5276,"_20":5277,"_22":5278,"_23":5279,"_29":4598,"_31":5282,"_2222":5283},"c = hermeadd(c1, c2)","Add two HermiteE polynomials","Adds two HermiteE coefficient arrays.",[5280,5281],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5284,5255],"hermesub",{"_16":5284,"_18":5286,"_20":5287,"_22":5288,"_23":5289,"_29":4611,"_31":5292,"_2222":5293},"c = hermesub(c1, c2)","Subtract two HermiteE polynomials","Subtracts two HermiteE coefficient arrays.",[5290,5291],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5265,5255],{"_16":5295,"_18":5296,"_20":5297,"_22":5298,"_23":5299,"_29":4627,"_31":5302,"_2222":5303},"hermepow","c = hermepow(c, n)","Raise HermiteE polynomial to a power","Raises a HermiteE polynomial to a non-negative integer power.",[5300,5301],{"_16":4481,"_22":4624},{"_16":629,"_22":4626},[],[5255],{"_16":5305,"_18":5306,"_20":5307,"_22":5308,"_23":5309,"_29":4639,"_31":5311,"_2222":5312},"hermeroots","r = hermeroots(c)","Find HermiteE polynomial roots","Finds roots of a HermiteE polynomial.",[5310],{"_16":4481,"_22":5229},[],[5313,5314],"hermefromroots","hermecompanion",{"_16":5313,"_18":5316,"_20":5317,"_22":5318,"_23":5319,"_29":5229,"_31":5321,"_2222":5322},"c = hermefromroots(r)","Construct HermiteE polynomial from roots","Constructs HermiteE coefficient array from roots.",[5320],{"_16":4652,"_22":4639},[],[5305],{"_16":5314,"_18":5324,"_20":5325,"_22":5326,"_23":5327,"_29":4663,"_31":5329,"_2222":5330},"C = hermecompanion(c)","HermiteE companion matrix","Generates the companion matrix for a HermiteE polynomial.",[5328],{"_16":4481,"_22":5229},[],[5305],{"_16":5332,"_18":5333,"_20":5334,"_22":5335,"_23":5336,"_29":4679,"_31":5339,"_2222":5340},"hermevander","V = hermevander(x, deg)","HermiteE Vandermonde matrix","Generates a HermiteE Vandermonde matrix.",[5337,5338],{"_16":1350,"_22":4675},{"_16":4677,"_22":4678},[],[5232],{"_16":5232,"_18":5342,"_20":5343,"_22":5344,"_23":5345,"_29":5229,"_31":5349,"_2222":5350},"c = hermefit(x, y, deg)","Least-squares HermiteE fit","Fits a HermiteE polynomial of the given degree to data using least squares.",[5346,5347,5348],{"_16":1350,"_22":4690},{"_16":2349,"_22":4692},{"_16":4677,"_22":4694},[],[5222,5332],{"_16":5352,"_18":5353,"_20":5354,"_22":5355,"_23":5356,"_29":4927,"_31":5359,"_2222":5360},"herme2poly","p = herme2poly(c)","Convert HermiteE to power series","Converts HermiteE coefficients to power series coefficients.",[5357],{"_16":4481,"_22":5358},"HermiteE coefficients",[],[5361],"poly2herme",{"_16":5363,"_18":5364,"_20":5365,"_22":5366,"_23":5367,"_29":4483,"_31":5371,"_2222":5374},"lagval","y = lagval(x, c)","Evaluate Laguerre polynomial","Evaluates a Laguerre polynomial at point x.",[5368,5369],{"_16":1350,"_22":4479},{"_16":4481,"_22":5370},"Laguerre coefficient array",[5372],{"_2215":5373},"lagval(1, [1 2 3])",[5375,5376],"lagfit","lagder",{"_16":5376,"_18":5378,"_20":5379,"_22":5380,"_23":5381,"_29":4534,"_31":5384,"_2222":5385},"dc = lagder(c)\ndc = lagder(c, m)","Laguerre derivative","Differentiates a Laguerre polynomial m times.",[5382,5383],{"_16":4481,"_22":5370},{"_16":1130,"_22":4533,"_28":11},[],[5386,5363],"lagint",{"_16":5386,"_18":5388,"_20":5389,"_22":5390,"_23":5391,"_29":4550,"_31":5395,"_2222":5396},"ic = lagint(c)\nic = lagint(c, m)\nic = lagint(c, m, k)","Laguerre integral","Integrates a Laguerre polynomial m times.",[5392,5393,5394],{"_16":4481,"_22":5370},{"_16":1130,"_22":4547,"_28":11},{"_16":430,"_22":4802,"_28":11},[],[5376,5363],{"_16":5398,"_18":5399,"_20":5400,"_22":5401,"_23":5402,"_29":4568,"_31":5405,"_2222":5406},"lagmul","c = lagmul(c1, c2)","Multiply two Laguerre polynomials","Multiplies two Laguerre coefficient arrays.",[5403,5404],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5407,5408],"lagdiv","lagadd",{"_16":5407,"_18":5410,"_20":5411,"_22":5412,"_23":5413,"_29":4829,"_31":5416,"_2222":5417},"[q, r] = lagdiv(c1, c2)","Divide two Laguerre polynomials","Divides two Laguerre coefficient arrays.",[5414,5415],{"_16":4563,"_22":4583},{"_16":4566,"_22":4585},[],[5398],{"_16":5408,"_18":5419,"_20":5420,"_22":5421,"_23":5422,"_29":4598,"_31":5425,"_2222":5426},"c = lagadd(c1, c2)","Add two Laguerre polynomials","Adds two Laguerre coefficient arrays.",[5423,5424],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5427,5398],"lagsub",{"_16":5427,"_18":5429,"_20":5430,"_22":5431,"_23":5432,"_29":4611,"_31":5435,"_2222":5436},"c = lagsub(c1, c2)","Subtract two Laguerre polynomials","Subtracts two Laguerre coefficient arrays.",[5433,5434],{"_16":4563,"_22":4564},{"_16":4566,"_22":4567},[],[5408,5398],{"_16":5438,"_18":5439,"_20":5440,"_22":5441,"_23":5442,"_29":4627,"_31":5445,"_2222":5446},"lagpow","c = lagpow(c, n)","Raise Laguerre polynomial to a power","Raises a Laguerre polynomial to a non-negative integer power.",[5443,5444],{"_16":4481,"_22":4624},{"_16":629,"_22":4626},[],[5398],{"_16":5448,"_18":5449,"_20":5450,"_22":5451,"_23":5452,"_29":4639,"_31":5454,"_2222":5455},"lagroots","r = lagroots(c)","Find Laguerre polynomial roots","Finds roots of a Laguerre polynomial.",[5453],{"_16":4481,"_22":5370},[],[5456,5457],"lagfromroots","lagcompanion",{"_16":5456,"_18":5459,"_20":5460,"_22":5461,"_23":5462,"_29":5370,"_31":5464,"_2222":5465},"c = lagfromroots(r)","Construct Laguerre polynomial from roots","Constructs Laguerre coefficient array from roots.",[5463],{"_16":4652,"_22":4639},[],[5448],{"_16":5457,"_18":5467,"_20":5468,"_22":5469,"_23":5470,"_29":4663,"_31":5472,"_2222":5473},"C = lagcompanion(c)","Laguerre companion matrix","Generates the companion matrix for a Laguerre polynomial.",[5471],{"_16":4481,"_22":5370},[],[5448],{"_16":5475,"_18":5476,"_20":5477,"_22":5478,"_23":5479,"_29":4679,"_31":5482,"_2222":5483},"lagvander","V = lagvander(x, deg)","Laguerre Vandermonde matrix","Generates a Laguerre Vandermonde matrix.",[5480,5481],{"_16":1350,"_22":4675},{"_16":4677,"_22":4678},[],[5375],{"_16":5375,"_18":5485,"_20":5486,"_22":5487,"_23":5488,"_29":5370,"_31":5492,"_2222":5493},"c = lagfit(x, y, deg)","Least-squares Laguerre fit","Fits a Laguerre polynomial of the given degree to data using least squares.",[5489,5490,5491],{"_16":1350,"_22":4690},{"_16":2349,"_22":4692},{"_16":4677,"_22":4694},[],[5363,5475],{"_16":5495,"_18":5496,"_20":5497,"_22":5498,"_23":5499,"_29":4927,"_31":5502,"_2222":5503},"lag2poly","p = lag2poly(c)","Convert Laguerre to power series","Converts Laguerre coefficients to power series coefficients.",[5500],{"_16":4481,"_22":5501},"Laguerre coefficients",[],[5504],"poly2lag",{"_16":4932,"_18":5506,"_20":5507,"_22":5508,"_23":5509,"_29":4926,"_31":5511,"_2222":5514},"cc = poly2cheb(c)","Convert power series to Chebyshev","Converts power series coefficients to Chebyshev coefficients.",[5510],{"_16":4481,"_22":4927},[5512],{"_2215":5513},"poly2cheb([1 0 1])",[4920],{"_16":5077,"_18":5516,"_20":5517,"_22":5518,"_23":5519,"_29":5074,"_31":5521,"_2222":5522},"lc = poly2leg(c)","Convert power series to Legendre","Converts power series coefficients to Legendre coefficients.",[5520],{"_16":4481,"_22":4927},[],[5068],{"_16":5220,"_18":5524,"_20":5525,"_22":5526,"_23":5527,"_29":5217,"_31":5529,"_2222":5530},"hc = poly2herm(c)","Convert power series to Hermite","Converts power series coefficients to Hermite coefficients.",[5528],{"_16":4481,"_22":4927},[],[5211],{"_16":5361,"_18":5532,"_20":5533,"_22":5534,"_23":5535,"_29":5358,"_31":5537,"_2222":5538},"hc = poly2herme(c)","Convert power series to HermiteE","Converts power series coefficients to HermiteE coefficients.",[5536],{"_16":4481,"_22":4927},[],[5352],{"_16":5504,"_18":5540,"_20":5541,"_22":5542,"_23":5543,"_29":5501,"_31":5545,"_2222":5546},"lc = poly2lag(c)","Convert power series to Laguerre","Converts power series coefficients to Laguerre coefficients.",[5544],{"_16":4481,"_22":4927},[],[5495],{"_16":5548,"_18":5549,"_20":5550,"_22":5551,"_23":5552,"_29":5556,"_31":5557,"_2222":5561},"trimcoef","ct = trimcoef(c)\nct = trimcoef(c, tol)","Remove small trailing coefficients","Removes trailing elements with absolute value less than or equal to tol.",[5553,5554],{"_16":4481,"_22":4624},{"_16":243,"_22":5555,"_28":11},"Tolerance (default: 0)","Trimmed coefficient array",[5558],{"_2215":5559,"_2217":5560},"trimcoef([1 2 3 0 0])","[1 2 3]",[5562],"trimseq",{"_16":5562,"_18":5564,"_20":5565,"_22":5566,"_23":5567,"_29":5570,"_31":5571,"_2222":5575},"ct = trimseq(c)","Remove trailing zeros","Removes trailing zeros from a coefficient sequence.",[5568],{"_16":4481,"_22":5569},"Coefficient sequence","Trimmed sequence",[5572],{"_2215":5573,"_2217":5574},"trimseq([1 2 0 0])","[1 2]",[5548],{"_16":5577,"_18":5578,"_20":5579,"_22":5580,"_23":5581,"_29":5584,"_31":5585,"_2222":5589},"getdomain","d = getdomain(x)","Get domain from data points","Returns the minimum and maximum of the data as the domain [min, max].",[5582],{"_16":1350,"_22":5583},"Data points","[min, max] domain",[5586],{"_2215":5587,"_2217":5588},"getdomain([1 2 3 4 5])","[1 5]",[5590,5591],"mapdomain","mapparms",{"_16":5590,"_18":5593,"_20":5594,"_22":5595,"_23":5596,"_29":5603,"_31":5604,"_2222":5607},"y = mapdomain(x, old, new)","Map values between domains","Maps x from the old domain to the new domain using a linear transformation.",[5597,5599,5601],{"_16":1350,"_22":5598},"Values to map",{"_16":3066,"_22":5600},"Original domain [min, max]",{"_16":3069,"_22":5602},"Target domain [min, max]","Mapped values",[5605],{"_2215":5606,"_2217":2524},"mapdomain(0.5, [0 1], [-1 1])",[5591,5577],{"_16":5591,"_18":5609,"_20":5610,"_22":5611,"_23":5612,"_29":5615,"_31":5616,"_2222":5620},"[off, scl] = mapparms(old, new)","Get linear mapping parameters","Returns [offset, scale] such that new = offset + scale * old.",[5613,5614],{"_16":3066,"_22":5600},{"_16":3069,"_22":5602},"[offset, scale]",[5617],{"_2215":5618,"_2217":5619},"mapparms([0 1], [-1 1])","[-1 2]",[5590,5577],{"_35":5622,"_16":5623,"_22":5624,"_39":40,"_41":5625,"_45":5626},"symbolic","Symbolic Mathematics","MATLAB-compatible symbolic mathematics functions for creating symbolic variables, solving equations, expanding expressions, and more. Powered by SymEngine via symngwasm.","🔣",[5627,5652,5670,5689,5709,5726,5741,5767,5788,5809],{"_16":5628,"_18":5629,"_20":5630,"_22":5631,"_23":5632,"_29":5636,"_31":5637,"_2222":5648},"sym","x = sym(s)\nx = sym(n)","Create symbolic variable or expression","Creates a symbolic variable from a string name or converts a number to a symbolic number. Supports both function syntax sym('x') and command syntax sym x.\n\nWhen given a simple variable name, creates a symbolic variable. When given an expression string, parses it into a symbolic expression.",[5633],{"_16":5634,"_22":5635},"s","Variable name (string) or numeric value to convert","Symbolic variable or expression",[5638,5640,5642,5645],{"_2215":5639,"_2217":1350},"x = sym('x')",{"_2215":5641,"_2217":1350},"sym x",{"_2215":5643,"_2217":5644},"f = sym('x^2 + 2*x + 1')","x^2 + 2*x + 1",{"_2215":5646,"_2217":5647},"half = sym(1/2)","1/2",[5649,5650,5651],"syms","solve","expand",{"_16":5649,"_18":5653,"_20":5654,"_22":5655,"_23":5656,"_29":5660,"_31":5661,"_2222":5668},"syms x y z\nsyms('x', 'y', 'z')","Create multiple symbolic variables","Creates multiple symbolic variables and assigns them to the workspace. Supports both command syntax syms x y z and function syntax syms('x', 'y', 'z').\n\nEach variable name becomes a symbolic variable in the current workspace.",[5657],{"_16":5658,"_22":5659},"vars","Variable names (space-separated for command syntax, or multiple string arguments)","Creates variables in workspace (no return value)",[5662,5665],{"_2215":5663,"_2217":5664},"syms x y z","% Creates x, y, z as symbolic variables",{"_2215":5666,"_2217":5667},"syms('a', 'b')","% Creates a, b as symbolic variables",[5628,5650,5669],"subs",{"_16":5650,"_18":5671,"_20":5672,"_22":5673,"_23":5674,"_29":5680,"_31":5681,"_2222":5688},"S = solve(eqn, var)\nS = solve(eqn)","Solve symbolic equation","Solves a symbolic equation for the specified variable. The equation can be an expression (assumed equal to zero) or an equation created with ==.\n\nReturns an array of solutions. For polynomial equations, includes all roots (real and complex).",[5675,5678],{"_16":5676,"_22":5677},"eqn","Symbolic equation or expression (assumed = 0)",{"_16":2704,"_22":5679,"_28":11},"Variable to solve for","Array of symbolic solutions",[5682,5685],{"_2215":5683,"_2217":5684},"syms x; solve(x^2 - 1, x)","[-1, 1]",{"_2215":5686,"_2217":5687},"syms x; solve(x^2 + x - 6, x)","[-3, 2]",[5628,5649,5651,5669],{"_16":5669,"_18":5690,"_20":5691,"_22":5692,"_23":5693,"_29":5701,"_31":5702,"_2222":5708},"g = subs(f, old, new)\ng = subs(f, var, value)","Substitute in symbolic expression","Substitutes old with new in the symbolic expression f. Can substitute a variable with a value or an expression with another expression.\n\nUseful for evaluating symbolic expressions at specific values or simplifying by replacement.",[5694,5697,5699],{"_16":5695,"_22":5696},"f","Symbolic expression",{"_16":3066,"_22":5698},"Symbol or expression to replace",{"_16":3069,"_22":5700},"Replacement value or expression","Expression with substitution applied",[5703,5705],{"_2215":5704,"_2217":2629},"syms x; subs(x^2 + 1, x, 2)",{"_2215":5706,"_2217":5707},"syms x y; subs(x + y, x, y^2)","y^2 + y",[5628,5650,5651],{"_16":5651,"_18":5710,"_20":5711,"_22":5712,"_23":5713,"_29":5716,"_31":5717,"_2222":5723},"g = expand(f)","Expand symbolic expression","Expands products and powers in the symbolic expression. Distributes multiplication over addition and expands powers of sums.\n\nExample: expand((x+1)^2) returns x^2 + 2*x + 1",[5714],{"_16":5695,"_22":5715},"Symbolic expression to expand","Expanded expression",[5718,5720],{"_2215":5719,"_2217":5644},"syms x; expand((x + 1)^2)",{"_2215":5721,"_2217":5722},"syms x y; expand((x + y)*(x - y))","x^2 - y^2",[5628,5724,5725],"simplify","factor",{"_16":5724,"_18":5727,"_20":5728,"_22":5729,"_23":5730,"_29":5733,"_31":5734,"_2222":5739},"g = simplify(f)","Simplify symbolic expression","Simplifies a symbolic expression using various algebraic rules. Combines like terms, cancels common factors, and applies trigonometric identities.",[5731],{"_16":5695,"_22":5732},"Symbolic expression to simplify","Simplified expression",[5735,5737],{"_2215":5736,"_2217":1350},"syms x; simplify(x^2/x)",{"_2215":5738,"_2217":2434},"syms x; simplify(sin(x)^2 + cos(x)^2)",[5651,5725,5740],"collect",{"_16":5742,"_18":5743,"_20":5744,"_22":5745,"_23":5746,"_29":5753,"_31":5754,"_2222":5764},"diff","df = diff(f, x)\ndf = diff(f, x, n)","Symbolic differentiation","Computes the symbolic derivative of f with respect to x. If n is specified, computes the nth derivative.\n\nSupports all elementary functions including trigonometric, exponential, and logarithmic.",[5747,5749,5751],{"_16":5695,"_22":5748},"Symbolic expression to differentiate",{"_16":1350,"_22":5750},"Variable to differentiate with respect to",{"_16":629,"_22":5752,"_28":11},"Order of derivative (default: 1)","Derivative expression",[5755,5758,5761],{"_2215":5756,"_2217":5757},"syms x; diff(x^3, x)","3*x^2",{"_2215":5759,"_2217":5760},"syms x; diff(sin(x), x)","cos(x)",{"_2215":5762,"_2217":5763},"syms x; diff(x^3, x, 2)","6*x",[5765,5766,5628],"int","taylor",{"_16":5766,"_18":5768,"_20":5769,"_22":5770,"_23":5771,"_29":5779,"_31":5780,"_2222":5787},"T = taylor(f, x)\nT = taylor(f, x, a)\nT = taylor(f, x, a, n)","Taylor series expansion","Computes the Taylor series expansion of f around the point a (default 0). Returns a polynomial approximation with n terms (default 6).\n\nThe result is a symbolic polynomial representing the truncated Taylor series.",[5772,5773,5775,5777],{"_16":5695,"_22":5715},{"_16":1350,"_22":5774},"Expansion variable",{"_16":2283,"_22":5776,"_28":11},"Expansion point (default: 0)",{"_16":629,"_22":5778,"_28":11},"Number of terms (default: 6)","Taylor polynomial",[5781,5784],{"_2215":5782,"_2217":5783},"syms x; taylor(exp(x), x, 0, 4)","1 + x + x^2/2 + x^3/6",{"_2215":5785,"_2217":5786},"syms x; taylor(sin(x), x)","x - x^3/6 + x^5/120",[5742,5651,5628],{"_16":5789,"_18":5790,"_20":5791,"_22":5792,"_23":5793,"_29":5799,"_31":5800,"_2222":5807},"assume","assume(x, prop)\nassume x prop","Set assumption on symbolic variable","Sets an assumption on a symbolic variable. Assumptions affect simplification and solving.\n\nCommon assumptions: positive, negative, real, integer, rational",[5794,5796],{"_16":1350,"_22":5795},"Symbolic variable",{"_16":5797,"_22":5798},"prop","Property to assume (e.g., 'positive', 'real', 'integer')","Nothing (modifies variable in place)",[5801,5804],{"_2215":5802,"_2217":5803},"syms x; assume(x, 'positive')","% x is now assumed positive",{"_2215":5805,"_2217":5806},"assume x real","% x is now assumed real",[5808,5628,5649],"assumptions",{"_16":5808,"_18":5810,"_20":5811,"_22":5812,"_23":5813,"_29":5816,"_31":5817,"_2222":5821},"a = assumptions(x)","Get assumptions on symbolic variable","Returns the current assumptions on a symbolic variable as a string.",[5814],{"_16":1350,"_22":5815},"Symbolic variable to query","String describing assumptions",[5818],{"_2215":5819,"_2217":5820},"syms x; assume(x, 'positive'); assumptions(x)","'positive'",[5789,5628,5649],{"_35":5823,"_16":5824,"_22":5825,"_39":40,"_41":5826,"_43":5823,"_45":5827},"vtk","3D Visualization (VTK)","Advanced 3D visualization functions powered by VTK.js for volumetric data, FEM meshes, and scientific visualization.","🧊",[5828,5851,5874,5895,5916,5940,5959,5982,6000,6016,6027,6039,6050,6059,6068,6081,6094,6110],{"_16":5829,"_18":5830,"_20":5831,"_22":5832,"_23":5833,"_29":5843,"_31":5844,"_2222":5847},"vtk.polydata","vtk.polydata(points, polys)\nvtk.polydata(points, polys, scalars)","Create PolyData geometry","Creates a VTK PolyData visualization from points and polygon connectivity. Points should be an Nx3 matrix of [x, y, z] coordinates. Polys defines polygon connectivity. Optional scalars provide per-point coloring.",[5834,5837,5840],{"_16":5835,"_22":5836},"points","Nx3 matrix of point coordinates",{"_16":5838,"_22":5839},"polys","Polygon connectivity array (VTK format: [npts, p1, p2, ...])",{"_16":5841,"_22":5842,"_28":11},"scalars","Per-point scalar values for coloring","null (renders VTK visualization inline)",[5845],{"_2215":5846},"% Create a simple triangle\npoints = [0 0 0; 1 0 0; 0.5 1 0];\npolys = [3 0 1 2]; % triangle with 3 vertices\nvtk.polydata(points, polys)",[5848,5849,5850],"vtk.volume","vtk.femgrid","vtk.sphere",{"_16":5848,"_18":5852,"_20":5853,"_22":5854,"_23":5855,"_29":5867,"_31":5868,"_2222":5871},"vtk.volume(data, dims)\nvtk.volume(data, dims, spacing)\nvtk.volume(data, dims, spacing, origin)","Create volumetric visualization","Creates a VTK volume rendering from 3D scalar data. The data array contains voxel values in row-major order. Dims specifies [nx, ny, nz] dimensions. Optional spacing and origin control physical coordinates.",[5856,5858,5861,5864],{"_16":117,"_22":5857},"Flat array of scalar values (nx*ny*nz elements)",{"_16":5859,"_22":5860},"dims","3-element vector [nx, ny, nz] specifying grid dimensions",{"_16":5862,"_22":5863,"_28":11},"spacing","3-element vector [dx, dy, dz] for voxel spacing (default: [1,1,1])",{"_16":5865,"_22":5866,"_28":11},"origin","3-element vector [x0, y0, z0] for grid origin (default: [0,0,0])","null (renders VTK volume inline)",[5869],{"_2215":5870},"% Create a 3D Gaussian blob\n[X, Y, Z] = meshgrid(-2:0.1:2);\ndata = exp(-(X.^2 + Y.^2 + Z.^2));\nvtk.volume(data(:), size(data))",[5872,5873,5829],"vtk.isosurface","vtk.slice",{"_16":5872,"_18":5875,"_20":5876,"_22":5877,"_23":5878,"_29":5890,"_31":5891,"_2222":5894},"vtk.isosurface(data, dims, isovalue)\nvtk.isosurface(data, dims, spacing, origin, isovalue)","Extract and render isosurface","Extracts an isosurface from 3D volumetric data at the specified scalar value. Creates a surface representation of the contour where data equals the isovalue.",[5879,5881,5883,5885,5887],{"_16":117,"_22":5880},"Flat array of scalar values",{"_16":5859,"_22":5882},"3-element vector [nx, ny, nz]",{"_16":5862,"_22":5884,"_28":11},"Voxel spacing (default: [1,1,1])",{"_16":5865,"_22":5886,"_28":11},"Grid origin (default: [0,0,0])",{"_16":5888,"_22":5889},"isovalue","Scalar value for the isosurface","null (renders isosurface inline)",[5892],{"_2215":5893},"% Extract isosurface from a sphere function\n[X, Y, Z] = meshgrid(-2:0.1:2);\ndata = X.^2 + Y.^2 + Z.^2;\nvtk.isosurface(data(:), size(data), 1.0) % sphere of radius 1",[5848,5829],{"_16":5849,"_18":5896,"_20":5897,"_22":5898,"_23":5899,"_29":5911,"_31":5912,"_2222":5915},"vtk.femgrid(nodes, elements, elementTypes)\nvtk.femgrid(nodes, elements, elementTypes, scalars)","Visualize FEM unstructured grid","Creates a VTK unstructured grid visualization for finite element meshes. Nodes is an Nx3 matrix of coordinates. Elements defines cell connectivity. ElementTypes specifies VTK cell types (10=tetra, 12=hex, 5=tri, 9=quad).",[5900,5903,5906,5909],{"_16":5901,"_22":5902},"nodes","Nx3 matrix of node coordinates",{"_16":5904,"_22":5905},"elements","Cell connectivity in VTK format [npts, n1, n2, ...]",{"_16":5907,"_22":5908},"elementTypes","Array of VTK cell type codes for each element",{"_16":5841,"_22":5910,"_28":11},"Per-node or per-cell scalar field (e.g., stress, temperature)","null (renders FEM mesh inline)",[5913],{"_2215":5914},"% Create a simple tetrahedral mesh\nnodes = [0 0 0; 1 0 0; 0.5 1 0; 0.5 0.5 1];\nelements = [4 0 1 2 3]; % one tetrahedron\ntypes = [10]; % VTK_TETRA\nvtk.femgrid(nodes, elements, types)",[5829,5848],{"_16":5850,"_18":5917,"_20":5918,"_22":5919,"_23":5920,"_29":5930,"_31":5931,"_2222":5936},"vtk.sphere()\nvtk.sphere(radius)\nvtk.sphere(radius, center)\nvtk.sphere(radius, center, resolution)","Create sphere geometry","Creates a VTK sphere source with specified radius, center, and resolution. Useful for quick testing and demonstrations.",[5921,5924,5927],{"_16":5922,"_22":5923,"_28":11},"radius","Sphere radius (default: 1)",{"_16":5925,"_22":5926,"_28":11},"center","3-element vector [x, y, z] for center (default: [0,0,0])",{"_16":5928,"_22":5929,"_28":11},"resolution","Number of phi/theta divisions (default: 32)","null (renders sphere inline)",[5932,5934],{"_2215":5933},"vtk.sphere() % unit sphere at origin",{"_2215":5935},"vtk.sphere(2, [1 0 0], 64) % radius 2, centered at (1,0,0), high resolution",[5937,5938,5939],"vtk.cone","vtk.cube","vtk.cylinder",{"_16":5937,"_18":5941,"_20":5942,"_22":5943,"_23":5944,"_29":5952,"_31":5953,"_2222":5958},"vtk.cone()\nvtk.cone(height, radius)\nvtk.cone(height, radius, center)","Create cone geometry","Creates a VTK cone source with specified height, radius, and center.",[5945,5948,5950],{"_16":5946,"_22":5947,"_28":11},"height","Cone height (default: 1)",{"_16":5922,"_22":5949,"_28":11},"Base radius (default: 0.5)",{"_16":5925,"_22":5951,"_28":11},"3-element center position (default: [0,0,0])","null (renders cone inline)",[5954,5956],{"_2215":5955},"vtk.cone()",{"_2215":5957},"vtk.cone(2, 1, [0 0 1])",[5850,5938,5939],{"_16":5938,"_18":5960,"_20":5961,"_22":5962,"_23":5963,"_29":5975,"_31":5976,"_2222":5981},"vtk.cube()\nvtk.cube(size)\nvtk.cube(xLen, yLen, zLen)","Create cube/box geometry","Creates a VTK cube (box) source with specified dimensions.",[5964,5966,5969,5972],{"_16":93,"_22":5965,"_28":11},"Uniform size for all dimensions (default: 1)",{"_16":5967,"_22":5968,"_28":11},"xLen","X dimension length",{"_16":5970,"_22":5971,"_28":11},"yLen","Y dimension length",{"_16":5973,"_22":5974,"_28":11},"zLen","Z dimension length","null (renders cube inline)",[5977,5979],{"_2215":5978},"vtk.cube()",{"_2215":5980},"vtk.cube(2, 1, 0.5) % rectangular box",[5850,5937,5939],{"_16":5939,"_18":5983,"_20":5984,"_22":5985,"_23":5986,"_29":5993,"_31":5994,"_2222":5999},"vtk.cylinder()\nvtk.cylinder(height, radius)\nvtk.cylinder(height, radius, resolution)","Create cylinder geometry","Creates a VTK cylinder source with specified height, radius, and resolution.",[5987,5989,5991],{"_16":5946,"_22":5988,"_28":11},"Cylinder height (default: 1)",{"_16":5922,"_22":5990,"_28":11},"Cylinder radius (default: 0.5)",{"_16":5928,"_22":5992,"_28":11},"Number of facets around circumference (default: 32)","null (renders cylinder inline)",[5995,5997],{"_2215":5996},"vtk.cylinder()",{"_2215":5998},"vtk.cylinder(3, 0.5, 64)",[5850,5937,5938],{"_16":6001,"_18":6002,"_20":6003,"_22":6004,"_23":6005,"_29":4068,"_31":6008,"_2222":6013},"vtk.colormap","vtk.colormap('name')","Set VTK colormap","Sets the colormap for subsequent VTK visualizations. Available colormaps: 'viridis', 'rainbow', 'coolwarm', 'grayscale', 'jet', 'hot'.",[6006],{"_16":16,"_22":6007},"Colormap name",[6009,6011],{"_2215":6010},"vtk.colormap('coolwarm')",{"_2215":6012},"vtk.colormap('viridis'); vtk.volume(data, dims)",[6014,6015],"vtk.opacity","vtk.edges",{"_16":6014,"_18":6017,"_20":6018,"_22":6019,"_23":6020,"_29":4068,"_31":6023,"_2222":6026},"vtk.opacity(value)","Set