# F08 - Least-squares and Eigenvalue Problems (LAPACK)

 Chapter Introduction F08AEF (SGEQRF/DGEQRF) QR factorization of real general rectangular matrix F08AFF (SORGQR/DORGQR) Form all or part of orthogonal Q from QR factorization determined by F08AEF or F08BEF F08AGF (SORMQR/DORMQR) Apply orthogonal transformation determined by F08AEF or F08BEF F08AHF (SGELQF/DGELQF) LQ factorization of real general rectangular matrix F08AJF (SORGLQ/DORGLQ) Form all or part of orthogonal Q from LQ factorization determined by F08AHF F08AKF (SORMLQ/DORMLQ) Apply orthogonal transformation determined by F08AHF F08ASF (CGEQRF/ZGEQRF) QR factorization of complex general rectangular matrix F08ATF (CUNGQR/ZUNGQR) Form all or part of unitary Q from QR factorization determined by F08ASF or F08BSF F08AUF (CUNMQR/ZUNMQR) Apply unitary transformation determined by F08ASF or F08BSF F08AVF (CGELQF/ZGELQF) LQ factorization of complex general rectangular matrix F08AWF (CUNGLQ/ZUNGLQ) Form all or part of unitary Q from LQ factorization determined by F08AVF F08AXF (CUNMLQ/ZUNMLQ) Apply unitary transformation determined by F08AVF F08BEF (SGEQPF/DGEQPF) QR factorization of real general rectangular matrix with column pivoting F08BSF (CGEQPF/ZGEQPF) QR factorization of complex general rectangular matrix with column pivoting F08FCF (SSYEVD/DSYEVD) All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer F08FEF (SSYTRD/DSYTRD) Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form F08FFF (SORGTR/DORGTR) Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF F08FGF (SORMTR/DORMTR) Apply orthogonal transformation determined by F08FEF F08FQF (CHEEVD/ZHEEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer F08FSF (CHETRD/ZHETRD) Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form F08FTF (CUNGTR/ZUNGTR) Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF F08FUF (CUNMTR/ZUNMTR) Apply unitary transformation matrix determined by F08FSF F08GCF (SSPEVD/DSPEVD) All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer F08GEF (SSPTRD/DSPTRD) Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage F08GFF (SOPGTR/DOPGTR) Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF F08GGF (SOPMTR/DOPMTR) Apply orthogonal transformation determined by F08GEF F08GQF (CHPEVD/ZHPEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer F08GSF (CHPTRD/ZHPTRD) Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage F08GTF (CUPGTR/ZUPGTR) Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF F08GUF (CUPMTR/ZUPMTR) Apply unitary transformation matrix determined by F08GSF F08HCF (SSBEVD/DSBEVD) All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer F08HEF (SSBTRD/DSBTRD) Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form F08HQF (CHBEVD/ZHBEVD) All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer F08HSF (CHBTRD/ZHBTRD) Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form F08JCF (SSTEVD/DSTEVD) All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer F08JEF (SSTEQR/DSTEQR) All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR F08JFF (SSTERF/DSTERF) All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR F08JGF (SPTEQR/DPTEQR) All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix F08JJF (SSTEBZ/DSTEBZ) Selected eigenvalues of real symmetric tridiagonal matrix by bisection F08JKF (SSTEIN/DSTEIN) Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array F08JSF (CSTEQR/ZSTEQR) All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR F08JUF (CPTEQR/ZPTEQR) All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix F08JXF (CSTEIN/ZSTEIN) Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array F08KEF (SGEBRD/DGEBRD) Orthogonal reduction of real general rectangular matrix to bidiagonal form F08KFF (SORGBR/DORGBR) Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF F08KGF (SORMBR/DORMBR) Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF F08KSF (CGEBRD/ZGEBRD) Unitary reduction of complex general rectangular matrix to bidiagonal form F08KTF (CUNGBR/ZUNGBR) Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF F08KUF (CUNMBR/ZUNMBR) Apply unitary transformations from reduction to bidiagonal form determined by F08KSF F08LEF (SGBBRD/DGBBRD) Reduction of real rectangular band matrix to upper bidiagonal form F08LSF (CGBBRD/ZGBBRD) Reduction of complex rectangular band matrix to upper bidiagonal form F08MEF (SBDSQR/DBDSQR) SVD of real bidiagonal matrix reduced from real general matrix F08MSF (CBDSQR/ZBDSQR) SVD of real bidiagonal matrix reduced from complex general matrix F08NEF (SGEHRD/DGEHRD) Orthogonal reduction of real general matrix to upper Hessenberg form F08NFF (SORGHR/DORGHR) Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF F08NGF (SORMHR/DORMHR) Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF F08NHF (SGEBAL/DGEBAL) Balance real general matrix F08NJF (SGEBAK/DGEBAK) Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF F08NSF (CGEHRD/ZGEHRD) Unitary reduction of complex general matrix to upper Hessenberg form F08NTF (CUNGHR/ZUNGHR) Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF F08NUF (CUNMHR/ZUNMHR) Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF F08NVF (CGEBAL/ZGEBAL) Balance complex general matrix F08NWF (CGEBAK/ZGEBAK) Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF F08PEF (SHSEQR/DHSEQR) Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix F08PKF (SHSEIN/DHSEIN) Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration F08PSF (CHSEQR/ZHSEQR) Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix F08PXF (CHSEIN/ZHSEIN) Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration F08QFF (STREXC/DTREXC) Reorder Schur factorization of real matrix using orthogonal similarity transformation F08QGF (STRSEN/DTRSEN) Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities F08QHF (STRSYL/DTRSYL) Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes F08QKF (STREVC/DTREVC) Left and right eigenvectors of real upper quasi-triangular matrix F08QLF (STRSNA/DTRSNA) Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix F08QTF (CTREXC/ZTREXC) Reorder Schur factorization of complex matrix using unitary similarity transformation F08QUF (CTRSEN/ZTRSEN) Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities F08QVF (CTRSYL/ZTRSYL) Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes F08QXF (CTREVC/ZTREVC) Left and right eigenvectors of complex upper triangular matrix F08QYF (CTRSNA/ZTRSNA) Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix F08SEF (SSYGST/DSYGST) Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = lamda Bx, ABx = lamda x or BAx = lamda x, B factorized by F07FDF F08SSF (CHEGST/ZHEGST) Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = lamda Bx, ABx = lamda x or BAx = lamda x, B factorized by F07FRF F08TEF (SSPGST/DSPGST) Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = lamda Bx, ABx = lamda x or BAx = lamda x, packed storage, B factorized by F07GDF F08TSF (CHPGST/ZHPGST) Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = lamda Bx, ABx = lamda x or BAx = lamda x, packed storage, B factorized by F07GRF F08UEF (SSBGST/DSBGST) Reduction of real symmetric-definite banded generalized eigenproblem Ax = lamda Bx to standard form Cy = lamda y, such that C has the same bandwidth as A F08UFF (SPBSTF/DPBSTF) Computes a split Cholesky factorization of real symmetric positive-definite band matrix A F08USF (CHBGST/ZHBGST) Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = lamda Bx to standard form Cy = lamda y, such that C has the same bandwidth as A F08UTF (CPBSTF/ZPBSTF) Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A

© The Numerical Algorithms Group Ltd, Oxford UK. 1999