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# Notes

1.
This index lists related pairs of real and complex routines together, for example, SBDSQR and CBDSQR.

2.
Driver routines are listed in bold type, for example SGBSV and CGBSV.

3.
Routines are listed in alphanumeric order of the real (single precision) routine name (which always begins with S-). (See subsection 2.2.3 for details of the LAPACK naming scheme.)

4.
Double precision routines are not listed here; they have names beginning with D- instead of S-, or Z- instead of C-.

5.
This index gives only a brief description of the purpose of each routine. For a precise description, consult the specifications in Part 2, where the routines appear in the same order as here.

6.
The text of the descriptions applies to both real and complex routines, except where alternative words or phrases are indicated, for example symmetric/Hermitian'', orthogonal/unitary'' or quasi-triangular/triangular''. For the real routines AH is equivalent to AT. (The same convention is used in Part 2.)

7.
In a few cases, three routines are listed together, one for real symmetric, one for complex symmetric, and one for complex Hermitian matrices (for example SSPCON, CSPCON and CHPCON).

8.
A few routines for real matrices have no complex equivalent (for example SSTEBZ).

 Routine Description real complex SBDSDC Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using a divide and conquer method. SBDSQR CBDSQR Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using the bidiagonal QR algorithm. SDISNA Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix. SGBBRD CGBBRD Reduces a general band matrix to real upper bidiagonal form by an orthogonal/unitary transformation. SGBCON CGBCON Estimates the reciprocal of the condition number of a general band matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF/CGBTRF. SGBEQU CGBEQU Computes row and column scalings to equilibrate a general band matrix and reduce its condition number. SGBRFS CGBRFS Improves the computed solution to a general banded system of linear equations AX=B, AT X=B or AH X=B, and provides forward and backward error bounds for the solution. SGBSV CGBSV Solves a general banded system of linear equations AX=B. SGBSVX CGBSVX Solves a general banded system of linear equations AX=B, AT X=B or AH X=B, and provides an estimate of the condition number and error bounds on the solution. SGBTRF CGBTRF Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges. SGBTRS CGBTRS Solves a general banded system of linear equations AX=B, AT X=B or AH X=B, using the LU factorization computed by SGBTRF/CGBTRF. SGEBAK CGEBAK Transforms eigenvectors of a balanced matrix to those of the original matrix supplied to SGEBAL/CGEBAL. SGEBAL CGEBAL Balances a general matrix in order to improve the accuracy of computed eigenvalues. SGEBRD CGEBRD Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/unitary transformation. SGECON CGECON Estimates the reciprocal of the condition number of a general matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF/CGETRF. SGEEQU CGEEQU Computes row and column scalings to equilibrate a general rectangular matrix and reduce its condition number. SGEES CGEES Computes the eigenvalues and Schur factorization of a general matrix, and orders the factorization so that selected eigenvalues are at the top left of the Schur form.

 Routine Description real complex SGEESX CGEESX Computes the eigenvalues and Schur factorization of a general matrix, orders the factorization so that selected eigenvalues are at the top left of the Schur form, and computes reciprocal condition numbers for the average of the selected eigenvalues, and for the associated right invariant subspace. SGEEV CGEEV Computes the eigenvalues and left and right eigenvectors of a general matrix. SGEEVX CGEEVX Computes the eigenvalues and left and right eigenvectors of a general matrix, with preliminary balancing of the matrix, and computes reciprocal condition numbers for the eigenvalues and right eigenvectors. SGEHRD CGEHRD Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation. SGELQF CGELQF Computes an LQ factorization of a general rectangular matrix. SGELS CGELS Computes the least squares solution to an overdetermined system of linear equations, A X=B or AH X=B, or the minimum norm solution of an underdetermined system, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A. SGELSD CGELSD Computes the minimum norm least squares solution to an over- or underdetermined system of linear equations A X=B, using the singular value decomposition of A and a divide and conquer method. SGELSS CGELSS Computes the minimum norm least squares solution to an over- or underdetermined system of linear equations A X=B, using the singular value decomposition of A. SGELSY CGELSY Computes the minimum norm least squares solution to an over- or underdetermined system of linear equations A X=B, using a complete orthogonal factorization of A via xGEQP3. SGEQLF CGEQLF Computes a QL factorization of a general rectangular matrix. SGEQP3 CGEQP3 Computes a QR factorization with column pivoting of a general rectangular matrix using Level 3 BLAS. SGEQRF CGEQRF Computes a QR factorization of a general rectangular matrix. SGERFS CGERFS Improves the computed solution to a general system of linear equations AX=B, AT X=B or AH X=B, and provides forward and backward error bounds for the solution. SGERQF CGERQF Computes an RQ factorization of a general rectangular matrix. SGESDD CGESDD Computes the singular value decomposition (SVD) of a general rectangular matrix using a divide and conquer method. SGESV CGESV Solves a general system of linear equations AX=B.