VTK opacity","Sets the opacity (0-1) for subsequent VTK visualizations.",[6021],{"_16":457,"_22":6022},"Opacity value between 0 (transparent) and 1 (opaque)",[6024],{"_2215":6025},"vtk.opacity(0.7)",[6001,6015],{"_16":6015,"_18":6028,"_20":6029,"_22":6030,"_23":6031,"_29":4068,"_31":6034,"_2222":6037},"vtk.edges('on')\nvtk.edges('off')","Toggle edge visibility","Enables or disables edge rendering for surface meshes. Useful for FEM visualization.",[6032],{"_16":4206,"_22":6033},"'on' or 'off'",[6035],{"_2215":6036},"vtk.edges('on')",[6001,6038],"vtk.wireframe",{"_16":6038,"_18":6040,"_20":6041,"_22":6042,"_23":6043,"_29":4068,"_31":6044,"_2222":6047},"vtk.wireframe()","Set wireframe rendering","Sets the rendering mode to wireframe for subsequent VTK visualizations.",[],[6045],{"_2215":6046},"vtk.wireframe(); vtk.sphere()",[6048,6049,6015],"vtk.surface","vtk.points",{"_16":6048,"_18":6051,"_20":6052,"_22":6053,"_23":6054,"_29":4068,"_31":6055,"_2222":6058},"vtk.surface()","Set surface rendering","Sets the rendering mode to filled surface for subsequent VTK visualizations (default mode).",[],[6056],{"_2215":6057},"vtk.surface(); vtk.sphere()",[6038,6049],{"_16":6049,"_18":6060,"_20":6061,"_22":6062,"_23":6063,"_29":4068,"_31":6064,"_2222":6067},"vtk.points()","Set point rendering","Sets the rendering mode to points only for subsequent VTK visualizations.",[],[6065],{"_2215":6066},"vtk.points(); vtk.sphere()",[6038,6048],{"_16":6069,"_18":6070,"_20":6071,"_22":6072,"_23":6073,"_29":5843,"_31":6076,"_2222":6079},"vtk.mesh","vtk.mesh(mesh)","Visualize an MFEM mesh","Renders an MFEM mesh object directly. The mesh is exported to VTK format internally and displayed as an unstructured grid visualization. For solution visualization with scalar coloring, use vtk.gridfunction() instead.",[6074],{"_16":2365,"_22":6075},"MFEM Mesh object (from mfem.mesh.makeCartesian2D, etc.)",[6077],{"_2215":6078},"mesh = mfem.mesh.makeCartesian2D(10, 10, 'TRIANGLE', true, 1.0, 1.0)\nvtk.edges('on')\nvtk.mesh(mesh)",[6080,5849,6001],"vtk.gridfunction",{"_16":6082,"_18":6083,"_20":6084,"_22":6085,"_23":6086,"_29":6089,"_31":6090,"_2222":6093},"vtk.meshCoordinates","coords = vtk.meshCoordinates(mesh)","Get mesh vertex coordinates","Extracts the x, y, and z coordinates of all mesh vertices. Returns a struct with x, y, z arrays and the number of vertices.",[6087],{"_16":2365,"_22":6088},"MFEM Mesh object","Struct with fields: x, y, z (NDArrays) and numVertices (number)",[6091],{"_2215":6092},"mesh = mfem.mesh.makeCartesian2D(10, 10)\ncoords = vtk.meshCoordinates(mesh)\ndisp(coords.x) % x-coordinates of all vertices\ndisp(coords.y) % y-coordinates of all vertices",[6069,6080],{"_16":6080,"_18":6095,"_20":6096,"_22":6097,"_23":6098,"_29":5843,"_31":6104,"_2222":6109},"vtk.gridfunction(mesh, gf)","Visualize MFEM GridFunction with scalar coloring","Renders an MFEM GridFunction on its mesh, with vertices colored by the solution values. Use vtk.colormap() to set the color scheme before calling this function.",[6099,6101],{"_16":2365,"_22":6100},"MFEM Mesh object (the mesh on which the GridFunction is defined)",{"_16":6102,"_22":6103},"gf","MFEM GridFunction object containing the finite element solution",[6105,6107],{"_2215":6106},"vtk.colormap('viridis')\nvtk.gridfunction(mesh, solution)",{"_2215":6108},"vtk.colormap('coolwarm')\nvtk.edges('on')\nvtk.gridfunction(mesh, x)",[6069,6001,6015],{"_16":6111,"_18":6112,"_20":6113,"_22":6114,"_23":6115,"_29":6122,"_31":6123,"_2222":6126},"vtk.displacement","vtk.displacement(mesh, u)\nvtk.displacement(mesh, u, scaleFactor)","Visualize displacement field on deformed mesh","Renders a vector displacement field by deforming the mesh and coloring by displacement magnitude. The scaleFactor amplifies the deformation for visualization of small displacements (default: 1).",[6116,6117,6119],{"_16":2365,"_22":6088},{"_16":1995,"_22":6118},"Vector GridFunction containing displacement [ux, uy, uz] per node",{"_16":6120,"_22":6121,"_28":11},"scaleFactor","Deformation amplification factor (default: 1)","null (renders deformed mesh inline)",[6124],{"_2215":6125},"vtk.colormap('coolwarm')\nvtk.displacement(mesh, u, 100) % amplify by 100x",[6080,6069],{"_35":6128,"_16":6129,"_22":6130,"_39":40,"_41":6131,"_45":6132},"sparse","Sparse Matrices","Sparse matrix creation, manipulation, and iterative solvers for large-scale linear systems.","🔳",[6133,6161,6173,6190,6203,6215,6232,6248,6262,6276,6291,6302,6314,6325,6337,6352,6367,6392,6406,6420,6436,6452,6465,6482,6496],{"_16":6128,"_18":6134,"_20":6135,"_22":6136,"_23":6137,"_29":6148,"_31":6149,"_2222":6156},"S = sparse(A)\nS = sparse(m, n)\nS = sparse(i, j, v)\nS = sparse(i, j, v, m, n)","Create sparse matrix","Creates a sparse matrix. With one argument, converts a dense matrix to sparse CSR format. With two arguments (m,n), creates an empty m-by-n sparse matrix. With three arguments (i,j,v), creates a sparse matrix from row indices i, column indices j, and values v. With five arguments, additionally specifies the m-by-n dimensions.",[6138,6141,6144,6146,6147],{"_16":6139,"_22":6140},"A/i","Dense matrix, or row index vector (1-based)",{"_16":6142,"_22":6143,"_28":11},"j/n","Column index vector (1-based), or number of columns",{"_16":1604,"_22":6145,"_28":11},"Values vector",{"_16":1130,"_22":2209,"_28":11},{"_16":629,"_22":2211,"_28":11},"Sparse matrix (CSR format)",[6150,6152,6154],{"_2215":6151},"S = sparse(eye(5))",{"_2215":6153},"S = sparse([1 2 3], [1 2 3], [10 20 30], 3, 3)",{"_2215":6155},"S = sparse(5, 5) % empty 5x5 sparse",[6157,6158,6159,6160],"speye","sprand","full","issparse",{"_16":6157,"_18":6162,"_20":6163,"_22":6164,"_23":6165,"_29":6163,"_31":6169,"_2222":6172},"S = speye(n)\nS = speye(m, n)","Sparse identity matrix","Creates a sparse identity matrix. speye(n) creates an n-by-n sparse identity. speye(m,n) creates an m-by-n sparse matrix with ones on the main diagonal.",[6166,6168],{"_16":1130,"_22":6167},"Size (or number of rows)",{"_16":629,"_22":2211,"_28":11},[6170],{"_2215":6171},"I = speye(100)",[6128,2225,6158],{"_16":6158,"_18":6174,"_20":6175,"_22":6176,"_23":6177,"_29":6183,"_31":6184,"_2222":6187},"S = sprand(m, n, density)","Sparse uniformly distributed random matrix","Generates an m-by-n sparse matrix with approximately density*m*n uniformly distributed nonzero entries on [0,1).",[6178,6179,6180],{"_16":1130,"_22":2209},{"_16":629,"_22":2211},{"_16":6181,"_22":6182},"density","Approximate density (0 to 1)","Sparse random matrix",[6185],{"_2215":6186},"S = sprand(100, 100, 0.05)",[6188,6189,6128],"sprandn","sprandsym",{"_16":6188,"_18":6191,"_20":6192,"_22":6193,"_23":6194,"_29":6198,"_31":6199,"_2222":6202},"S = sprandn(m, n, density)","Sparse normally distributed random matrix","Generates an m-by-n sparse matrix with approximately density*m*n normally distributed nonzero entries.",[6195,6196,6197],{"_16":1130,"_22":2209},{"_16":629,"_22":2211},{"_16":6181,"_22":6182},"Sparse random matrix with normal distribution",[6200],{"_2215":6201},"S = sprandn(100, 100, 0.05)",[6158,6189,6128],{"_16":6189,"_18":6204,"_20":6205,"_22":6206,"_23":6207,"_29":6205,"_31":6211,"_2222":6214},"S = sprandsym(n, density)","Sparse symmetric random matrix","Generates an n-by-n sparse symmetric random matrix with approximately density*n*n/2 nonzero entries.",[6208,6210],{"_16":629,"_22":6209},"Matrix size",{"_16":6181,"_22":6182},[6212],{"_2215":6213},"S = sprandsym(50, 0.1)",[6158,6188],{"_16":6216,"_18":6217,"_20":6218,"_22":6219,"_23":6220,"_29":6227,"_31":6228,"_2222":6231},"spdiags","S = spdiags(B, d, m, n)","Sparse matrix formed from diagonals","Creates a sparse m-by-n matrix by placing the columns of B along the diagonals specified by d. Each column of B is placed along the corresponding diagonal in d.",[6221,6223,6225,6226],{"_16":505,"_22":6222},"Matrix whose columns are the diagonals",{"_16":1096,"_22":6224},"Vector of diagonal positions (0 = main, positive = above, negative = below)",{"_16":1130,"_22":2209},{"_16":629,"_22":2211},"Sparse matrix with specified diagonals",[6229],{"_2215":6230},"e = ones(5,1);\nS = spdiags([-e 2*e -e], [-1 0 1], 5, 5)",[6128,6157,2253],{"_16":6233,"_18":6234,"_20":6235,"_22":6236,"_23":6237,"_29":6243,"_31":6244,"_2222":6247},"spalloc","S = spalloc(m, n, nz)","Allocate space for sparse matrix","Creates an m-by-n all-zero sparse matrix with space preallocated for nz nonzero elements. Returns an empty sparse matrix (JS sparse matrices auto-resize).",[6238,6239,6240],{"_16":1130,"_22":2209},{"_16":629,"_22":2211},{"_16":6241,"_22":6242},"nz","Number of nonzero elements to allocate (hint)","Empty sparse matrix",[6245],{"_2215":6246},"S = spalloc(10, 10, 50)",[6128,6157],{"_16":6249,"_18":6250,"_20":6251,"_22":6252,"_23":6253,"_29":6257,"_31":6258,"_2222":6261},"spconvert","S = spconvert(D)","Import sparse matrix from triplet data","Converts a matrix D with rows [i j v] into a sparse matrix. Row indices are in column 1, column indices in column 2, values in column 3. The last row may specify the matrix dimensions as [m n 0].",[6254],{"_16":6255,"_22":6256},"D","Dense matrix with columns [i, j, v]","Sparse matrix",[6259],{"_2215":6260},"D = [1 1 10; 2 2 20; 3 3 30];\nS = spconvert(D)",[6128,2774],{"_16":6160,"_18":6263,"_20":6264,"_22":6265,"_23":6266,"_29":6269,"_31":6270,"_2222":6275},"tf = issparse(S)","Determine if matrix is sparse","Returns true (1) if S is a sparse matrix, false (0) otherwise.",[6267],{"_16":1113,"_22":6268},"Input value to test","Logical 1 or 0",[6271,6273],{"_2215":6272,"_2217":2434},"issparse(speye(5))",{"_2215":6274,"_2217":2524},"issparse(eye(5))",[6128,6159],{"_16":3970,"_18":6277,"_20":6278,"_22":6279,"_23":6280,"_29":6283,"_31":6284,"_2222":6288},"n = nnz(S)","Number of nonzero matrix elements","Returns the number of nonzero elements in sparse matrix S, or the number of nonzero elements in a full matrix.",[6281],{"_16":1113,"_22":6282},"Sparse or full matrix","Number of nonzeros",[6285],{"_2215":6286,"_2217":6287},"nnz(speye(100))","100",[6289,6290,6160],"nonzeros","nzmax",{"_16":6289,"_18":6292,"_20":6293,"_22":6294,"_23":6295,"_29":6297,"_31":6298,"_2222":6301},"v = nonzeros(S)","Nonzero matrix elements","Returns a column vector of the nonzero elements in sparse matrix S.",[6296],{"_16":1113,"_22":6257},"Column vector of nonzero values",[6299],{"_2215":6300},"nonzeros(sparse([1 0; 0 2]))",[3970,2774,6290],{"_16":6290,"_18":6303,"_20":6304,"_22":6305,"_23":6306,"_29":6308,"_31":6309,"_2222":6313},"n = nzmax(S)","Amount of storage allocated for nonzero elements","Returns the amount of storage allocated for nonzero matrix elements. Returns the same as nnz(S) since JS arrays auto-resize.",[6307],{"_16":1113,"_22":6257},"Allocated storage size",[6310],{"_2215":6311,"_2217":6312},"nzmax(speye(10))","10",[3970,6289],{"_16":6159,"_18":6315,"_20":6316,"_22":6317,"_23":6318,"_29":6320,"_31":6321,"_2222":6324},"A = full(S)","Convert sparse matrix to full storage","Converts a sparse matrix S to full (dense) matrix form. If S is already a full matrix, returns it unchanged.",[6319],{"_16":1113,"_22":6282},"Full (dense) matrix",[6322],{"_2215":6323},"full(speye(3))",[6128,6160,3947],{"_16":6326,"_18":6327,"_20":6328,"_22":6329,"_23":6330,"_29":6332,"_31":6333,"_2222":6336},"spones","R = spones(S)","Replace nonzero sparse matrix elements with ones","Returns a matrix with the same sparsity pattern as S but with all nonzero values replaced by 1.",[6331],{"_16":1113,"_22":6257},"Sparse matrix with ones at nonzero positions",[6334],{"_2215":6335},"full(spones(sparse([1 0; 0 5])))",[3970,6289,6128],{"_16":6338,"_18":6339,"_20":6340,"_22":6341,"_23":6342,"_29":6347,"_31":6348,"_2222":6351},"spfun","F = spfun(func, S)","Apply function to nonzero sparse matrix elements","Applies the function func to the nonzero elements of sparse matrix S. The sparsity pattern is preserved.",[6343,6346],{"_16":6344,"_22":6345},"func","Function handle to apply (e.g., @sqrt, @exp)",{"_16":1113,"_22":6257},"Sparse matrix with function applied to nonzeros",[6349],{"_2215":6350},"full(spfun(@sqrt, sparse([4 0; 0 9])))",[6326,6289],{"_16":6353,"_18":6354,"_20":6355,"_22":6356,"_23":6357,"_29":6363,"_31":6364,"_2222":6366},"spparms","spparms\nspparms(key)\nspparms(key, value)","Set parameters for sparse matrix routines","Gets or sets parameters for sparse matrix routines. This is a compatibility stub that accepts but ignores configuration.",[6358,6361],{"_16":6359,"_22":6360,"_28":11},"key","Parameter name",{"_16":457,"_22":6362,"_28":11},"Parameter value","Current parameter values, or null",[6365],{"_2215":6353},[6128],{"_16":6368,"_18":6369,"_20":6370,"_22":6371,"_23":6372,"_29":6385,"_31":6386,"_2222":6389},"gmres","x = gmres(A, b)\nx = gmres(A, b, restart, tol, maxit)\n[x, flag, relres, iter] = gmres(...)","Generalized minimum residual method","Solves the linear system Ax = b using the GMRES iterative method. Suitable for general (non-symmetric) sparse systems.",[6373,6375,6377,6380,6382],{"_16":26,"_22":6374},"Sparse coefficient matrix (n x n)",{"_16":983,"_22":6376},"Right-hand side vector",{"_16":6378,"_22":6379,"_28":11},"restart","Restart parameter (default 20)",{"_16":243,"_22":6381,"_28":11},"Convergence tolerance (default 1e-6)",{"_16":6383,"_22":6384,"_28":11},"maxit","Maximum iterations","Solution vector x, or [x, flag, relres, iter]",[6387],{"_2215":6388},"A = speye(3); b = [1;2;3];\nx = gmres(A, b)",[6390,6391,6128],"bicgstab","pcg",{"_16":6390,"_18":6393,"_20":6394,"_22":6395,"_23":6396,"_29":6385,"_31":6402,"_2222":6405},"x = bicgstab(A, b)\n[x, flag, relres, iter] = bicgstab(A, b, tol, maxit)","BiConjugate Gradients Stabilized method","Solves the linear system Ax = b using the BiCGSTAB iterative method. Works for general (non-symmetric) sparse matrices.",[6397,6399,6400,6401],{"_16":26,"_22":6398},"Sparse coefficient matrix",{"_16":983,"_22":6376},{"_16":243,"_22":6381,"_28":11},{"_16":6383,"_22":6384,"_28":11},[6403],{"_2215":6404},"x = bicgstab(A, b)",[6368,6391],{"_16":6391,"_18":6407,"_20":6408,"_22":6409,"_23":6410,"_29":6385,"_31":6416,"_2222":6419},"x = pcg(A, b)\n[x, flag, relres, iter] = pcg(A, b, tol, maxit)","Preconditioned conjugate gradients","Solves the symmetric positive definite linear system Ax = b using the Preconditioned Conjugate Gradient method.",[6411,6413,6414,6415],{"_16":26,"_22":6412},"Symmetric positive definite sparse matrix",{"_16":983,"_22":6376},{"_16":243,"_22":6381,"_28":11},{"_16":6383,"_22":6384,"_28":11},[6417],{"_2215":6418},"x = pcg(A, b)",[6368,6390],{"_16":6421,"_18":6422,"_20":6423,"_22":6424,"_23":6425,"_29":6431,"_31":6432,"_2222":6435},"lsqr","x = lsqr(A, b)\n[x, flag] = lsqr(A, b, tol, maxit)","Least-squares solution via iterative method","Solves the least-squares problem min ||Ax - b||_2 using an iterative method. Delegates to conjugate gradients on the normal equations.",[6426,6428,6429,6430],{"_16":26,"_22":6427},"Sparse matrix (possibly non-square)",{"_16":983,"_22":6376},{"_16":243,"_22":6381,"_28":11},{"_16":6383,"_22":6384,"_28":11},"Solution vector x, or [x, flag]",[6433],{"_2215":6434},"x = lsqr(A, b)",[6391,6368],{"_16":6437,"_18":6438,"_20":6439,"_22":6440,"_23":6441,"_29":6446,"_31":6447,"_2222":6450},"eigs","d = eigs(A, k)\n[V, D] = eigs(A, k)","Largest eigenvalues and eigenvectors of sparse matrix","Finds the k largest eigenvalues and optionally eigenvectors of a sparse matrix using ARPACK.",[6442,6444],{"_16":26,"_22":6443},"Sparse matrix or LinearOperator",{"_16":430,"_22":6445,"_28":11},"Number of eigenvalues (default 6)","Eigenvalues vector, or [V, D] decomposition",[6448],{"_2215":6449},"d = eigs(speye(10), 3)",[3311,6451],"svds",{"_16":6451,"_18":6453,"_20":6454,"_22":6455,"_23":6456,"_29":6460,"_31":6461,"_2222":6464},"s = svds(A, k)\n[U, S, V] = svds(A, k)","Largest singular values of sparse matrix","Computes the k largest singular values and optionally singular vectors of a sparse matrix.",[6457,6458],{"_16":26,"_22":6257},{"_16":430,"_22":6459,"_28":11},"Number of singular values (default 6)","Singular values vector, or [U, S, V] decomposition",[6462],{"_2215":6463},"s = svds(A, 3)",[3326,6437],{"_16":6466,"_18":6467,"_20":6468,"_22":6469,"_23":6470,"_29":6476,"_31":6477,"_2222":6480},"ilu","[L, U] = ilu(A)\n[L, U] = ilu(A, setup)","Incomplete LU factorization","Computes the incomplete LU factorization of sparse matrix A, suitable for use as a preconditioner in iterative solvers.",[6471,6473],{"_16":26,"_22":6472},"Sparse square matrix",{"_16":6474,"_22":6475,"_28":11},"setup","Options struct with type and droptol","[L, U] incomplete factors",[6478],{"_2215":6479},"[L, U] = ilu(speye(5))",[6481,6391,6368],"ichol",{"_16":6481,"_18":6483,"_20":6484,"_22":6485,"_23":6486,"_29":6491,"_31":6492,"_2222":6495},"L = ichol(A)\nL = ichol(A, opts)","Incomplete Cholesky factorization","Computes the incomplete Cholesky factorization of a symmetric positive definite sparse matrix A. Useful as a preconditioner for pcg.",[6487,6488],{"_16":26,"_22":6412},{"_16":6489,"_22":6490,"_28":11},"opts","Options struct","Lower triangular incomplete factor L",[6493],{"_2215":6494},"L = ichol(speye(5))",[6466,6391],{"_16":6497,"_18":6498,"_20":6499,"_22":6500,"_23":6501,"_29":6503,"_31":6504,"_2222":6507},"sprank","r = sprank(A)","Structural rank of sparse matrix","Returns the structural rank of sparse matrix A, which is an upper bound on the numerical rank. Uses a greedy maximum matching algorithm.",[6502],{"_16":26,"_22":6257},"Structural rank (integer)",[6505],{"_2215":6506,"_2217":2629},"sprank(speye(5))",[3970,6128],{"_35":6509,"_16":6510,"_22":6511,"_39":40,"_41":6512,"_43":6513,"_45":6514},"mfem-generated","Finite Element (MFEM)","Finite element library powered by MFEM compiled to WebAssembly. Provides mesh generation, finite element spaces, bilinear/linear forms, coefficients, and iterative solvers.","🔷","mfem",[6515,6528,6541,6550,6566,6584,6598,6607,6616,6628,6635,6644,6653,6662,6672,6680,6690,6707,6717,6724,6737,6745,6757,6767,6779,6788,6796,6804,6813,6822,6833,6851,6868,6883,6894,6906,6915,6928,6943,6954,6967,6976,6985,6998,7007,7019,7028,7036,7046,7055,7067,7076,7087,7096,7105,7118,7129,7138,7147,7156,7165,7177,7188,7198,7207,7220,7231,7244,7255,7266,7275,7285,7294,7304,7315,7324,7332,7340,7349,7357,7365,7373,7381,7391,7403,7414,7422,7429,7437,7446,7453,7461,7469,7477,7484,7492,7500,7510,7519,7527,7534,7542,7551,7561,7569,7582,7593,7605,7617,7629,7639,7647,7654,7662,7674,7681,7696,7707,7718,7729,7739,7749,7759,7772,7782,7791,7802,7813,7823,7831,7841,7853,7868,7878,7890,7899,7914,7926,7936,7947,7957,7967,7976,7987,8002,8020,8031,8042,8055,8067,8079,8089,8100,8111,8121,8132,8141,8149,8157,8170,8183,8192,8205,8214,8226,8236,8245,8255,8264,8272,8284,8292,8300,8308,8316,8327,8333,8340,8346,8352,8359,8365,8371,8378,8385,8392,8398,8404,8411,8420,8431,8440,8449,8457,8464,8474,8483,8493,8503,8516,8523,8538,8545,8554,8562,8575,8585,8595,8603,8617,8627,8634,8641,8648,8655,8670,8680,8687,8693,8700,8712,8723,8733,8743,8757,8766,8776,8785,8792,8799,8807,8814,8825,8831,8839,8846,8854,8861,8870,8877,8884,8891,8900,8909,8915,8925,8932,8938,8944,8951,8958,8965,8972,8978,8984,8991,9003,9011,9019,9026,9038,9049,9058,9067,9076,9085,9094,9103,9112,9121,9134,9143,9152,9159,9171,9182,9194,9206,9226,9244,9256,9269,9280,9290,9301,9310,9321,9334,9345,9356,9369,9377,9392,9405,9414,9422,9430,9438,9447,9455,9466,9478,9486,9493,9503,9514,9525,9537,9545,9555,9564,9575,9585,9597,9604,9614,9623,9630,9637,9644,9651,9658,9665,9672,9679,9686,9693,9700,9707,9714,9724,9731,9738,9745,9754,9761,9768,9775,9782,9789,9796,9803,9810,9817,9824,9831,9839,9848,9855,9867,9875,9886,9894,9904,9914,9921,9928,9935,9944,9951,9958,9965,9972,9979,9988,9996,10003,10010,10018,10026,10034,10041,10048,10054,10061,10067,10073,10080,10089,10097,10106,10112,10119,10125,10131,10142,10150,10161,10177,10187,10200,10211,10220,10226,10233,10240,10247,10254,10261,10267,10275,10285,10294,10301,10308,10321,10331],{"_16":6516,"_18":6517,"_20":6518,"_22":6519,"_23":6520,"_29":30,"_31":6527},"mfem.bilinearForms.addBoundaryMassIntegrator","mfem.bilinearForms.addBoundaryMassIntegrator(blf, coeff?)","Add a boundary mass integrator to the bilinear form.\r","Add a boundary mass integrator to the bilinear form.\r\n\r\nComputes: ∫_∂Ω c * u * v ds",[6521,6524],{"_16":6522,"_22":6523,"_28":6},"blf","- BilinearForm instance",{"_16":6525,"_22":6526,"_28":11},"coeff","- Optional scalar coefficient",[],{"_16":6529,"_18":6530,"_20":6531,"_22":6532,"_23":6533,"_29":30,"_31":6540},"mfem.bilinearForms.addConvectionIntegrator","mfem.bilinearForms.addConvectionIntegrator(blf, velocity, alpha?)","Add a convection integrator (v · ∇u) to the bilinear form.\r","Add a convection integrator (v · ∇u) to the bilinear form.\r\n\r\nComputes: ∫ α * (β · ∇u) * v dx",[6534,6535,6538],{"_16":6522,"_22":6523,"_28":6},{"_16":6536,"_22":6537,"_28":6},"velocity","- Vector coefficient for velocity field",{"_16":1022,"_22":6539,"_28":11},"- Scaling factor (defaults to 1.0)",[],{"_16":6542,"_18":6543,"_20":6544,"_22":6545,"_23":6546,"_29":30,"_31":6549},"mfem.bilinearForms.addCurlCurlIntegrator","mfem.bilinearForms.addCurlCurlIntegrator(blf, coeff?)","Add a curl-curl integrator (∇×u · ∇×v) to the bilinear form.\r","Add a curl-curl integrator (∇×u · ∇×v) to the bilinear form.\r\nUsed for H(curl) finite element spaces.\r\n\r\nComputes: ∫ c * (∇×u) · (∇×v) dx",[6547,6548],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6551,"_18":6552,"_20":6553,"_22":6554,"_23":6555,"_29":30,"_31":6565},"mfem.bilinearForms.addDGDiffusionIntegrator","mfem.bilinearForms.addDGDiffusionIntegrator(blf, coeff, sigma, kappa)","Add DG diffusion integrator for interior penalty method.\r","Add DG diffusion integrator for interior penalty method.\r\nAdds integrators for both interior and boundary faces.",[6556,6557,6559,6562],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6558,"_28":6},"- Diffusion coefficient (optional)",{"_16":6560,"_22":6561,"_28":6},"sigma","- Symmetry parameter (-1 = SIPG, 0 = IIPG, 1 = NIPG)",{"_16":6563,"_22":6564,"_28":6},"kappa","- Penalty parameter (typically 10 * p^2 / h)",[],{"_16":6567,"_18":6568,"_20":6569,"_22":6570,"_23":6571,"_29":30,"_31":6583},"mfem.bilinearForms.addDGElasticityIntegrator","mfem.bilinearForms.addDGElasticityIntegrator(blf, lambda, mu, alpha?, kappa?)","Add a discontinuous Galerkin (DG) elasticity integrator.\r","Add a discontinuous Galerkin (DG) elasticity integrator.\r\n\r\nUsed for elasticity problems with discontinuous Galerkin methods\r\nwhere displacement jumps occur across element boundaries.\r\nThis adds interior face integrators for the DG formulation.",[6572,6573,6576,6579,6581],{"_16":6522,"_22":6523,"_28":6},{"_16":6574,"_22":6575,"_28":6},"lambda","- Lamé first parameter",{"_16":6577,"_22":6578,"_28":6},"mu","- Shear modulus",{"_16":1022,"_22":6580,"_28":11},"- Symmetry parameter (default: -1.0 for symmetric form)",{"_16":6563,"_22":6582,"_28":11},"- Penalty parameter for stability",[],{"_16":6585,"_18":6586,"_20":6587,"_22":6588,"_23":6589,"_29":30,"_31":6597},"mfem.bilinearForms.addDGTraceIntegrator","mfem.bilinearForms.addDGTraceIntegrator(blf, coeff?, alpha?, beta?)","Add DG trace integrator for face terms.\r","Add DG trace integrator for face terms.\r\nUsed for upwinding in DG advection problems.",[6590,6591,6593,6595],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6592,"_28":11},"- Optional coefficient (VectorCoefficient)",{"_16":1022,"_22":6594,"_28":11},"- Upwinding parameter (default: 0)",{"_16":1027,"_22":6596,"_28":11},"- Penalty parameter (default: 0)",[],{"_16":6599,"_18":6600,"_20":6601,"_22":6602,"_23":6603,"_29":30,"_31":6606},"mfem.bilinearForms.addDiffusionIntegrator","mfem.bilinearForms.addDiffusionIntegrator(blf, coeff?)","Add a diffusion integrator (∇u · ∇v) to the bilinear form.\r","Add a diffusion integrator (∇u · ∇v) to the bilinear form.\r\n\r\nComputes: ∫ c * ∇u · ∇v dx",[6604,6605],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6608,"_18":6609,"_20":6610,"_22":6611,"_23":6612,"_29":30,"_31":6615},"mfem.bilinearForms.addDivDivIntegrator","mfem.bilinearForms.addDivDivIntegrator(blf, coeff?)","Add a div-div integrator (∇·u)(∇·v) to the bilinear form.\r","Add a div-div integrator (∇·u)(∇·v) to the bilinear form.\r\nUsed for H(div) finite element spaces.\r\n\r\nComputes: ∫ c * (∇·u)(∇·v) dx",[6613,6614],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6617,"_18":6618,"_20":6619,"_22":6620,"_23":6621,"_29":30,"_31":6627},"mfem.bilinearForms.addElasticityIntegrator","mfem.bilinearForms.addElasticityIntegrator(blf, lambda, mu)","Add a linear elasticity integrator to the bilinear form.\r","Add a linear elasticity integrator to the bilinear form.