Sun Performance Library Routines

Sun Performance Library User's Guide

Appendix A

Sun Performance Library Routines

This appendix lists the Sun Performance Library routines by library, routine name, and function.

For a description of the function and a listing of the Fortran and C interfaces, refer to the section 3P man pages for the individual routines. For example, to display the man page for the SBDSQR routine, type man -s 3P sbdsqr. The man page routine names use lowercase letters.

For many routines, separate routines exist that operate on different data types. Rather than list each routine separately, a lowercase x is used in a routine name to denote single, double, complex, and double complex data types. For example, the routine xBDSQR is available as four routines that operate with the following data types:

SBDSQR - Single data type
BBDSQR - Double data type
CBDSQR - Complex data type
ZBDSQR - Double complex data type

If a routine name is not available for S, B, C, and Z, the x prefix will not be used and each routine name will be listed.

LAPACK Routines

TABLE A-1   LAPACK (Linear Algebra Package) Routines
Routine Function

Bidiagonal Matrix

SBDSDC or DBDSDC Computes the singular value decomposition (SVD) of a bidirectional matrix, using a divide and conquer method.

xBDSQR Computes SVD of real upper or lower bidiagonal matrix, using the bidirectional QR algorithm.

Diagonal Matrix

SDISNA or DDISNA Computes the reciprocal condition numbers for eigenvectors of real symmetric or complex Hermitian matrix.

General Band Matrix

xGBBRD Reduces real or complex general band matrix to upper bidiagonal form.

xGBCON Estimates the reciprocal of the condition number of general band matrix using LU factorization.

xGBEQU Computes row and column scalings to equilibrate a general band matrix and reduce its condition number.

xGBRFS Refines solution to general banded system of linear equations.

xGBSV Solves a general banded system of linear equations (simple driver).

xGBSVX Solves a general banded system of linear equations (expert driver).

xGBTRF LU factorization of a general band matrix using partial pivoting with row interchanges.

xGBTRS Solves a general banded system of linear equations, using the factorization computed by xGBTRF.

General Matrix (Unsymmetric or Rectangular)

xGEBAK Forms the right or left eigenvectors of a general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by xGEBAL.

xGEBAL Balances a general matrix.

xGEBRD Reduces a general matrix to upper or lower bidiagonal form by an orthogonal transformation.

xGECON Estimates the reciprocal of the condition number of a general matrix, using the factorization computed by xGETRF.

xGEEQU Computes row and column scalings intended to equilibrate a general rectangular matrix and reduce its condition number.

xGEES Computes the eigenvalues and Schur factorization of a general matrix (simple driver).

xGEESX Computes the eigenvalues and Schur factorization of a general matrix (expert driver).

xGEEV Computes the eigenvalues and left and right eigenvectors of a general matrix (simple driver).

xGEEVX Computes the eigenvalues and left and right eigenvectors of a general matrix (expert driver).

xGEGS Depreciated routine replaced by xGGES.

xGEGV Depreciated routine replaced by xGGEV.

xGEHRD Reduces a general matrix to upper Hessenberg form by an orthogonal similarity transformation.

xGELQF Computes LQ factorization of a general rectangular matrix.

xGELS Computes the least squares solution to an over-determined system of linear equations using a QR or LQ factorization of A.

xGELSD Computes the least squares solution to an over-determined system of linear equations using a divide and conquer method using a QR or LQ factorization of A.

xGELSS Computes the minimum-norm solution to a linear least squares problem by using the SVD of a general rectangular matrix (simple driver).

xGELSX Depreciated routine replaced by xSELSY.

xGELSY Computes the minimum-norm solution to a linear least squares problem using a complete orthogonal factorization.

xGEQLF Computes QL factorization of a general rectangular matrix.

xGEQP3 Computes QR factorization of general rectangular matrix using Level 3 BLAS.

xGEQPF Depreciated routine replaced by xGEQP3.

xGEQRF Computes QR factorization of a general rectangular matrix.

xGERFS Refines solution to a system of linear equations.

xGERQF Computes RQ factorization of a general rectangular matrix.

xGESDD Computes SVD of general rectangular matrix using a divide and conquer method.

xGESV Solves a general system of linear equations (simple driver).

xGESVX Solves a general system of linear equations (expert driver).

xGESVD Computes SVD of general rectangular matrix.

xGETRF Computes an LU factorization of a general rectangular matrix using partial pivoting with row interchanges.

xGETRI Computes inverse of a general matrix using the factorization computed by xGETRF.

xGETRS Solves a general system of linear equations using the factorization computed by xGETRF.

General Matrix-Generalized Problem (Pair of General Matrices)

xGGBAK Forms the right or left eigenvectors of a generalized eigenvalue problem based on the output by xGGBAL.

xGGBAL Balances a pair of general matrices for the generalized eigenvalue problem.

xGGES Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for two nonsymmetric matrices.

xGGESX Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors.

xGGEV Computes the generalized eigenvalues and the left and/or right generalized eigenvalues for two nonsymmetric matrices.

xGGEVX Computes the generalized eigenvalues and the left and/or right generalized eigenvectors.

xGGGLM Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization.

xGGHRD Reduces two matrices to generalized upper Hessenberg form using orthogonal transformations.

xGGLSE Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization.

xGGQRF Computes generalized QR factorization of two matrices.

xGGRQF Computes generalized RQ factorization of two matrices.

xGGSVD Computes the generalized singular value decomposition.

xGGSVP Computes an orthogonal or unitary matrix as a preprocessing step for calculating the generalized singular value decomposition.

General Tridiagonal Matrix

xGTCON Estimates the reciprocal of the condition number of a tridiagonal matrix, using the LU factorization as computed by xGTTRF.

xGTRFS Refines solution to a general tridiagonal system of linear equations.

xGTSV Solves a general tridiagonal system of linear equations (simple driver).

xGTSVX Solves a general tridiagonal system of linear equations (expert driver).

xGTTRF Computes an LU factorization of a general tridiagonal matrix using partial pivoting and row exchanges.

xGTTRS Solves general tridiagonal system of linear equations using the factorization computed by x.

