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 A^H is equivalent to A^T. (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 $Ax = \lambda Bx$, 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 $Ax = \lambda Bx$ 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 $Ax = \lambda Bx$.
SSBGVD	CHBGVD	Computes all eigenvalues, and optionally, the eigenvectors of a real/complex generalized symmetric-/Hermitian-definite banded eigenproblem $Ax = \lambda Bx$. 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 $Ax = \lambda Bx$.
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 $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$, 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, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$, 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, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$, 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, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$, 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 $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$, 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, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$.
SSYGVD	CHEGVD	Computes all eigenvalues, and optionally, the eigenvectors of a generalized symmetric/Hermitian definite generalized eigenproblem, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$. 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, $Ax = \lambda Bx$, $ABx=\lambda x$, or $BAx=\lambda x$.
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 $AX \pm XB=C$ 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).