\r\n\r\nImplements the bilinear form for linear elasticity:\r\na(u,v) = ∫ λ(∇·u)(∇·v) + 2μ ε(u):ε(v) dx\r\n\r\nwhere:\r\n- λ (lambda) is the first Lamé parameter\r\n- μ (mu) is the second Lamé parameter (shear modulus)\r\n- ε is the strain tensor: ε(u) = (∇u + (∇u)ᵀ)/2",[6622,6623,6625],{"_16":6522,"_22":6523,"_28":6},{"_16":6574,"_22":6624,"_28":6},"- Lamé first parameter (scalar coefficient)",{"_16":6577,"_22":6626,"_28":6},"- Shear modulus / Lamé second parameter (scalar coefficient)",[],{"_16":6629,"_18":6630,"_20":6631,"_22":6631,"_23":6632,"_29":30,"_31":6634},"mfem.bilinearForms.addGradientIntegrator","mfem.bilinearForms.addGradientIntegrator(blf)","Add a gradient integrator to the bilinear form.",[6633],{"_16":6522,"_22":6523,"_28":6},[],{"_16":6636,"_18":6637,"_20":6638,"_22":6639,"_23":6640,"_29":30,"_31":6643},"mfem.bilinearForms.addMassIntegrator","mfem.bilinearForms.addMassIntegrator(blf, coeff?)","Add a mass integrator (u, v) to the bilinear form.\r","Add a mass integrator (u, v) to the bilinear form.\r\n\r\nComputes: ∫ c * u * v dx",[6641,6642],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6645,"_18":6646,"_20":6647,"_22":6648,"_23":6649,"_29":30,"_31":6652},"mfem.bilinearForms.addVectorDiffusionIntegrator","mfem.bilinearForms.addVectorDiffusionIntegrator(blf, coeff?)","Add a vector diffusion integrator to the bilinear form.\r","Add a vector diffusion integrator to the bilinear form.\r\nFor vector-valued finite element functions.",[6650,6651],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6654,"_18":6655,"_20":6656,"_22":6657,"_23":6658,"_29":30,"_31":6661},"mfem.bilinearForms.addVectorMassIntegrator","mfem.bilinearForms.addVectorMassIntegrator(blf, coeff?)","Add a vector mass integrator (u · v) to the bilinear form.\r","Add a vector mass integrator (u · v) to the bilinear form.\r\nFor vector-valued finite element functions.\r\n\r\nComputes: ∫ c * u · v dx",[6659,6660],{"_16":6522,"_22":6523,"_28":6},{"_16":6525,"_22":6526,"_28":11},[],{"_16":6663,"_18":6664,"_20":6665,"_22":6665,"_23":6666,"_29":30,"_31":6671},"mfem.bilinearForms.assemble","mfem.bilinearForms.assemble(blf, skipZeros?)","Assemble bilinear form into sparse matrix.",[6667,6668],{"_16":6522,"_22":6523,"_28":6},{"_16":6669,"_22":6670,"_28":11},"skipZeros","- If true, skip storing zeros in the matrix (default: true)",[],{"_16":6673,"_18":6674,"_20":6675,"_22":6676,"_23":6677,"_29":30,"_31":6679},"mfem.bilinearForms.assemblePartial","mfem.bilinearForms.assemblePartial(blf)","Partial assembly for matrix-free operations.\r","Partial assembly for matrix-free operations.\r\nSets the assembly level to PARTIAL and then assembles.",[6678],{"_16":6522,"_22":6523,"_28":6},[],{"_16":6681,"_18":6682,"_20":6683,"_22":6683,"_23":6684,"_29":6688,"_31":6689},"mfem.bilinearForms.create","mfem.bilinearForms.create(fespace)","Create a bilinear form on a finite element space.",[6685],{"_16":6686,"_22":6687,"_28":6},"fespace","- FiniteElementSpace instance","Promise",[],{"_16":6691,"_18":6692,"_20":6693,"_22":6694,"_23":6695,"_29":30,"_31":6706},"mfem.bilinearForms.eliminateEssentialBC","mfem.bilinearForms.eliminateEssentialBC(blf, essentialDofs, sol, rhs)","Eliminate essential BCs from system.\r","Eliminate essential BCs from system.\r\nModifies the RHS vector in place for non-homogeneous boundary conditions.",[6696,6697,6700,6703],{"_16":6522,"_22":6523,"_28":6},{"_16":6698,"_22":6699,"_28":6},"essentialDofs","- Essential DOF indices",{"_16":6701,"_22":6702,"_28":6},"sol","- Solution vector with boundary values",{"_16":6704,"_22":6705,"_28":6},"rhs","- Right-hand side vector (modified in place)",[],{"_16":6708,"_18":6709,"_20":6710,"_22":6711,"_23":6712,"_29":1402,"_31":6716},"mfem.bilinearForms.formSystemMatrix","mfem.bilinearForms.formSystemMatrix(blf, essentialDofs)","Form system matrix with essential BC elimination.\r","Form system matrix with essential BC elimination.\r\nWorks with static condensation if enabled.",[6713,6715],{"_16":6522,"_22":6714,"_28":6},"- BilinearForm instance (must be assembled first)",{"_16":6698,"_22":6699,"_28":6},[],{"_16":6718,"_18":6719,"_20":6720,"_22":6720,"_23":6721,"_29":1402,"_31":6723},"mfem.bilinearForms.getMatrix","mfem.bilinearForms.getMatrix(blf)","Get assembled sparse matrix from a bilinear form.",[6722],{"_16":6522,"_22":6714,"_28":6},[],{"_16":6725,"_18":6726,"_20":6727,"_22":6727,"_23":6728,"_29":6735,"_31":6736},"mfem.bilinearForms.createMixed","mfem.bilinearForms.createMixed(trialFES, testFES)","Create a mixed bilinear form on trial and test spaces.",[6729,6732],{"_16":6730,"_22":6731,"_28":6},"trialFES","- Trial FiniteElementSpace",{"_16":6733,"_22":6734,"_28":6},"testFES","- Test FiniteElementSpace","Promise",[],{"_16":6738,"_18":6739,"_20":6740,"_22":6740,"_23":6741,"_29":6688,"_31":6744},"mfem.bilinearForms.BilinearForm.create","mfem.bilinearForms.BilinearForm.create(fespace)","Creates a new bilinear form on the specified finite element space.",[6742],{"_16":6686,"_22":6743,"_28":6},"- The finite element space",[],{"_16":6746,"_18":6747,"_20":6748,"_22":6748,"_23":6749,"_29":6735,"_31":6756},"mfem.bilinearForms.MixedBilinearForm.create","mfem.bilinearForms.MixedBilinearForm.create(trialFespace, testFespace)","Creates a new mixed bilinear form.",[6750,6753],{"_16":6751,"_22":6752,"_28":6},"trialFespace","- The trial finite element space",{"_16":6754,"_22":6755,"_28":6},"testFespace","- The test finite element space",[],{"_16":6758,"_18":6759,"_20":6760,"_22":6760,"_23":6761,"_29":6765,"_31":6766},"mfem.block.BlockMatrix.createSquare","mfem.block.BlockMatrix.createSquare(offsets)","Create a square BlockMatrix with the same offsets for rows and columns.",[6762],{"_16":6763,"_22":6764,"_28":6},"offsets","- Block offsets array (used for both rows and columns)","Promise",[],{"_16":6768,"_18":6769,"_20":6770,"_22":6770,"_23":6771,"_29":6765,"_31":6778},"mfem.block.BlockMatrix.create","mfem.block.BlockMatrix.create(rowOffsets, colOffsets)","Create a rectangular BlockMatrix with different row and column offsets.",[6772,6775],{"_16":6773,"_22":6774,"_28":6},"rowOffsets","- Row block offsets array",{"_16":6776,"_22":6777,"_28":6},"colOffsets","- Column block offsets array",[],{"_16":6780,"_18":6781,"_20":6782,"_22":6783,"_23":6784,"_29":6765,"_31":6787},"mfem.block.BlockMatrix.fromPointer","mfem.block.BlockMatrix.fromPointer(ptr)","Creates a BlockMatrix from an existing WASM pointer.\r","Creates a BlockMatrix from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[6785],{"_16":133,"_22":6786,"_28":6},"- WASM pointer to an existing MFEM BlockMatrix",[],{"_16":6789,"_18":6790,"_20":6791,"_22":6791,"_23":6792,"_29":6794,"_31":6795},"mfem.block.BlockOperator.createSquare","mfem.block.BlockOperator.createSquare(offsets)","Create a square BlockOperator with the same offsets for rows and columns.",[6793],{"_16":6763,"_22":6764,"_28":6},"Promise",[],{"_16":6797,"_18":6798,"_20":6799,"_22":6799,"_23":6800,"_29":6794,"_31":6803},"mfem.block.BlockOperator.create","mfem.block.BlockOperator.create(rowOffsets, colOffsets)","Create a rectangular BlockOperator with different row and column offsets.",[6801,6802],{"_16":6773,"_22":6774,"_28":6},{"_16":6776,"_22":6777,"_28":6},[],{"_16":6805,"_18":6806,"_20":6807,"_22":6808,"_23":6809,"_29":6794,"_31":6812},"mfem.block.BlockOperator.fromPointer","mfem.block.BlockOperator.fromPointer(ptr)","Creates a BlockOperator from an existing WASM pointer.\r","Creates a BlockOperator from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[6810],{"_16":133,"_22":6811,"_28":6},"- WASM pointer to an existing MFEM BlockOperator",[],{"_16":6814,"_18":6815,"_20":6816,"_22":6816,"_23":6817,"_29":6820,"_31":6821},"mfem.block.BlockVector.create","mfem.block.BlockVector.create(offsets)","Create a new BlockVector with the specified block offsets.",[6818],{"_16":6763,"_22":6819,"_28":6},"- Array where offsets[i+1] - offsets[i] defines block i size","Promise",[],{"_16":6823,"_18":6824,"_20":6825,"_22":6826,"_23":6827,"_29":6820,"_31":6832},"mfem.block.BlockVector.fromPointer","mfem.block.BlockVector.fromPointer(ptr, offsets)","Creates a BlockVector from an existing WASM pointer.\r","Creates a BlockVector from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[6828,6830],{"_16":133,"_22":6829,"_28":6},"- WASM pointer to an existing MFEM BlockVector",{"_16":6763,"_22":6831,"_28":6},"- Block offsets array",[],{"_16":6834,"_18":6835,"_20":6836,"_22":6836,"_23":6837,"_29":6849,"_31":6850},"mfem.boundaryConditions.addBoundaryRobinIntegrator","mfem.boundaryConditions.addBoundaryRobinIntegrator(blf, lf, alpha, g, bdrAttrs)","Add Robin boundary condition integrator (legacy name)",[6838,6840,6843,6845,6847],{"_16":6522,"_22":6839,"_28":6},"BilinearForm",{"_16":6841,"_22":6842,"_28":6},"lf","LinearForm",{"_16":1022,"_22":6844,"_28":6},"number | CoefficientLike_15",{"_16":6846,"_22":6844,"_28":6},"g",{"_16":6848,"_22":954,"_28":6},"bdrAttrs","Promise",[],{"_16":6852,"_18":6853,"_20":6854,"_22":6855,"_23":6856,"_29":6849,"_31":6867},"mfem.boundaryConditions.addRobinBC","mfem.boundaryConditions.addRobinBC(bf, lf, alpha, g, bdrAttrs)","Add Robin boundary condition: alpha*u + du/dn = g\r","Add Robin boundary condition: alpha*u + du/dn = g\r\n\r\nThis function adds the necessary integrators to both the bilinear form\r\nand linear form to implement Robin boundary conditions on specified\r\nboundary attributes.",[6857,6859,6861,6863,6865],{"_16":6858,"_22":6523,"_28":6},"bf",{"_16":6841,"_22":6860,"_28":6},"- LinearForm instance",{"_16":1022,"_22":6862,"_28":6},"- Coefficient for u term (scalar value or CoefficientLike)",{"_16":6846,"_22":6864,"_28":6},"- RHS coefficient g (scalar value or CoefficientLike)",{"_16":6848,"_22":6866,"_28":6},"- Array of boundary attributes where Robin BC applies",[],{"_16":6869,"_18":6870,"_20":6871,"_22":6872,"_23":6873,"_29":30,"_31":6882},"mfem.boundaryConditions.applyEssentialBC","mfem.boundaryConditions.applyEssentialBC(blf, essentialDofs, x, b)","Apply essential boundary conditions to a linear system.\r","Apply essential boundary conditions to a linear system.\r\nThis modifies the RHS vector to account for known Dirichlet values.",[6874,6876,6878,6880],{"_16":6522,"_22":6875,"_28":6},"- BilinearForm instance (system matrix)",{"_16":6698,"_22":6877,"_28":6},"- Array of essential DOF indices",{"_16":1350,"_22":6879,"_28":6},"- GridFunction with Dirichlet values set",{"_16":983,"_22":6881,"_28":6},"- LinearForm (RHS) to modify",[],{"_16":6884,"_18":6885,"_20":6886,"_22":6887,"_23":6888,"_29":147,"_31":6893},"mfem.boundaryConditions.createBdrMarkerArray","mfem.boundaryConditions.createBdrMarkerArray(mesh, bdrAttrs)","Create a boundary marker array from a mesh and list of boundary attributes.\r","Create a boundary marker array from a mesh and list of boundary attributes.\r\n\r\nThis function creates an array where each element corresponds to a boundary\r\nattribute. The value is 1 if the attribute is in the given list, 0 otherwise.",[6889,6891],{"_16":2365,"_22":6890,"_28":6},"- Mesh instance",{"_16":6848,"_22":6892,"_28":6},"- Array of boundary attribute numbers to mark (1-based)",[],{"_16":6895,"_18":6896,"_20":6897,"_22":6898,"_23":6899,"_29":30,"_31":6905},"mfem.boundaryConditions.eliminateEssentialBC","mfem.boundaryConditions.eliminateEssentialBC(blf, essentialDofs, diagPolicy?)","Eliminate essential boundary conditions from a bilinear form.\r","Eliminate essential boundary conditions from a bilinear form.\r\nModifies the system matrix to enforce the essential BCs.",[6900,6901,6902],{"_16":6522,"_22":6523,"_28":6},{"_16":6698,"_22":6877,"_28":6},{"_16":6903,"_22":6904,"_28":11},"diagPolicy","- Diagonal policy (default: DIAG_ONE)",[],{"_16":6907,"_18":6908,"_20":6909,"_22":6909,"_23":6910,"_29":954,"_31":6914},"mfem.boundaryConditions.getEssentialTrueDofs","mfem.boundaryConditions.getEssentialTrueDofs(fespace, bdrAttrs)","Get essential true DOF indices for given boundary attributes.",[6911,6912],{"_16":6686,"_22":6687,"_28":6},{"_16":6848,"_22":6913,"_28":6},"- Array of boundary attribute numbers",[],{"_16":6916,"_18":6917,"_20":6918,"_22":6919,"_23":6920,"_29":6926,"_31":6927},"mfem.boundaryConditions.getPeriodicDofMapping","mfem.boundaryConditions.getPeriodicDofMapping(fespace, options)","Get periodic DOF correspondence for a finite element space.\r","Get periodic DOF correspondence for a finite element space.\r\n\r\nThis function computes which DOFs are identified as equivalent due to\r\nperiodicity, based on the provided translation vectors. DOFs whose\r\ncoordinates differ by a translation vector (within tolerance) are\r\nidentified as master/slave pairs.\r\n\r\n**Note:** In MFEM, periodic DOF identification is often handled internally\r\nthrough mesh vertex mapping when `Mesh::MakePeriodic` is called. This\r\nfunction provides explicit DOF mapping when needed for custom handling.",[6921,6923],{"_16":6686,"_22":6922,"_28":6},"- FiniteElementSpace (typically on a periodic mesh)",{"_16":6924,"_22":6925,"_28":6},"options","- Configuration including translation vectors and tolerance","Promise",[],{"_16":6929,"_18":6930,"_20":6931,"_22":6932,"_23":6933,"_29":6941,"_31":6942},"mfem.boundaryConditions.createPeriodicMesh","mfem.boundaryConditions.createPeriodicMesh(mesh, translations, tol?)","Create a periodic mesh from translation vectors.\r","Create a periodic mesh from translation vectors.\r\n\r\nThis function identifies vertices that should be treated as equivalent\r\nunder the given translations and creates a new mesh with these vertices\r\nmerged. The result is a mesh suitable for periodic boundary conditions.",[6934,6936,6939],{"_16":2365,"_22":6935,"_28":6},"- Original mesh",{"_16":6937,"_22":6938,"_28":6},"translations","- Array of translation vectors defining periodicity.\r\n For 2D: `[[Lx, 0], [0, Ly]]` for x and y periodicity\r\n For 3D: `[[Lx, 0, 0], [0, Ly, 0], [0, 0, Lz]]`",{"_16":243,"_22":6940,"_28":11},"- Tolerance for vertex matching (relative to mesh diameter).\r\n Default is 1e-8.","Promise",[],{"_16":6944,"_18":6945,"_20":6946,"_22":6946,"_23":6947,"_29":6950,"_31":6953},"mfem.boundaryConditions.makePeriodic","mfem.boundaryConditions.makePeriodic(_fespace, _mesh)","Create periodic finite element space (legacy name).",[6948,6951],{"_16":6949,"_22":6950,"_28":6},"_fespace","unknown",{"_16":6952,"_22":6950,"_28":6},"_mesh",[],{"_16":6955,"_18":6956,"_20":6957,"_22":6958,"_23":6959,"_29":6965,"_31":6966},"mfem.boundaryConditions.createPeriodicVertexMapping","mfem.boundaryConditions.createPeriodicVertexMapping(mesh, translations, tol?)","Create periodic vertex mapping from translation vectors.\r","Create periodic vertex mapping from translation vectors.\r\n\r\nThis function identifies which vertices should be treated as equivalent\r\nunder the given translations. The returned mapping array can be used\r\nwith `makePeriodic` for advanced use cases.\r\n\r\nFor most use cases, prefer `createPeriodicMesh` which handles both\r\nthe mapping and mesh creation in one step.",[6960,6962,6964],{"_16":2365,"_22":6961,"_28":6},"- Mesh to analyze",{"_16":6937,"_22":6963,"_28":6},"- Array of translation vectors defining periodicity",{"_16":243,"_22":6940,"_28":11},"Promise",[],{"_16":6968,"_18":6969,"_20":6970,"_22":6970,"_23":6971,"_29":30,"_31":6975},"mfem.boundaryConditions.makePeriodicVertices","mfem.boundaryConditions.makePeriodicVertices(_mesh, _v2v)","Set periodic vertex mapping on mesh (legacy name).",[6972,6973],{"_16":6952,"_22":6950,"_28":6},{"_16":6974,"_22":125,"_28":6},"_v2v",[],{"_16":6977,"_18":6978,"_20":6979,"_22":6979,"_23":6980,"_29":6983,"_31":6984},"mfem.coefficients.constant","mfem.coefficients.constant(value)","Create a constant scalar coefficient.",[6981],{"_16":457,"_22":6982,"_28":6},"- Constant value","Promise",[],{"_16":6986,"_18":6987,"_20":6988,"_22":6988,"_23":6989,"_29":6996,"_31":6997},"mfem.coefficients.crossProduct","mfem.coefficients.crossProduct(v1, v2)","Create a cross product coefficient from two vector coefficients.",[6990,6993],{"_16":6991,"_22":6992,"_28":6},"v1","- First vector coefficient (must be 3D)",{"_16":6994,"_22":6995,"_28":6},"v2","- Second vector coefficient (must be 3D)","Promise",[],{"_16":6999,"_18":7000,"_20":7001,"_22":7001,"_23":7002,"_29":7005,"_31":7006},"mfem.coefficients.curl","mfem.coefficients.curl(gf)","Create a curl vector coefficient from a vector GridFunction.",[7003],{"_16":6102,"_22":7004,"_28":6},"- Vector GridFunction instance","Promise",[],{"_16":7008,"_18":7009,"_20":7010,"_22":7010,"_23":7011,"_29":7017,"_31":7018},"mfem.coefficients.delta","mfem.coefficients.delta(center, weight?)","Create a Dirac delta coefficient (point source).",[7012,7014],{"_16":5925,"_22":7013,"_28":6},"- Center point of the delta function",{"_16":7015,"_22":7016,"_28":11},"weight","- Weight (scale) of the delta function (defaults to 1.0)","Promise",[],{"_16":7020,"_18":7021,"_20":7022,"_22":7022,"_23":7023,"_29":7026,"_31":7027},"mfem.coefficients.diagonal","mfem.coefficients.diagonal(values)","Create a diagonal matrix coefficient from an array of values.",[7024],{"_16":620,"_22":7025,"_28":6},"- Array of diagonal values","Promise",[],{"_16":7029,"_18":7030,"_20":7031,"_22":7031,"_23":7032,"_29":7034,"_31":7035},"mfem.coefficients.divergence","mfem.coefficients.divergence(gf)","Create a divergence scalar coefficient from a vector GridFunction.",[7033],{"_16":6102,"_22":7004,"_28":6},"Promise",[],{"_16":7037,"_18":7038,"_20":7039,"_22":7039,"_23":7040,"_29":7044,"_31":7045},"mfem.coefficients.functionCoefficient","mfem.coefficients.functionCoefficient(fn)","Create a coefficient from a JavaScript function.",[7041],{"_16":7042,"_22":7043,"_28":6},"fn","- Function (x, y, z) => number","Promise",[],{"_16":7047,"_18":7048,"_20":7049,"_22":7049,"_23":7050,"_29":7053,"_31":7054},"mfem.coefficients.gradient","mfem.coefficients.gradient(gf)","Create a gradient vector coefficient from a scalar GridFunction.",[7051],{"_16":6102,"_22":7052,"_28":6},"- Scalar GridFunction instance","Promise",[],{"_16":7056,"_18":7057,"_20":7058,"_22":7058,"_23":7059,"_29":7065,"_31":7066},"mfem.coefficients.gridFunctionCoefficient","mfem.coefficients.gridFunctionCoefficient(gf, component?)","Create a coefficient from a GridFunction.",[7060,7062],{"_16":6102,"_22":7061,"_28":6},"- GridFunction instance",{"_16":7063,"_22":7064,"_28":11},"component","- Component to use (1-based, for vector GridFunctions)","Promise",[],{"_16":7068,"_18":7069,"_20":7070,"_22":7070,"_23":7071,"_29":7074,"_31":7075},"mfem.coefficients.identity","mfem.coefficients.identity(dim)","Create an identity matrix coefficient.",[7072],{"_16":2675,"_22":7073,"_28":6},"- Dimension of the identity matrix","Promise",[],{"_16":7077,"_18":7078,"_20":7079,"_22":7079,"_23":7080,"_29":7085,"_31":7086},"mfem.coefficients.innerProduct","mfem.coefficients.innerProduct(v1, v2)","Create an inner product coefficient from two vector coefficients.",[7081,7083],{"_16":6991,"_22":7082,"_28":6},"- First vector coefficient",{"_16":6994,"_22":7084,"_28":6},"- Second vector coefficient","Promise",[],{"_16":7088,"_18":7089,"_20":7090,"_22":7090,"_23":7091,"_29":7094,"_31":7095},"mfem.coefficients.inverse","mfem.coefficients.inverse(m)","Create an inverse of a matrix coefficient.",[7092],{"_16":1130,"_22":7093,"_28":6},"- Matrix coefficient to invert","Promise",[],{"_16":7097,"_18":7098,"_20":7099,"_22":7099,"_23":7100,"_29":7103,"_31":7104},"mfem.coefficients.matrixConstant","mfem.coefficients.matrixConstant(values)","Create a constant matrix coefficient.",[7101],{"_16":620,"_22":7102,"_28":6},"- 2D array of values (row-major)","Promise",[],{"_16":7106,"_18":7107,"_20":7108,"_22":7108,"_23":7109,"_29":7116,"_31":7117},"mfem.coefficients.matrixFunction","mfem.coefficients.matrixFunction(fn, height, width?)","Create a matrix coefficient from a JavaScript function.",[7110,7112,7113],{"_16":7042,"_22":7111,"_28":6},"- Function (x, y, z) => number[][]",{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":7115,"_28":11},"width","- Number of columns (defaults to height)","Promise",[],{"_16":7119,"_18":7120,"_20":7121,"_22":7121,"_23":7122,"_29":7127,"_31":7128},"mfem.coefficients.matrixProduct","mfem.coefficients.matrixProduct(a, b)","Create a matrix product coefficient from two matrix coefficients.",[7123,7125],{"_16":2283,"_22":7124,"_28":6},"- First matrix coefficient",{"_16":983,"_22":7126,"_28":6},"- Second matrix coefficient","Promise",[],{"_16":7130,"_18":7131,"_20":7132,"_22":7132,"_23":7133,"_29":7136,"_31":7137},"mfem.coefficients.normalizedVector","mfem.coefficients.normalizedVector(v)","Create a normalized vector coefficient from a vector coefficient.",[7134],{"_16":1604,"_22":7135,"_28":6},"- Vector coefficient to normalize","Promise",[],{"_16":7139,"_18":7140,"_20":7141,"_22":7141,"_23":7142,"_29":7145,"_31":7146},"mfem.coefficients.outerProduct","mfem.coefficients.outerProduct(a, b)","Create an outer product coefficient from two vector coefficients.",[7143,7144],{"_16":2283,"_22":7082,"_28":6},{"_16":983,"_22":7084,"_28":6},"Promise",[],{"_16":7148,"_18":7149,"_20":7150,"_22":7150,"_23":7151,"_29":7154,"_31":7155},"mfem.coefficients.piecewiseConstant","mfem.coefficients.piecewiseConstant(values)","Create a piecewise constant coefficient by element attribute.",[7152],{"_16":620,"_22":7153,"_28":6},"- Map of attribute number (1-based) to value","Promise",[],{"_16":7157,"_18":7158,"_20":7159,"_22":7159,"_23":7160,"_29":7163,"_31":7164},"mfem.coefficients.position","mfem.coefficients.position(dim?)","Create a position vector coefficient that returns the spatial position x.",[7161],{"_16":2675,"_22":7162,"_28":11},"- Spatial dimension (1, 2, or 3). Defaults to 3.","Promise",[],{"_16":7166,"_18":7167,"_20":7168,"_22":7168,"_23":7169,"_29":7175,"_31":7176},"mfem.coefficients.power","mfem.coefficients.power(c, exponent)","Create a power of a coefficient.",[7170,7172],{"_16":4481,"_22":7171,"_28":6},"- Base coefficient",{"_16":7173,"_22":7174,"_28":6},"exponent","- Exponent value","Promise",[],{"_16":7178,"_18":7179,"_20":7180,"_22":7180,"_23":7181,"_29":7186,"_31":7187},"mfem.coefficients.product","mfem.coefficients.product(c1, c2)","Create a product of two coefficients.",[7182,7184],{"_16":4563,"_22":7183,"_28":6},"- First coefficient",{"_16":4566,"_22":7185,"_28":6},"- Second coefficient","Promise",[],{"_16":7189,"_18":7190,"_20":7191,"_22":7191,"_23":7192,"_29":7196,"_31":7197},"mfem.coefficients.quadratureFunctionCoefficient","mfem.coefficients.quadratureFunctionCoefficient(qf)","Create a coefficient from a scalar quadrature function.",[7193],{"_16":7194,"_22":7195,"_28":6},"qf","- The quadrature function (vdim=1)","Promise",[],{"_16":7199,"_18":7200,"_20":7201,"_22":7201,"_23":7202,"_29":7205,"_31":7206},"mfem.coefficients.vectorQuadratureFunctionCoefficient","mfem.coefficients.vectorQuadratureFunctionCoefficient(qf)","Create a vector coefficient from a quadrature function.",[7203],{"_16":7194,"_22":7204,"_28":6},"- The quadrature function","Promise",[],{"_16":7208,"_18":7209,"_20":7210,"_22":7210,"_23":7211,"_29":7218,"_31":7219},"mfem.coefficients.restricted","mfem.coefficients.restricted(baseCoeff, attributes)","Create a restricted coefficient from a base coefficient.",[7212,7215],{"_16":7213,"_22":7214,"_28":6},"baseCoeff","- The base coefficient to restrict",{"_16":7216,"_22":7217,"_28":6},"attributes","- Array of mesh attributes where the coefficient is active (1-based)","Promise",[],{"_16":7221,"_18":7222,"_20":7223,"_22":7223,"_23":7224,"_29":7229,"_31":7230},"mfem.coefficients.scalarVectorProduct","mfem.coefficients.scalarVectorProduct(s, v)","Create a scalar-vector product coefficient.",[7225,7227],{"_16":5634,"_22":7226,"_28":6},"- Scalar coefficient",{"_16":1604,"_22":7228,"_28":6},"- Vector coefficient","Promise",[],{"_16":7232,"_18":7233,"_20":7234,"_22":7234,"_23":7235,"_29":7242,"_31":7243},"mfem.coefficients.sum","mfem.coefficients.sum(c1, c2, alpha?, beta?)","Create a sum of two coefficients.",[7236,7237,7238,7240],{"_16":4563,"_22":7183,"_28":6},{"_16":4566,"_22":7185,"_28":6},{"_16":1022,"_22":7239,"_28":11},"- Scale factor for c1 (default 1.0)",{"_16":1027,"_22":7241,"_28":11},"- Scale factor for c2 (default 1.0)","Promise",[],{"_16":7245,"_18":7246,"_20":7247,"_22":7247,"_23":7248,"_29":7253,"_31":7254},"mfem.coefficients.symmetric","mfem.coefficients.symmetric(fn, dim)","Create a symmetric matrix coefficient from a JavaScript function.",[7249,7251],{"_16":7042,"_22":7250,"_28":6},"- Function (position: number[]) => number[][]",{"_16":2675,"_22":7252,"_28":6},"- Dimension of the symmetric matrix","Promise",[],{"_16":7256,"_18":7257,"_20":7258,"_22":7258,"_23":7259,"_29":7264,"_31":7265},"mfem.coefficients.transformed","mfem.coefficients.transformed(coeff, fn)","Create a transformed coefficient that applies a function to another coefficient.",[7260,7262],{"_16":6525,"_22":7261,"_28":6},"- Source coefficient to transform",{"_16":7042,"_22":7263,"_28":6},"- Transformation function (value) => transformedValue","Promise",[],{"_16":7267,"_18":7268,"_20":7269,"_22":7269,"_23":7270,"_29":7273,"_31":7274},"mfem.coefficients.transpose","mfem.coefficients.transpose(m)","Create a transpose of a matrix