Hermitian Band Matrix

CHBEV or ZHBEV (Replacement with newer version CHBEVD or ZHBEVD suggested) Computes all eigenvalues and eigenvectors of a Hermitian band matrix.

CHBEVD or ZHBEVD Computes all eigenvalues and eigenvectors of a Hermitian band matrix and uses a divide and conquer method to calculate eigenvectors.

CHBEVX or ZHBEVX Computes selected eigenvalues and eigenvectors of a Hermitian band matrix.

CHBGST or ZHBGST Reduces Hermitian-definite banded generalized eigenproblem to standard form.

CHBGV or ZHBGV (Replacement with newer version CHBGVD or ZHBGVD suggested) Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.

CHBGVD or ZHBGVD Computes all eigenvalues and eigenvectors of generalized Hermitian-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.

CHBGVX or ZHBGVX Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.

CHBTRD or ZHBTRD Reduces Hermitian band matrix to real symmetric tridiagonal form by using a unitary similarity transform.

Hermitian Matrix

CHECON or ZHECON Estimates the reciprocal of the condition number of a Hermitian matrix using the factorization computed by CHETRF or ZHETRF.

CHEEV or ZHEEV (Replacement with newer version CHEEVR or ZHEEVR suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix (simple driver).

CHEEVD or ZHEEVD (Replacement with newer version CHEEVR or ZHEEVR suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix and uses a divide and conquer method to calculate eigenvectors.

CHEEVR or ZHEEVR Computes selected eigenvalues and the eigenvectors of a complex Hermitian matrix.

CHEEVX or ZHEEVX Computes selected eigenvalues and eigenvectors of a Hermitian matrix (expert driver).

CHEGST or ZHEGST Reduces a Hermitian-definite generalized eigenproblem to standard form using the factorization computed by CPOTRF or ZPOTRF.

CHEGV or ZHEGV (Replacement with newer version CHEGVD or ZHEGVD suggested) Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.

CHEGVD or ZHEGVD Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.

CHEGVX or ZHEGVX Computes selected eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.

CHERFS or ZHERFS Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite.

CHESV or ZHESV Solves a complex Hermitian indefinite system of linear equations (simple driver).

CHESVX or ZHESVX Solves a complex Hermitian indefinite system of linear equations (simple driver).

CHETRD or ZHETRD Reduces a Hermitian matrix to real symmetric tridiagonal form by using a unitary similarity transformation.

CHETRF or ZHERTF Computes the factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.

CHETRI or ZHETRI Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF or ZHETRF.

CHETRS or ZHETRS Solves a complex Hermitian indefinite matrix, using the factorization computed by CHETRF or ZHETRF.

Hermitian Matrix in Packed Storage

CHPCON or ZHPCON Estimates the reciprocal of the condition number of a Hermitian indefinite matrix in packed storage using the factorization computed by CHPTRF or ZHPTRF.

CHPEV or ZHPEV (Replacement with newer version CHPEVD or ZHPEVD suggested) Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage (simple driver).

CHPEVX or ZHPEVX Computes selected eigenvalues and eigenvectors of a Hermitian matrix in packed storage (expert driver).

CHPEVD or ZHPEVD Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.

CHPGST or ZHPGST Reduces a Hermitian-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by CPPTRF or ZPPTRF.

CHPGV or ZHPGV (Replacement with newer version CHPGVD or ZHPGVD suggested) Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).

CHPGVX or ZHPGVX Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).

CHPGVD or ZHPGVD Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.

CHPRFS or ZHPRFS Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite in packed storage.

CHPSV or ZHPSV Computes the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (simple driver).

CHPSVX or ZHPSVX Uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (expert driver).

CHPTRD or ZHPTRD Reduces a complex Hermitian matrix stored in packed form to real symmetric tridiagonal form.

CHPTRF or ZHPTRF Computes the factorization of a complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method.

CHPTRI or ZHPTRI Computes the inverse of a complex Hermitian indefinite matrix in packed storage using the factorization computed by CHPTRF or ZHPTRF.

CHPTRS or ZHPTRS Solves a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF or ZHPTRF.

Upper Hessenberg Matrix

xHSEIN Computes right and/or left eigenvectors of upper Hessenberg matrix using inverse iteration.

xHSEQR Computes eigenvectors and Shur factorization of upper Hessenberg matrix using multishift QR algorithm.

Upper Hessenberg Matrix-Generalized Problem (Hessenberg and Triangular Matrix)

xHGEQZ Implements single-/double-shift version of QZ method for finding the generalized eigenvalues of the equation det(A - w(i) * B) = 0.

Real Orthogonal Matrix in Packed Storage

SOPGTR or DOPGTR Generates an orthogonal transformation matrix from a tridiagonal matrix determined by SSPTRD or DSPTRD.

SOPMTR or DOPMTR Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by SSPTRD or DSPTRD.

Real Orthogonal Matrix

SORGBR or DORGBR Generates the orthogonal transformation matrices from reduction to bidiagonal form, as determined by SGEBRD or DGEBRD.

SORGHR or DORGHR Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by SGEHRD or DGEHRD.

SORGLQ or DORGLQ Generates an orthogonal matrix Q from an LQ factorization, as returned by SGELQF or DGELQF.

SORGQL or DORGQL Generates an orthogonal matrix Q from a QL factorization, as returned by SGEQLF or DGEQLF.

SORGQR or DORGQR Generates an orthogonal matrix Q from a QR factorization, as returned by SGEQRF or DGEQRF.

SORGRQ or DORGRQ Generates orthogonal matrix Q from an RQ factorization, as returned by SGERQF or DGERQF.

SORGTR or DORGTR Generates an orthogonal matrix reduced to tridiagonal form by SSYTRD or DSYTRD.

SORMBR or DORMBR Multiplies a general matrix with the orthogonal matrix reduced to bidiagonal form, as determined by SGEBRD or DGEBRD.