 Routine Description real complex SGESVD CGESVD Computes the singular value decomposition (SVD) of a general rectangular matrix. SGESVX CGESVX Solves a general system of linear equations AX=B, AT X=B or AH X=B, and provides an estimate of the condition number and error bounds on the solution. SGETRF CGETRF Computes an LU factorization of a general matrix, using partial pivoting with row interchanges. SGETRI CGETRI Computes the inverse of a general matrix, using the LU factorization computed by SGETRF/CGETRF. SGETRS CGETRS Solves a general system of linear equations AX=B, AT X=B or AH X=B, using the LU factorization computed by SGETRF/CGETRF. SGGBAK CGGBAK Forms the right or left eigenvectors of a real generalized eigenvalue problem , by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL/CGGBAL. SGGBAL CGGBAL Balances a pair of general matrices to improve the accuracy of computed eigenvalues and/or eigenvectors. SGGES CGGES Computes the generalized eigenvalues, Schur form, and the left and/or right Schur vectors for a pair of nonsymmetric matrices. SGGESX CGGESX Computes the generalized eigenvalues, Schur form, and, optionally, the left and/or right matrices of Schur vectors. SGGEV CGGEV Computes the generalized eigenvalues and the left and/or right generalized eigenvectors for a pair of nonsymmetric matrices. SGGEVX CGGEVX Computes the generalized eigenvalues and, optionally, the left and/or right generalized eigenvectors. SGGGLM CGGGLM Solves a general Gauss-Markov linear model (GLM) problem using a generalized QR factorization. SGGHRD CGGHRD Reduces a pair of matrices to generalized upper Hessenberg form using orthogonal/unitary transformations. SGGLSE CGGLSE Solves the linear equality-constrained least squares (LSE) problem using a generalized RQ factorization. SGGQRF CGGQRF Computes a generalized QR factorization of a pair of matrices. SGGRQF CGGRQF Computes a generalized RQ factorization of a pair of matrices. SGGSVD CGGSVD Computes the generalized singular value decomposition (GSVD) of a pair of general rectangular matrices. SGGSVP CGGSVP Computes orthogonal/unitary matrices U, V, and Q as the preprocessing step for computing the generalized singular value decomposition (GSVD).
 Routine Description real complex SGTCON CGTCON Estimates the reciprocal of the condition number of a general tridiagonal matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGTTRF/CGTTRF. SGTRFS CGTRFS Improves the computed solution to a general tridiagonal system of linear equations AX=B, AT X=B or AH X=B, and provides forward and backward error bounds for the solution. SGTSV CGTSV Solves a general tridiagonal system of linear equations AX=B. SGTSVX CGTSVX Solves a general tridiagonal system of linear equations AX=B, AT X=B or AH X=B, and provides an estimate of the condition number and error bounds on the solution. SGTTRF CGTTRF Computes an LU factorization of a general tridiagonal matrix, using partial pivoting with row interchanges. SGTTRS CGTTRS Solves a general tridiagonal system of linear equations AX=B, AT X=B or AH X=B, using the LU factorization computed by SGTTRF/CGTTRF. SHGEQZ CHGEQZ Implements a single-/double-shift version of the QZ method for finding the generalized eigenvalues of a pair of general matrices, which can simultaneously be reduced to generalized Schur form using orthogonal/unitary transformations. SHSEIN CHSEIN Computes specified right and/or left eigenvectors of an upper Hessenberg matrix by inverse iteration. SHSEQR CHSEQR Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the multishift QR algorithm. SOPGTR CUPGTR Generates the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSPTRD/CHPTRD. SOPMTR CUPMTR Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSPTRD/CHPTRD. SORGBR CUNGBR Generates the orthogonal/unitary transformation matrices from a reduction to bidiagonal form determined by SGEBRD/CGEBRD. SORGHR CUNGHR Generates the orthogonal/unitary transformation matrix from a reduction to Hessenberg form determined by SGEHRD/CGEHRD. SORGLQ CUNGLQ Generates all or part of the orthogonal/unitary matrix Q from an LQ factorization determined by SGELQF/CGELQF. SORGQL CUNGQL Generates all or part of the orthogonal/unitary matrix Q from a QL factorization determined by SGEQLF/CGEQLF. SORGQR CUNGQR Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by SGEQRF/CGEQRF. SORGRQ CUNGRQ Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by SGERQF/CGERQF. SORGTR CUNGTR Generates the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSYTRD/CHETRD.
 Routine Description real complex SORMBR CUNMBR Multiplies a general matrix by one of the orthogonal/unitary transformation matrices from a reduction to bidiagonal form determined by SGEBRD/CGEBRD. SORMHR CUNMHR Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to Hessenberg form determined by SGEHRD/CGEHRD. SORMLQ CUNMLQ Multiplies a general matrix by the orthogonal/unitary matrix from an LQ factorization determined by SGELQF/CGELQF. SORMQL CUNMQL Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by SGEQLF/CGEQLF. SORMQR CUNMQR Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by SGEQRF/CGEQRF. SORMRQ CUNMRQ Multiplies a general matrix by the orthogonal/unitary matrix from an RQ factorization determined by SGERQF/CGERQF. SORMRZ CUNMRZ Multiplies a general matrix by the orthogonal/unitary