coefficient.",[7271],{"_16":1130,"_22":7272,"_28":6},"- Matrix coefficient to transpose","Promise",[],{"_16":7276,"_18":7277,"_20":7278,"_22":7278,"_23":7279,"_29":7283,"_31":7284},"mfem.coefficients.vectorArray","mfem.coefficients.vectorArray(coeffs)","Create a vector coefficient from an array of scalar coefficients.",[7280],{"_16":7281,"_22":7282,"_28":6},"coeffs","- Array of scalar coefficients for each component","Promise",[],{"_16":7286,"_18":7287,"_20":7288,"_22":7288,"_23":7289,"_29":7292,"_31":7293},"mfem.coefficients.vectorConstant","mfem.coefficients.vectorConstant(values)","Create a constant vector coefficient.",[7290],{"_16":620,"_22":7291,"_28":6},"- Array of constant values","Promise",[],{"_16":7295,"_18":7296,"_20":7297,"_22":7297,"_23":7298,"_29":7302,"_31":7303},"mfem.coefficients.vectorDelta","mfem.coefficients.vectorDelta(center, direction)","Create a vector Dirac delta coefficient (directional point source).",[7299,7300],{"_16":5925,"_22":7013,"_28":6},{"_16":2801,"_22":7301,"_28":6},"- Direction vector of the source","Promise",[],{"_16":7305,"_18":7306,"_20":7307,"_22":7307,"_23":7308,"_29":7313,"_31":7314},"mfem.coefficients.vectorFunction","mfem.coefficients.vectorFunction(fn, dim?)","Create a vector coefficient from a JavaScript function.",[7309,7311],{"_16":7042,"_22":7310,"_28":6},"- Function (x, y, z) => number[]",{"_16":2675,"_22":7312,"_28":11},"- Output vector dimension (defaults to 3)","Promise",[],{"_16":7316,"_18":7317,"_20":7318,"_22":7318,"_23":7319,"_29":7322,"_31":7323},"mfem.coefficients.vectorRotProduct","mfem.coefficients.vectorRotProduct(a, b)","Create a 2D cross product (rotation product) of two vector coefficients.",[7320,7321],{"_16":2283,"_22":7082,"_28":6},{"_16":983,"_22":7084,"_28":6},"Promise",[],{"_16":7325,"_18":7326,"_20":7327,"_22":7327,"_23":7328,"_29":6983,"_31":7331},"mfem.coefficients.ConstantCoefficient.create","mfem.coefficients.ConstantCoefficient.create(value)","Creates a new constant coefficient with the specified value.",[7329],{"_16":457,"_22":7330,"_28":6},"- The constant value",[],{"_16":7333,"_18":7334,"_20":7335,"_22":7335,"_23":7336,"_29":7005,"_31":7339},"mfem.coefficients.CurlCoefficient.create","mfem.coefficients.CurlCoefficient.create(gf)","Creates a new curl coefficient from a vector GridFunction.",[7337],{"_16":6102,"_22":7338,"_28":6},"- The vector GridFunction whose curl to compute",[],{"_16":7341,"_18":7342,"_20":7343,"_22":7343,"_23":7344,"_29":7017,"_31":7348},"mfem.coefficients.DeltaCoefficient.create","mfem.coefficients.DeltaCoefficient.create(center, weight?)","Creates a new delta coefficient (point source).",[7345,7347],{"_16":5925,"_22":7346,"_28":6},"- Center point of the delta function [x] or [x, y] or [x, y, z]",{"_16":7015,"_22":7016,"_28":11},[],{"_16":7350,"_18":7351,"_20":7352,"_22":7352,"_23":7353,"_29":7026,"_31":7356},"mfem.coefficients.DiagonalMatrixCoefficient.create","mfem.coefficients.DiagonalMatrixCoefficient.create(values)","Creates a new diagonal matrix coefficient.",[7354],{"_16":620,"_22":7355,"_28":6},"- Array of diagonal values. The length determines the matrix dimension.",[],{"_16":7358,"_18":7359,"_20":7360,"_22":7360,"_23":7361,"_29":7034,"_31":7364},"mfem.coefficients.DivergenceCoefficient.create","mfem.coefficients.DivergenceCoefficient.create(gf)","Creates a new divergence coefficient from a vector GridFunction.",[7362],{"_16":6102,"_22":7363,"_28":6},"- The vector GridFunction whose divergence to compute",[],{"_16":7366,"_18":7367,"_20":7368,"_22":7368,"_23":7369,"_29":7044,"_31":7372},"mfem.coefficients.FunctionCoefficient.create","mfem.coefficients.FunctionCoefficient.create(fn)","Creates a new function coefficient with the specified evaluation function.",[7370],{"_16":7042,"_22":7371,"_28":6},"- Function that takes (x, y, z) coordinates and returns a scalar value",[],{"_16":7374,"_18":7375,"_20":7376,"_22":7376,"_23":7377,"_29":7053,"_31":7380},"mfem.coefficients.GradientCoefficient.create","mfem.coefficients.GradientCoefficient.create(gf)","Creates a new gradient coefficient from a scalar GridFunction.",[7378],{"_16":6102,"_22":7379,"_28":6},"- The scalar GridFunction whose gradient to compute",[],{"_16":7382,"_18":7383,"_20":7384,"_22":7384,"_23":7385,"_29":7065,"_31":7390},"mfem.coefficients.GridFunctionCoefficient.create","mfem.coefficients.GridFunctionCoefficient.create(gf, component?)","Creates a new GridFunction coefficient.",[7386,7388],{"_16":6102,"_22":7387,"_28":6},"- The GridFunction to evaluate",{"_16":7063,"_22":7389,"_28":11},"- Component to use for vector GridFunctions (1-based, default 1)",[],{"_16":7392,"_18":7393,"_20":7394,"_22":7394,"_23":7395,"_29":7103,"_31":7402},"mfem.coefficients.MatrixConstantCoefficient.create","mfem.coefficients.MatrixConstantCoefficient.create(values, height?, width?)","Creates a new constant matrix coefficient with the specified values.",[7396,7398,7400],{"_16":620,"_22":7397,"_28":6},"- 2D array of values (row-major) or 1D array with explicit dimensions",{"_16":5946,"_22":7399,"_28":11},"- Number of rows (required if values is 1D array)",{"_16":7114,"_22":7401,"_28":11},"- Number of columns (required if values is 1D array)",[],{"_16":7404,"_18":7405,"_20":7406,"_22":7406,"_23":7407,"_29":7116,"_31":7413},"mfem.coefficients.MatrixFunctionCoefficient.create","mfem.coefficients.MatrixFunctionCoefficient.create(fn, height, width?)","Creates a new matrix function coefficient.",[7408,7410,7411],{"_16":7042,"_22":7409,"_28":6},"- Function that takes (x, y, z) and returns a 2D array",{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":7412,"_28":11},"- Number of columns (defaults to height for square matrices)",[],{"_16":7415,"_18":7416,"_20":7417,"_22":7417,"_23":7418,"_29":7127,"_31":7421},"mfem.coefficients.MatrixProductCoefficient.create","mfem.coefficients.MatrixProductCoefficient.create(a, b)","Creates a new matrix product coefficient: A * B",[7419,7420],{"_16":2283,"_22":7124,"_28":6},{"_16":983,"_22":7126,"_28":6},[],{"_16":7423,"_18":7424,"_20":7425,"_22":7425,"_23":7426,"_29":7136,"_31":7428},"mfem.coefficients.NormalizedVectorCoefficient.create","mfem.coefficients.NormalizedVectorCoefficient.create(v)","Creates a new normalized vector coefficient: v / ||v||",[7427],{"_16":1604,"_22":7135,"_28":6},[],{"_16":7430,"_18":7431,"_20":7432,"_22":7432,"_23":7433,"_29":7154,"_31":7436},"mfem.coefficients.PWConstCoefficient.create","mfem.coefficients.PWConstCoefficient.create(values)","Creates a new piecewise constant coefficient.",[7434],{"_16":620,"_22":7435,"_28":6},"- Array of values for each attribute (index i corresponds to attribute i+1)",[],{"_16":7438,"_18":7439,"_20":7440,"_22":7440,"_23":7441,"_29":7154,"_31":7445},"mfem.coefficients.PWConstCoefficient.createFromMap","mfem.coefficients.PWConstCoefficient.createFromMap(attrValues)","Creates a new piecewise constant coefficient from a Map.",[7442],{"_16":7443,"_22":7444,"_28":6},"attrValues","- Map of attribute numbers (1-based) to values",[],{"_16":7447,"_18":7448,"_20":7449,"_22":7449,"_23":7450,"_29":7163,"_31":7452},"mfem.coefficients.PositionVectorCoefficient.create","mfem.coefficients.PositionVectorCoefficient.create(dim?)","Creates a new position vector coefficient.",[7451],{"_16":2675,"_22":7162,"_28":11},[],{"_16":7454,"_18":7455,"_20":7456,"_22":7456,"_23":7457,"_29":7175,"_31":7460},"mfem.coefficients.PowerCoefficient.create","mfem.coefficients.PowerCoefficient.create(c, exponent)","Creates a new power coefficient: c^p",[7458,7459],{"_16":4481,"_22":7171,"_28":6},{"_16":7173,"_22":553,"_28":6},[],{"_16":7462,"_18":7463,"_20":7464,"_22":7464,"_23":7465,"_29":7186,"_31":7468},"mfem.coefficients.ProductCoefficient.create","mfem.coefficients.ProductCoefficient.create(c1, c2)","Creates a new product coefficient: c1 * c2",[7466,7467],{"_16":4563,"_22":7183,"_28":6},{"_16":4566,"_22":7185,"_28":6},[],{"_16":7470,"_18":7471,"_20":7472,"_22":7472,"_23":7473,"_29":7196,"_31":7476},"mfem.coefficients.QuadratureFunctionCoefficient.create","mfem.coefficients.QuadratureFunctionCoefficient.create(qf)","Creates a new coefficient from a scalar quadrature function.",[7474],{"_16":7194,"_22":7475,"_28":6},"- The quadrature function (must have vdim=1)",[],{"_16":7478,"_18":7479,"_20":7480,"_22":7480,"_23":7481,"_29":7205,"_31":7483},"mfem.coefficients.VectorQuadratureFunctionCoefficient.create","mfem.coefficients.VectorQuadratureFunctionCoefficient.create(qf)","Creates a new vector coefficient from a quadrature function.",[7482],{"_16":7194,"_22":7204,"_28":6},[],{"_16":7485,"_18":7486,"_20":7487,"_22":7487,"_23":7488,"_29":7218,"_31":7491},"mfem.coefficients.RestrictedCoefficient.create","mfem.coefficients.RestrictedCoefficient.create(baseCoeff, attributes)","Creates a new restricted coefficient.",[7489,7490],{"_16":7213,"_22":7214,"_28":6},{"_16":7216,"_22":7217,"_28":6},[],{"_16":7493,"_18":7494,"_20":7495,"_22":7495,"_23":7496,"_29":7229,"_31":7499},"mfem.coefficients.ScalarVectorProductCoefficient.create","mfem.coefficients.ScalarVectorProductCoefficient.create(s, v)","Creates a new scalar-vector product coefficient: s * v",[7497,7498],{"_16":5634,"_22":7226,"_28":6},{"_16":1604,"_22":7228,"_28":6},[],{"_16":7501,"_18":7502,"_20":7503,"_22":7503,"_23":7504,"_29":7242,"_31":7509},"mfem.coefficients.SumCoefficient.create","mfem.coefficients.SumCoefficient.create(c1, c2, alpha?, beta?)","Creates a new sum coefficient: alpha * c1 + beta * c2",[7505,7506,7507,7508],{"_16":4563,"_22":7183,"_28":6},{"_16":4566,"_22":7185,"_28":6},{"_16":1022,"_22":7239,"_28":11},{"_16":1027,"_22":7241,"_28":11},[],{"_16":7511,"_18":7512,"_20":7513,"_22":7513,"_23":7514,"_29":7253,"_31":7518},"mfem.coefficients.SymmetricMatrixCoefficient.create","mfem.coefficients.SymmetricMatrixCoefficient.create(fn, dim)","Creates a new symmetric matrix function coefficient.",[7515,7517],{"_16":7042,"_22":7516,"_28":6},"- Function that takes position [x, y, z] and returns a symmetric 2D array",{"_16":2675,"_22":7252,"_28":6},[],{"_16":7520,"_18":7521,"_20":7522,"_22":7522,"_23":7523,"_29":7264,"_31":7526},"mfem.coefficients.TransformedCoefficient.create","mfem.coefficients.TransformedCoefficient.create(coeff, fn)","Creates a new transformed coefficient: F(Q)",[7524,7525],{"_16":6525,"_22":7261,"_28":6},{"_16":7042,"_22":7263,"_28":6},[],{"_16":7528,"_18":7529,"_20":7530,"_22":7530,"_23":7531,"_29":7283,"_31":7533},"mfem.coefficients.VectorArrayCoefficient.create","mfem.coefficients.VectorArrayCoefficient.create(dim)","Creates a new vector array coefficient of the specified dimension.",[7532],{"_16":2675,"_22":1105,"_28":6},[],{"_16":7535,"_18":7536,"_20":7537,"_22":7537,"_23":7538,"_29":7292,"_31":7541},"mfem.coefficients.VectorConstantCoefficient.create","mfem.coefficients.VectorConstantCoefficient.create(values)","Creates a new constant vector coefficient with the specified values.",[7539],{"_16":620,"_22":7540,"_28":6},"- Array of constant values for each component",[],{"_16":7543,"_18":7544,"_20":7545,"_22":7545,"_23":7546,"_29":7302,"_31":7550},"mfem.coefficients.VectorDeltaCoefficient.create","mfem.coefficients.VectorDeltaCoefficient.create(center, direction)","Creates a new vector delta coefficient (directional point source).",[7547,7548],{"_16":5925,"_22":7346,"_28":6},{"_16":2801,"_22":7549,"_28":6},"- Direction vector of the source (must match spatial dimension)",[],{"_16":7552,"_18":7553,"_20":7554,"_22":7554,"_23":7555,"_29":7313,"_31":7560},"mfem.coefficients.VectorFunctionCoefficient.create","mfem.coefficients.VectorFunctionCoefficient.create(fn, dim)","Creates a new vector function coefficient.",[7556,7558],{"_16":7042,"_22":7557,"_28":6},"- Function that takes (x, y, z) and returns a vector",{"_16":2675,"_22":7559,"_28":6},"- Output vector dimension",[],{"_16":7562,"_18":7563,"_20":7564,"_22":7564,"_23":7565,"_29":7322,"_31":7568},"mfem.coefficients.VectorRotProductCoefficient.create","mfem.coefficients.VectorRotProductCoefficient.create(a, b)","Creates a new VectorRotProductCoefficient: A_x * B_y - A_y * B_x",[7566,7567],{"_16":2283,"_22":7082,"_28":6},{"_16":983,"_22":7084,"_28":6},[],{"_16":7570,"_18":7571,"_20":7572,"_22":7573,"_23":7574,"_29":137,"_31":7581},"mfem.eigenvalue.getEigenvalues","mfem.eigenvalue.getEigenvalues(solver, numEigs?)","Get computed eigenvalues after solve.\r","Get computed eigenvalues after solve.\r\n\r\nCall this after solve() to retrieve the computed eigenvalues.\r\nIf numEigs is not specified, returns all converged eigenvalues.",[7575,7578],{"_16":7576,"_22":7577,"_28":6},"solver","- LOBPCG solver instance with solved eigenvalues",{"_16":7579,"_22":7580,"_28":11},"numEigs","- Number of eigenvalues to retrieve (defaults to number of converged)",[],{"_16":7583,"_18":7584,"_20":7585,"_22":7586,"_23":7587,"_29":7591,"_31":7592},"mfem.eigenvalue.getEigenvectors","mfem.eigenvalue.getEigenvectors(eigenvectorMatrix)","getEigenvectors","",[7588],{"_16":7589,"_22":7590,"_28":6},"eigenvectorMatrix","DenseMatrix","Float64Array[]",[],{"_16":7594,"_18":7595,"_20":7596,"_22":7597,"_23":7598,"_29":30,"_31":7604},"mfem.eigenvalue.setNumModes","mfem.eigenvalue.setNumModes(solver, numModes)","Set the number of eigenvalues/eigenvectors to compute.\r","Set the number of eigenvalues/eigenvectors to compute.\r\n\r\nThis should match the number of columns in the eigenvector DenseMatrix\r\npassed to solve().",[7599,7601],{"_16":7576,"_22":7600,"_28":6},"- LOBPCG solver instance",{"_16":7602,"_22":7603,"_28":6},"numModes","- Number of eigenpairs to compute",[],{"_16":7606,"_18":7607,"_20":7608,"_22":7609,"_23":7610,"_29":30,"_31":7616},"mfem.eigenvalue.setOperators","mfem.eigenvalue.setOperators(solver, A, B?)","Set A and B operators for generalized eigenvalue problem Ax = λBx.\r","Set A and B operators for generalized eigenvalue problem Ax = λBx.\r\n\r\nFor standard eigenvalue problems (Ax = λx), only pass A.\r\nFor generalized problems (Ax = λBx), pass both A and B.",[7611,7612,7614],{"_16":7576,"_22":7600,"_28":6},{"_16":26,"_22":7613,"_28":6},"- Stiffness matrix/operator A (e.g., SparseMatrix, BilinearForm)",{"_16":505,"_22":7615,"_28":11},"- Mass matrix/operator B for generalized problem (optional)",[],{"_16":7618,"_18":7619,"_20":7620,"_22":7621,"_23":7622,"_29":30,"_31":7628},"mfem.eigenvalue.solve","mfem.eigenvalue.solve(solver, eigenvectors)","Solve the eigenvalue problem using LOBPCG.\r","Solve the eigenvalue problem using LOBPCG.\r\n\r\nSolves: Ax = λBx (generalized) or Ax = λx (standard if B is not set)\r\n\r\nThe eigenvectors will be stored as columns in the provided DenseMatrix.\r\nThe matrix should be pre-allocated with dimensions [nDofs × numModes].",[7623,7625],{"_16":7576,"_22":7624,"_28":6},"- LOBPCG solver instance (must have operators set)",{"_16":7626,"_22":7627,"_28":6},"eigenvectors","- DenseMatrix to store computed eigenvectors (columns are eigenvectors)",[],{"_16":7630,"_18":7631,"_20":7632,"_22":7633,"_23":7634,"_29":7637,"_31":7638},"mfem.eigenvalue.DenseMatrix.create","mfem.eigenvalue.DenseMatrix.create(height, width)","Creates a new dense matrix of specified dimensions.\r","Creates a new dense matrix of specified dimensions.\r\nElements are uninitialized.",[7635,7636],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},"Promise",[],{"_16":7640,"_18":7641,"_20":7642,"_22":7642,"_23":7643,"_29":7637,"_31":7646},"mfem.eigenvalue.DenseMatrix.zeros","mfem.eigenvalue.DenseMatrix.zeros(height, width)","Creates a zero matrix of specified dimensions.",[7644,7645],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},[],{"_16":7648,"_18":7649,"_20":7650,"_22":7650,"_23":7651,"_29":7637,"_31":7653},"mfem.eigenvalue.DenseMatrix.identity","mfem.eigenvalue.DenseMatrix.identity(n)","Creates an identity matrix of size n x n.",[7652],{"_16":629,"_22":1458,"_28":6},[],{"_16":7655,"_18":7656,"_20":7657,"_22":7657,"_23":7658,"_29":7637,"_31":7661},"mfem.eigenvalue.DenseMatrix.fromArray","mfem.eigenvalue.DenseMatrix.fromArray(data)","Creates a DenseMatrix from a 2D array.",[7659],{"_16":117,"_22":7660,"_28":6},"- 2D array in row-major order (data[row][col])",[],{"_16":7663,"_18":7664,"_20":7665,"_22":7666,"_23":7667,"_29":7637,"_31":7673},"mfem.eigenvalue.DenseMatrix.fromPointer","mfem.eigenvalue.DenseMatrix.fromPointer(ptr, ownsMemory?)","Creates a DenseMatrix from an existing WASM pointer.\r","Creates a DenseMatrix from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[7668,7670],{"_16":133,"_22":7669,"_28":6},"- WASM pointer to an existing MFEM DenseMatrix",{"_16":7671,"_22":7672,"_28":11},"ownsMemory","- Whether this wrapper owns the memory (default: false)",[],{"_16":7675,"_18":7676,"_20":7677,"_22":7677,"_23":7678,"_29":7679,"_31":7680},"mfem.eigenvalue.LOBPCGSolver.create","mfem.eigenvalue.LOBPCGSolver.create()","Creates a new LOBPCG solver.",[],"Promise",[],{"_16":7682,"_18":7683,"_20":7684,"_22":7685,"_23":7686,"_29":7694,"_31":7695},"mfem.fespace.createDG","mfem.fespace.createDG(mesh, order, vdim?)","Creates a Discontinuous Galerkin (DG) finite element space.\r","Creates a Discontinuous Galerkin (DG) finite element space.\r\n\r\nThis is an alias for . DG spaces are L2 spaces used in\r\nDiscontinuous Galerkin methods, where numerical fluxes connect elements.\r\n\r\nDG methods are popular for:\r\n- Hyperbolic conservation laws\r\n- Advection-dominated transport\r\n- Problems with sharp gradients or shocks\r\n- hp-adaptivity",[7687,7689,7691],{"_16":2365,"_22":7688,"_28":6},"- The mesh on which to define the space",{"_16":1532,"_22":7690,"_28":6},"- Polynomial order (0 = piecewise constant, 1 = linear, etc.)",{"_16":7692,"_22":7693,"_28":11},"vdim","- Vector dimension (default 1 for scalar fields)","Promise",[],{"_16":7697,"_18":7698,"_20":7699,"_22":7700,"_23":7701,"_29":7694,"_31":7706},"mfem.fespace.createH1","mfem.fespace.createH1(mesh, order, vdim?)","Creates an H1 (continuous Lagrange) finite element space.\r","Creates an H1 (continuous Lagrange) finite element space.\r\n\r\nH1 spaces use continuous piecewise polynomial functions that are globally\r\nconforming in H1 (functions with square-integrable first derivatives).\r\nThey are the most common choice for:\r\n- Scalar problems (heat transfer, Poisson equation)\r\n- Vector problems (elasticity, Stokes flow)",[7702,7703,7705],{"_16":2365,"_22":7688,"_28":6},{"_16":1532,"_22":7704,"_28":6},"- Polynomial order (1 = linear, 2 = quadratic, 3 = cubic, etc.)",{"_16":7692,"_22":7693,"_28":11},[],{"_16":7708,"_18":7709,"_20":7710,"_22":7711,"_23":7712,"_29":7694,"_31":7717},"mfem.fespace.createH1Positive","mfem.fespace.createH1Positive(mesh, order, vdim?)","Creates an H1 finite element space with positive (Bernstein) basis.\r","Creates an H1 finite element space with positive (Bernstein) basis.\r\n\r\nBernstein basis functions are non-negative and form a partition of unity,\r\nmaking them ideal for applications requiring positivity preservation:\r\n- Concentration fields that must remain positive\r\n- Probability distributions\r\n- NURBS-like representations\r\n\r\nThe space has the same approximation properties as standard H1 but with\r\ndifferent basis function properties.",[7713,7714,7716],{"_16":2365,"_22":7688,"_28":6},{"_16":1532,"_22":7715,"_28":6},"- Polynomial order (1 = linear, 2 = quadratic, etc.)",{"_16":7692,"_22":7693,"_28":11},[],{"_16":7719,"_18":7720,"_20":7721,"_22":7722,"_23":7723,"_29":7694,"_31":7728},"mfem.fespace.createHcurl","mfem.fespace.createHcurl(mesh, order)","Creates an H(curl) (Nedelec) finite element space.\r","Creates an H(curl) (Nedelec) finite element space.\r\n\r\nH(curl) spaces are designed for vector fields where the curl is well-defined\r\nand square-integrable. They are essential for:\r\n- Electromagnetics (electric field, magnetic vector potential)\r\n- Maxwell's equations\r\n- Edge element discretizations\r\n\r\nThe tangential component is continuous across element faces while the\r\nnormal component may be discontinuous.",[7724,7726],{"_16":2365,"_22":7725,"_28":6},"- The mesh on which to define the space (must be 2D or 3D)",{"_16":1532,"_22":7727,"_28":6},"- Polynomial order (1 = lowest order Nedelec, etc.)",[],{"_16":7730,"_18":7731,"_20":7732,"_22":7733,"_23":7734,"_29":7694,"_31":7738},"mfem.fespace.createHdiv","mfem.fespace.createHdiv(mesh, order)","Creates an H(div) (Raviart-Thomas) finite element space.\r","Creates an H(div) (Raviart-Thomas) finite element space.\r\n\r\nH(div) spaces are designed for vector fields where the divergence is\r\nwell-defined and square-integrable. They are essential for:\r\n- Fluid flow (velocity fields)\r\n- Mixed finite element methods\r\n- Darcy flow and porous media\r\n- Magnetic flux density in electromagnetics\r\n\r\nThe normal component is continuous across element faces while the\r\ntangential component may be discontinuous.",[7735,7736],{"_16":2365,"_22":7725,"_28":6},{"_16":1532,"_22":7737,"_28":6},"- Polynomial order (0 = lowest order RT, etc.)",[],{"_16":7740,"_18":7741,"_20":7742,"_22":7743,"_23":7744,"_29":7694,"_31":7748},"mfem.fespace.createL2","mfem.fespace.createL2(mesh, order, vdim?)","Creates an L2 (discontinuous) finite element space.\r","Creates an L2 (discontinuous) finite element space.\r\n\r\nL2 spaces use piecewise polynomial functions with no continuity constraints\r\nacross element boundaries. This allows for:\r\n- Discontinuous Galerkin (DG) methods\r\n- Higher accuracy for advection-dominated problems\r\n- Local conservation properties\r\n- Representation of discontinuous fields\r\n\r\nL2 spaces have more DOFs than H1 spaces for the same mesh and order,\r\nas each element has its own independent polynomial representation.",[7745,7746,7747],{"_16":2365,"_22":7688,"_28":6},{"_16":1532,"_22":7690,"_28":6},{"_16":7692,"_22":7693,"_28":11},[],{"_16":7750,"_18":7751,"_20":7752,"_22":7753,"_23":7754,"_29":7694,"_31":7758},"mfem.fespace.createND","mfem.fespace.createND(mesh, order)","Creates a Nedelec (ND) finite element space.\r","Creates a Nedelec (ND) finite element space.\r\n\r\nThis is an alias for . Nedelec elements are edge elements\r\nthat conform to H(curl), named after Jean-Claude Nédélec who introduced them.\r\n\r\nCommon applications:\r\n- Electric field in electromagnetics\r\n- Magnetic vector potential\r\n- Any vector field where curl is the primary differential operator",[7755,7756],{"_16":2365,"_22":7725,"_28":6},{"_16":1532,"_22":7757,"_28":6},"- Polynomial order (1 = lowest order, etc.)",[],{"_16":7760,"_18":7761,"_20":7762,"_22":7763,"_23":7764,"_29":7770,"_31":7771},"mfem.fespace.createNURBS","mfem.fespace.createNURBS(mesh, order?, vdim?)","Creates a NURBS finite element space.\r","Creates a NURBS finite element space.\r\n\r\nNURBS (Non-Uniform Rational B-Splines) spaces are used for isogeometric\r\nanalysis (IGA), where the same basis functions used for CAD geometry\r\nrepresentation are used for the finite element analysis. This provides\r\nexact geometry representation and higher continuity across elements.\r\n\r\nThe mesh must be a NURBS mesh (created from NURBS patch data). Standard\r\nmeshes created with `makeCartesian2D` or similar functions cannot be used.",[7765,7767,7769],{"_16":2365,"_22":7766,"_28":6},"- A NURBS mesh instance (must have NURBS extension)",{"_16":1532,"_22":7768,"_28":11},"- Polynomial order. Use -1 or 0 for variable order (uses\r\n the mesh's native NURBS order from each patch)",{"_16":7692,"_22":7693,"_28":11},"FiniteElementSpace",[],{"_16":7773,"_18":7774,"_20":7775,"_22":7776,"_23":7777,"_29":7694,"_31":7781},"mfem.fespace.createRT","mfem.fespace.createRT(mesh, order)","Creates a Raviart-Thomas (RT) finite element space.\r","Creates a Raviart-Thomas (RT) finite element space.\r\n\r\nThis is an alias for . Raviart-Thomas elements are face\r\nelements that conform to H(div), named after Pierre-Arnaud Raviart and\r\nJean-Marie Thomas who introduced them.\r\n\r\nCommon applications:\r\n- Velocity in mixed formulations\r\n- Flux variables in conservation laws\r\n- Magnetic flux density",[7778,7779],{"_16":2365,"_22":7725,"_28":6},{"_16":1532,"_22":7780,"_28":6},"- Polynomial order (0 = lowest order, etc.)",[],{"_16":7783,"_18":7784,"_20":7785,"_22":7786,"_23":7787,"_29":7789,"_31":7790},"mfem.fespace.getAllDofCoordinates","mfem.fespace.getAllDofCoordinates(fespace)","Gets the physical coordinates for all degrees of freedom in a finite element space.\r","Gets the physical coordinates for all degrees of freedom in a finite element space.\r\n\r\nThis function iterates over all elements in the mesh and collects the physical\r\ncoordinates of each DOF. For DOFs shared between elements, the coordinates from\r\nthe first encountered element are used.\r\n\r\n**Performance note:** This function allocates temporary WASM memory and iterates\r\nover all elements. For large meshes, consider caching the result.",[7788],{"_16":6686,"_22":6743,"_28":6},"Promise>",[],{"_16":7792,"_18":7793,"_20":7794,"_22":7795,"_23":7796,"_29":954,"_31":7801},"mfem.fespace.getBoundaryDofs","mfem.fespace.getBoundaryDofs(fespace, bdrAttr)","Gets the DOF indices on a boundary with a specific attribute.