SORMHR or DORMHR Multiplies a general matrix by the orthogonal matrix reduced to Hessenberg form by SGEHRD or DGEHRD.

SORMLQ or DORMLQ Multiplies a general matrix by the orthogonal matrix from an LQ factorization, as returned by SGELQF or DGELQF.

SORMQL or DORMQL Multiplies a general matrix by the orthogonal matrix from a QL factorization, as returned by SGEQLF or DGEQLF.

SORMQR or DORMQR Multiplies a general matrix by the orthogonal matrix from a QR factorization, as returned by SGEQRF or DGEQRF.

SORMR3 or DORMR3 Multiplies a general matrix by the orthogonal matrix returned by STZRZF or DTZRZF.

SORMRQ or DORMRQ Multiplies a general matrix by the orthogonal matrix from an RQ factorization returned by SGERQF or DGERQF.

SORMRZ or DORMRZ Multiplies a general matrix by the orthogonal matrix from an RZ factorization, as returned by STZRZF or DTZRZF.

SORMTR or DORMTR Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by SSYTRD or DSYTRD.

Symmetric or Hermitian Positive Definite Band Matrix

xPBCON Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite band matrix, using the Cholesky factorization returned by xPBTRF.

xPBEQU Computes equilibration scale factors for a symmetric or Hermitian positive definite band matrix.

xPBRFS Refines solution to a symmetric or Hermitian positive definite banded system of linear equations.

xPBSTF Computes a split Cholesky factorization of a real symmetric positive definite band matrix.

xPBSV Solves a symmetric or Hermitian positive definite banded system of linear equations (simple driver).

xPBSVX Solves a symmetric or Hermitian positive definite banded system of linear equations (expert driver).

xPBTRF Computes Cholesky factorization of a symmetric or Hermitian positive definite band matrix.

xPBTRS Solves symmetric positive definite banded matrix, using the Cholesky factorization computed by xPBTRF.

Symmetric or Hermitian Positive Definite Matrix

xPOCON Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite matrix, using the Cholesky factorization returned by xPOTRF.

xPOEQU Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix.

xPORFS Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix.

xPOSV Solves a symmetric or Hermitian positive definite system of linear equations (simple driver).

xPOSVX Solves a symmetric or Hermitian positive definite system of linear equations (expert driver).

xPOTRF Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix.

xPOTRI Computes the inverse of a symmetric or Hermitian positive definite matrix using the Cholesky-factorization returned by xPOTRF.

xPOTRS Solves a symmetric or Hermitian positive definite system of linear equations, using the Cholesky factorization returned by xPOTRF.

Symmetric or Hermitian Positive Definite Matrix in Packed Storage

xPPCON Reciprocal condition number of a Cholesky-factored symmetric positive definite matrix in packed storage.

xPPEQU Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix in packed storage.

xPPRFS Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix in packed storage.

xPPSV Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (simple driver).

xPPSVX Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (expert driver).

xPPTRF Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix in packed storage.

xPPTRI Computes the inverse of a symmetric or Hermitian positive definite matrix in packed storage using the Cholesky-factorization returned by xPPTRF.

xPPTRS Solves a symmetric or Hermitian positive definite system of linear equations where the coefficient matrix is in packed storage, using the Cholesky factorization returned by xPPTRF.

Symmetric or Hermitian Positive Definite Tridiagonal Matrix

xPTCON Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite tridiagonal matrix using the Cholesky factorization returned by xPTTRF.

xPTEQR Computes all eigenvectors and eigenvalues of a real symmetric or Hermitian positive definite system of linear equations.

xPTRFS Refines solution to a symmetric or Hermitian positive definite tridiagonal system of linear equations.

xPTSV Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (simple driver).

xPTSVX Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (expert driver).

xPTTRF Computes the LDL^H factorization of a symmetric or Hermitian positive definite tridiagonal matrix.

xPTTRS Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations using the LDL^H factorization returned by xPTTRF.

Real Symmetric Band Matrix

SSBEV or DSBEV (Replacement with newer version SSBEVD or DSBEVD suggested) Computes all eigenvalues and eigenvectors of a symmetric band matrix.

SSBEVD or DSBEVD Computes all eigenvalues and eigenvectors of a symmetric band matrix and uses a divide and conquer method to calculate eigenvectors.

SSBEVX or DSBEVX Computes selected eigenvalues and eigenvectors of a symmetric band matrix.

SSBGST or DSBGST Reduces symmetric-definite banded generalized eigenproblem to standard form.

SSBGV or DSBGV (Replacement with newer version SSBGVD or DSBGVD suggested) Computes all eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.

SSBGVD or DSBGVD Computes all eigenvalues and eigenvectors of generalized symmetric-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.

SSBGVX or DSBGVX Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.

SSBTRD or DSBTRD Reduces symmetric band matrix to real symmetric tridiagonal form by using an orthogonal similarity transform.

Symmetric Matrix in Packed Storage

xSPCON Estimates the reciprocal of the condition number of a symmetric packed matrix using the factorization computed by xSPTRF.

SSPEV or DSPEV (Replacement with newer version SSPEVD or DSPEVD suggested) Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage (simple driver).

SSPEVX or DSPEVX Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage (expert driver).

SSPEVD or DSPEVD Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.

SSPGST or DSPGST Reduces a real symmetric-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by SPPTRF or DPPTRF.

SSPGVD or DSPGVD Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.

SSPGV or DSPGV (Replacement with newer version SSPGVD or DSPGVD suggested) Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).

SSPGVX or DSPGVX Computes selected eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).

xSPRFS Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite in packed storage.

xSPSV Computes the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (simple driver).

xSPSVX Uses the diagonal pivoting factorization to compute the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (expert driver).

SSPTRD or DSPTRD Reduces a real symmetric matrix stored in packed form to real symmetric tridiagonal form using an orthogonal similarity transform.

xSPTRF Computes the factorization of a symmetric packed matrix using the Bunch-Kaufman diagonal pivoting method.

xSPTRI Computes the inverse of a symmetric indefinite matrix in packed storage using the factorization computed by xSPTRF.

xSPTRS Solves a system of linear equations by the symmetric matrix stored in packed format using the factorization computed by xSPTRF.

