Equana

Function Reference

Docs/Eigenvalue Solvers (ARPACK)

Eigenvalue Solvers (ARPACK)

ARPACK eigenvalue solvers for large sparse matrices.

ar.advanced.bucklingEigs

Compute buckling eigenvalues and modes.

ar.advanced.bucklingEigs(Kmatvec, Kgmatvec, solveShifted, n, nev, sigma, options?)

ar.advanced.criticalBucklingLoad

Compute critical buckling load and mode.

ar.advanced.criticalBucklingLoad(Kmatvec, Kgmatvec, solveShifted, n, options?)

ar.advanced.cayleyEigs

Compute eigenvalues using the Cayley transform.

ar.advanced.cayleyEigs(Amatvec, Bmatvec, solveCayleyMinus, n, nev, sigma, options?)

ar.advanced.eigsInInterval

Compute eigenvalues in an interval using Cayley transform.

ar.advanced.eigsInInterval(Amatvec, Bmatvec, createSolver, n, nev, interval, options?)

ar.complex.zeigs

Compute eigenvalues and eigenvectors of a complex matrix.

ar.complex.zeigs(matvec, n, nev, options?)

ar.complex.zeigsh

Compute eigenvalues and eigenvectors of a complex Hermitian matrix.

ar.complex.zeigsh(matvec, n, nev, options?)

ar.continuation.eigsDeflated

Compute eigenvalues with deflation against known eigenvectors.

ar.continuation.eigsDeflated(matvec, n, nev, knownEigenvectors, knownEigenvalues?, options?)

ar.continuation.eigsContinue

Continue eigenvalue computation from a previous result.

ar.continuation.eigsContinue(matvec, n, additionalNev, previousResult, options?)

ar.continuation.eignDeflated

Compute non-symmetric eigenvalues with deflation.

ar.continuation.eignDeflated(matvec, n, nev, knownEigenvectors, options?)

Compute eigenvalues and eigenvectors of a real non-symmetric matrix.

ar.core.eign(matvec, n, nev, options?)

Compute eigenvalues and eigenvectors of a real symmetric matrix.

ar.core.eigs(matvec, n, nev, options?)

Compute eigenvalues and eigenvectors of a sparse matrix.

ar.core.eigsh(matvec, n, nev, options?)

ar.core.isEigsResult

Type guard to check if a result is from the symmetric solver.

ar.core.isEigsResult(result)

ar.core.isEignResult

Type guard to check if a result is from the non-symmetric solver.

ar.core.isEignResult(result)

ar.dimred.spectralEmbedding

Compute spectral embedding (Laplacian Eigenmaps) for dimensionality reduction.

ar.dimred.spectralEmbedding(affinityMatvec, degrees, n, nComponents, options?)

ar.dimred.truncatedPCA

Compute truncated PCA via eigendecomposition of the covariance matrix.

ar.dimred.truncatedPCA(covarianceMatvec, n, nComponents, options?)

ar.dimred.truncatedPCAfromData

Compute truncated PCA directly from a data matrix via SVD.

ar.dimred.truncatedPCAfromData(dataMatvec, dataMatvecT, nSamples, nFeatures, nComponents, options?)

ar.generalized.eignNear

Find eigenvalues of a non-symmetric matrix nearest to a target value.

ar.generalized.eignNear(matvec, solveShifted, n, nev, sigma, options?)

ar.generalized.eigsNear

Find eigenvalues of a symmetric matrix nearest to a target value.

ar.generalized.eigsNear(matvec, solveShifted, n, nev, sigma, options?)

ar.generalized.geigs

Compute eigenvalues and eigenvectors of a generalized eigenvalue problem.

ar.generalized.geigs(Amatvec, Bmatvec, n, nev, options?)

ar.graph.laplacianEigs

Compute eigenvalues of the graph Laplacian for spectral clustering.

ar.graph.laplacianEigs(adjacencyMatvec, degrees, n, nev, options?)

ar.graph.pagerank

Compute PageRank scores for a directed graph.

ar.graph.pagerank(outlinksMatvec, n, options?)

ar.graph.pagerankEigs

Alternative PageRank using ARPACK eigenvalue solver.

ar.graph.pagerankEigs(outlinksMatvec, n, options?)

ar.linalg.condest

Estimate the condition number of a matrix.

ar.linalg.condest(matvec, matvecT, n, options?)