\r","Gets the DOF indices on a boundary with a specific attribute.\r\n\r\nReturns the true (global) DOF indices that lie on boundary elements\r\nwith the specified attribute. This is useful for applying Dirichlet\r\nboundary conditions on specific parts of the domain boundary.",[7797,7798],{"_16":6686,"_22":6743,"_28":6},{"_16":7799,"_22":7800,"_28":6},"bdrAttr","- The boundary attribute (1-based, as defined in the mesh)",[],{"_16":7803,"_18":7804,"_20":7805,"_22":7806,"_23":7807,"_29":147,"_31":7812},"mfem.fespace.getDofMap","mfem.fespace.getDofMap(fespace, elemIndex)","Gets the DOF indices for a specific element.\r","Gets the DOF indices for a specific element.\r\n\r\nReturns the global DOF indices associated with the specified element.\r\nThis is useful for assembling local element contributions into global\r\nmatrices and vectors.",[7808,7809],{"_16":6686,"_22":6743,"_28":6},{"_16":7810,"_22":7811,"_28":6},"elemIndex","- The element index (0-based)",[],{"_16":7814,"_18":7815,"_20":7816,"_22":7817,"_23":7818,"_29":954,"_31":7822},"mfem.fespace.getEssentialDofs","mfem.fespace.getEssentialDofs(fespace, bdrAttrs)","Gets the essential (Dirichlet) DOF indices for specified boundary attributes.\r","Gets the essential (Dirichlet) DOF indices for specified boundary attributes.\r\n\r\nReturns the true (global) DOF indices that should be constrained for\r\nDirichlet boundary conditions on the specified boundary attributes.\r\nMultiple boundary attributes can be specified to get DOFs from several\r\nboundary regions at once.",[7819,7820],{"_16":6686,"_22":6743,"_28":6},{"_16":6848,"_22":7821,"_28":6},"- Array of boundary attributes (1-based, as defined in the mesh)",[],{"_16":7824,"_18":7825,"_20":7826,"_22":7827,"_23":7828,"_29":95,"_31":7830},"mfem.fespace.order","mfem.fespace.order(fespace)","Gets the maximum polynomial order of the finite element space.\r","Gets the maximum polynomial order of the finite element space.\r\n\r\nFor spaces with variable order (hp-adaptivity), this returns the\r\nmaximum order across all elements.",[7829],{"_16":6686,"_22":6743,"_28":6},[],{"_16":7832,"_18":7833,"_20":7699,"_22":7834,"_23":7835,"_29":7694,"_31":7840},"mfem.fespace.FiniteElementSpace.createH1","mfem.fespace.FiniteElementSpace.createH1(mesh, order, vdim?)","Creates an H1 (continuous Lagrange) finite element space.\r\n\r\nH1 spaces use continuous piecewise polynomial functions. They are the most\r\ncommon choice for scalar problems like heat transfer, and for vector problems\r\nlike elasticity.\r\n\r\n**Basis functions:**\r\n- Order 1: Linear (nodal values at vertices)\r\n- Order 2: Quadratic (nodal values at vertices and edge midpoints)\r\n- Order p: Polynomial of degree p",[7836,7837,7838],{"_16":2365,"_22":7688,"_28":6},{"_16":1532,"_22":7715,"_28":6},{"_16":7692,"_22":7839,"_28":11},"- Vector dimension (default 1 for scalar fields, 2 or 3 for vector fields)",[],{"_16":7842,"_18":7843,"_20":7844,"_22":7845,"_23":7846,"_29":95,"_31":7852},"mfem.gridfunction.computeError","mfem.gridfunction.computeError(gf, exactValue)","Computes the L2 error between a grid function and a constant exact solution.\r","Computes the L2 error between a grid function and a constant exact solution.\r\n\r\nThe L2 error is defined as:\r\n```\r\n||u - u_exact||_L2 = sqrt( ∫_Ω |u(x) - u_exact|² dx )\r\n```\r\n\r\nThis is useful for verifying solutions against known manufactured solutions\r\nor for convergence studies.",[7847,7849],{"_16":6102,"_22":7848,"_28":6},"- GridFunction (numerical solution)",{"_16":7850,"_22":7851,"_28":6},"exactValue","- The constant exact solution value",[],{"_16":7854,"_18":7855,"_20":7856,"_22":7857,"_23":7858,"_29":95,"_31":7867},"mfem.gridfunction.computeH1Error","mfem.gridfunction.computeH1Error(gf, coeffPtr?, dcoeffPtr?)","Computes the H1 error between a grid function and an exact solution.\r","Computes the H1 error between a grid function and an exact solution.\r\n\r\nThe H1 error combines the L2 error of the function and its gradient:\r\n||u - u_exact||_H1 = sqrt(||u - u_exact||²_L2 + ||∇u - ∇u_exact||²_L2)\r\n\r\nYou can provide either or both of:\r\n- The exact solution coefficient (for the L2 part)\r\n- The gradient of the exact solution (for the gradient part)",[7859,7861,7864],{"_16":6102,"_22":7860,"_28":6},"- The grid function (numerical solution)",{"_16":7862,"_22":7863,"_28":11},"coeffPtr","- Pointer to Coefficient for exact solution (or 0 to skip L2 part)",{"_16":7865,"_22":7866,"_28":11},"dcoeffPtr","- Pointer to VectorCoefficient for exact gradient (or 0 to skip gradient part)",[],{"_16":7869,"_18":7870,"_20":7871,"_22":7872,"_23":7873,"_29":95,"_31":7877},"mfem.gridfunction.computeL2ErrorCoeff","mfem.gridfunction.computeL2ErrorCoeff(gf, coeffPtr)","Computes the L2 error between a grid function and an exact solution\r","Computes the L2 error between a grid function and an exact solution\r\nrepresented as a scalar coefficient.\r\n\r\nThe L2 error is defined as:\r\n||u - u_exact||_L2 = sqrt(∫ |u(x) - u_exact(x)|² dx)",[7874,7875],{"_16":6102,"_22":7860,"_28":6},{"_16":7862,"_22":7876,"_28":6},"- Pointer to a Coefficient representing the exact solution",[],{"_16":7879,"_18":7880,"_20":7881,"_22":7882,"_23":7883,"_29":95,"_31":7889},"mfem.gridfunction.computeL2ErrorVCoeff","mfem.gridfunction.computeL2ErrorVCoeff(gf, vcoeffPtr)","Computes the L2 error between a vector grid function and an exact solution\r","Computes the L2 error between a vector grid function and an exact solution\r\nrepresented as a vector coefficient.\r\n\r\nThe L2 error is defined as:\r\n||u - u_exact||_L2 = sqrt(∫ |u(x) - u_exact(x)|² dx)\r\n\r\nwhere |·| is the Euclidean norm of the vector difference.",[7884,7886],{"_16":6102,"_22":7885,"_28":6},"- The vector grid function (numerical solution)",{"_16":7887,"_22":7888,"_28":6},"vcoeffPtr","- Pointer to a VectorCoefficient representing the exact solution",[],{"_16":7891,"_18":7892,"_20":7893,"_22":7894,"_23":7895,"_29":95,"_31":7898},"mfem.gridfunction.computeMaxError","mfem.gridfunction.computeMaxError(gf, coeffPtr)","Computes the maximum (L-infinity) error between a grid function and\r","Computes the maximum (L-infinity) error between a grid function and\r\nan exact solution represented as a coefficient.\r\n\r\nThe max error is defined as:\r\n||u - u_exact||_L∞ = max_x |u(x) - u_exact(x)|\r\n\r\nThis is useful for checking pointwise accuracy of a solution.",[7896,7897],{"_16":6102,"_22":7860,"_28":6},{"_16":7862,"_22":7876,"_28":6},[],{"_16":7900,"_18":7901,"_20":7902,"_22":7903,"_23":7904,"_29":95,"_31":7913},"mfem.gridfunction.computeW11Error","mfem.gridfunction.computeW11Error(gf, coeffPtr?, dcoeffPtr?, normType?)","Computes the W^{1,1} error between a grid function and an exact solution.\r","Computes the W^{1,1} error between a grid function and an exact solution.\r\n\r\nThe W^{1,1} norm uses L1 integrals instead of L2:\r\n||u - u_exact||_{W^{1,1}} = ∫ |u - u_exact| dx + ∫ |∇u - ∇u_exact| dx\r\n\r\nThis error measure is more robust to outliers than L2-based errors.",[7905,7906,7908,7910],{"_16":6102,"_22":7860,"_28":6},{"_16":7862,"_22":7907,"_28":11},"- Pointer to Coefficient for exact solution (or 0 to skip)",{"_16":7865,"_22":7909,"_28":11},"- Pointer to VectorCoefficient for exact gradient (or 0 to skip)",{"_16":7911,"_22":7912,"_28":11},"normType","- Which components to include (default: BOTH)",[],{"_16":7915,"_18":7916,"_20":7917,"_22":7918,"_23":7919,"_29":7924,"_31":7925},"mfem.gridfunction.fromBinary","mfem.gridfunction.fromBinary(fespace, data)","Loads a grid function from a base64-encoded binary string with an existing FE space.\r","Loads a grid function from a base64-encoded binary string with an existing FE space.\r\n\r\nThis is the inverse of . The base64 string is decoded\r\nand parsed as an MFEM format grid function. You must provide the\r\nFiniteElementSpace that matches the saved data.",[7920,7922],{"_16":6686,"_22":7921,"_28":6},"- The finite element space for the grid function",{"_16":117,"_22":7923,"_28":6},"- Base64-encoded string containing grid function data","Promise",[],{"_16":7927,"_18":7928,"_20":7929,"_22":7930,"_23":7931,"_29":7924,"_31":7935},"mfem.gridfunction.fromBinaryWithMesh","mfem.gridfunction.fromBinaryWithMesh(mesh, data)","Loads a grid function from a base64-encoded binary string with auto-detected FE space.\r","Loads a grid function from a base64-encoded binary string with auto-detected FE space.\r\n\r\nThis is the inverse of . The base64 string is decoded\r\nand parsed as an MFEM format grid function. The FE space is automatically\r\nreconstructed from the saved header information.\r\n\r\nThe returned GridFunction owns its FESpace.",[7932,7934],{"_16":2365,"_22":7933,"_28":6},"- The mesh for the grid function",{"_16":117,"_22":7923,"_28":6},[],{"_16":7937,"_18":7938,"_20":7939,"_22":7940,"_23":7941,"_29":7924,"_31":7946},"mfem.gridfunction.fromCoefficient","mfem.gridfunction.fromCoefficient(fespace, value)","Creates a new grid function initialized with a constant value.\r","Creates a new grid function initialized with a constant value.\r\n\r\nThis is a convenience function that creates a grid function and projects\r\na constant coefficient onto it. For more complex coefficients, create a\r\ngrid function manually and use projection functions.",[7942,7944],{"_16":6686,"_22":7943,"_28":6},"- The finite element space on which to define the function",{"_16":457,"_22":7945,"_28":6},"- The constant value to project",[],{"_16":7948,"_18":7949,"_20":7950,"_22":7951,"_23":7952,"_29":7924,"_31":7956},"mfem.gridfunction.fromFunction","mfem.gridfunction.fromFunction(fespace, fn)","Creates a new grid function initialized by evaluating a function at DOF locations.\r","Creates a new grid function initialized by evaluating a function at DOF locations.\r\n\r\nThe function is evaluated at the physical coordinates of each degree of freedom\r\n(node) in the finite element space. For Lagrange elements, these are the nodal\r\ninterpolation points.\r\n\r\n**Note:** This performs nodal interpolation, not L2 projection. For smoother\r\nresults with non-smooth functions, consider using L2 projection methods.",[7953,7954],{"_16":6686,"_22":7943,"_28":6},{"_16":7042,"_22":7955,"_28":6},"- Function that takes coordinates [x, y?, z?] and returns a scalar value",[],{"_16":7958,"_18":7959,"_20":7960,"_22":7961,"_23":7962,"_29":7924,"_31":7966},"mfem.gridfunction.fromMFEM","mfem.gridfunction.fromMFEM(fespace, data)","Loads a grid function from an MFEM format string into an existing GridFunction.\r","Loads a grid function from an MFEM format string into an existing GridFunction.\r\n\r\nThe GridFunction must already have an associated FiniteElementSpace that\r\nmatches the data being loaded. Use this when you already know the FE type\r\nand have created the space.",[7963,7964],{"_16":6686,"_22":7921,"_28":6},{"_16":117,"_22":7965,"_28":6},"- MFEM format grid function string",[],{"_16":7968,"_18":7969,"_20":7970,"_22":7971,"_23":7972,"_29":7924,"_31":7975},"mfem.gridfunction.fromMFEMWithMesh","mfem.gridfunction.fromMFEMWithMesh(mesh, data)","Creates a grid function from an MFEM format string with auto-detected FE space.\r","Creates a grid function from an MFEM format string with auto-detected FE space.\r\n\r\nThis function parses the FE collection information from the saved data header\r\nand automatically creates the appropriate FiniteElementSpace. Use this when\r\nloading a solution where you don't know the FE type in advance.\r\n\r\nThe returned GridFunction owns its FESpace, which will be destroyed when\r\nthe GridFunction is destroyed.",[7973,7974],{"_16":2365,"_22":7933,"_28":6},{"_16":117,"_22":7965,"_28":6},[],{"_16":7977,"_18":7978,"_20":7979,"_22":7980,"_23":7981,"_29":137,"_31":7986},"mfem.gridfunction.getAllNodalValues","mfem.gridfunction.getAllNodalValues(gf, vdim?)","Gets the values of a grid function at all vertices of the mesh.\r","Gets the values of a grid function at all vertices of the mesh.\r\n\r\nThis returns one value per vertex for the entire mesh, which is useful\r\nfor visualization or post-processing. For vector-valued grid functions,\r\nyou can specify which component to extract.",[7982,7984],{"_16":6102,"_22":7983,"_28":6},"- The grid function to evaluate",{"_16":7692,"_22":7985,"_28":11},"- Vector component to extract (1-based, default 1 for scalar)",[],{"_16":7988,"_18":7989,"_20":7990,"_22":7991,"_23":7992,"_29":954,"_31":8001},"mfem.gridfunction.getCurl","mfem.gridfunction.getCurl(gf, elemIdx, ip)","Computes the curl of a vector grid function at a point within an element.\r","Computes the curl of a vector grid function at a point within an element.\r\n\r\nThe curl is computed in physical coordinates:\r\n- In 3D: curl = [∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y]\r\n- In 2D: curl is a scalar (z-component of the 3D curl)\r\n\r\nThis is typically used with H(curl) finite element spaces (Nedelec elements).",[7993,7995,7998],{"_16":6102,"_22":7994,"_28":6},"- Vector GridFunction (e.g., from H(curl) space)",{"_16":7996,"_22":7997,"_28":6},"elemIdx","- Index of the element containing the point (0-based)",{"_16":7999,"_22":8000,"_28":6},"ip","- Integration point in reference coordinates",[],{"_16":8003,"_18":8004,"_20":8005,"_22":8006,"_23":8007,"_29":30,"_31":8019},"mfem.gridfunction.getDerivative","mfem.gridfunction.getDerivative(gf, comp, derComp, destGf)","Computes the derivative of a grid function component in a specified direction\r","Computes the derivative of a grid function component in a specified direction\r\nand projects it onto another grid function.\r\n\r\nThis computes ∂u_comp/∂x_derComp where comp is the component of a\r\nvector-valued function and derComp is the spatial direction.",[8008,8010,8013,8016],{"_16":6102,"_22":8009,"_28":6},"- The source grid function",{"_16":8011,"_22":8012,"_28":6},"comp","- Component to differentiate (1-based: 1, 2, or 3)",{"_16":8014,"_22":8015,"_28":6},"derComp","- Direction of differentiation (1=x, 2=y, 3=z)",{"_16":8017,"_22":8018,"_28":6},"destGf","- Destination grid function (must be pre-created on same mesh)",[],{"_16":8021,"_18":8022,"_20":8023,"_22":8024,"_23":8025,"_29":95,"_31":8030},"mfem.gridfunction.getDivergence","mfem.gridfunction.getDivergence(gf, elemIdx, ip)","Computes the divergence of a vector grid function at a point within an element.\r","Computes the divergence of a vector grid function at a point within an element.\r\n\r\nThe divergence is computed in physical coordinates:\r\ndiv(F) = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z\r\n\r\nThis is typically used with H(div) finite element spaces (Raviart-Thomas elements).",[8026,8028,8029],{"_16":6102,"_22":8027,"_28":6},"- Vector GridFunction (e.g., from H(div) space)",{"_16":7996,"_22":7997,"_28":6},{"_16":7999,"_22":8000,"_28":6},[],{"_16":8032,"_18":8033,"_20":8034,"_22":8035,"_23":8036,"_29":954,"_31":8041},"mfem.gridfunction.getGradient","mfem.gridfunction.getGradient(gf, elemIdx, ip)","Computes the gradient of a scalar grid function at a point within an element.\r","Computes the gradient of a scalar grid function at a point within an element.\r\n\r\nThe gradient is computed in physical (not reference) coordinates. The result\r\nis a vector with components [∂f/∂x, ∂f/∂y, ∂f/∂z] (depending on dimension).",[8037,8039,8040],{"_16":6102,"_22":8038,"_28":6},"- Scalar GridFunction to differentiate",{"_16":7996,"_22":7997,"_28":6},{"_16":7999,"_22":8000,"_28":6},[],{"_16":8043,"_18":8044,"_20":8045,"_22":8046,"_23":8047,"_29":8053,"_31":8054},"mfem.gridfunction.getGradients","mfem.gridfunction.getGradients(gf, elemIdx, points)","Computes gradients of a grid function at multiple integration points\r","Computes gradients of a grid function at multiple integration points\r\nwithin an element.\r\n\r\nThis is more efficient than calling multiple times\r\nwhen you need gradients at many points in the same element.",[8048,8049,8051],{"_16":6102,"_22":7983,"_28":6},{"_16":7996,"_22":8050,"_28":6},"- Element index (0-based)",{"_16":5835,"_22":8052,"_28":6},"- Array of integration points in reference element coordinates","GradientsResult",[],{"_16":8056,"_18":8057,"_20":8058,"_22":8059,"_23":8060,"_29":8065,"_31":8066},"mfem.gridfunction.getHessian","mfem.gridfunction.getHessian(gf, elemIdx, ip)","Computes the Hessian matrix of a grid function at a point within an element.\r","Computes the Hessian matrix of a grid function at a point within an element.\r\n\r\nThe Hessian is the matrix of second partial derivatives:\r\n```\r\nH = | ∂²u/∂x² ∂²u/∂x∂y ∂²u/∂x∂z |\r\n | ∂²u/∂y∂x ∂²u/∂y² ∂²u/∂y∂z |\r\n | ∂²u/∂z∂x ∂²u/∂z∂y ∂²u/∂z² |\r\n```",[8061,8062,8063],{"_16":6102,"_22":7983,"_28":6},{"_16":7996,"_22":8050,"_28":6},{"_16":7999,"_22":8064,"_28":6},"- Integration point in reference element coordinates","HessianResult",[],{"_16":8068,"_18":8069,"_20":8070,"_22":8071,"_23":8072,"_29":95,"_31":8078},"mfem.gridfunction.getLaplacian","mfem.gridfunction.getLaplacian(gf, elemIdx, ip, vdim?)","Computes the Laplacian of a grid function at a point within an element.\r","Computes the Laplacian of a grid function at a point within an element.\r\n\r\nThe Laplacian is the sum of second partial derivatives:\r\nΔu = ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z²",[8073,8074,8075,8076],{"_16":6102,"_22":7983,"_28":6},{"_16":7996,"_22":8050,"_28":6},{"_16":7999,"_22":8064,"_28":6},{"_16":7692,"_22":8077,"_28":11},"- Vector component (1-based, default 1 for scalar)",[],{"_16":8080,"_18":8081,"_20":8082,"_22":8083,"_23":8084,"_29":954,"_31":8088},"mfem.gridfunction.getNodalValues","mfem.gridfunction.getNodalValues(gf, elemIdx, vdim?)","Gets the values of a grid function at the vertices of a specific element.\r","Gets the values of a grid function at the vertices of a specific element.\r\n\r\nThis is simpler than using for extracting vertex values,\r\nas it directly returns all nodal values for an element without requiring\r\nintegration point coordinates.",[8085,8086,8087],{"_16":6102,"_22":7983,"_28":6},{"_16":7996,"_22":8050,"_28":6},{"_16":7692,"_22":7985,"_28":11},[],{"_16":8090,"_18":8091,"_20":8092,"_22":8093,"_23":8094,"_29":95,"_31":8099},"mfem.gridfunction.getValue","mfem.gridfunction.getValue(gf, elemIdx, ip)","Evaluates a grid function at a point within a specific element.\r","Evaluates a grid function at a point within a specific element.\r\n\r\nThe point is specified in reference (local) coordinates of the element.\r\nFor most elements, these coordinates range from 0 to 1.",[8095,8097,8098],{"_16":6102,"_22":8096,"_28":6},"- GridFunction to evaluate",{"_16":7996,"_22":7997,"_28":6},{"_16":7999,"_22":8000,"_28":6},[],{"_16":8101,"_18":8102,"_20":8103,"_22":8104,"_23":8105,"_29":137,"_31":8110},"mfem.gridfunction.getVectorFieldNodalValues","mfem.gridfunction.getVectorFieldNodalValues(gf, component)","Gets the values of a specific component of a vector-valued grid function\r","Gets the values of a specific component of a vector-valued grid function\r\nat all vertices of the mesh.\r\n\r\nThis is useful for extracting individual components (e.g., x-velocity,\r\ny-velocity) from a vector field for visualization or analysis.",[8106,8108],{"_16":6102,"_22":8107,"_28":6},"- The vector GridFunction to evaluate",{"_16":7063,"_22":8109,"_28":6},"- Component index (1-based: 1=x, 2=y, 3=z)",[],{"_16":8112,"_18":8113,"_20":8114,"_22":8115,"_23":8116,"_29":954,"_31":8120},"mfem.gridfunction.getVectorValue","mfem.gridfunction.getVectorValue(gf, elemIdx, ip)","Evaluates a vector-valued grid function at a point within an element.\r","Evaluates a vector-valued grid function at a point within an element.\r\n\r\nThis is the vector analog of . It returns all components\r\nof the vector field at the specified point.",[8117,8118,8119],{"_16":6102,"_22":8107,"_28":6},{"_16":7996,"_22":8050,"_28":6},{"_16":7999,"_22":8064,"_28":6},[],{"_16":8122,"_18":8123,"_20":8124,"_22":8125,"_23":8126,"_29":8130,"_31":8131},"mfem.gridfunction.getVectorValues","mfem.gridfunction.getVectorValues(gf, elemIdx, points)","Evaluates a vector-valued grid function at multiple integration points within an element.\r","Evaluates a vector-valued grid function at multiple integration points within an element.\r\n\r\nThis is more efficient than calling multiple times\r\nwhen you need values at many points in the same element.",[8127,8128,8129],{"_16":6102,"_22":8107,"_28":6},{"_16":7996,"_22":8050,"_28":6},{"_16":5835,"_22":8052,"_28":6},"VectorValuesResult",[],{"_16":8133,"_18":8134,"_20":8135,"_22":8136,"_23":8137,"_29":95,"_31":8140},"mfem.gridfunction.normH1","mfem.gridfunction.normH1(gf)","Computes the H1 norm of a grid function.\r","Computes the H1 norm of a grid function.\r\n\r\nThe H1 norm is defined as:\r\n```\r\n||u||_H1 = sqrt( ||u||²_L2 + ||∇u||²_L2 )\r\n = sqrt( ∫_Ω |u(x)|² dx + ∫_Ω |∇u(x)|² dx )\r\n```\r\n\r\nThis norm measures both the function values and their derivatives,\r\nmaking it suitable for error analysis in elliptic PDEs.\r\n\r\n**Note:** This function returns the H1 seminorm (gradient norm only).\r\nTo get the full H1 norm, combine with the L2 norm:\r\n`sqrt(normL2(gf)**2 + normH1(gf)**2)`",[8138],{"_16":6102,"_22":8139,"_28":6},"- GridFunction to compute norm of",[],{"_16":8142,"_18":8143,"_20":8144,"_22":8145,"_23":8146,"_29":95,"_31":8148},"mfem.gridfunction.normL2","mfem.gridfunction.normL2(gf)","Computes the L2 norm of a grid function.\r","Computes the L2 norm of a grid function.\r\n\r\nThe L2 norm is defined as:\r\n```\r\n||u||_L2 = sqrt( ∫_Ω |u(x)|² dx )\r\n```\r\n\r\nThis is computed using numerical quadrature over all elements in the mesh.",[8147],{"_16":6102,"_22":8139,"_28":6},[],{"_16":8150,"_18":8151,"_20":8152,"_22":8153,"_23":8154,"_29":95,"_31":8156},"mfem.gridfunction.normLinf","mfem.gridfunction.normLinf(gf)","Computes the L-infinity (maximum) norm of a grid function.\r","Computes the L-infinity (maximum) norm of a grid function.\r\n\r\nThe L-infinity norm is defined as:\r\n```\r\n||u||_∞ = max |u(x)| over all x in Ω\r\n```\r\n\r\nIn practice, this is computed as the maximum absolute value of the DOF coefficients.",[8155],{"_16":6102,"_22":8139,"_28":6},[],{"_16":8158,"_18":8159,"_20":8160,"_22":8161,"_23":8162,"_29":30,"_31":8169},"mfem.gridfunction.projectBdrCoefficient","mfem.gridfunction.projectBdrCoefficient(gf, value, bdrAttrs)","Projects a constant value onto boundary DOFs for specified boundary attributes.\r","Projects a constant value onto boundary DOFs for specified boundary attributes.\r\n\r\nThis sets the DOF values on the specified boundaries to the given constant value.\r\nIt is useful for applying Dirichlet boundary conditions where the boundary\r\nvalue is known.\r\n\r\nOnly DOFs that lie on boundary elements with the specified attributes are modified.\r\nInterior DOFs remain unchanged.",[8163,8165,8167],{"_16":6102,"_22":8164,"_28":6},"- GridFunction to modify",{"_16":457,"_22":8166,"_28":6},"- The constant value to project on boundary",{"_16":6848,"_22":8168,"_28":6},"- Array of boundary attributes (1-based) to apply the value to",[],{"_16":8171,"_18":8172,"_20":8173,"_22":8174,"_23":8175,"_29":30,"_31":8182},"mfem.gridfunction.projectBdrVectorCoefficient","mfem.gridfunction.projectBdrVectorCoefficient(gf, vcoeffPtr, bdrAttrs)","Projects a vector coefficient onto boundary DOFs of a grid function.\r","Projects a vector coefficient onto boundary DOFs of a grid function.\r\n\r\nThis sets the values of the grid function at boundary DOFs to match\r\nthe given vector coefficient. Interior DOFs are not modified.",[8176,8178,8180],{"_16":6102,"_22":8177,"_28":6},"- The grid function to modify",{"_16":7887,"_22":8179,"_28":6},"- Pointer to a VectorCoefficient in WASM memory",{"_16":6848,"_22":8181,"_28":6},"- Array of boundary attribute markers (1 = apply, 0 = skip)",[],{"_16":8184,"_18":8185,"_20":8186,"_22":8187,"_23":8188,"_29":30,"_31":8191},"mfem.gridfunction.projectCoefficient","mfem.gridfunction.projectCoefficient(gf, value)","Projects a constant coefficient onto a grid function.\r","Projects a constant coefficient onto a grid function.\r\n\r\nThis sets all DOF values such that the grid function represents\r\nthe constant function f(x) = value everywhere in the domain.\r\nThis is equivalent to calling `gf.projectConstant(value)`.",[8189,8190],{"_16":6102,"_22":8164,"_28":6},{"_16":457,"_22":7945,"_28":6},[],{"_16":8193,"_18":8194,"_20":8195,"_22":8196,"_23":8197,"_29":30,"_31":8204},"mfem.gridfunction.projectDiscCoefficient","mfem.gridfunction.projectDiscCoefficient(gf, coeffPtr, avgType?)","Projects a discontinuous coefficient onto a grid function with averaging.\r","Projects a discontinuous coefficient onto a grid function with averaging.