Real Symmetric Tridiagonal Matrix

SSTEBZ or DSTEBZ Computes the eigenvalues of a real symmetric tridiagonal matrix.

xSTEDC Computes all the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using a divide and conquer method.

xSTEGR Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.

xSTEIN Computes selected eigenvectors of a real symmetric tridiagonal matrix using inverse iteration.

xSTEQR Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using the implicit QL or QR algorithm.

SSTERF or DSTERF Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a root-free QL or QR algorithm variant.

SSTEV or DSTEV (Replacement with newer version SSTEVR or DSTEVR suggested) Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (simple driver).

SSTEVX or DSTEVX Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (expert driver).

SSTEVD or DSTEVD (Replacement with newer version SSTEVR or DSTEVR suggested) Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a divide and conquer method.

SSTEVR or DSTEVR Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.

xSTSV Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.

xSTTRF Computes the factorization of a symmetric tridiagonal matrix.

xSTTRS Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.

Symmetric Matrix

xSYCON Estimates the reciprocal of the condition number of a symmetric matrix using the factorization computed by SSYTRF or DSYTRF.

SSYEV or DSYEV (Replacement with newer version SSYEVR or DSYEVR suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix.

SSYEVX or DSYEVX Computes eigenvalues and eigenvectors of a symmetric matrix (expert driver).

SSYEVD or DSYEVD (Replacement with newer version SSYEVR or DSYEVR suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix and uses a divide and conquer method to calculate eigenvectors.

SSYEVR or DSYEVR Computes selected eigenvalues and eigenvectors of a symmetric tridiagonal matrix.

SSYGST or DSYGST Reduces a symmetric-definite generalized eigenproblem to standard form using the factorization computed by SPOTRF or DPOTRF.

SSYGV or DSYGV (Replacement with newer version SSYGVD or DSYGVD suggested) Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.

SSYGVX or DSYGVX Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.

SSYGVD or DSYGVD Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.

xSYRFS Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite.

xSYSV Solves a real symmetric indefinite system of linear equations (simple driver).

xSYSVX Solves a real symmetric indefinite system of linear equations (expert driver).

SSYTRD or DSYTRD Reduces a symmetric matrix to real symmetric tridiagonal form by using a orthogonal similarity transformation.

xSYTRF Computes the factorization of a real symmetric indefinite matrix using the diagonal pivoting method.

xSYTRI Computes the inverse of a symmetric indefinite matrix using the factorization computed by xSYTRF.

xSYTRS Solves a system of linear equations by the symmetric matrix using the factorization computed by xSYTRF.

Triangular Band Matrix

xTBCON Estimates the reciprocal condition number of a triangular band matrix.

xTBRFS Determines error bounds and estimates for solving a triangular banded system of linear equations.

xTBTRS Solves a triangular banded system of linear equations.

Triangular Matrix-Generalized Problem (Pair of Triangular Matrices)

xTGEVC Computes right and/or left generalized eigenvectors of two upper triangular matrices.

xTGEXC Reorders the generalized Schur decomposition of a real or complex matrix pair using an orthogonal or unitary equivalence transformation.

xTGSEN Reorders the generalized real-Schur or Schur decomposition of two matrixes and computes the generalized eigenvalues.

xTGSJA Computes the generalized SVD from two upper triangular matrices obtained from xGGSVP.

xTGSNA Estimates reciprocal condition numbers for specified eigenvalues and eigenvectors of two matrices in real-Schur or Schur canonical form.

xTGSYL Solves the generalized Sylvester equation.

Triangular Matrix in Packed Storage

xTPCON Estimates the reciprocal or the condition number of a triangular matrix in packed storage.

xTPRFS Determines error bounds and estimates for solving a triangular system of linear equations where the coefficient matrix is in packed storage.

xTPTRI Computes the inverse of a triangular matrix in packed storage.

xTPTRS Solves a triangular system of linear equations where the coefficient matrix is in packed storage.

Triangular Matrix

xTRCON Estimates the reciprocal or the condition number of a triangular matrix.

xTREVC Computes right and/or left eigenvectors of an upper triangular matrix.

xTREXC Reorders Schur factorization of matrix using an orthogonal or unitary similarity transformation.

xTRRFS Determines error bounds and estimates for triangular system of a linear equations.

xTRSEN Reorders Schur factorization of matrix to group selected cluster of eigenvalues in the leading positions on the diagonal of the upper triangular matrix T and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.

xTRSNA Estimates the reciprocal condition numbers of selected eigenvalues and eigenvectors of an upper quasi-triangular matrix.

xTRSYL Solves Sylvester matrix equation.

xTRTRI Computes the inverse of a triangular matrix.

xTRTRS Solves a triangular system of linear equations.

Trapezoidal Matrix

xTZRQF Depreciated routine replaced by routine xTZRZF.

xTZRZF Reduces a rectangular upper trapezoidal matrix to upper triangular form by means of orthogonal transformations.

Unitary Matrix

CUNGBR or ZUNGBR Generates the unitary transformation matrices from reduction to bidiagonal form, as determined by CGEBRD or ZGEBRD.

CUNGHR or ZUNGHR Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by CGEHRD or ZGEHRD.

CUNGLQ or ZUNGLQ Generates a unitary matrix Q from an LQ factorization, as returned by CGELQF or ZGELQF.

CUNGQL or ZUNGQL Generates a unitary matrix Q from a QL factorization, as returned by CGEQLF or ZGEQLF.

CUNGQR or ZUNGQR Generates a unitary matrix Q from a QR factorization, as returned by CGEQRF or ZGEQRF.

CUNGRQ or ZUNGRQ Generates a unitary matrix Q from an RQ factorization, as returned by CGERQF or ZGERQF.

CUNGTR or ZUNGTR Generates a unitary matrix reduced to tridiagonal form, by CHETRD or ZHETRD.

CUNMBR or ZUNMBR Multiplies a general matrix with the unitary transformation matrix reduced to bidiagonal form, as determined by CGEBRD or ZGEBRD.

