| Routine Name |
Mark of Introduction |
Purpose |
| f08aec Example Text Example Data |
7 | nag_dgeqrf QR factorization of real general rectangular matrix |
| f08afc Example Text Example Data |
7 | nag_dorgqr Form all or part of orthogonal Q from QR factorization determined by nag_dgeqrf (f08aec) or nag_dgeqpf (f08bec) |
| f08agc | 7 | nag_dormqr Apply orthogonal transformation determined by nag_dgeqrf (f08aec) or nag_dgeqpf (f08bec) |
| f08ahc Example Text Example Data |
7 | nag_dgelqf LQ factorization of real general rectangular matrix |
| f08ajc Example Text Example Data |
7 | nag_dorglq Form all or part of orthogonal Q from LQ factorization determined by nag_dgelqf (f08ahc) |
| f08akc | 7 | nag_dormlq Apply orthogonal transformation determined by nag_dgelqf (f08ahc) |
| f08asc Example Text Example Data |
7 | nag_zgeqrf QR factorization of complex general rectangular matrix |
| f08atc Example Text Example Data |
7 | nag_zungqr Form all or part of unitary Q from QR factorization determined by nag_zgeqrf (f08asc) or nag_zgeqpf (f08bsc) |
| f08auc | 7 | nag_zunmqr Apply unitary transformation determined by nag_zgeqrf (f08asc) or nag_zgeqpf (f08bsc) |
| f08avc Example Text Example Data |
7 | nag_zgelqf LQ factorization of complex general rectangular matrix |
| f08awc Example Text Example Data |
7 | nag_zunglq Form all or part of unitary Q from LQ factorization determined by nag_zgelqf (f08avc) |
| f08axc | 7 | nag_zunmlq Apply unitary transformation determined by nag_zgelqf (f08avc) |
| f08bec Example Text Example Data |
7 | nag_dgeqpf QR factorization of real general rectangular matrix with column pivoting |
| f08bsc Example Text Example Data |
7 | nag_zgeqpf QR factorization of complex general rectangular matrix with column pivoting |
| f08fcc Example Text Example Data |
7 | nag_dsyevd All eigenvalues and optionally all eigenvectors of real symmetric matrix (divide-and-conquer) |
| f08fec Example Text Example Data |
7 | nag_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| f08ffc Example Text Example Data |
7 | nag_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsytrd (f08fec) |
| f08fgc Example Text Example Data |
7 | nag_dormtr Apply orthogonal transformation determined by nag_dsytrd (f08fec) |
| f08fqc Example Text Example Data |
7 | nag_zheevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| f08fsc Example Text Example Data |
7 | nag_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| f08ftc Example Text Example Data |
7 | nag_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhetrd (f08fsc) |
| f08fuc Example Text Example Data |
7 | nag_zunmtr Apply unitary transformation matrix determined by nag_zhetrd (f08fsc) |
| f08gcc Example Text Example Data |
7 | nag_dspevd All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) |
| f08gec Example Text Example Data |
7 | nag_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| f08gfc Example Text Example Data |
7 | nag_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsptrd (f08gec) |
| f08ggc Example Text Example Data |
7 | nag_dopmtr Apply orthogonal transformation determined by nag_dsptrd (f08gec) |
| f08gqc Example Text Example Data |
7 | nag_zhpevd All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer) |
| f08gsc Example Text Example Data |
7 | nag_zhptrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
| f08gtc Example Text Example Data |
7 | nag_zupgtr Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhptrd (f08gsc) |
| f08guc Example Text Example Data |
7 | nag_zupmtr Apply unitary transformation matrix determined by nag_zhptrd (f08gsc) |
| f08hcc Example Text Example Data |
7 | nag_dsbevd All eigenvalues and optionally all eigenvectors of real symmetric band matrix (divide-and-conquer) |
| f08hec Example Text Example Data |
7 | nag_dsbtrd Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| f08hqc Example Text Example Data |
7 | nag_zhbevd All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |
| f08hsc Example Text Example Data |
7 | nag_zhbtrd Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| f08jcc Example Text Example Data |
7 | nag_dstevd All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |
| f08jec Example Text Example Data |
7 | nag_dsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR |
| f08jfc Example Text Example Data |
7 | nag_dsterf All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR |
| f08jgc Example Text Example Data |
7 | nag_dpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix |
| f08jjc | 7 | nag_dstebz Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| f08jkc | 7 | nag_dstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| f08jsc | 7 | nag_zsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR |
| f08juc Example Text Example Data |
7 | nag_zpteqr All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix |
| f08jxc | 7 | nag_zstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| f08kec Example Text Example Data |
7 | nag_dgebrd Orthogonal reduction of real general rectangular matrix to bidiagonal form |
| f08kfc Example Text Example Data |
7 | nag_dorgbr Generate orthogonal transformation matrices from reduction to bidiagonal form determined by nag_dgebrd (f08kec) |
| f08kgc Example Text Example Data |
7 | nag_dormbr Apply orthogonal transformations from reduction to bidiagonal form determined by nag_dgebrd (f08kec) |
| f08ksc Example Text Example Data |