\r\n\r\nWhen a coefficient has different values on different sides of an element\r\ninterface, this function uses the specified averaging type to determine\r\nthe value at shared DOFs.",[8198,8199,8201],{"_16":6102,"_22":8177,"_28":6},{"_16":7862,"_22":8200,"_28":6},"- Pointer to a Coefficient in WASM memory",{"_16":8202,"_22":8203,"_28":11},"avgType","- Averaging type for interface values (default: ARITHMETIC)",[],{"_16":8206,"_18":8207,"_20":8208,"_22":8209,"_23":8210,"_29":6849,"_31":8213},"mfem.gridfunction.projectFunction","mfem.gridfunction.projectFunction(gf, fn)","Projects a JavaScript function onto a grid function using nodal interpolation.\r","Projects a JavaScript function onto a grid function using nodal interpolation.\r\n\r\nThe function is evaluated at the physical coordinates of each degree of freedom\r\nto determine the DOF values. For standard Lagrange elements, this corresponds\r\nto interpolation at the nodal points.\r\n\r\n**Note:** This function is async because it needs to compute DOF coordinates.",[8211,8212],{"_16":6102,"_22":8164,"_28":6},{"_16":7042,"_22":7955,"_28":6},[],{"_16":8215,"_18":8216,"_20":8217,"_22":8218,"_23":8219,"_29":30,"_31":8225},"mfem.gridfunction.projectGridFunction","mfem.gridfunction.projectGridFunction(destGf, srcGf)","Projects a source grid function onto a destination grid function.\r","Projects a source grid function onto a destination grid function.\r\n\r\nThis is useful for transferring solutions between different finite element\r\nspaces on the same mesh, or for initializing a grid function from an\r\nexisting solution.",[8220,8222],{"_16":8017,"_22":8221,"_28":6},"- The destination grid function to modify",{"_16":8223,"_22":8224,"_28":6},"srcGf","- The source grid function to project from",[],{"_16":8227,"_18":8228,"_20":8229,"_22":8230,"_23":8231,"_29":8234,"_31":8235},"mfem.gridfunction.save","mfem.gridfunction.save(gf)","Exports a grid function to MFEM format string.\r","Exports a grid function to MFEM format string.\r\n\r\nThe returned string can be saved to a file and later loaded back using\r\nMFEM's GridFunction constructor that takes a mesh and input stream.\r\n\r\nThe format includes the finite element collection type, ordering,\r\nand all DOF values.",[8232],{"_16":6102,"_22":8233,"_28":6},"- GridFunction to export","string",[],{"_16":8237,"_18":8238,"_20":8239,"_22":8240,"_23":8241,"_29":8234,"_31":8244},"mfem.gridfunction.toBinary","mfem.gridfunction.toBinary(gf)","Exports a grid function to a base64-encoded binary string.\r","Exports a grid function to a base64-encoded binary string.\r\n\r\nThis provides a compact representation of the grid function suitable for\r\nstorage in JSON, localStorage, or transmission. The grid function is first\r\nserialized to MFEM format (including FE space info) and then base64-encoded.",[8242],{"_16":6102,"_22":8243,"_28":6},"- The grid function to export",[],{"_16":8246,"_18":8247,"_20":8248,"_22":8249,"_23":8250,"_29":8234,"_31":8254},"mfem.gridfunction.toVTK","mfem.gridfunction.toVTK(gf, options?)","Exports a grid function to VTK format string for visualization.\r","Exports a grid function to VTK format string for visualization.\r\n\r\nThe returned string contains VTK data for the grid function values.\r\n**Note:** This exports only the field data. For complete VTK output,\r\nyou also need to export the mesh using `mesh.toVTK()`.\r\n\r\nFor visualization in ParaView or similar tools, combine the mesh\r\nand field data into a complete VTK file.",[8251,8252],{"_16":6102,"_22":8233,"_28":6},{"_16":6924,"_22":8253,"_28":11},"- Export options",[],{"_16":8256,"_18":8257,"_20":8258,"_22":8259,"_23":8260,"_29":137,"_31":8263},"mfem.gridfunction.getTrueDofs","mfem.gridfunction.getTrueDofs(gf)","Gets the true DOF values from a grid function.\r","Gets the true DOF values from a grid function.\r\n\r\nFor conforming meshes, this returns the same as `getData()`.\r\nFor non-conforming meshes, this returns only the independent DOF values,\r\nwhich may be fewer than the total number of DOFs.",[8261],{"_16":6102,"_22":8262,"_28":6},"- The grid function to query",[],{"_16":8265,"_18":8266,"_20":8267,"_22":8268,"_23":8269,"_29":95,"_31":8271},"mfem.gridfunction.getTrueVectorSize","mfem.gridfunction.getTrueVectorSize(gf)","Gets the size of the true DOF vector.\r","Gets the size of the true DOF vector.\r\n\r\nFor conforming meshes, this equals the total number of DOFs.\r\nFor non-conforming meshes, this may be smaller.",[8270],{"_16":6102,"_22":8262,"_28":6},[],{"_16":8273,"_18":8274,"_20":8275,"_22":8276,"_23":8277,"_29":30,"_31":8283},"mfem.gridfunction.setFromTrueDofs","mfem.gridfunction.setFromTrueDofs(gf, trueDofs)","Sets grid function values from true DOF values.\r","Sets grid function values from true DOF values.\r\n\r\nThis applies the prolongation operator to populate all DOFs from\r\nthe independent true DOFs. For conforming meshes, this is equivalent\r\nto `setData()`. For non-conforming meshes, this properly distributes\r\nvalues to hanging nodes.",[8278,8280],{"_16":6102,"_22":8279,"_28":6},"- The grid function to update",{"_16":8281,"_22":8282,"_28":6},"trueDofs","- Array of true DOF values",[],{"_16":8285,"_18":8286,"_20":8287,"_22":8288,"_23":8289,"_29":30,"_31":8291},"mfem.gridfunction.setTrueVector","mfem.gridfunction.setTrueVector(gf)","Extracts true DOFs from the grid function to internal storage.\r","Extracts true DOFs from the grid function to internal storage.\r\n\r\nFor conforming meshes, this is a no-op. For non-conforming meshes\r\n(with hanging nodes), this extracts the independent DOF values.\r\nCall this before solving to prepare the true DOF vector.",[8290],{"_16":6102,"_22":8279,"_28":6},[],{"_16":8293,"_18":8294,"_20":8295,"_22":8296,"_23":8297,"_29":7924,"_31":8299},"mfem.gridfunction.GridFunction.create","mfem.gridfunction.GridFunction.create(fespace)","Creates a new grid function on the specified finite element space.\r","Creates a new grid function on the specified finite element space.\r\n\r\nThe grid function is initialized with unspecified values. Use\r\n| projectConstant() or\r\n| setData() to initialize the values.",[8298],{"_16":6686,"_22":7943,"_28":6},[],{"_16":8301,"_18":8302,"_20":8303,"_22":8303,"_23":8304,"_29":137,"_31":8307},"mfem.linalg.createDoubleArray","mfem.linalg.createDoubleArray(size)","Create a zero-initialized Float64Array.",[8305],{"_16":93,"_22":8306,"_28":6},"- Array size",[],{"_16":8309,"_18":8310,"_20":8311,"_22":8312,"_23":8313,"_29":147,"_31":8315},"mfem.linalg.createIntArray","mfem.linalg.createIntArray(size)","Array utility functions for creating typed arrays.\r","Array utility functions for creating typed arrays.\r\n\r\nThese are pure JavaScript utilities that don't require WASM.",[8314],{"_16":93,"_22":8306,"_28":6},[],{"_16":8317,"_18":8318,"_20":8319,"_22":8320,"_23":8321,"_29":147,"_31":8326},"mfem.linalg.createMarkerArray","mfem.linalg.createMarkerArray(size, markedIndices)","Create a marker array (0/1 values) with specified indices marked as 1.\r","Create a marker array (0/1 values) with specified indices marked as 1.\r\n\r\nThis is useful for creating boundary marker arrays or element selection arrays.",[8322,8323],{"_16":93,"_22":8306,"_28":6},{"_16":8324,"_22":8325,"_28":6},"markedIndices","- Indices to mark as 1",[],{"_16":8328,"_18":8329,"_20":6760,"_22":6760,"_23":8330,"_29":6765,"_31":8332},"mfem.linalg.BlockMatrix.createSquare","mfem.linalg.BlockMatrix.createSquare(offsets)",[8331],{"_16":6763,"_22":6764,"_28":6},[],{"_16":8334,"_18":8335,"_20":6770,"_22":6770,"_23":8336,"_29":6765,"_31":8339},"mfem.linalg.BlockMatrix.create","mfem.linalg.BlockMatrix.create(rowOffsets, colOffsets)",[8337,8338],{"_16":6773,"_22":6774,"_28":6},{"_16":6776,"_22":6777,"_28":6},[],{"_16":8341,"_18":8342,"_20":6782,"_22":6783,"_23":8343,"_29":6765,"_31":8345},"mfem.linalg.BlockMatrix.fromPointer","mfem.linalg.BlockMatrix.fromPointer(ptr)",[8344],{"_16":133,"_22":6786,"_28":6},[],{"_16":8347,"_18":8348,"_20":6791,"_22":6791,"_23":8349,"_29":6794,"_31":8351},"mfem.linalg.BlockOperator.createSquare","mfem.linalg.BlockOperator.createSquare(offsets)",[8350],{"_16":6763,"_22":6764,"_28":6},[],{"_16":8353,"_18":8354,"_20":6799,"_22":6799,"_23":8355,"_29":6794,"_31":8358},"mfem.linalg.BlockOperator.create","mfem.linalg.BlockOperator.create(rowOffsets, colOffsets)",[8356,8357],{"_16":6773,"_22":6774,"_28":6},{"_16":6776,"_22":6777,"_28":6},[],{"_16":8360,"_18":8361,"_20":6807,"_22":6808,"_23":8362,"_29":6794,"_31":8364},"mfem.linalg.BlockOperator.fromPointer","mfem.linalg.BlockOperator.fromPointer(ptr)",[8363],{"_16":133,"_22":6811,"_28":6},[],{"_16":8366,"_18":8367,"_20":6816,"_22":6816,"_23":8368,"_29":6820,"_31":8370},"mfem.linalg.BlockVector.create","mfem.linalg.BlockVector.create(offsets)",[8369],{"_16":6763,"_22":6819,"_28":6},[],{"_16":8372,"_18":8373,"_20":6825,"_22":6826,"_23":8374,"_29":6820,"_31":8377},"mfem.linalg.BlockVector.fromPointer","mfem.linalg.BlockVector.fromPointer(ptr, offsets)",[8375,8376],{"_16":133,"_22":6829,"_28":6},{"_16":6763,"_22":6831,"_28":6},[],{"_16":8379,"_18":8380,"_20":7632,"_22":7633,"_23":8381,"_29":7637,"_31":8384},"mfem.linalg.DenseMatrix.create","mfem.linalg.DenseMatrix.create(height, width)",[8382,8383],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},[],{"_16":8386,"_18":8387,"_20":7642,"_22":7642,"_23":8388,"_29":7637,"_31":8391},"mfem.linalg.DenseMatrix.zeros","mfem.linalg.DenseMatrix.zeros(height, width)",[8389,8390],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},[],{"_16":8393,"_18":8394,"_20":7650,"_22":7650,"_23":8395,"_29":7637,"_31":8397},"mfem.linalg.DenseMatrix.identity","mfem.linalg.DenseMatrix.identity(n)",[8396],{"_16":629,"_22":1458,"_28":6},[],{"_16":8399,"_18":8400,"_20":7657,"_22":7657,"_23":8401,"_29":7637,"_31":8403},"mfem.linalg.DenseMatrix.fromArray","mfem.linalg.DenseMatrix.fromArray(data)",[8402],{"_16":117,"_22":7660,"_28":6},[],{"_16":8405,"_18":8406,"_20":7665,"_22":7666,"_23":8407,"_29":7637,"_31":8410},"mfem.linalg.DenseMatrix.fromPointer","mfem.linalg.DenseMatrix.fromPointer(ptr, ownsMemory?)",[8408,8409],{"_16":133,"_22":7669,"_28":6},{"_16":7671,"_22":7672,"_28":11},[],{"_16":8412,"_18":8413,"_20":8414,"_22":8414,"_23":8415,"_29":8418,"_31":8419},"mfem.linalg.SparseMatrix.create","mfem.linalg.SparseMatrix.create(height, width)","Creates a new empty sparse matrix of the specified dimensions.",[8416,8417],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},"Promise",[],{"_16":8421,"_18":8422,"_20":8423,"_22":8424,"_23":8425,"_29":8418,"_31":8430},"mfem.linalg.SparseMatrix.fromPointer","mfem.linalg.SparseMatrix.fromPointer(ptr, ownsMemory?)","Creates a SparseMatrix from an existing WASM pointer.\r","Creates a SparseMatrix from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[8426,8428],{"_16":133,"_22":8427,"_28":6},"- WASM pointer to an existing MFEM SparseMatrix",{"_16":7671,"_22":8429,"_28":11},"- If true, destroy() will free the memory; if false, it won't",[],{"_16":8432,"_18":8433,"_20":8434,"_22":8434,"_23":8435,"_29":8438,"_31":8439},"mfem.linalg.Vector.create","mfem.linalg.Vector.create(size)","Creates a new vector of the specified size.",[8436],{"_16":93,"_22":8437,"_28":6},"- The number of elements in the vector","Promise",[],{"_16":8441,"_18":8442,"_20":8443,"_22":8444,"_23":8445,"_29":8438,"_31":8448},"mfem.linalg.Vector.fromPointer","mfem.linalg.Vector.fromPointer(ptr)","Creates a Vector from an existing WASM pointer.\r","Creates a Vector from an existing WASM pointer.\r\nUse with caution - the caller is responsible for pointer validity.",[8446],{"_16":133,"_22":8447,"_28":6},"- WASM pointer to an existing MFEM Vector",[],{"_16":8450,"_18":8451,"_20":8452,"_22":8452,"_23":8453,"_29":95,"_31":8456},"mfem.linear.getFinalNorm","mfem.linear.getFinalNorm(solver)","Get the final residual norm from the last solve.",[8454],{"_16":7576,"_22":8455,"_28":6},"- Iterative solver instance",[],{"_16":8458,"_18":8459,"_20":8460,"_22":8460,"_23":8461,"_29":95,"_31":8463},"mfem.linear.getNumIterations","mfem.linear.getNumIterations(solver)","Get the number of iterations from the last solve.",[8462],{"_16":7576,"_22":8455,"_28":6},[],{"_16":8465,"_18":8466,"_20":1224,"_22":1224,"_23":8467,"_29":30,"_31":8473},"mfem.linear.mult","mfem.linear.mult(solver, b, x)",[8468,8469,8471],{"_16":7576,"_22":8455,"_28":6},{"_16":983,"_22":8470,"_28":6},"- Right-hand side vector",{"_16":1350,"_22":8472,"_28":6},"- Solution vector (modified in place)",[],{"_16":8475,"_18":8476,"_20":8477,"_22":8477,"_23":8478,"_29":30,"_31":8482},"mfem.linear.setMaxIterations","mfem.linear.setMaxIterations(solver, max)","Set maximum number of iterations for an iterative solver.",[8479,8480],{"_16":7576,"_22":8455,"_28":6},{"_16":2688,"_22":8481,"_28":6},"- Maximum iterations",[],{"_16":8484,"_18":8485,"_20":8486,"_22":8486,"_23":8487,"_29":30,"_31":8492},"mfem.linear.setPreconditioner","mfem.linear.setPreconditioner(solver, prec)","Set preconditioner for an iterative solver.",[8488,8489],{"_16":7576,"_22":8455,"_28":6},{"_16":8490,"_22":8491,"_28":6},"prec","- Preconditioner (Solver)",[],{"_16":8494,"_18":8495,"_20":8496,"_22":8496,"_23":8497,"_29":30,"_31":8502},"mfem.linear.setPrintLevel","mfem.linear.setPrintLevel(solver, level)","Set verbosity level for an iterative solver.",[8498,8499],{"_16":7576,"_22":8455,"_28":6},{"_16":8500,"_22":8501,"_28":6},"level","- Print level (0=silent, 1=summary, 2=iteration details)",[],{"_16":8504,"_18":8505,"_20":8506,"_22":8506,"_23":8507,"_29":30,"_31":8515},"mfem.linear.setTolerance","mfem.linear.setTolerance(solver, rtol, atol?)","Set convergence tolerances for an iterative solver.",[8508,8509,8512],{"_16":7576,"_22":8455,"_28":6},{"_16":8510,"_22":8511,"_28":6},"rtol","- Relative tolerance",{"_16":8513,"_22":8514,"_28":11},"atol","- Absolute tolerance (optional)",[],{"_16":8517,"_18":8518,"_20":8519,"_22":8519,"_23":8520,"_29":8521,"_31":8522},"mfem.linear.BiCGSTABSolver.create","mfem.linear.BiCGSTABSolver.create()","Creates a new BiCGSTAB solver.",[],"Promise",[],{"_16":8524,"_18":8525,"_20":8526,"_22":8526,"_23":8527,"_29":8536,"_31":8537},"mfem.linear.BlockILU.create","mfem.linear.BlockILU.create(matrixPtr, blockSize?, options?)","Creates a new BlockILU preconditioner.",[8528,8531,8534],{"_16":8529,"_22":8530,"_28":6},"matrixPtr","- Pointer to SparseMatrix or Operator",{"_16":8532,"_22":8533,"_28":11},"blockSize","- Block size for ILU factorization. Default: 1",{"_16":6924,"_22":8535,"_28":11},"- Optional configuration options","Promise",[],{"_16":8539,"_18":8540,"_20":8541,"_22":8541,"_23":8542,"_29":8543,"_31":8544},"mfem.linear.CGSolver.create","mfem.linear.CGSolver.create()","Creates a new CG solver.",[],"Promise",[],{"_16":8546,"_18":8547,"_20":8548,"_22":8548,"_23":8549,"_29":8552,"_31":8553},"mfem.linear.ChebyshevSmoother.create","mfem.linear.ChebyshevSmoother.create(options)","Creates a new Chebyshev smoother with explicit maximum eigenvalue.",[8550],{"_16":6924,"_22":8551,"_28":6},"- Smoother configuration options","Promise",[],{"_16":8555,"_18":8556,"_20":8557,"_22":8558,"_23":8559,"_29":8552,"_31":8561},"mfem.linear.ChebyshevSmoother.createAuto","mfem.linear.ChebyshevSmoother.createAuto(options)","Creates a new Chebyshev smoother with automatic eigenvalue estimation.\r","Creates a new Chebyshev smoother with automatic eigenvalue estimation.\r\nUses power iteration to estimate the maximum eigenvalue.",[8560],{"_16":6924,"_22":8551,"_28":6},[],{"_16":8563,"_18":8564,"_20":8565,"_22":8565,"_23":8566,"_29":8573,"_31":8574},"mfem.linear.DirectSubBlockSolver.create","mfem.linear.DirectSubBlockSolver.create(APtr, blockDofPtr)","Creates a new DirectSubBlockSolver.",[8567,8570],{"_16":8568,"_22":8569,"_28":6},"APtr","- Pointer to the system SparseMatrix",{"_16":8571,"_22":8572,"_28":6},"blockDofPtr","- Pointer to SparseMatrix defining block-DOF membership","Promise",[],{"_16":8576,"_18":8577,"_20":8578,"_22":8578,"_23":8579,"_29":8583,"_31":8584},"mfem.linear.DSmoother.create","mfem.linear.DSmoother.create(matrixPtr, options?)","Creates a new DSmoother.",[8580,8582],{"_16":8529,"_22":8581,"_28":6},"- Pointer to SparseMatrix",{"_16":6924,"_22":8535,"_28":11},"Promise",[],{"_16":8586,"_18":8587,"_20":8588,"_22":8588,"_23":8589,"_29":8593,"_31":8594},"mfem.linear.FGMRESSolver.create","mfem.linear.FGMRESSolver.create(kdim?)","Creates a new Flexible GMRES solver.",[8590],{"_16":8591,"_22":8592,"_28":11},"kdim","- Krylov space dimension (restart parameter, default 50)","Promise",[],{"_16":8596,"_18":8597,"_20":8598,"_22":8598,"_23":8599,"_29":8601,"_31":8602},"mfem.linear.GMRESSolver.create","mfem.linear.GMRESSolver.create(kdim?)","Creates a new GMRES solver.",[8600],{"_16":8591,"_22":8592,"_28":11},"Promise",[],{"_16":8604,"_18":8605,"_20":8606,"_22":8606,"_23":8607,"_29":8615,"_31":8616},"mfem.linear.GSSmoother.create","mfem.linear.GSSmoother.create(matrixPtr, type?, iterations?)","Creates a new Gauss-Seidel smoother.",[8608,8609,8612],{"_16":8529,"_22":8581,"_28":6},{"_16":8610,"_22":8611,"_28":11},"type","- Type of GS iteration (default: SYMMETRIC)",{"_16":8613,"_22":8614,"_28":11},"iterations","- Number of iterations (default: 1)","Promise",[],{"_16":8618,"_18":8619,"_20":8620,"_22":8620,"_23":8621,"_29":8625,"_31":8626},"mfem.linear.JacobiSmoother.create","mfem.linear.JacobiSmoother.create(matrixPtr, essentialDofs?)","Creates a new Jacobi smoother.",[8622,8623],{"_16":8529,"_22":8581,"_28":6},{"_16":6698,"_22":8624,"_28":11},"- Optional array of essential DOF indices to exclude","Promise",[],{"_16":8628,"_18":8629,"_20":8630,"_22":8630,"_23":8631,"_29":8632,"_31":8633},"mfem.linear.KLUSolver.isAvailable","mfem.linear.KLUSolver.isAvailable()","Checks if KLU (SuiteSparse) is available.",[],"Promise",[],{"_16":8635,"_18":8636,"_20":8637,"_22":8637,"_23":8638,"_29":8639,"_31":8640},"mfem.linear.KLUSolver.create","mfem.linear.KLUSolver.create()","Creates a new KLU solver.",[],"Promise",[],{"_16":8642,"_18":8643,"_20":8644,"_22":8644,"_23":8645,"_29":8646,"_31":8647},"mfem.linear.MINRESSolver.create","mfem.linear.MINRESSolver.create()","Creates a new MINRES solver.",[],"Promise",[],{"_16":8649,"_18":8650,"_20":8651,"_22":8651,"_23":8652,"_29":8653,"_31":8654},"mfem.linear.OrthoSolver.create","mfem.linear.OrthoSolver.create()","Creates a new orthogonalizing solver wrapper.",[],"Promise",[],{"_16":8656,"_18":8657,"_20":8658,"_22":8658,"_23":8659,"_29":8668,"_31":8669},"mfem.linear.ProductSolver.create","mfem.linear.ProductSolver.create(s0Ptr, s1Ptr, options?)","Creates a new product solver: S = S1 * S0.",[8660,8663,8666],{"_16":8661,"_22":8662,"_28":6},"s0Ptr","- Pointer to first solver (applied first)",{"_16":8664,"_22":8665,"_28":6},"s1Ptr","- Pointer to second solver (applied second)",{"_16":6924,"_22":8667,"_28":11},"- Ownership options","Promise",[],{"_16":8656,"_18":8671,"_20":8658,"_22":8658,"_23":8672,"_29":8668,"_31":8679},"mfem.linear.ProductSolver.create(s0, s1, options?)",[8673,8676,8678],{"_16":8674,"_22":8675,"_28":6},"s0","- First solver (applied first)",{"_16":3013,"_22":8677,"_28":6},"- Second solver (applied second)",{"_16":6924,"_22":8667,"_28":11},[],{"_16":8681,"_18":8682,"_20":8683,"_22":8683,"_23":8684,"_29":8685,"_31":8686},"mfem.linear.SLISolver.create","mfem.linear.SLISolver.create()","Creates a new SLI solver.",[],"Promise",[],{"_16":8688,"_18":8689,"_20":8690,"_22":8690,"_23":8691,"_29":8632,"_31":8692},"mfem.linear.UMFPackSolver.isAvailable","mfem.linear.UMFPackSolver.isAvailable()","Checks if UMFPack (SuiteSparse) is available.",[],[],{"_16":8694,"_18":8695,"_20":8696,"_22":8696,"_23":8697,"_29":8698,"_31":8699},"mfem.linear.UMFPackSolver.create","mfem.linear.UMFPackSolver.create()","Creates a new UMFPack solver.",[],"Promise",[],{"_16":8701,"_18":8702,"_20":8703,"_22":8704,"_23":8705,"_29":30,"_31":8711},"mfem.linearForms.addBoundaryFluxIntegrator","mfem.linearForms.addBoundaryFluxIntegrator(lf, coeff, bdrAttrs?)","Add a VectorFE boundary flux integrator for H(div) spaces.\r","Add a VectorFE boundary flux integrator for H(div) spaces.\r\n\r\nComputes: ∫_∂Ω f * (v · n) ds",[8706,8707,8709],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":8708,"_28":6},"- Scalar flux coefficient",{"_16":6848,"_22":8710,"_28":11},"- Optional boundary attributes to restrict to",[],{"_16":8713,"_18":8714,"_20":8715,"_22":8716,"_23":8717,"_29":30,"_31":8722},"mfem.linearForms.addBoundaryIntegrator","mfem.linearForms.addBoundaryIntegrator(lf, coeff, bdrAttrs?)","Add a boundary integrator (g, v) to the linear form.\r","Add a boundary integrator (g, v) to the linear form.\r\n\r\nComputes: ∫_∂Ω g * v ds",[8718,8719,8721],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":8720,"_28":6},"- Boundary source coefficient",{"_16":6848,"_22":8710,"_28":11},[],{"_16":8724,"_18":8725,"_20":8726,"_22":8727,"_23":8728,"_29":30,"_31":8732},"mfem.linearForms.addBoundaryNormalIntegrator","mfem.linearForms.addBoundaryNormalIntegrator(lf, coeff, bdrAttrs?)","Add a boundary normal integrator (F · n, v) to the linear form.\r","Add a boundary normal integrator (F · n, v) to the linear form.\r\n\r\nComputes: ∫_∂Ω (F · n) * v ds",[8729,8730,8731],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":7228,"_28":6},{"_16":6848,"_22":8710,"_28":11},[],{"_16":8734,"_18":8735,"_20":8736,"_22":8737,"_23":8738,"_29":30,"_31":8742},"mfem.linearForms.addBoundaryTangentialIntegrator","mfem.linearForms.addBoundaryTangentialIntegrator(lf, coeff, bdrAttrs?)","Add a boundary tangential integrator (F × n, v) to the linear form.\r","Add a boundary tangential integrator (F × n, v) to the linear form.\r\nFor 2D: takes the tangential component of the vector field.\r\n\r\nComputes: ∫_∂Ω (F · t) * v ds",[8739,8740,8741],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":7228,"_28":6},{"_16":6848,"_22":8710,"_28":11},[],{"_16":8744,"_18":8745,"_20":8746,"_22":8747,"_23":8748,"_29":30,"_31":8756},"mfem.linearForms.addDGDirichletIntegrator","mfem.linearForms.addDGDirichletIntegrator(lf, coeff, sigma, kappa)","Add a DG Dirichlet boundary integrator for discontinuous Galerkin methods.\r","Add a DG Dirichlet boundary integrator for discontinuous Galerkin methods.\r\n\r\nNote: This integrator is not yet implemented in the WASM bindings.\r\nIt requires additional C++ support for DG-specific integrators.",[8749,8750,8752,8754],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":8751,"_28":6},"- Dirichlet value coefficient",{"_16":6560,"_22":8753,"_28":6},"- Symmetry parameter (-1 for SIPG, 0 for IIPG, 1 for NIPG)",{"_16":6563,"_22":8755,"_28":6},"- Penalty parameter",[],{"_16":8758,"_18":8759,"_20":8760,"_22":8761,"_23":8762,"_29":30,"_31":8765},"mfem.linearForms.addDomainGradientIntegrator","mfem.linearForms.addDomainGradientIntegrator(lf, coeff)","Add a domain gradient integrator (F, ∇v) to the linear form.\r","Add a domain gradient integrator (F, ∇v) to the linear form.\r\n\r\nComputes: ∫ F · ∇v dx",[8763,8764],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":7228,"_28":6},[],{"_16":8767,"_18":8768,"_20":8769,"_22":8770,"_23":8771,"_29":30,"_31":8775},"mfem.linearForms.addDomainIntegrator","mfem.linearForms.addDomainIntegrator(lf, coeff)","Add a domain integrator (f, v) to the linear form.\r","Add a domain integrator (f, v) to the linear form.\r\n\r\nComputes: ∫ f * v dx",[8772,8773],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":8774,"_28":6},"- Source coefficient",[],{"_16":8777,"_18":8778,"_20":8779,"_22":8780,"_23":8781,"_29":30,"_31":8784},"mfem.linearForms.addVectorDomainIntegrator","mfem.linearForms.addVectorDomainIntegrator(lf, coeff)","Add a vector domain integrator (F, v) to the linear form.\r","Add a vector domain integrator (F, v) to the linear form.\r\nFor vector-valued test functions.