CUNMHR or ZUNMHR Multiplies a general matrix by the unitary matrix reduced to Hessenberg form by CGEHRD or ZGEHRD.

CUNMLQ or ZUNMLQ Multiplies a general matrix by the unitary matrix from an LQ factorization, as returned by CGELQF or ZGELQF.

CUNMQL or ZUNMQL Multiplies a general matrix by the unitary matrix from a QL factorization, as returned by CGEQLF or ZGEQLF.

CUNMQR or ZUNMQR Multiplies a general matrix by the unitary matrix from a QR factorization, as returned by CGEQRF or ZGEQRF.

CUNMRQ or ZUNMRQ Multiplies a general matrix by the unitary matrix from an RQ factorization, as returned by CGERQF or ZGERQF.

CUNMRZ or ZUNMRZ Multiplies a general matrix by the unitary matrix from an RZ factorization, as returned by CTZRZF or ZTZRZF.

CUNMTR or ZUNMTR Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by CHETRD or ZHETRD.

Unitary Matrix in Packed Storage

CUPGTR or ZUPGTR Generates the unitary transformation matrix from a tridiagonal matrix determined by CHPTRD or ZHPTRD.

CUPMTR or ZUPMTR Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by CHPTRD or ZHPTRD.

BLAS1 Routines

TABLE A-2   BLAS1 (Basic Linear Algebra Subprograms, Level 1) Routines
Routine Function

SASUM, DASUM, SCASUM, DZASUM Sum of the absolute values of a vector

xAXPY Product of a scalar and vector plus a vector

xCOPY Copy a vector

SDOT, DDOT, DSDOT, SDSDOT, CDOTU, ZDOTU, DQDOTA, DQDOTI Dot product (inner product)

CDOTC, ZDOTC Dot product conjugating first vector

SNRM2, DNRM2, SCNRM2, DCNRM2, DZNRM2 Euclidean norm of a vector

xROTG Set up Givens plane rotation

xROT, CSROT, ZDROT Apply Given's plane rotation

SROTMG, DROTMG Set up modified Given's plane rotation

SROTM, DROTM Apply modified Given's rotation

ISAMAX, DAMAX, ICAMAX, IZAMAX Index of element with maximum absolute value

xSCAL, CSSCAL, ZDSCAL Scale a vector

xSWAP Swap two vectors

CVMUL, ZVMUL Compute scaled product of complex vectors

BLAS2 Routines

TABLE A-3   BLAS2 (Basic Linear Algebra Subprograms, Level 2) Routines
Routine Function

xGBMV Product of a matrix in banded storage and a vector

xGEMV Product of a general matrix and a vector

SGER, DGER, CGERC, ZGERC, CGERU, ZGERU Rank-1 update to a general matrix

CHBMV, ZHBMV Product of a Hermitian matrix in banded storage and a vector

CHEMV, ZHEMV Product of a Hermitian matrix and a vector

CHER, ZHER Rank-1 update to a Hermitian matrix

CHER2, ZHER2 Rank-2 update to a Hermitian matrix

CHPMV, ZHPMV Product of a Hermitian matrix in packed storage and a vector

CHPR, ZHPR Rank-1 update to a Hermitian matrix in packed storage

CHPR2, ZHPR2 Rank-2 update to a Hermitian matrix in packed storage

SSBMV, DSBMV Product of a symmetric matrix in banded storage and a vector

xSPMV Product of a Symmetric matrix in packed storage and a vector

SSPR, DSPR Rank-1 update to a real symmetric matrix in packed storage

SSPR2, DSPR2 Rank-2 update to a real symmetric matrix in packed storage

SSYMV, DSYMV Product of a symmetric matrix and a vector

SSYR, DSYR Rank-1 update to a real symmetric matrix

SSYR2, DSYR2 Rank-2 update to a real symmetric matrix

xTBMV Product of a triangular matrix in banded storage and a vector

xTBSV Solution to a triangular system in banded storage of linear equations

xTPMV Product of a triangular matrix in packed storage and a vector

xTPSV Solution to a triangular system of linear equations in packed storage

xTRMV Product of a triangular matrix and a vector

xTRSV Solution to a triangular system of linear equations

BLAS3 Routines

TABLE A-4   BLAS3 (Basic Linear Algebra Subprograms, Level 3) Routines
Routine Function

xGEMM Product of two general matrices

CHEMM or ZHEMM Product of a Hermitian matrix and a general matrix

CHERK or ZHERK Rank-k update of a Hermitian matrix

CHER2K or ZHER2K Rank-2k update of a Hermitian matrix

xSYMM Product of a symmetric matrix and a general matrix

xSYRK Rank-k update of a symmetric matrix

xSYR2K Rank-2k update of a symmetric matrix

xTRMM Product of a triangular matrix and a general matrix

xTRSM Solution for a triangular system of equations

Sparse BLAS Routines

TABLE A-5   Sparse BLAS Routines
Routines Function

xAXPYI Adds a scalar multiple of a sparse vector X to a full vector Y.

SBCOMM or DBCOMM Block coordinate matrix-matrix multiply.

SBDIMM or DBDIMM Block diagonal format matrix-matrix multiply.

SBDISM or DBDISM Block Diagonal format triangular solve.

SBELMM or DBELMM Block Ellpack format matrix-matrix multiply.

SBELSM or DBELSM Block Ellpack format triangular solve.

SBSCMM or DBSCMM Block compressed sparse column format matrix-matrix multiply.

SBSCSM or DBSCSM Block compressed sparse column format triangular solve.

SBSRMM or DBSRMM Block compressed sparse row format matrix-matrix multiply.

SBSRSM or DBSRSM Block compressed sparse row format triangular solve.

SCOOMM or DCOOMM Coordinate format matrix-matrix multiply.

SCSCMM or DCSCMM Compressed sparse column format matrix-matrix multiply

SCSCSM or DCSCSM Compressed sparse column format triangular solve

SCSRMM or DCSRMM Compressed sparse row format matrix-matrix multiply.