matrix from an RZ factorization determined by STZRZF/CTZRZF. SORMTR CUNMTR Multiplies a general matrix by the orthogonal/unitary transformation matrix from a reduction to tridiagonal form determined by SSYTRD/CHETRD. SPBCON CPBCON Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite band matrix, using the Cholesky factorization computed by SPBTRF/CPBTRF. SPBEQU CPBEQU Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite band matrix and reduce its condition number. SPBRFS CPBRFS Improves the computed solution to a symmetric/Hermitian positive definite banded system of linear equations A X=B, and provides forward and backward error bounds for the solution. SPBSTF CPBSTF Computes a split Cholesky factorization of a real/complex symmetric/Hermitian positive definite band matrix. SPBSV CPBSV Solves a symmetric/Hermitian positive definite banded system of linear equations A X=B. SPBSVX CPBSVX Solves a symmetric/Hermitian positive definite banded system of linear equations A X=B, and provides an estimate of the condition number and error bounds on the solution. SPBTRF CPBTRF Computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix. SPBTRS CPBTRS Solves a symmetric/Hermitian positive definite banded system of linear equations A X=B, using the Cholesky factorization computed by SPBTRF/CPBTRF. SPOCON CPOCON Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by SPOTRF/CPOTRF.
 Routine Description real complex SPOEQU CPOEQU Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix and reduce its condition number. SPORFS CPORFS Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations A X=B, and provides forward and backward error bounds for the solution. SPOSV CPOSV Solves a symmetric/Hermitian positive definite system of linear equations A X=B. SPOSVX CPOSVX Solves a symmetric/Hermitian positive definite system of linear equations A X=B, and provides an estimate of the condition number and error bounds on the solution. SPOTRF CPOTRF Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix. SPOTRI CPOTRI Computes the inverse of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by SPOTRF/CPOTRF. SPOTRS CPOTRS Solves a symmetric/Hermitian positive definite system of linear equations A X=B, using the Cholesky factorization computed by SPOTRF/CPOTRF. SPPCON CPPCON Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF. SPPEQU CPPEQU Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix in packed storage and reduce its condition number. SPPRFS CPPRFS Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations A X=B, where A is held in packed storage, and provides forward and backward error bounds for the solution. SPPSV CPPSV Solves a symmetric/Hermitian positive definite system of linear equations A X=B, where A is held in packed storage. SPPSVX CPPSVX Solves a symmetric/Hermitian positive definite system of linear equations A X=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution. SPPTRF CPPTRF Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix in packed storage. SPPTRI CPPTRI Computes the inverse of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF. SPPTRS CPPTRS Solves a symmetric/Hermitian positive definite system of linear equations A X=B, where A is held in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF.
 Routine Description real complex SPTCON CPTCON Computes the reciprocal of the condition number of a symmetric/Hermitian positive definite tridiagonal matrix, using the LDLH factorization computed by SPTTRF/CPTTRF. SPTEQR CPTEQR Computes all eigenvalues and eigenvectors of a real symmetric positive definite tridiagonal matrix, by computing the SVD of its bidiagonal Cholesky factor. SPTRFS CPTRFS Improves the computed solution to a symmetric/Hermitian positive definite tridiagonal system of linear equations A X=B, and provides forward and backward error bounds for the solution. SPTSV CPTSV Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations A X=B. SPTSVX CPTSVX Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations A X=B, and provides an estimate of the condition number and error bounds on the solution. SPTTRF CPTTRF Computes the LDLH factorization of a symmetric/Hermitian positive definite tridiagonal matrix. SPTTRS CPTTRS Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations, using the LDLH factorization computed by SPTTRF/CPTTRF. SSBEV CHBEV Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian band matrix. SSBEVD CHBEVD Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm. SSBEVX CHBEVX Computes selected eigenvalues and eigenvectors of a symmetric/Hermitian band matrix. SSBGST CHBGST Reduces a real/complex symmetric-/Hermitian-definite banded generalized eigenproblem to standard form, where B has been factorized by SPBSTF/CPBSTF (Crawford's algorithm). SSBGV CHBGV Computes all of the eigenvalues, and optionally, the eigenvectors of a real/complex generalized symmetric-/Hermitian-definite banded eigenproblem . SSBGVD CHBGVD Computes all eigenvalues, and optionally, the eigenvectors of a real/complex generalized symmetric-/Hermitian-definite banded eigenproblem . If eigenvectors are desired, it uses a divide and conquer algorithm. SSBGVX CHBGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real/complex generalized symmetric-/Hermitian-definite banded eigenproblem . SSBTRD CHBTRD Reduces a symmetric/Hermitian band matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation.