ar.linalg.nuclearNormApprox

Approximate the nuclear norm by summing the k largest singular values.

ar.linalg.nuclearNormApprox(matvec, matvecT, m, n, k, options?)

ar.linalg.spectralNorm

Compute the spectral norm (2-norm) of a matrix.

ar.linalg.spectralNorm(matvec, matvecT, m, n, options?)

ar.linalg.spectralRadius

Compute the spectral radius of a matrix.

ar.linalg.spectralRadius(matvec, n, options?)

ar.matfun.expmv

Compute y = exp(t*A) * v using Krylov subspace approximation.

ar.matfun.expmv(matvec, v, t, options?)

ar.matfun.expmvMultiple

Compute y = exp(t*A) * v for multiple time points.

ar.matfun.expmvMultiple(matvec, v, times, options?)

ar.matfun.sqrtmv

Compute y = A^(1/2) * v for symmetric positive definite A.

ar.matfun.sqrtmv(matvec, v, options?)

ar.matfun.invsqrtmv

Compute y = A^(-1/2) * v for symmetric positive definite A.

ar.matfun.invsqrtmv(matvec, v, options?)

ar.matfun.matpowv

Compute y = A^p * v for symmetric positive definite A and any real power p.

ar.matfun.matpowv(matvec, v, p, options?)

ar.operators.addMatvec

ARWasm - ARPACK WebAssembly Module

ar.operators.addMatvec(A, B, alpha?, beta?)

ar.operators.mulMatvec

Create a product operator: y = A * B * x

ar.operators.mulMatvec(A, B)

ar.operators.shiftMatvec

Create a shifted operator: y = (A - σI) * x

ar.operators.shiftMatvec(matvec, sigma)

ar.operators.scaleMatvec

Create a scaled operator: y = α * A * x

ar.operators.scaleMatvec(matvec, alpha)

ar.operators.transposeMatvec

Create a transpose operator via explicit computation.

ar.operators.transposeMatvec(matvec, m, n)

ar.operators.symmetrizeMatvec

Create a symmetrized operator: y = (A + A^T)/2 * x

ar.operators.symmetrizeMatvec(matvec, matvecT)

ar.operators.identityMatvec

Create an identity operator: y = x

ar.operators.identityMatvec(n)

ar.operators.negateMatvec

Create a negated operator: y = -A * x

ar.operators.negateMatvec(matvec)

ar.operators.powerMatvec

Create a power operator: y = A^k * x

ar.operators.powerMatvec(matvec, k)

ar.operators.blockDiagMatvec

Create a block diagonal operator from multiple sub-operators.

ar.operators.blockDiagMatvec(operators, sizes)

ar.sparse.bandedMatvec

Create a matrix-vector product function from a banded matrix.

ar.sparse.bandedMatvec(bands, offsets, n)

ar.sparse.symBandedMatvec

Create a symmetric banded matrix-vector product function.

ar.sparse.symBandedMatvec(bands, n)

ar.sparse.toeplitzBandedMatvec

Create a Toeplitz banded matrix-vector product function.

ar.sparse.toeplitzBandedMatvec(bandValues, offsets, n)

ar.sparse.cooMatvec

Create a matrix-vector product function from COO sparse matrix format.

ar.sparse.cooMatvec(rows, cols, values, shape)

ar.sparse.cooMatvecT

Create a transpose matrix-vector product function from COO format.

ar.sparse.cooMatvecT(rows, cols, values, shape)

ar.sparse.cscMatvec

Create a matrix-vector product function from CSC sparse matrix format.

ar.sparse.cscMatvec(indptr, indices, data, shape)

ar.sparse.cscMatvecT

Create a transpose matrix-vector product function from CSC format.

ar.sparse.cscMatvecT(indptr, indices, data, shape)

ar.sparse.csrMatvec

Create a matrix-vector product function from CSR sparse matrix format.

ar.sparse.csrMatvec(indptr, indices, data, shape)

ar.sparse.csrMatvecT

Create a transpose matrix-vector product function from CSR format.

ar.sparse.csrMatvecT(indptr, indices, data, shape)

ar.sparse.denseMatvec

Create a matrix-vector product function from a dense matrix.

ar.sparse.denseMatvec(matrix, m, n, rowMajor?)

ar.sparse.denseMatvecT

Create a transpose matrix-vector product function from a dense matrix.