SCSRSM or DCSRSM Compressed sparse row format triangular solve.

SDIAMM or DDIAMM Diagonal format matrix-matrix multiply.

SDIASM or DDIASM Diagonal format triangular solve.

SDOTI, DDOTI, CDOTUI, or ZDOTUI Computes the dot product of a sparse vector and a full vector.

CDOTCI, or ZDOTCI, Computes the conjugate dot product of a sparse vector and a full vector.

SELLMM or DELLMM Ellpack format matrix-matrix multiply.

SELLSM or DELLSM Ellpack format triangular solve.

xCGTHR Given a full vector, creates a sparse vector and corresponding index vector.

xCGTHRZ Given a full vector, creates a sparse vector and corresponding index vector and zeros the full vector.

SJADMM or DJADMM Jagged diagonal matrix-matrix multiply.

SJADRP or DJADRP Right permutation of a jagged diagonal matrix.

SJADSM or DJADSM Jagged diagonal triangular solve.

SROTI or DROTI Applies a Givens rotation to a sparse vector and a full vector.

xCSCTR Given a sparse vector and corresponding index vector, puts those elements into a full vector.

SSKYMM or DSKYMM Skyline format matrix-matrix multiply.

SSKYSM or DSKYSM Skyline format triangular solve.

SVBRMM or DVBRMM Variable block sparse row format matrix-matrix multiply.

SVBRSM or DVBRSM Variable block sparse row format triangular solve.

Sparse Solver Routines

TABLE A-6   Sparse Solver Routines
Routines Function

DGSSFS One call interface to sparse solver.

DGSSIN Sparse solver initialization.

DGSSOR Fill reducing ordering and symbolic factorization.

DGSSFA Matrix value input and numeric factorization.

DGSSSL Triangular solve.

DGSSUO Sets user-specified ordering permutation.

DGSSRP Returns permutation used by solver.

DGSSCO Returns condition number estimate of coefficient matrix.

DGSSDA De-allocates sparse solver.

DGSSPS Prints solver statistics.

FFTPACK and VFFTPACK Routines

Routines with a V prefix are vectorized routines that belong to VFFTPACK.

TABLE A-7   FFTPACK and VFFTPACK (Fast Fourier Transform and Vectorized Fast Fourier Transform) Routines
Routine Function

COSQB, DCOSQB, VCOSQB, VDCOSQB Cosine quarter-wave synthesis

COSQF, DCOSQF, VCOSQF, VDCOSQF Cosine quarter-wave transform

COSQI, DCOSQI, VCOSQI, VDCOSQI Initialize cosine quarter-wave transform and synthesis

COST, DCOST, VCOST, VDCOST Cosine even-wave transform

COSTI, DCOSTI, VCOSTI, VDCOSTI Initialize cosine even-wave transform

EZFFTB EZ Fourier synthesis

EZFFTF EZ Fourier transform

EZFFTI Initialize EZ Fourier transform and synthesis

RFFTB, DFFTB, CFFTB, ZFFTB, VRFFTB, VDFFTB, VCFFTB, VZFFTB Fourier synthesis

RFFTF, DFFTF, CFFTF, ZFFTF, VRFFTF, VDFFTF, VCFFTF, VZFFTF Fourier transform

RFFTI, DFFTI, CFFTI, ZFFTI, VRFFTI, VDFFTI, VCFFTI, VZFFTI Initialize Fourier transform and synthesis

SINQB, DSINQB, VSINQB, VDSINQB Sine quarter-wave synthesis

SINQF, DSINQF, VSINQF, VDSINQF Sine quarter-wave transform

SINQI, DSINQI, VSINQI, VDSINQI Initialize sine quarter-wave transform and synthesis

SINT, DSINT, VSINT, VDSINT Sine odd-wave transform

SINTI, DSINT, VSINTI, VDSINTI Initialize sine odd-wave transform

RFFT2B, DFFT2B, CFFT2B, ZFFT2B Two-dimensional Fourier synthesis

RFFT2F, DFFT2F, CFFT2F, ZFFT2F Two-dimensional Fourier transform

RFFT2I, DFFT2I, CFFT2I, ZFFT2I Initialize two-dimensional Fourier transform or synthesis

RFFT3B, DFFT3B, CFFT3B, ZFFT3B Three-dimensional Fourier synthesis

RFFT3F, DFFT3F, CFFT3F, DFFT3F Three-dimensional Fourier transform

RFFT3I, DFFT3I, CFFT3I, DFFT3I Initialize three-dimensional Fourier transform or synthesis

Other Routines

TABLE A-8   Other Routines
Routines Function

xCNVCOR Computes convolution or correlation

xCNVCOR2 Computes two-dimensional convolution or correlation

xTRANS Transposes array

SWIENER or DWEINER Performs Wiener deconvolution of two signals

LINPACK Routines

TABLE A-9   LINPACK Routines
Routine Function

xCHDC Cholesky decomposition of a symmetric positive definite matrix

xCHDD Downdate an augmented Cholesky decomposition

xCHEX Update an augmented Cholesky decomposition with permutations

xCHUD Update an augmented Cholesky decomposition

xGBCO LU Factorization and condition number of a general matrix in banded storage

xGBDI Determinant of an LU-factored general matrix in banded storage

xGBFA LU factorization of a general matrix in banded storage

xGBSL Solution to a linear system in an LU-factored matrix in banded storage

xGECO LU factorization and condition number of a general matrix

xGEDI Determinant and inverse of an LU-factored general matrix

xGEFA LU factorization of a general matrix

xGESL Solution to a linear system in an LU-factored general matrix

xGTSL Solution to a linear system in a tridiagonal matrix

CHICO or ZHICO UDU factorization and condition number of a Hermitian matrix

CHIDI or ZHIDI Determinant, inertia, and inverse of a UDU-factored Hermitian matrix