 Routine Description real complex SSPCON CSPCON CHPCON Estimates the reciprocal of the condition number of a real symmetric/complex symmetric/complex Hermitian indefinite matrix in packed storage, using the factorization computed by SSPTRF/CSPTRF/CHPTRF. SSPEV CHPEV Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix in packed storage. SSPEVD CHPEVD Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. SSPEVX CHPEVX Computes selected eigenvalues and eigenvectors of a symmetric/Hermitian matrix in packed storage. SSPGST CHPGST Reduces a symmetric/Hermitian definite generalized eigenproblem , , or , to standard form, where A and B are held in packed storage, and B has been factorized by SPPTRF/CPPTRF. SSPGV CHPGV Computes all eigenvalues and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or , where A and B are in packed storage. SSPGVD CHPGVD Computes all eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or , where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. SSPGVX CHPGVX Computes selected eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or , where A and B are in packed storage. SSPRFS CSPRFS CHPRFS Improves the computed solution to a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, where A is held in packed storage, and provides forward and backward error bounds for the solution. SSPSV CSPSV CHPSV Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, where A is held in packed storage. SSPSVX CSPSVX CHPSVX Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution. SSPTRD CHPTRD Reduces a symmetric/Hermitian matrix in packed storage to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation.
 Routine Description real complex SSPTRF CSPTRF CHPTRF Computes the factorization of a real symmetric/complex symmetric/complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method. SSPTRI CSPTRI CHPTRI Computes the inverse of a real symmetric/complex symmetric/complex Hermitian indefinite matrix in packed storage, using the factorization computed by SSPTRF/CSPTRF/CHPTRF. SSPTRS CSPTRS CHPTRS Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, where A is held in packed storage, using the factorization computed by SSPTRF/CSPTRF/CHPTRF. SSTEBZ Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection. SSTEDC CSTEDC Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer algorithm. SSTEGR CSTEGR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representations. SSTEIN CSTEIN Computes selected eigenvectors of a real symmetric tridiagonal matrix by inverse iteration. SSTEQR CSTEQR Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm. SSTERF Computes all eigenvalues of a real symmetric tridiagonal matrix, using a root-free variant of the QL or QR algorithm. SSTEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix. SSTEVD Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm. SSTEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix using the Relatively Robust Representations. SSTEVX Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. SSYCON CSYCON CHECON Estimates the reciprocal of the condition number of a real symmetric/complex symmetric/complex Hermitian indefinite matrix, using the factorization computed by SSYTRF/CSYTRF/CHETRF. SSYEV CHEEV Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix. SSYEVD CHEEVD Computes all eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
 Routine Description real complex SSYEVR CHEEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric/Hermitian matrix using the Relatively Robust Representations. SSYEVX CHEEVX Computes selected eigenvalues and, optionally, eigenvectors of a symmetric/Hermitian matrix. SSYGST CHEGST Reduces a symmetric/Hermitian definite generalized eigenproblem , , or , to standard form, where B has been factorized by SPOTRF/CPOTRF. SSYGV CHEGV Computes all eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or . SSYGVD CHEGVD Computes all eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or . If eigenvectors are desired, it uses a divide and conquer algorithm. SSYGVX CHEGVX Computes selected eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, , , or . SSYRFS CSYRFS CHERFS Improves the computed solution to a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, and provides forward and backward error bounds for the solution. SSYSV CSYSV CHESV Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B. SSYSVX CSYSVX CHESVX Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, and provides an estimate of the condition number and error bounds on the solution. SSYTRD CHETRD Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation. SSYTRF CSYTRF CHETRF Computes the factorization of a real symmetric/complex symmetric/complex Hermitian indefinite matrix, using the diagonal pivoting method. SSYTRI CSYTRI CHETRI Computes the inverse of a real symmetric/complex symmetric/complex Hermitian indefinite matrix, using the factorization computed by SSYTRF/CSYTRF/CHETRF. SSYTRS CSYTRS CHETRS Solves a real symmetric/complex symmetric/complex Hermitian indefinite system of linear equations A X=B, using the factorization computed by SSPTRF/CSPTRF/CHPTRF. STBCON CTBCON Estimates the reciprocal of the condition number of a triangular band matrix, in either the 1-norm or the infinity-norm.