\r\n\r\nComputes: ∫ F · v dx",[8782,8783],{"_16":6841,"_22":6860,"_28":6},{"_16":6525,"_22":7228,"_28":6},[],{"_16":8786,"_18":8787,"_20":8788,"_22":8788,"_23":8789,"_29":30,"_31":8791},"mfem.linearForms.assemble","mfem.linearForms.assemble(lf)","Assemble the linear form into a vector.",[8790],{"_16":6841,"_22":6860,"_28":6},[],{"_16":8793,"_18":8794,"_20":8795,"_22":8795,"_23":8796,"_29":137,"_31":8798},"mfem.linearForms.getVector","mfem.linearForms.getVector(lf)","Get the assembled vector data from the linear form.",[8797],{"_16":6841,"_22":6860,"_28":6},[],{"_16":8800,"_18":8801,"_20":8802,"_22":8802,"_23":8803,"_29":8805,"_31":8806},"mfem.linearForms.create","mfem.linearForms.create(fespace)","Create a linear form on a finite element space.",[8804],{"_16":6686,"_22":6687,"_28":6},"Promise",[],{"_16":8808,"_18":8809,"_20":8810,"_22":8810,"_23":8811,"_29":8805,"_31":8813},"mfem.linearForms.LinearForm.create","mfem.linearForms.LinearForm.create(fespace)","Creates a new linear form on the specified finite element space.",[8812],{"_16":6686,"_22":6743,"_28":6},[],{"_16":8815,"_18":8816,"_20":8817,"_22":7586,"_23":8818,"_29":30,"_31":8824},"mfem.matrix.add","mfem.matrix.add(dm, alpha, other)","add",[8819,8821,8822],{"_16":8820,"_22":7590,"_28":6},"dm",{"_16":1022,"_22":95,"_28":6},{"_16":8823,"_22":7590,"_28":6},"other",[],{"_16":8826,"_18":8827,"_20":123,"_22":7586,"_23":8828,"_29":95,"_31":8830},"mfem.matrix.cols","mfem.matrix.cols(dm)",[8829],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8832,"_18":8833,"_20":8834,"_22":7586,"_23":8835,"_29":7637,"_31":8838},"mfem.matrix.create","mfem.matrix.create(rows, cols)","create_2",[8836,8837],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},[],{"_16":8840,"_18":8841,"_20":8842,"_22":7586,"_23":8843,"_29":95,"_31":8845},"mfem.matrix.determinant","mfem.matrix.determinant(dm)","determinant",[8844],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8847,"_18":8848,"_20":8849,"_22":7586,"_23":8850,"_29":8852,"_31":8853},"mfem.matrix.eigenvalues","mfem.matrix.eigenvalues(dm)","eigenvalues",[8851],{"_16":8820,"_22":7590,"_28":6},"Promise",[],{"_16":8855,"_18":8856,"_20":8857,"_22":7586,"_23":8858,"_29":7637,"_31":8860},"mfem.matrix.fromArray","mfem.matrix.fromArray(data)","fromArray",[8859],{"_16":117,"_22":125,"_28":6},[],{"_16":8862,"_18":8863,"_20":8864,"_22":7586,"_23":8865,"_29":95,"_31":8869},"mfem.matrix.get","mfem.matrix.get(dm, i, j)","get_2",[8866,8867,8868],{"_16":8820,"_22":7590,"_28":6},{"_16":409,"_22":95,"_28":6},{"_16":412,"_22":95,"_28":6},[],{"_16":8871,"_18":8872,"_20":8873,"_22":7586,"_23":8874,"_29":137,"_31":8876},"mfem.matrix.getData","mfem.matrix.getData(dm)","getData",[8875],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8878,"_18":8879,"_20":8880,"_22":7586,"_23":8881,"_29":7637,"_31":8883},"mfem.matrix.identity","mfem.matrix.identity(n)","identity_2",[8882],{"_16":629,"_22":95,"_28":6},[],{"_16":8885,"_18":8886,"_20":8887,"_22":7586,"_23":8888,"_29":30,"_31":8890},"mfem.matrix.invert","mfem.matrix.invert(dm)","invert",[8889],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8892,"_18":8893,"_20":8894,"_22":7586,"_23":8895,"_29":30,"_31":8899},"mfem.matrix.mult","mfem.matrix.mult(dm, x, y)","mult",[8896,8897,8898],{"_16":8820,"_22":7590,"_28":6},{"_16":1350,"_22":2145,"_28":6},{"_16":2349,"_22":2145,"_28":6},[],{"_16":8901,"_18":8902,"_20":8903,"_22":7586,"_23":8904,"_29":30,"_31":8908},"mfem.matrix.multTranspose","mfem.matrix.multTranspose(dm, x, y)","multTranspose",[8905,8906,8907],{"_16":8820,"_22":7590,"_28":6},{"_16":1350,"_22":2145,"_28":6},{"_16":2349,"_22":2145,"_28":6},[],{"_16":8910,"_18":8911,"_20":120,"_22":7586,"_23":8912,"_29":95,"_31":8914},"mfem.matrix.rows","mfem.matrix.rows(dm)",[8913],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8916,"_18":8917,"_20":8918,"_22":7586,"_23":8919,"_29":30,"_31":8924},"mfem.matrix.set","mfem.matrix.set(dm, i, j, value)","set_2",[8920,8921,8922,8923],{"_16":8820,"_22":7590,"_28":6},{"_16":409,"_22":95,"_28":6},{"_16":412,"_22":95,"_28":6},{"_16":457,"_22":95,"_28":6},[],{"_16":8926,"_18":8927,"_20":5650,"_22":7586,"_23":8928,"_29":8438,"_31":8931},"mfem.matrix.solve","mfem.matrix.solve(dm, b)",[8929,8930],{"_16":8820,"_22":7590,"_28":6},{"_16":983,"_22":2145,"_28":6},[],{"_16":8933,"_18":8934,"_20":3326,"_22":7586,"_23":8935,"_29":8852,"_31":8937},"mfem.matrix.svd","mfem.matrix.svd(dm)",[8936],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8939,"_18":8940,"_20":3429,"_22":7586,"_23":8941,"_29":95,"_31":8943},"mfem.matrix.trace","mfem.matrix.trace(dm)",[8942],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8945,"_18":8946,"_20":8947,"_22":7586,"_23":8948,"_29":7637,"_31":8950},"mfem.matrix.transpose","mfem.matrix.transpose(dm)","transpose_2",[8949],{"_16":8820,"_22":7590,"_28":6},[],{"_16":8952,"_18":8953,"_20":2203,"_22":7586,"_23":8954,"_29":7637,"_31":8957},"mfem.matrix.zeros","mfem.matrix.zeros(rows, cols)",[8955,8956],{"_16":120,"_22":95,"_28":6},{"_16":123,"_22":95,"_28":6},[],{"_16":8959,"_18":8960,"_20":7632,"_22":7633,"_23":8961,"_29":7637,"_31":8964},"mfem.matrix.DenseMatrix.create","mfem.matrix.DenseMatrix.create(height, width)",[8962,8963],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},[],{"_16":8966,"_18":8967,"_20":7642,"_22":7642,"_23":8968,"_29":7637,"_31":8971},"mfem.matrix.DenseMatrix.zeros","mfem.matrix.DenseMatrix.zeros(height, width)",[8969,8970],{"_16":5946,"_22":121,"_28":6},{"_16":7114,"_22":124,"_28":6},[],{"_16":8973,"_18":8974,"_20":7650,"_22":7650,"_23":8975,"_29":7637,"_31":8977},"mfem.matrix.DenseMatrix.identity","mfem.matrix.DenseMatrix.identity(n)",[8976],{"_16":629,"_22":1458,"_28":6},[],{"_16":8979,"_18":8980,"_20":7657,"_22":7657,"_23":8981,"_29":7637,"_31":8983},"mfem.matrix.DenseMatrix.fromArray","mfem.matrix.DenseMatrix.fromArray(data)",[8982],{"_16":117,"_22":7660,"_28":6},[],{"_16":8985,"_18":8986,"_20":7665,"_22":7666,"_23":8987,"_29":7637,"_31":8990},"mfem.matrix.DenseMatrix.fromPointer","mfem.matrix.DenseMatrix.fromPointer(ptr, ownsMemory?)",[8988,8989],{"_16":133,"_22":7669,"_28":6},{"_16":7671,"_22":7672,"_28":11},[],{"_16":8992,"_18":8993,"_20":8994,"_22":8995,"_23":8996,"_29":30,"_31":9002},"mfem.mesh.derefine","mfem.mesh.derefine(mesh, derefinements)","Derefines (coarsens) specified elements in a non-conforming mesh.\r","Derefines (coarsens) specified elements in a non-conforming mesh.\r\n\r\nDerefinement is the reverse of refinement - it merges previously refined\r\nelements back into their parent elements. This is useful for adaptive\r\nmesh refinement (AMR) where elements may need to be coarsened after\r\nsolution features have moved or diminished.\r\n\r\n**Requirements:**\r\n- The mesh must have NCMesh (non-conforming mesh) support enabled\r\n- The elements must have been previously refined\r\n- The derefinement indices refer to rows in the NCMesh derefinement table\r\n\r\nTo enable NCMesh support before refinement, use .",[8997,8999],{"_16":2365,"_22":8998,"_28":6},"- Mesh instance with NCMesh support",{"_16":9000,"_22":9001,"_28":6},"derefinements","- Array of derefinement table row indices",[],{"_16":9004,"_18":9005,"_20":9006,"_22":9007,"_23":9008,"_29":30,"_31":9010},"mfem.mesh.enableNCMesh","mfem.mesh.enableNCMesh(mesh)","Enables non-conforming mesh (NCMesh) support.\r","Enables non-conforming mesh (NCMesh) support.\r\n\r\nNCMesh support is required for local refinement with hanging nodes\r\nand for derefinement (coarsening). This function must be called\r\nbefore any local refinement operations if derefinement is desired later.",[9009],{"_16":2365,"_22":6890,"_28":6},[],{"_16":9012,"_18":9013,"_20":9014,"_22":9015,"_23":9016,"_29":95,"_31":9018},"mfem.mesh.getDerefTableSize","mfem.mesh.getDerefTableSize(mesh)","Gets the size of the derefinement table.\r","Gets the size of the derefinement table.\r\n\r\nThe derefinement table contains information about which element groups\r\ncan be coarsened. Each row in the table represents one possible\r\nderefinement operation.",[9017],{"_16":2365,"_22":8998,"_28":6},[],{"_16":9020,"_18":9021,"_20":9022,"_22":9022,"_23":9023,"_29":69,"_31":9025},"mfem.mesh.isNCMesh","mfem.mesh.isNCMesh(mesh)","Checks if a mesh has NCMesh (non-conforming mesh) support.",[9024],{"_16":2365,"_22":6890,"_28":6},[],{"_16":9027,"_18":9028,"_20":9029,"_22":9030,"_23":9031,"_29":30,"_31":9037},"mfem.mesh.elevateNURBSDegree","mfem.mesh.elevateNURBSDegree(mesh, relDegree)","Elevates the polynomial degree of a NURBS mesh.\r","Elevates the polynomial degree of a NURBS mesh.\r\n\r\nThis modifies the mesh in place by increasing the polynomial order of\r\nall NURBS patches. The geometry is preserved exactly while adding\r\nadditional control points.",[9032,9034],{"_16":2365,"_22":9033,"_28":6},"- NURBS mesh to elevate",{"_16":9035,"_22":9036,"_28":6},"relDegree","- Relative degree increase (e.g., 1 to go from order 2 to 3)",[],{"_16":9039,"_18":9040,"_20":9041,"_22":9042,"_23":9043,"_29":30,"_31":9048},"mfem.mesh.setNURBSOrder","mfem.mesh.setNURBSOrder(mesh, order)","Sets the NURBS order uniformly.\r","Sets the NURBS order uniformly.\r\n\r\nThis sets the curvature order of the mesh, which affects the underlying\r\nNURBS representation. Note that this may perform degree elevation or\r\nreduction depending on the current order.",[9044,9046],{"_16":2365,"_22":9045,"_28":6},"- NURBS mesh",{"_16":1532,"_22":9047,"_28":6},"- New polynomial order",[],{"_16":9050,"_18":9051,"_20":9052,"_22":9053,"_23":9054,"_29":6941,"_31":9057},"mfem.mesh.fromBinary","mfem.mesh.fromBinary(data)","Loads a mesh from a base64-encoded binary string.\r","Loads a mesh from a base64-encoded binary string.\r\n\r\nThis is the inverse of . The base64 string is decoded\r\nand parsed as an MFEM format mesh.",[9055],{"_16":117,"_22":9056,"_28":6},"- Base64-encoded string containing mesh data",[],{"_16":9059,"_18":9060,"_20":9061,"_22":9062,"_23":9063,"_29":6941,"_31":9066},"mfem.mesh.fromGmsh","mfem.mesh.fromGmsh(data)","Loads a mesh from a Gmsh format string.\r","Loads a mesh from a Gmsh format string.\r\n\r\nParses mesh data in Gmsh MSH format (versions 2.x and 4.x are supported).\r\nThis is useful for importing meshes created with the Gmsh mesh generator\r\nor exported from other tools in Gmsh format.",[9064],{"_16":117,"_22":9065,"_28":6},"- Gmsh mesh format string (MSH file contents)",[],{"_16":9068,"_18":9069,"_20":9070,"_22":9071,"_23":9072,"_29":6941,"_31":9075},"mfem.mesh.fromMFEM","mfem.mesh.fromMFEM(data)","Loads a mesh from an MFEM native format string.\r","Loads a mesh from an MFEM native format string.\r\n\r\nThis is an alias for provided for API consistency.\r\nMFEM's native mesh format is automatically detected by the parser.",[9073],{"_16":117,"_22":9074,"_28":6},"- MFEM native format mesh string (.mesh file contents)",[],{"_16":9077,"_18":9078,"_20":9079,"_22":9080,"_23":9081,"_29":6941,"_31":9084},"mfem.mesh.fromNetgen","mfem.mesh.fromNetgen(data)","Loads a mesh from a Netgen format string.\r","Loads a mesh from a Netgen format string.\r\n\r\nParses mesh data in Netgen neutral format. MFEM automatically detects\r\nthe format based on file headers:\r\n- 2D meshes typically start with \"areasmesh2\" or \"curved_areamesh2\"\r\n- 3D meshes typically start with \"NETGEN\" or \"NETGEN_Neutral_Format\"",[9082],{"_16":117,"_22":9083,"_28":6},"- Netgen format mesh string",[],{"_16":9086,"_18":9087,"_20":9088,"_22":9089,"_23":9090,"_29":6941,"_31":9093},"mfem.mesh.fromTrueGrid","mfem.mesh.fromTrueGrid(data)","Loads a mesh from a TrueGrid format string.\r","Loads a mesh from a TrueGrid format string.\r\n\r\nParses mesh data in TrueGrid format. MFEM automatically detects\r\nthe format based on file headers. TrueGrid files typically start\r\nwith \"TrueGrid\".",[9091],{"_16":117,"_22":9092,"_28":6},"- TrueGrid format mesh string",[],{"_16":9095,"_18":9096,"_20":9097,"_22":9098,"_23":9099,"_29":6941,"_31":9102},"mfem.mesh.fromVTK","mfem.mesh.fromVTK(data)","Loads a mesh from a VTK format string.\r","Loads a mesh from a VTK format string.\r\n\r\nParses mesh data in VTK legacy format (.vtk). This is useful for importing\r\nmeshes from visualization tools like ParaView or VTK-based applications.",[9100],{"_16":117,"_22":9101,"_28":6},"- VTK legacy format string (.vtk file contents)",[],{"_16":9104,"_18":9105,"_20":9106,"_22":9107,"_23":9108,"_29":125,"_31":9111},"mfem.mesh.getElementCentroids","mfem.mesh.getElementCentroids(mesh)","Computes the centroid (geometric center) of each element in the mesh.\r","Computes the centroid (geometric center) of each element in the mesh.\r\n\r\nThe centroid is the average of the element's vertex coordinates and\r\nrepresents the center of mass assuming uniform density.",[9109],{"_16":2365,"_22":9110,"_28":6},"- The mesh to compute element centroids for",[],{"_16":9113,"_18":9114,"_20":9115,"_22":9116,"_23":9117,"_29":137,"_31":9120},"mfem.mesh.getElementVolumes","mfem.mesh.getElementVolumes(mesh)","Computes the volume (or area/length) of each element in the mesh.\r","Computes the volume (or area/length) of each element in the mesh.\r\n\r\nReturns the measure of each element according to the mesh dimension:\r\n- 1D: element lengths\r\n- 2D: element areas\r\n- 3D: element volumes\r\n\r\nThis is useful for computing integrals, checking mesh quality,\r\nor applying element-based operations.",[9118],{"_16":2365,"_22":9119,"_28":6},"- The mesh to compute element volumes for",[],{"_16":9122,"_18":9123,"_20":9124,"_22":9124,"_23":9125,"_29":137,"_31":9133},"mfem.mesh.getNURBSKnotVector","mfem.mesh.getNURBSKnotVector(mesh, patchIdx, dir)","Gets the knot vector for a NURBS patch in a specific direction.",[9126,9127,9130],{"_16":2365,"_22":9045,"_28":6},{"_16":9128,"_22":9129,"_28":6},"patchIdx","- Patch index",{"_16":9131,"_22":9132,"_28":6},"dir","- Direction (0, 1, or 2 for x, y, z)",[],{"_16":9135,"_18":9136,"_20":9137,"_22":9137,"_23":9138,"_29":9141,"_31":9142},"mfem.mesh.getNURBSPatch","mfem.mesh.getNURBSPatch(mesh, patchIdx)","Gets full NURBS patch data including knot vectors.",[9139,9140],{"_16":2365,"_22":9045,"_28":6},{"_16":9128,"_22":9129,"_28":6},"NURBSPatch",[],{"_16":9144,"_18":9145,"_20":9146,"_22":9146,"_23":9147,"_29":9150,"_31":9151},"mfem.mesh.getNURBSPatchInfo","mfem.mesh.getNURBSPatchInfo(mesh, patchIdx)","Gets information about a NURBS patch.",[9148,9149],{"_16":2365,"_22":9045,"_28":6},{"_16":9128,"_22":9129,"_28":6},"NURBSPatchInfo",[],{"_16":9153,"_18":9154,"_20":9155,"_22":9155,"_23":9156,"_29":95,"_31":9158},"mfem.mesh.getNumNURBSPatches","mfem.mesh.getNumNURBSPatches(mesh)","Gets the number of NURBS patches in the mesh.",[9157],{"_16":2365,"_22":9045,"_28":6},[],{"_16":9160,"_18":9161,"_20":9162,"_22":9162,"_23":9163,"_29":30,"_31":9170},"mfem.mesh.insertNURBSKnot","mfem.mesh.insertNURBSKnot(mesh, direction, knot)","Inserts a single knot into a NURBS mesh.",[9164,9165,9167],{"_16":2365,"_22":9045,"_28":6},{"_16":2801,"_22":9166,"_28":6},"- Parametric direction (0=x, 1=y, 2=z)",{"_16":9168,"_22":9169,"_28":6},"knot","- Knot value to insert (must be within the parametric domain)",[],{"_16":9172,"_18":9173,"_20":9174,"_22":9174,"_23":9175,"_29":30,"_31":9181},"mfem.mesh.insertNURBSKnots","mfem.mesh.insertNURBSKnots(mesh, direction, knots)","Inserts multiple knots into a NURBS mesh in a specific direction.",[9176,9177,9178],{"_16":2365,"_22":9045,"_28":6},{"_16":2801,"_22":9166,"_28":6},{"_16":9179,"_22":9180,"_28":6},"knots","- Array of knot values to insert",[],{"_16":9183,"_18":9184,"_20":9185,"_22":9186,"_23":9187,"_29":30,"_31":9193},"mfem.mesh.uniformNURBSRefinement","mfem.mesh.uniformNURBSRefinement(mesh, refFactor?)","Performs uniform refinement on a NURBS mesh.\r","Performs uniform refinement on a NURBS mesh.\r\n\r\nThis inserts new knots uniformly within each existing span, refining\r\nthe NURBS mesh while preserving the geometry exactly.",[9188,9190],{"_16":2365,"_22":9189,"_28":6},"- NURBS mesh to refine",{"_16":9191,"_22":9192,"_28":11},"refFactor","- Refinement factor (1 = 1 new knot per span, etc.)",[],{"_16":9195,"_18":9196,"_20":9197,"_22":9198,"_23":9199,"_29":6941,"_31":9205},"mfem.mesh.makeCartesian1D","mfem.mesh.makeCartesian1D(n, sx?)","Creates a 1D Cartesian (line segment) mesh.\r","Creates a 1D Cartesian (line segment) mesh.\r\n\r\nGenerates a uniform mesh on the interval [0, sx] with `n` line segment elements.\r\nThis is useful for 1D finite element problems like ODEs, 1D heat transfer,\r\nor testing numerical methods.",[9200,9202],{"_16":629,"_22":9201,"_28":6},"- Number of elements (must be ≥ 1)",{"_16":9203,"_22":9204,"_28":11},"sx","- Domain size / length of the interval (default 1.0)",[],{"_16":9207,"_18":9208,"_20":9209,"_22":9210,"_23":9211,"_29":6941,"_31":9225},"mfem.mesh.makeCartesian2D","mfem.mesh.makeCartesian2D(nx, ny, type?, sx?, sy?)","Creates a 2D Cartesian (rectangular) mesh.\r","Creates a 2D Cartesian (rectangular) mesh.\r\n\r\nGenerates a structured mesh on the rectangular domain [0, sx] × [0, sy]\r\nwith the specified number of elements in each direction.",[9212,9215,9218,9220,9222],{"_16":9213,"_22":9214,"_28":6},"nx","- Number of elements in the x-direction (must be ≥ 1)",{"_16":9216,"_22":9217,"_28":6},"ny","- Number of elements in the y-direction (must be ≥ 1)",{"_16":8610,"_22":9219,"_28":11},"- Element type: `'quad'` for quadrilaterals (default), `'tri'` for triangles",{"_16":9203,"_22":9221,"_28":11},"- Domain size in x-direction (default 1.0)",{"_16":9223,"_22":9224,"_28":11},"sy","- Domain size in y-direction (default 1.0)",[],{"_16":9227,"_18":9228,"_20":9229,"_22":9230,"_23":9231,"_29":6941,"_31":9243},"mfem.mesh.makeCartesian3D","mfem.mesh.makeCartesian3D(nx, ny, nz, type?, sx?, sy?, sz?)","Creates a 3D Cartesian (box) mesh.\r","Creates a 3D Cartesian (box) mesh.\r\n\r\nGenerates a structured mesh on the box domain [0, sx] × [0, sy] × [0, sz]\r\nwith the specified number of elements in each direction.",[9232,9233,9234,9236,9238,9239,9240],{"_16":9213,"_22":9214,"_28":6},{"_16":9216,"_22":9217,"_28":6},{"_16":6241,"_22":9235,"_28":6},"- Number of elements in the z-direction (must be ≥ 1)",{"_16":8610,"_22":9237,"_28":11},"- Element type: `'hex'` for hexahedra (default), `'tet'` for tetrahedra, `'wedge'` for wedges",{"_16":9203,"_22":9221,"_28":11},{"_16":9223,"_22":9224,"_28":11},{"_16":9241,"_22":9242,"_28":11},"sz","- Domain size in z-direction (default 1.0)",[],{"_16":9245,"_18":9246,"_20":9247,"_22":9248,"_23":9249,"_29":6941,"_31":9255},"mfem.mesh.makeCircle","mfem.mesh.makeCircle(npts, radius?)","Creates a 2D circular disk mesh.\r","Creates a 2D circular disk mesh.\r\n\r\nGenerates a triangulated mesh approximating a circular disk by creating a\r\nsquare mesh and applying an elliptic conformal mapping. This mapping\r\npreserves mesh quality while smoothly transforming the square to a circle.\r\n\r\nThe mesh is centered at the origin with the specified radius.",[9250,9253],{"_16":9251,"_22":9252,"_28":6},"npts","- Controls mesh density. Higher values create finer meshes (minimum 3)",{"_16":5922,"_22":9254,"_28":11},"- Radius of the circular disk (default 1.0)",[],{"_16":9257,"_18":9258,"_20":9259,"_22":9260,"_23":9261,"_29":6941,"_31":9268},"mfem.mesh.makeCylinder","mfem.mesh.makeCylinder(npts, length?, radius?)","Creates a 3D solid cylinder mesh.\r","Creates a 3D solid cylinder mesh.\r\n\r\nGenerates a hexahedral mesh of a solid cylinder by creating a box mesh\r\nand applying an elliptic conformal mapping to the x-y cross-section while\r\npreserving the z-coordinate. The cylinder is centered on the z-axis with\r\nz ∈ [0, length].",[9262,9264,9266],{"_16":9251,"_22":9263,"_28":6},"- Controls mesh density via ∛npts elements per side (minimum 4)",{"_16":2834,"_22":9265,"_28":11},"- Length of the cylinder in the z-direction (default 1.0)",{"_16":5922,"_22":9267,"_28":11},"- Radius of the cylinder in the x-y plane (default 1.0)",[],{"_16":9270,"_18":9271,"_20":9272,"_22":9273,"_23":9274,"_29":6941,"_31":9279},"mfem.mesh.makeDisk","mfem.mesh.makeDisk(npts, radius?)","Creates a 2D disk mesh using elliptic mapping.\r","Creates a 2D disk mesh using elliptic mapping.\r\n\r\nGenerates a triangulated mesh of a circular disk by mapping a square mesh\r\nto a disk using the elliptic conformal mapping:\r\n```\r\nx = u × √(1 - v²/2) × radius\r\ny = v × √(1 - u²/2) × radius\r\n```\r\n\r\nThis mapping produces high-quality elements with smooth variation across\r\nthe domain, making it suitable for finite element analysis.",[9275,9277],{"_16":9251,"_22":9276,"_28":6},"- Controls mesh density via √npts elements per side (minimum 3)",{"_16":5922,"_22":9278,"_28":11},"- Radius of the disk (default 1.0)",[],{"_16":9281,"_18":9282,"_20":9283,"_22":9284,"_23":9285,"_29":6941,"_31":9289},"mfem.mesh.makeSphere","mfem.mesh.makeSphere(npts, radius?)","Creates a 3D solid sphere (ball) mesh.\r","Creates a 3D solid sphere (ball) mesh.\r\n\r\nGenerates a tetrahedral mesh of a solid ball by creating a cube mesh\r\nand applying a radial projection transformation. Interior points are\r\nmapped proportionally while boundary points are projected to the sphere surface.\r\n\r\nThe mesh is centered at the origin with the specified radius.",[9286,9287],{"_16":9251,"_22":9263,"_28":6},{"_16":5922,"_22":9288,"_28":11},"- Radius of the sphere (default 1.0)",[],{"_16":9291,"_18":9292,"_20":9293,"_22":9294,"_23":9295,"_29":30,"_31":9300},"mfem.mesh.refineLocal","mfem.mesh.refineLocal(mesh, elements)","Locally refines specified elements in the mesh.\r","Locally refines specified elements in the mesh.\r\n\r\nPerforms adaptive refinement by subdividing only the specified elements,\r\nleaving other elements unchanged. This is useful for adaptive mesh refinement\r\n(AMR) strategies where refinement is focused on regions with high error.\r\n\r\nThe mesh maintains conformity by adding necessary transition elements between\r\nrefined and unrefined regions.",[9296,9298],{"_16":2365,"_22":9297,"_28":6},"- The mesh to refine (modified in place)",{"_16":5904,"_22":9299,"_28":6},"- Array of element indices to refine (0-based)",[],{"_16":9302,"_18":9303,"_20":9304,"_22":9305,"_23":9306,"_29":30,"_31":9309},"mfem.mesh.refineNonconforming","mfem.mesh.refineNonconforming(mesh, elements)","Performs non-conforming refinement of specified elements.\r","Performs non-conforming refinement of specified elements.\r\n\r\nNon-conforming refinement allows hanging nodes (vertices that lie on\r\nedges/faces of neighboring elements) which enables more flexible local\r\nrefinement without requiring transition elements.\r\n\r\n**Note:** The current implementation uses the same mechanism as\r\n. True non-conforming refinement with hanging node\r\nsupport requires full NCMesh integration which is not yet available.",[9307,9308],{"_16":2365,"_22":9297,"_28":6},{"_16":5904,"_22":9299,"_28":6},[],{"_16":9311,"_18":9312,"_20":9313,"_22":9314,"_23":9315,"_29":30,"_31":9320},"mfem.mesh.refineUniform","mfem.mesh.refineUniform(mesh, times?)","Uniformly refines a mesh one or more times.\r","Uniformly refines a mesh one or more times.\r\n\r\nEach refinement level subdivides every element into smaller elements:\r\n- 2D triangles → 4 triangles\r\n- 2D quadrilaterals → 4 quadrilaterals\r\n- 3D tetrahedra → 8 tetrahedra\r\n- 3D hexahedra → 8 hexahedra\r\n\r\nThe number of elements grows exponentially: after `times` refinements,\r\na 2D mesh will have 4^times × original elements.",[9316,9317],{"_16":2365,"_22":9297,"_28":6},{"_16":9318,"_22":9319,"_28":11},"times","- Number of refinement levels to apply (default 1)",[],{"_16":9322,"_18":9323,"_20":9324,"_22":9325,"_23":9326,"_29":30,"_31":9333},"mfem.mesh.rotate","mfem.mesh.rotate(mesh, angle, axis?)","Rotates a mesh around an axis.\r","Rotates a mesh around an axis.\r\n\r\nFor 2D meshes, rotates around the origin (z-axis).\r\nFor 3D meshes, rotates around the specified coordinate axis passing\r\nthrough the origin.\r\n\r\nRotation follows the right-hand rule: positive angles rotate\r\ncounterclockwise when looking along the axis toward the origin.",[9327,9329,9331],{"_16":2365,"_22":9328,"_28":6},"- The mesh to rotate (modified in place)",{"_16":4182,"_22":9330,"_28":6},"- Rotation angle in radians (positive = counterclockwise)",{"_16":4138,"_22":9332,"_28":11},"- Rotation axis for 3D: 0=x, 1=y, 2=z (default). Ignored for 2D.",[],{"_16":9335,"_18":9336,"_20":9337,"_22":9338,"_23":9339,"_29":30,"_31":9344},"mfem.mesh.scale","mfem.mesh.scale(mesh, factor)","Scales a mesh uniformly or along each axis.\r","Scales a mesh uniformly or along each axis.\r\n\r\nMultiplies all vertex coordinates by the scale factor(s), effectively\r\nresizing the mesh. Scaling is performed relative to the origin.",[9340,9342],{"_16":2365,"_22":9341,"_28":6},"- The mesh to scale (modified in place)",{"_16":5725,"_22":9343,"_28":6},"- Either a single uniform scale factor, or an array of\r\n per-axis factors [sx, sy] (2D) or [sx, sy, sz] (3D)",[],{"_16":9346,"_18":9347,"_20":9348,"_22":9349,"_23":9350,"_29":30,"_31":9355},"mfem.mesh.setCurvature","mfem.mesh.setCurvature(mesh, order)","Sets the curvature order for high-order geometry representation.\r","Sets the curvature order for high-order geometry representation.\r\n\r\nConverts the mesh to use high-order polynomial nodes for representing\r\ncurved element boundaries. This is essential for accurately representing\r\ncurved domains (circles, spheres, etc.) and achieving optimal convergence\r\nrates with high-order finite elements.\r\n\r\nHigher orders provide better approximation of curved boundaries but\r\nincrease the number of geometry nodes per element.",[9351,9353],{"_16":2365,"_22":9352,"_28":6},"- The mesh to set curvature on (modified in place)",{"_16":1532,"_22":9354,"_28":6},"- Polynomial order for geometry representation (≥ 1)",[],{"_16":9357,"_18":9358,"_20":9359,"_22":9360,"_23":9361,"_29":9367,"_31":9368},"mfem.mesh.getBoundaryNormals","mfem.mesh.getBoundaryNormals(mesh, bdrAttribute?)","Computes unit normal vectors for all boundary elements (or a subset).\r","Computes unit normal vectors for all boundary elements (or a subset).\r\n\r\nThis is a convenience function that calls for each\r\nboundary element and collects the results. The normals are computed at the\r\ncentroid of each boundary element.",[9362,9364],{"_16":2365,"_22":9363,"_28":6},"- The mesh to compute boundary normals for",{"_16":9365,"_22":9366,"_28":11},"bdrAttribute","- Optional: If provided, only compute normals for boundary\r\n elements with this attribute. If undefined, compute for all.","Map",[],{"_16":9370,"_18":9371,"_20":9372,"_22":9373,"_23":9374,"_29":137,"_31":9376},"mfem.mesh.getBoundaryNormalsFlat","mfem.mesh.getBoundaryNormalsFlat(mesh)","Computes unit normal vectors for all boundary elements as a flat array.