CHIFA or ZHIFA UDU factorization of a Hermitian matrix

CHISL or ZHISL Solution to a linear system in a UDU-factored Hermitian matrix

CHPCO or ZHPCO UDU factorization and condition number of a Hermitian matrix in packed storage

CHPDI or ZHPDI Determinant, inertia, and inverse of a UDU-factored Hermitian matrix in packed storage

CHPFA or ZHPFA UDU factorization of a Hermitian matrix in packed storage

CHPSL or ZHPSL Solution to a linear system in a UDU-factored Hermitian matrix in packed storage

xPBCO Cholesky factorization and condition number of a symmetric positive definite matrix in banded storage

xPBDI Determinant of a Cholesky-factored symmetric positive definite matrix in banded storage

xPBFA Cholesky factorization of a symmetric positive definite matrix in banded storage

xPBSL Solution to a linear system in a Cholesky-factored symmetric positive definite matrix in banded storage

xPOCO Cholesky factorization and condition number of a symmetric positive definite matrix

xPODI Determinant and inverse of a Cholesky-factored symmetric positive definite matrix

xPOFA Cholesky factorization of a symmetric positive definite matrix

xPOSL Solution to a linear system in a Cholesky-factored symmetric positive definite matrix

xPPCO Cholesky factorization and condition number of a symmetric positive definite matrix in packed storage

xPPDI Determinant and inverse of a Cholesky-factored symmetric positive definite matrix in packed storage

xPPFA Cholesky factorization of a symmetric positive definite matrix in packed storage

xPPSL Solution to a linear system in a Cholesky-factored symmetric positive definite matrix in packed storage

xPTSL Solution to a linear system in a symmetric positive definite tridiagonal matrix

xQRDC QR factorization of a general matrix

xQRSL Solution to a linear system in a QR-factored general matrix

xSICO UDU factorization and condition number of a symmetric matrix

xSIDI Determinant, inertia, and inverse of a UDU-factored symmetric matrix

xSIFA UDU factorization of a symmetric matrix

xSISL Solution to a linear system in a UDU-factored symmetric matrix

xSPCO UDU factorization and condition number of a symmetric matrix in packed storage

xSPDI Determinant, inertia, and inverse of a UDU-factored symmetric matrix in packed storage

xSPFA UDU factorization of a symmetric matrix in packed storage

xSPSL Solution to a linear system in a UDU-factored symmetric matrix in packed storage

