Chapter F08

Least-squares and Eigenvalue Problems (LAPACK)

Chapter Introduction
F08AEF	QR factorization of real general rectangular matrix
F08AFF	Form all or part of orthogonal Q from QR factorization determined by F08AEF or F08BEF
F08AGF	Apply orthogonal transformation determined by F08AEF or F08BEF
F08AHF	LQ factorization of real general rectangular matrix
F08AJF	Form all or part of orthogonal Q from LQ factorization determined by F08AHF
F08AKF	Apply orthogonal transformation determined by F08AHF
F08ASF	QR factorization of complex general rectangular matrix
F08ATF	Form all or part of unitary Q from QR factorization determined by F08ASF or F08BSF
F08AUF	Apply unitary transformation determined by F08ASF or F08BSF
F08AVF	LQ factorization of complex general rectangular matrix
F08AWF	Form all or part of unitary Q from LQ factorization determined by F08AVF
F08AXF	Apply unitary transformation determined by F08AVF
F08BEF	QR factorization of real general rectangular matrix with column pivoting
F08BSF	QR factorization of complex general rectangular matrix with column pivoting
F08FCF	All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
F08FEF	Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF	Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF
F08FGF	Apply orthogonal transformation determined by F08FEF
F08FQF	All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
F08FSF	Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF	Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF
F08FUF	Apply unitary transformation matrix determined by F08FSF
F08GCF	All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
F08GEF	Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF	Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF
F08GGF	Apply orthogonal transformation determined by F08GEF
F08GQF	All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
F08GSF	Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF	Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF
F08GUF	Apply unitary transformation matrix determined by F08GSF
F08HCF	All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
F08HEF	Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HQF	All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
F08HSF	Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JCF	All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
F08JEF	All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
F08JFF	All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
F08JGF	All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JJF	Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF	Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JSF	All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
F08JUF	All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JXF	Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KEF	Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF	Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF
F08KGF	Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF
F08KSF	Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF	Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF
F08KUF	Apply unitary transformations from reduction to bidiagonal form determined by F08KSF
F08LEF	Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF	Reduction of complex rectangular band matrix to upper bidiagonal form
F08MEF	SVD of real bidiagonal matrix reduced from real general matrix
F08MSF	SVD of real bidiagonal matrix reduced from complex general matrix
F08NEF	Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF	Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
F08NGF	Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF
F08NHF	Balance real general matrix
F08NJF	Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF
F08NSF	Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF	Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
F08NUF	Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF
F08NVF	Balance complex general matrix
F08NWF	Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF
F08PEF	Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF	Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PSF	Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF	Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF	Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF	Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF	Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
F08QKF	Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF	Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF	Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF	Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF	Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
F08QXF	Left and right eigenvectors of complex upper triangular matrix
F08QYF	Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SEF	Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FDF
F08SSF	Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FRF
F08TEF	Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GDF
F08TSF	Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = lamda x or BAx = λ x, packed storage, B factorized by F07GRF
F08UEF	Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UFF	Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08USF	Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UTF	Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F08WEF	Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF	Balance a pair of real general matrices
F08WJF	Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF
F08WSF	Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF	Balance a pair of complex general matrices
F08WWF	Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF
F08XEF	Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg matrix reduced from a pair of real general matrices
F08XSF	Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg matrix reduced from a pair of complex general matrices
F08YKF	Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YXF	Left and right eigenvectors of a pair of complex upper triangular matrices

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