\r","Computes unit normal vectors for all boundary elements as a flat array.\r\n\r\nThis is more efficient than when you need normals\r\nfor all boundary elements in a contiguous array format.",[9375],{"_16":2365,"_22":9363,"_28":6},[],{"_16":9378,"_18":9379,"_20":9380,"_22":9381,"_23":9382,"_29":954,"_31":9391},"mfem.mesh.getSurfaceNormal","mfem.mesh.getSurfaceNormal(mesh, bdrIndex, refPoint?)","Computes the unit outward normal vector at a point on a boundary element.\r","Computes the unit outward normal vector at a point on a boundary element.\r\n\r\nFor a 2D mesh (spaceDim=2, dim=1 on boundary):\r\n- The tangent is the Jacobian column\r\n- The normal is perpendicular (rotated 90 degrees)\r\n\r\nFor a 3D surface (spaceDim=3, dim=2 on boundary):\r\n- The two tangent vectors are the Jacobian columns\r\n- The normal is their cross product\r\n\r\nNote: The \"outward\" direction depends on the mesh orientation. MFEM typically\r\norients boundary elements so that the computed normal points outward.",[9383,9385,9388],{"_16":2365,"_22":9384,"_28":6},"- The mesh containing the boundary element",{"_16":9386,"_22":9387,"_28":6},"bdrIndex","- Zero-based boundary element index",{"_16":9389,"_22":9390,"_28":11},"refPoint","- Optional reference coordinates on the boundary element.\r\n If not provided, uses the element centroid.",[],{"_16":9393,"_18":9394,"_20":9395,"_22":9396,"_23":9397,"_29":125,"_31":9404},"mfem.mesh.getSurfaceTangents","mfem.mesh.getSurfaceTangents(mesh, bdrIndex, refPoint?, normalize?)","Gets the tangent vectors at a point on a boundary element.\r","Gets the tangent vectors at a point on a boundary element.\r\n\r\nThe tangent vectors are extracted directly from the Jacobian matrix columns.\r\nFor a 1D boundary element (edge), returns 1 tangent vector.\r\nFor a 2D boundary element (face), returns 2 tangent vectors.\r\n\r\nThe tangent vectors are NOT normalized - they represent the actual\r\ndifferential change in physical coordinates per unit change in reference\r\ncoordinates. Use this for computing surface metrics, arc lengths, or areas.",[9398,9399,9400,9401],{"_16":2365,"_22":9384,"_28":6},{"_16":9386,"_22":9387,"_28":6},{"_16":9389,"_22":9390,"_28":11},{"_16":9402,"_22":9403,"_28":11},"normalize","- If true, normalize the tangent vectors to unit length.\r\n Default is false.",[],{"_16":9406,"_18":9407,"_20":9408,"_22":9409,"_23":9410,"_29":8234,"_31":9413},"mfem.mesh.toBinary","mfem.mesh.toBinary(mesh)","Exports a mesh to a base64-encoded binary string.\r","Exports a mesh to a base64-encoded binary string.\r\n\r\nThis provides a compact representation of the mesh suitable for\r\nstorage in JSON, localStorage, or transmission. The mesh is first\r\nserialized to MFEM format and then base64-encoded.",[9411],{"_16":2365,"_22":9412,"_28":6},"- The mesh to export",[],{"_16":9415,"_18":9416,"_20":9417,"_22":9418,"_23":9419,"_29":8234,"_31":9421},"mfem.mesh.toGmsh","mfem.mesh.toGmsh(mesh)","Exports a mesh to Gmsh MSH 2.2 format string.\r","Exports a mesh to Gmsh MSH 2.2 format string.\r\n\r\nGenerates a string representation of the mesh in Gmsh MSH format,\r\nwhich can be used with Gmsh or other tools that support this format.\r\n\r\n**Note:** This is a simplified implementation that exports node coordinates\r\nand basic element information. Full element connectivity is not yet supported.\r\nFor complete mesh export, prefer or .",[9420],{"_16":2365,"_22":9412,"_28":6},[],{"_16":9423,"_18":9424,"_20":9425,"_22":9426,"_23":9427,"_29":8234,"_31":9429},"mfem.mesh.toMFEM","mfem.mesh.toMFEM(mesh)","Exports a mesh to MFEM native format string.\r","Exports a mesh to MFEM native format string.\r\n\r\nGenerates a string representation of the mesh in MFEM's native format,\r\nwhich can be saved to a file or used with other MFEM tools. This format\r\npreserves all mesh information including high-order geometry nodes.",[9428],{"_16":2365,"_22":9412,"_28":6},[],{"_16":9431,"_18":9432,"_20":9433,"_22":9434,"_23":9435,"_29":8234,"_31":9437},"mfem.mesh.toNetgen","mfem.mesh.toNetgen(mesh)","Exports a mesh to Netgen/TrueGrid format string.\r","Exports a mesh to Netgen/TrueGrid format string.\r\n\r\nUses MFEM's PrintXG() method which outputs a Netgen-compatible format.\r\nThis format can be imported by Netgen and related tools.",[9436],{"_16":2365,"_22":9412,"_28":6},[],{"_16":9439,"_18":9440,"_20":9441,"_22":9442,"_23":9443,"_29":8234,"_31":9446},"mfem.mesh.toParaView","mfem.mesh.toParaView(mesh, options?)","Exports a mesh to ParaView VTU (VTK XML Unstructured Grid) format string.\r","Exports a mesh to ParaView VTU (VTK XML Unstructured Grid) format string.\r\n\r\nVTU is an XML-based format that can be directly loaded by ParaView\r\nand other VTK-compatible visualization tools. It supports high-order\r\nelement visualization through refinement.",[9444,9445],{"_16":2365,"_22":9412,"_28":6},{"_16":6924,"_22":8253,"_28":11},[],{"_16":9448,"_18":9449,"_20":9450,"_22":9451,"_23":9452,"_29":8234,"_31":9454},"mfem.mesh.toVTK","mfem.mesh.toVTK(mesh)","Exports a mesh to VTK legacy format string.\r","Exports a mesh to VTK legacy format string.\r\n\r\nGenerates a string representation of the mesh in VTK legacy format (.vtk),\r\nwhich can be visualized in ParaView, VisIt, or other VTK-compatible tools.",[9453],{"_16":2365,"_22":9412,"_28":6},[],{"_16":9456,"_18":9457,"_20":9458,"_22":9459,"_23":9460,"_29":30,"_31":9465},"mfem.mesh.transform","mfem.mesh.transform(mesh, fn)","Transforms all mesh vertex coordinates using a custom function.\r","Transforms all mesh vertex coordinates using a custom function.\r\n\r\nThis function applies an arbitrary coordinate transformation to every vertex\r\nin the mesh. It's useful for creating curved domains, deforming meshes, or\r\napplying custom mappings.\r\n\r\nThe transformation function receives the current coordinates as an array\r\nand must return an array of the same length with the new coordinates.",[9461,9463],{"_16":2365,"_22":9462,"_28":6},"- The mesh to transform (modified in place)",{"_16":7042,"_22":9464,"_28":6},"- Transformation function that maps old coordinates to new coordinates",[],{"_16":9467,"_18":9468,"_20":9469,"_22":9470,"_23":9471,"_29":30,"_31":9477},"mfem.mesh.translate","mfem.mesh.translate(mesh, offset)","Translates a mesh by an offset vector.\r","Translates a mesh by an offset vector.\r\n\r\nAdds the offset to all vertex coordinates, effectively moving the entire\r\nmesh in space without changing its shape or size.",[9472,9474],{"_16":2365,"_22":9473,"_28":6},"- The mesh to translate (modified in place)",{"_16":9475,"_22":9476,"_28":6},"offset","- Translation vector [dx, dy] for 2D or [dx, dy, dz] for 3D",[],{"_16":9479,"_18":9480,"_20":9481,"_22":9482,"_23":9483,"_29":9484,"_31":9485},"mfem.mesh.IsoparametricTransformation.create","mfem.mesh.IsoparametricTransformation.create()","Creates a new IsoparametricTransformation.\r","Creates a new IsoparametricTransformation.\r\n\r\nThe transformation is initially unconfigured. You must call\r\n and before using it.",[],"Promise",[],{"_16":9487,"_18":9488,"_20":9489,"_22":9490,"_23":9491,"_29":6941,"_31":9492},"mfem.mesh.Mesh.create","mfem.mesh.Mesh.create()","Creates an empty mesh.\r","Creates an empty mesh.\r\n\r\nThe returned mesh has no elements, vertices, or boundaries. Use\r\n| loadFromString() to populate it with mesh data.",[],[],{"_16":9494,"_18":9495,"_20":9496,"_22":9497,"_23":9498,"_29":6941,"_31":9502},"mfem.mesh.Mesh.fromString","mfem.mesh.Mesh.fromString(meshData)","Loads a mesh from a string containing mesh data in MFEM format.\r","Loads a mesh from a string containing mesh data in MFEM format.\r\n\r\nSupports the MFEM mesh format (versions 1.0 and 1.1). The mesh format\r\nincludes sections for dimension, elements, boundary elements, and vertices.",[9499],{"_16":9500,"_22":9501,"_28":6},"meshData","- String containing the mesh data in MFEM format",[],{"_16":9504,"_18":9505,"_20":9506,"_22":9506,"_23":9507,"_29":30,"_31":9513},"mfem.nonlinear.mult","mfem.nonlinear.mult(solver, b, x)","Solve nonlinear system F(x) = b.",[9508,9510,9511],{"_16":7576,"_22":9509,"_28":6},"- Nonlinear solver instance (NewtonSolver or LBFGSSolver)",{"_16":983,"_22":8470,"_28":6},{"_16":1350,"_22":9512,"_28":6},"- Solution vector (modified in place, initial guess on input)",[],{"_16":9515,"_18":9516,"_20":9517,"_22":9518,"_23":9519,"_29":30,"_31":9524},"mfem.nonlinear.setHistorySize","mfem.nonlinear.setHistorySize(solver, m)","Set history size for L-BFGS solver.\r","Set history size for L-BFGS solver.\r\n\r\nThe history size determines how many gradient vectors are stored for\r\napproximating the inverse Hessian.",[9520,9522],{"_16":7576,"_22":9521,"_28":6},"- LBFGSSolver instance",{"_16":1130,"_22":9523,"_28":6},"- History size (number of vectors to store)",[],{"_16":9526,"_18":9527,"_20":9528,"_22":9529,"_23":9530,"_29":30,"_31":9536},"mfem.nonlinear.setLinearSolver","mfem.nonlinear.setLinearSolver(solver, linearSolver)","Set linear solver for Newton iterations.\r","Set linear solver for Newton iterations.\r\n\r\nThe linear solver is used to solve the Jacobian system at each Newton step.",[9531,9533],{"_16":7576,"_22":9532,"_28":6},"- Newton solver instance",{"_16":9534,"_22":9535,"_28":6},"linearSolver","- Linear solver for Jacobian systems (e.g., CGSolver, GMRESSolver)",[],{"_16":9538,"_18":9539,"_20":9540,"_22":9540,"_23":9541,"_29":30,"_31":9544},"mfem.nonlinear.setMaxIterations","mfem.nonlinear.setMaxIterations(solver, max)","Set maximum iterations for nonlinear solver.",[9542,9543],{"_16":7576,"_22":9509,"_28":6},{"_16":2688,"_22":8481,"_28":6},[],{"_16":9546,"_18":9547,"_20":9548,"_22":9548,"_23":9549,"_29":30,"_31":9554},"mfem.nonlinear.setOperator","mfem.nonlinear.setOperator(solver, oper)","Set nonlinear operator for the solver.",[9550,9551],{"_16":7576,"_22":9509,"_28":6},{"_16":9552,"_22":9553,"_28":6},"oper","- Nonlinear operator (e.g., NonlinearForm)",[],{"_16":9556,"_18":9557,"_20":9558,"_22":9558,"_23":9559,"_29":30,"_31":9563},"mfem.nonlinear.setTolerance","mfem.nonlinear.setTolerance(solver, rtol, atol?)","Set convergence tolerances for nonlinear solver.",[9560,9561,9562],{"_16":7576,"_22":9509,"_28":6},{"_16":8510,"_22":8511,"_28":6},{"_16":8513,"_22":8514,"_28":11},[],{"_16":9565,"_18":9566,"_20":9567,"_22":9568,"_23":9569,"_29":9573,"_31":9574},"mfem.nonlinear.HyperelasticIntegrator.create","mfem.nonlinear.HyperelasticIntegrator.create(modelPtr)","Creates a new hyperelastic integrator.\r","Creates a new hyperelastic integrator.\r\nNote: The integrator does NOT take ownership of the model.",[9570],{"_16":9571,"_22":9572,"_28":6},"modelPtr","Pointer to HyperelasticModel (e.g., NeoHookeanModel)","Promise",[],{"_16":9576,"_18":9577,"_20":9578,"_22":9578,"_23":9579,"_29":9583,"_31":9584},"mfem.nonlinear.LBFGSSolver.create","mfem.nonlinear.LBFGSSolver.create(historySize?)","Creates a new L-BFGS solver.",[9580],{"_16":9581,"_22":9582,"_28":11},"historySize","Number of vectors to store for history (default 10)","Promise",[],{"_16":9586,"_18":9587,"_20":9588,"_22":9588,"_23":9589,"_29":9595,"_31":9596},"mfem.nonlinear.NeoHookeanModel.create","mfem.nonlinear.NeoHookeanModel.create(mu, K)","Creates a new NeoHookean material model.",[9590,9592],{"_16":6577,"_22":9591,"_28":6},"Shear modulus (Lamé's second parameter)",{"_16":9593,"_22":9594,"_28":6},"K","Bulk 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alpha)",[10077,10078],{"_16":9994,"_22":2145,"_28":6},{"_16":1022,"_22":95,"_28":6},[],{"_16":10081,"_18":10082,"_20":10083,"_22":7586,"_23":10084,"_29":30,"_31":10088},"mfem.vector.set","mfem.vector.set(vec, i, value)","set_3",[10085,10086,10087],{"_16":9994,"_22":2145,"_28":6},{"_16":409,"_22":95,"_28":6},{"_16":457,"_22":95,"_28":6},[],{"_16":10090,"_18":10091,"_20":10092,"_22":7586,"_23":10093,"_29":30,"_31":10096},"mfem.vector.setAll","mfem.vector.setAll(vec, value)","setAll",[10094,10095],{"_16":9994,"_22":2145,"_28":6},{"_16":457,"_22":95,"_28":6},[],{"_16":10098,"_18":10099,"_20":10100,"_22":7586,"_23":10101,"_29":30,"_31":10105},"mfem.vector.setData","mfem.vector.setData(vec, data)","setData",[10102,10103],{"_16":9994,"_22":2145,"_28":6},{"_16":117,"_22":10104,"_28":6},"Float64Array | number[]",[],{"_16":10107,"_18":10108,"_20":93,"_22":7586,"_23":10109,"_29":95,"_31":10111},"mfem.vector.size","mfem.vector.size(vec)",[10110],{"_16":9994,"_22":2145,"_28":6},[],{"_16":10113,"_18":10114,"_20":10115,"_22":7586,"_23":10116,"_29":8438,"_31":10118},"mfem.vector.zeros","mfem.vector.zeros(size)","zeros_2",[10117],{"_16":93,"_22":95,"_28":6},[],{"_16":10120,"_18":10121,"_20":8434,"_22":8434,"_23":10122,"_29":8438,"_31":10124},"mfem.vector.Vector.create","mfem.vector.Vector.create(size)",[10123],{"_16":93,"_22":8437,"_28":6},[],{"_16":10126,"_18":10127,"_20":8443,"_22":8444,"_23":10128,"_29":8438,"_31":10130},"mfem.vector.Vector.fromPointer","mfem.vector.Vector.fromPointer(ptr)",[10129],{"_16":133,"_22":8447,"_28":6},[],{"_16":10132,"_18":10133,"_20":10134,"_22":10135,"_23":10136,"_29":10140,"_31":10141},"mfem.checkBoundaryDofs","mfem.checkBoundaryDofs(fespace, bdrAttrs)","Check boundary DOF extraction for specified boundary attributes.\r","Check boundary DOF extraction for specified boundary attributes.\r\n\r\nVerifies that DOFs can be correctly extracted for the given boundary attributes\r\nand validates the resulting DOF indices.",[10137,10138],{"_16":6686,"_22":6743,"_28":6},{"_16":6848,"_22":10139,"_28":6},"- Array of boundary attributes to check","Promise",[],{"_16":10143,"_18":10144,"_20":10145,"_22":10146,"_23":10147,"_29":10148,"_31":10149},"mfem.checkForLeaks","mfem.checkForLeaks()","Check for memory leaks.\r","Check for memory leaks.\r\n\r\nAnalyzes object tracking data to find undestroyed objects.",[],"LeakReport",[],{"_16":10151,"_18":10152,"_20":10153,"_22":10154,"_23":10155,"_29":10159,"_31":10160},"mfem.checkPositiveDefinite","mfem.checkPositiveDefinite(mat)","Check if a sparse matrix is positive definite.\r","Check if a sparse matrix is positive definite.\r\n\r\nPerforms diagonal check (necessary condition) and attempts to estimate\r\nthe smallest eigenvalue using power iteration.",[10156],{"_16":10157,"_22":10158,"_28":6},"mat","- The sparse matrix to check","Promise",[],{"_16":10162,"_18":10163,"_20":10164,"_22":10165,"_23":10166,"_29":10175,"_31":10176},"mfem.checkResidual","mfem.checkResidual(A, x, b, tol)","Check if a solution satisfies the residual tolerance.\r","Check if a solution satisfies the residual tolerance.\r\n\r\nComputes the relative residual ||b - Ax|| / ||b|| and checks if it's\r\nbelow the specified tolerance.",[10167,10169,10171,10173],{"_16":26,"_22":10168,"_28":6},"- The operator (SparseMatrix or BilinearForm)",{"_16":1350,"_22":10170,"_28":6},"- The solution vector",{"_16":983,"_22":10172,"_28":6},"- The right-hand side vector",{"_16":243,"_22":10174,"_28":6},"- Tolerance for the relative residual","Promise",[],{"_16":10178,"_18":10179,"_20":10180,"_22":10180,"_23":10181,"_29":10185,"_31":10186},"mfem.checkSymmetry","mfem.checkSymmetry(mat, tol?)","Check if a sparse matrix is symmetric within a given tolerance.",[10182,10183],{"_16":10157,"_22":10158,"_28":6},{"_16":243,"_22":10184,"_28":11},"- Tolerance for symmetry check (default: 1e-12)","Promise",[],{"_16":10188,"_18":10189,"_20":10190,"_22":10191,"_23":10192,"_29":10198,"_31":10199},"mfem.computeConditionNumber","mfem.computeConditionNumber(mat, maxIter?)","Estimate the condition number of a sparse matrix.\r","Estimate the condition number of a sparse matrix.\r\n\r\nUses power iteration to estimate the largest and smallest eigenvalues,\r\nthen computes their ratio.",[10193,10195],{"_16":10157,"_22":10194,"_28":6},"- The sparse matrix",{"_16":10196,"_22":10197,"_28":11},"maxIter","- Maximum iterations for power iteration (default: 100)","Promise",[],{"_16":10201,"_18":10202,"_20":10203,"_22":10203,"_23":10204,"_29":6849,"_31":10210},"mfem.computeResidual","mfem.computeResidual(A, x, b, r)","Compute the residual vector r = b - A*x.",[10205,10206,10207,10208],{"_16":26,"_22":10168,"_28":6},{"_16":1350,"_22":10170,"_28":6},{"_16":983,"_22":10172,"_28":6},{"_16":4652,"_22":10209,"_28":6},"- The output residual vector (must be pre-allocated with same size as b)",[],{"_16":10212,"_18":10213,"_20":10214,"_22":10215,"_23":10216,"_29":30,"_31":10219},"mfem.configureMFEM","mfem.configureMFEM(config)","Configure the MFEM WASM loader before initialization.\r","Configure the MFEM WASM loader before initialization.\r\nMust be called before loadMFEMModule().",[10217],{"_16":54,"_22":10218,"_28":6},"Configuration options",[],{"_16":10221,"_18":10222,"_20":10223,"_22":10223,"_23":10224,"_29":30,"_31":10225},"mfem.disableTiming","mfem.disableTiming()","Disable timing collection.",[],[],{"_16":10227,"_18":10228,"_20":10229,"_22":10230,"_23":10231,"_29":30,"_31":10232},"mfem.enableTiming","mfem.enableTiming()","Enable timing collection for MFEMWASM operations.\r","Enable timing collection for MFEMWASM operations.\r\n\r\nWhen enabled, operations can be timed using the `withTiming` helper\r\nor by manually calling `startTimer` and `stopTimer`.",[],[],{"_16":10234,"_18":10235,"_20":10236,"_22":10236,"_23":10237,"_29":10238,"_31":10239},"mfem.getMemoryUsage","mfem.getMemoryUsage()","Get current WASM memory usage.",[],"Promise",[],{"_16":10241,"_18":10242,"_20":10243,"_22":10243,"_23":10244,"_29":10245,"_31":10246},"mfem.getMFEMModule","mfem.getMFEMModule()","Get the loaded MFEM module synchronously.",[],"MFEMModule",[],{"_16":10248,"_18":10249,"_20":10250,"_22":10250,"_23":10251,"_29":10252,"_31":10253},"mfem.getObjectCount","mfem.getObjectCount()","Get the current object counts by type.",[],"ObjectCounts",[],{"_16":10255,"_18":10256,"_20":10257,"_22":10257,"_23":10258,"_29":10259,"_31":10260},"mfem.getTimingReport","mfem.getTimingReport()","Get the current timing report.",[],"TimingReport",[],{"_16":10262,"_18":10263,"_20":10264,"_22":10264,"_23":10265,"_29":69,"_31":10266},"mfem.isMFEMLoaded","mfem.isMFEMLoaded()","Check if the MFEM module has been loaded.",[],[],{"_16":10268,"_18":10269,"_20":10270,"_22":10271,"_23":10272,"_29":10273,"_31":10274},"mfem.loadMFEMModule","mfem.loadMFEMModule()","Load and initialize the MFEM WASM module.\r","Load and initialize the MFEM WASM module.\r\n\r\nThis function is idempotent - calling it multiple times returns the same\r\nmodule instance. The module is loaded lazily on first call.",[],"Promise",[],{"_16":10276,"_18":10277,"_20":10278,"_22":10279,"_23":10280,"_29":10283,"_31":10284},"mfem.loadSolution","mfem.loadSolution(data)","Loads a mesh and grid function pair from a JSON bundle string.\r","Loads a mesh and grid function pair from a JSON bundle string.\r\n\r\nThe bundle should contain both mesh and grid function in MFEM format,\r\nas created by . The grid function's FE space is\r\nautomatically reconstructed from the saved header information.",[10281],{"_16":117,"_22":10282,"_28":6},"- JSON string containing the solution bundle","Promise",[],{"_16":10286,"_18":10287,"_20":10288,"_22":10288,"_23":10289,"_29":10292,"_31":10293},"mfem.printDofInfo","mfem.printDofInfo(fespace)","Get comprehensive DOF information for a finite element space.",[10290],{"_16":6686,"_22":10291,"_28":6},"- The finite element space to inspect","Promise",[],{"_16":10295,"_18":10296,"_20":10297,"_22":10298,"_23":10299,"_29":30,"_31":10300},"mfem.resetMFEMModule","mfem.resetMFEMModule()","Reset the module state for testing purposes.\r","Reset the module state for testing purposes.\r\nAfter calling this, loadMFEMModule() will load a fresh instance.",[],[],{"_16":10302,"_18":10303,"_20":10304,"_22":10305,"_23":10306,"_29":30,"_31":10307},"mfem.resetTimers","mfem.resetTimers()","Reset all timing data.\r","Reset all timing data.\r\n\r\nClears all accumulated timing information.",[],[],{"_16":10309,"_18":10310,"_20":10311,"_22":10312,"_23":10313,"_29":8234,"_31":10320},"mfem.saveSolution","mfem.saveSolution(mesh, gf, options?)","Saves a mesh and grid function pair to a JSON bundle string.\r","Saves a mesh and grid function pair to a JSON bundle string.\r\n\r\nThe bundle contains both the mesh and grid function in MFEM format,\r\nalong with optional metadata. The grid function's FE space information\r\n(collection type, vdim, ordering) is preserved in the MFEM format header.",[10314,10316,10318],{"_16":2365,"_22":10315,"_28":6},"- The mesh to save",{"_16":6102,"_22":10317,"_28":6},"- The grid function to save",{"_16":6924,"_22":10319,"_28":11},"- Optional save options",[],{"_16":10322,"_18":10323,"_20":10324,"_22":10325,"_23":10326,"_29":10329,"_31":10330},"mfem.verifyAssembly","mfem.verifyAssembly(bf)","Verify that a bilinear form has been correctly assembled.\r","Verify that a bilinear form has been correctly assembled.\r\n\r\nChecks assembly status, matrix properties, and scans for NaN/Inf values.",[10327],{"_16":6858,"_22":10328,"_28":6},"- The bilinear form to verify","Promise",[],{"_16":10332,"_18":10333,"_20":10334,"_22":10334,"_23":10335,"_29":10339,"_31":10340},"mfem.visualizeDofs","mfem.visualizeDofs(fespace, elemIdx)","Get DOF locations for visualization/debugging of a specific element.",[10336,10337],{"_16":6686,"_22":6743,"_28":6},{"_16":7996,"_22":10338,"_28":6},"- Element index","Promise",[],{"_35":10342,"_16":10343,"_22":10344,"_39":40,"_41":10345,"_43":10346,"_45":10347},"sp-generated","Scientific Computing (SciPy)","SciPy-inspired scientific computing library with optimization, integration, linear algebra, and statistics.","🔬","sp",[10348,10364,10376,10387,10398,10410,10423,10434,10446,10457,10470,10479,10487,10498,10509,10520,10530,10545,10557,10568,10585,10597,10607,10616,10627,10639,10653,10665,10674,10682,10693,10703,10712,10722,10732,10741,10747,10755,10763,10771,10777,10784,10794,10802,10812,10820,10828,10837,10846,10853,10861,10868,10877,10888,10897,10910,10918,10926,10934,10942,10954,10963,10974,10982,10990,10998,11009,11020,11038,11050,11062,11070,11076,11083],{"_16":10349,"_18":10350,"_20":10351,"_22":10352,"_23":10353,"_29":10362,"_31":10363},"sp.integrate.quad","sp.integrate.quad(func, a, b, options?)","Compute a definite integral using adaptive quadrature.\r","Compute a definite integral using adaptive quadrature.\r\n\r\nIntegrates `func` from `a` to `b` (possibly infinite interval) using\r\nthe QUADPACK library compiled to WebAssembly.",[10354,10356,10358,10360],{"_16":6344,"_22":10355,"_28":6},"- The integrand function f(x, ...args).",{"_16":2283,"_22":10357,"_28":6},"- Lower limit of integration. Use -Infinity for -∞.",{"_16":983,"_22":10359,"_28":6},"- Upper limit of integration. Use Infinity for +∞.",{"_16":6924,"_22":10361,"_28":11},"- Integration options.","Promise",[],{"_16":10365,"_18":10366,"_20":10367,"_22":10368,"_23":10369,"_29":10374,"_31":10375},"sp.linalg.inv","sp.linalg.inv(A, options?)","Compute the inverse of a sparse matrix.\r","Compute the inverse of a sparse matrix.\r\n\r\nWarning: The inverse of a sparse matrix is typically dense!\r\nConsider using splu + solve for solving systems instead.",[10370,10372],{"_16":26,"_22":10371,"_28":6},"- Sparse square matrix (n x n)",{"_16":6924,"_22":10373,"_28":11},"- Options including output format","Promise",[],{"_16":10377,"_18":10378,"_20":10379,"_22":10380,"_23":10381,"_29":10385,"_31":10386},"sp.linalg.spilu","sp.linalg.spilu(A, options?)","Compute incomplete LU factorization for use as a preconditioner.\r","Compute incomplete LU factorization for use as a preconditioner.\r\n\r\nThe result implements LinearOperator and can be passed as the M\r\nparameter to iterative solvers (cg, gmres, bicgstab).",[10382,10383],{"_16":26,"_22":10371,"_28":6},{"_16":6924,"_22":10384,"_28":11},"- ILU options including drop tolerance","Promise",[],{"_16":10388,"_18":10389,"_20":10390,"_22":10391,"_23":10392,"_29":10396,"_31":10397},"sp.linalg.splu","sp.linalg.splu(A, options?)","Compute sparse LU decomposition of matrix A.\r","Compute sparse LU decomposition of matrix A.\r\n\r\nReturns a factorization object that can be reused for solving\r\nmultiple systems with the same matrix A.",[10393,10394],{"_16":26,"_22":10371,"_28":6},{"_16":6924,"_22":10395,"_28":11},"- Factorization options","Promise",[],{"_16":10399,"_18":10400,"_20":10401,"_22":10401,"_23":10402,"_29":10408,"_31":10409},"sp.linalg.spsolve","sp.linalg.spsolve(A, b, options?)","Solve the sparse linear system A @ x = b using SuperLU.",[10403,10404,10406],{"_16":26,"_22":10371,"_28":6},{"_16":983,"_22":10405,"_28":6},"- Right-hand side vector (length n) or matrix (n x nrhs)",{"_16":6924,"_22":10407,"_28":11},"- Solver options","Promise",[],{"_16":10411,

eigen.dense.destroy

Syntax

Description

Parameters

Returns