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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).

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