7 | nag_zgebrd Unitary reduction of complex general rectangular matrix to bidiagonal form |
| f08ktc Example Text Example Data |
7 | nag_zungbr Generate unitary transformation matrices from reduction to bidiagonal form determined by nag_zgebrd (f08ksc) |
| f08kuc Example Text Example Data |
7 | nag_zunmbr Apply unitary transformations from reduction to bidiagonal form determined by nag_zgebrd (f08ksc) |
| f08lec Example Text Example Data |
7 | nag_dgbbrd Reduction of real rectangular band matrix to upper bidiagonal form |
| f08lsc Example Text Example Data |
7 | nag_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |
| f08mec Example Text Example Data |
7 | nag_dbdsqr SVD of real bidiagonal matrix reduced from real general matrix |
| f08msc | 7 | nag_zbdsqr SVD of real bidiagonal matrix reduced from complex general matrix |
| f08nec Example Text Example Data |
7 | nag_dgehrd Orthogonal reduction of real general matrix to upper Hessenberg form |
| f08nfc Example Text Example Data |
7 | nag_dorghr Generate orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec) |
| f08ngc Example Text Example Data |
7 | nag_dormhr Apply orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec) |
| f08nhc Example Text Example Data |
7 | nag_dgebal Balance real general matrix |
| f08njc | 7 | nag_dgebak Transform eigenvectors of real balanced matrix to those of original matrix supplied to nag_dgebal (f08nhc) |
| f08nsc Example Text Example Data |
7 | nag_zgehrd Unitary reduction of complex general matrix to upper Hessenberg form |
| f08ntc Example Text Example Data |
7 | nag_zunghr Generate unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc) |
| f08nuc Example Text Example Data |
7 | nag_zunmhr Apply unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc) |
| f08nvc Example Text Example Data |
7 | nag_zgebal Balance complex general matrix |
| f08nwc | 7 | nag_zgebak Transform eigenvectors of complex balanced matrix to those of original matrix supplied to nag_zgebal (f08nvc) |
| f08pec Example Text Example Data |
7 | nag_dhseqr Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| f08pkc | 7 | nag_dhsein Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| f08psc Example Text Example Data |
7 | nag_zhseqr Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| f08pxc | 7 | nag_zhsein Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| f08qfc Example Text Example Data |
7 | nag_dtrexc Reorder Schur factorization of real matrix using orthogonal similarity transformation |
| f08qgc Example Text Example Data |
7 | nag_dtrsen Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| f08qhc Example Text Example Data |
7 | nag_dtrsyl Solve real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes |
| f08qkc | 7 | nag_dtrevc Left and right eigenvectors of real upper quasi-triangular matrix |
| f08qlc Example Text Example Data |
7 | nag_dtrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| f08qtc Example Text Example Data |
7 | nag_ztrexc Reorder Schur factorization of complex matrix using unitary similarity transformation |
| f08quc Example Text Example Data |
7 | nag_ztrsen Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| f08qvc Example Text Example Data |
7 | nag_ztrsyl Solve complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes |
| f08qxc | 7 | nag_ztrevc Left and right eigenvectors of complex upper triangular matrix |
| f08qyc Example Text Example Data |
7 | nag_ztrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| f08sec Example Text Example Data |
7 | nag_dsygst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_dpotrf (f07fdc) |
| f08ssc Example Text Example Data |
7 | nag_zhegst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_zpotrf (f07frc) |
| f08tec Example Text Example Data |
7 | nag_dspgst Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by nag_dpptrf (f07gdc) |
| f08tsc Example Text Example Data |
7 | nag_zhpgst Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by nag_zpptrf (f07grc) |
| f08uec Example Text Example Data |
7 | nag_dsbgst Reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A |
| f08ufc | 7 | nag_dpbstf Computes a split Cholesky factorization of real symmetric positive-definite band matrix A |
| f08usc Example Text Example Data |
7 | nag_zhbgst Reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λ y, such that C has the same bandwidth as A |
| f08utc | 7 | nag_zpbstf Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A |
| f08wec | 7 | nag_dgghrd Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08whc | 7 | nag_dggbal Balance a pair of real general matrices |
| f08wjc | 7 | nag_dggbak Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to nag_dggbal (f08whc) |
| f08wsc | 7 | nag_zgghrd Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wvc | 7 | nag_zggbal Balance a pair of complex general matrices |
| f08wwc | 7 | nag_zggbak Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to nag_zggbal (f08wvc) |
| f08xec Example Text Example Data |
7 | nag_dhgeqz Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
| f08xsc Example Text Example Data |
7 | nag_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices |
| f08ykc Example Text Example Data |
7 | nag_dtgevc Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| f08yxc Example Text Example Data |
7 | nag_ztgevc Left and right eigenvectors of a pair of complex upper triangular matrices |