 Routine Description real complex STBRFS CTBRFS Provides forward and backward error bounds for the solution of a triangular banded system of linear equations A X=B, AT X=B or AH X=B. STBTRS CTBTRS Solves a triangular banded system of linear equations A X=B, AT X=B or AH X=B. STGEVC CTGEVC Computes some or all of the right and/or left generalized eigenvectors of a pair of upper triangular matrices. STGEXC CTGEXC Reorders the generalized real-Schur/Schur decomposition of a matrix pair (A,B) using an orthogonal/unitary equivalence transformation so that the diagonal block of (A,B) with row index IFST is moved to row ILST. STGSEN CTGSEN Reorders the generalized real-Schur/Schur decomposition of a matrix pair (A,B), computes the generalized eigenvalues of the reordered matrix pair, and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces. STGSJA CTGSJA Computes the generalized singular value decomposition (GSVD) of a pair of upper triangular (or trapezoidal) matrices, which may be obtained by the preprocessing subroutine SGGSVP/CGGSVP. STGSNA CTGSNA Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A,B) in generalized real-Schur/Schur canonical form STGSYL CTGSYL Solves the generalized Sylvester equation STPCON CTPCON Estimates the reciprocal of the condition number of a triangular matrix in packed storage, in either the 1-norm or the infinity-norm. STPRFS CTPRFS Provides forward and backward error bounds for the solution of a triangular system of linear equations A X=B, AT X=B or AH X=B, where A is held in packed storage. STPTRI CTPTRI Computes the inverse of a triangular matrix in packed storage. STPTRS CTPTRS Solves a triangular system of linear equations A X=B, AT X=B or AH X=B, where A is held in packed storage. STRCON CTRCON Estimates the reciprocal of the condition number of a triangular matrix, in either the 1-norm or the infinity-norm. STREVC CTREVC Computes some or all of the right and/or left eigenvectors of an upper quasi-triangular/triangular matrix. STREXC CTREXC Reorders the Schur factorization of a matrix by an orthogonal/unitary similarity transformation. STRRFS CTRRFS Provides forward and backward error bounds for the solution of a triangular system of linear equations A X=B, AT X=B or AH X=B.

 Routine Description real complex STRSEN CTRSEN Reorders the Schur factorization of a matrix in order to find an orthonormal basis of a right invariant subspace corresponding to selected eigenvalues, and returns reciprocal condition numbers (sensitivities) of the average of the cluster of eigenvalues and of the invariant subspace. STRSNA CTRSNA Estimates the reciprocal condition numbers (sensitivities) of selected eigenvalues and eigenvectors of an upper quasi-triangular/triangular matrix. STRSYL CTRSYL Solves the Sylvester matrix equation where A and B are upper quasi-triangular/triangular, and may be transposed. STRTRI CTRTRI Computes the inverse of a triangular matrix. STRTRS CTRTRS Solves a triangular system of linear equations A X=B, AT X=B or AH X=B. STZRZF CTZRZF Computes an RZ factorization of an upper trapezoidal matrix (blocked algorithm).

Next: Index of Auxiliary Routines Up: Index of Driver and Previous: Index of Driver and   Contents   Index
Susan Blackford
1999-10-01