ar.sparse.denseMatvecT(matrix, m, n, rowMajor?)

ar.sparse.diagMatvec

Create a matrix-vector product function from a diagonal matrix.

ar.sparse.diagMatvec(diagonal)

ar.sparse.diagMatvecInv

Create an inverse diagonal matrix-vector product function.

ar.sparse.diagMatvecInv(diagonal, tol?)

ar.sparse.diagMatvecSqrt

Create a sqrt-diagonal matrix-vector product function.

ar.sparse.diagMatvecSqrt(diagonal)

ar.sparse.diagMatvecInvSqrt

Create an inverse-sqrt-diagonal matrix-vector product function.

ar.sparse.diagMatvecInvSqrt(diagonal, tol?)

ar.sparse.tridiagMatvec

Create a matrix-vector product function from a tridiagonal matrix.

ar.sparse.tridiagMatvec(lower, diag, upper)

ar.sparse.symTridiagMatvec

Create a symmetric tridiagonal matrix-vector product function.

ar.sparse.symTridiagMatvec(diag, offdiag)

ar.sparse.toeplitzTridiagMatvec

Create a Toeplitz tridiagonal matrix-vector product function.

ar.sparse.toeplitzTridiagMatvec(lower, diagVal, upper, n)

Compute partial singular value decomposition of a sparse matrix.

ar.svd.svds(matvec, matvecT, m, n, k, options?)

ar.validation.verifyEigs

Verify eigenvalue/eigenvector pairs.

ar.validation.verifyEigs(matvec, eigenvalues, eigenvectors, options?)

ar.validation.verifyEign

Verify non-symmetric eigenvalue/eigenvector pairs.

ar.validation.verifyEign(matvec, eigenvaluesReal, eigenvaluesImag, eigenvectors, options?)

ar.validation.verifySvds

Verify singular value decomposition.

ar.validation.verifySvds(matvec, matvecT, U, s, Vt, options?)

ar.validation.checkSymmetry

Check if a matrix is symmetric via random probing.

ar.validation.checkSymmetry(matvec, n, nProbes?, tol?)

ar.validation.checkPositiveDefinite

Check if a matrix is positive definite.

ar.validation.checkPositiveDefinite(matvec, n, tol?)

ar.validation.checkNormalization

Check normalization of eigenvectors.

ar.validation.checkNormalization(eigenvectors, tol?)

ar.configureARPACK

configureARPACK

ar.configureARPACK(config)

Calculate default ncv value.

ar.defaultNcv(n, nev, symmetric)

ar.dnaupdWorklSize

Calculate required workl size for non-symmetric problems (dnaupd).

ar.dnaupdWorklSize(ncv)

ar.dneupdWorkevSize

Calculate required workev size for non-symmetric extraction (dneupd).

ar.dneupdWorkevSize(ncv)

ar.dsaupdWorklSize

Calculate required workl size for symmetric problems (dsaupd).

ar.dsaupdWorklSize(ncv)

ar.getARPACKModule

getARPACKModule

ar.getARPACKModule()

ar.getDnaupdMessage

Get error message for dnaupd info code.

ar.getDnaupdMessage(info)

ar.getDneupdMessage

Get error message for dneupd info code.

ar.getDneupdMessage(info)

ar.getDsaupdMessage

Get error message for dsaupd info code.

ar.getDsaupdMessage(info)

ar.getDseupdMessage

Get error message for dseupd info code.

ar.getDseupdMessage(info)

ar.getZnaupdMessage

Get error message for znaupd info code.

ar.getZnaupdMessage(info)

ar.getZneupdMessage

Get error message for zneupd info code.

ar.getZneupdMessage(info)

ar.isARPACKLoaded

ar.isARPACKLoaded()

ar.loadARPACKModule

loadARPACKModule

ar.loadARPACKModule()

ar.resetARPACKModule

resetARPACKModule

ar.resetARPACKModule()

ar.znaupdRworkSize

Calculate required rwork size for complex problems (znaupd).

ar.znaupdRworkSize(ncv)

ar.znaupdWorklSize

Calculate required workl size for complex problems (znaupd).

ar.znaupdWorklSize(ncv)

ar.zneupdWorkevSize

Calculate required workev size for complex extraction (zneupd).

ar.zneupdWorkevSize(ncv)