xSVDC Singular value decomposition of a general matrix

xTRCO Condition number of a triangular matrix

xTRDI Determinant and inverse of a triangular matrix

xTRSL Solution to a linear system in a triangular matrix

**TABLE A-1** LAPACK (Linear Algebra Package) Routines
Routine	Function
Bidiagonal Matrix
`SBDSDC` or `DBDSDC`	Computes the singular value decomposition (SVD) of a bidirectional matrix, using a divide and conquer method.
x`BDSQR`	Computes SVD of real upper or lower bidiagonal matrix, using the bidirectional QR algorithm.
Diagonal Matrix
`SDISNA` or `DDISNA`	Computes the reciprocal condition numbers for eigenvectors of real symmetric or complex Hermitian matrix.
General Band Matrix
x`GBBRD`	Reduces real or complex general band matrix to upper bidiagonal form.
x`GBCON`	Estimates the reciprocal of the condition number of general band matrix using LU factorization.
x`GBEQU`	Computes row and column scalings to equilibrate a general band matrix and reduce its condition number.
x`GBRFS`	Refines solution to general banded system of linear equations.
x`GBSV`	Solves a general banded system of linear equations (simple driver).
x`GBSVX`	Solves a general banded system of linear equations (expert driver).
x`GBTRF`	LU factorization of a general band matrix using partial pivoting with row interchanges.
x`GBTRS`	Solves a general banded system of linear equations, using the factorization computed by x`GBTRF`.
General Matrix (Unsymmetric or Rectangular)
x`GEBAK`	Forms the right or left eigenvectors of a general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by x`GEBAL.`
x`GEBAL`	Balances a general matrix.
x`GEBRD`	Reduces a general matrix to upper or lower bidiagonal form by an orthogonal transformation.
x`GECON`	Estimates the reciprocal of the condition number of a general matrix, using the factorization computed by x`GETRF`.
x`GEEQU`	Computes row and column scalings intended to equilibrate a general rectangular matrix and reduce its condition number.
x`GEES`	Computes the eigenvalues and Schur factorization of a general matrix (simple driver).
x`GEESX`	Computes the eigenvalues and Schur factorization of a general matrix (expert driver).
x`GEEV`	Computes the eigenvalues and left and right eigenvectors of a general matrix (simple driver).
x`GEEVX`	Computes the eigenvalues and left and right eigenvectors of a general matrix (expert driver).
x`GEGS`	Depreciated routine replaced by x`GGES`.
x`GEGV`	Depreciated routine replaced by x`GGEV`.
x`GEHRD`	Reduces a general matrix to upper Hessenberg form by an orthogonal similarity transformation.
x`GELQF`	Computes LQ factorization of a general rectangular matrix.
x`GELS`	Computes the least squares solution to an over-determined system of linear equations using a QR or LQ factorization of A.
x`GELSD`	Computes the least squares solution to an over-determined system of linear equations using a divide and conquer method using a QR or LQ factorization of A.
x`GELSS`	Computes the minimum-norm solution to a linear least squares problem by using the SVD of a general rectangular matrix (simple driver).
x`GELSX`	Depreciated routine replaced by x`SELSY`.
x`GELSY`	Computes the minimum-norm solution to a linear least squares problem using a complete orthogonal factorization.
x`GEQLF`	Computes QL factorization of a general rectangular matrix.
x`GEQP3`	Computes QR factorization of general rectangular matrix using Level 3 BLAS.
x`GEQPF`	Depreciated routine replaced by x`GEQP3`.
x`GEQRF`	Computes QR factorization of a general rectangular matrix.
x`GERFS`	Refines solution to a system of linear equations.
x`GERQF`	Computes RQ factorization of a general rectangular matrix.
x`GESDD`	Computes SVD of general rectangular matrix using a divide and conquer method.
x`GESV`	Solves a general system of linear equations (simple driver).
x`GESVX`	Solves a general system of linear equations (expert driver).
x`GESVD`	Computes SVD of general rectangular matrix.
x`GETRF`	Computes an LU factorization of a general rectangular matrix using partial pivoting with row interchanges.
x`GETRI`	Computes inverse of a general matrix using the factorization computed by x`GETRF`.
x`GETRS`	Solves a general system of linear equations using the factorization computed by x`GETRF.`
General Matrix-Generalized Problem (Pair of General Matrices)
x`GGBAK`	Forms the right or left eigenvectors of a generalized eigenvalue problem based on the output by x`GGBAL`.
x`GGBAL`	Balances a pair of general matrices for the generalized eigenvalue problem.
x`GGES`	Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for two nonsymmetric matrices.
x`GGESX`	Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors.
x`GGEV`	Computes the generalized eigenvalues and the left and/or right generalized eigenvalues for two nonsymmetric matrices.
x`GGEVX`	Computes the generalized eigenvalues and the left and/or right generalized eigenvectors.
x`GGGLM`	Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization.
x`GGHRD`	Reduces two matrices to generalized upper Hessenberg form using orthogonal transformations.
x`GGLSE`	Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization.
x`GGQRF`	Computes generalized QR factorization of two matrices.
x`GGRQF`	Computes generalized RQ factorization of two matrices.
x`GGSVD`	Computes the generalized singular value decomposition.
x`GGSVP`	Computes an orthogonal or unitary matrix as a preprocessing step for calculating the generalized singular value decomposition.
General Tridiagonal Matrix
x`GTCON`	Estimates the reciprocal of the condition number of a tridiagonal matrix, using the LU factorization as computed by x`GTTRF`.
x`GTRFS`	Refines solution to a general tridiagonal system of linear equations.
x`GTSV`	Solves a general tridiagonal system of linear equations (simple driver).
x`GTSVX`	Solves a general tridiagonal system of linear equations (expert driver).
x`GTTRF`	Computes an LU factorization of a general tridiagonal matrix using partial pivoting and row exchanges.
x`GTTRS`	Solves general tridiagonal system of linear equations using the factorization computed by x.
Hermitian Band Matrix
`CHBEV` or `ZHBEV`	(Replacement with newer version `CHBEVD` or `ZHBEVD` suggested) Computes all eigenvalues and eigenvectors of a Hermitian band matrix.
`CHBEVD` or `ZHBEVD`	Computes all eigenvalues and eigenvectors of a Hermitian band matrix and uses a divide and conquer method to calculate eigenvectors.
`CHBEVX` or `ZHBEVX`	Computes selected eigenvalues and eigenvectors of a Hermitian band matrix.
`CHBGST` or `ZHBGST`	Reduces Hermitian-definite banded generalized eigenproblem to standard form.
`CHBGV` or `ZHBGV`	(Replacement with newer version `CHBGVD` or `ZHBGVD` suggested) Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.
`CHBGVD` or `ZHBGVD`	Computes all eigenvalues and eigenvectors of generalized Hermitian-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.
`CHBGVX` or `ZHBGVX`	Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite banded eigenproblem.
`CHBTRD` or `ZHBTRD`	Reduces Hermitian band matrix to real symmetric tridiagonal form by using a unitary similarity transform.
Hermitian Matrix
`CHECON` or `ZHECON`	Estimates the reciprocal of the condition number of a Hermitian matrix using the factorization computed by `CHETRF` or `ZHETRF`.
`CHEEV` or `ZHEEV`	(Replacement with newer version `CHEEVR` or `ZHEEVR` suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix (simple driver).
`CHEEVD` or `ZHEEVD`	(Replacement with newer version `CHEEVR` or `ZHEEVR` suggested) Computes all eigenvalues and eigenvectors of a Hermitian matrix and uses a divide and conquer method to calculate eigenvectors.
`CHEEVR` or `ZHEEVR`	Computes selected eigenvalues and the eigenvectors of a complex Hermitian matrix.
`CHEEVX` or `ZHEEVX`	Computes selected eigenvalues and eigenvectors of a Hermitian matrix (expert driver).
`CHEGST` or `ZHEGST`	Reduces a Hermitian-definite generalized eigenproblem to standard form using the factorization computed by `CPOTRF` or `ZPOTRF`.
`CHEGV` or `ZHEGV`	(Replacement with newer version `CHEGVD` or `ZHEGVD` suggested) Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.
`CHEGVD` or `ZHEGVD`	Computes all the eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.
`CHEGVX` or `ZHEGVX`	Computes selected eigenvalues and eigenvectors of a complex generalized Hermitian-definite eigenproblem.
`CHERFS` or `ZHERFS`	Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite.
`CHESV` or `ZHESV`	Solves a complex Hermitian indefinite system of linear equations (simple driver).
`CHESVX` or `ZHESVX`	Solves a complex Hermitian indefinite system of linear equations (simple driver).
`CHETRD` or `ZHETRD`	Reduces a Hermitian matrix to real symmetric tridiagonal form by using a unitary similarity transformation.
`CHETRF` or `ZHERTF`	Computes the factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.
`CHETRI` or `ZHETRI`	Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by `CHETRF` or `ZHETRF`.
`CHETRS` or `ZHETRS`	Solves a complex Hermitian indefinite matrix, using the factorization computed by `CHETRF` or `ZHETRF`.
Hermitian Matrix in Packed Storage
`CHPCON` or `ZHPCON`	Estimates the reciprocal of the condition number of a Hermitian indefinite matrix in packed storage using the factorization computed by `CHPTRF` or `ZHPTRF`.
`CHPEV` or `ZHPEV`	(Replacement with newer version `CHPEVD` or `ZHPEVD` suggested) Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage (simple driver).
`CHPEVX` or `ZHPEVX`	Computes selected eigenvalues and eigenvectors of a Hermitian matrix in packed storage (expert driver).
`CHPEVD` or `ZHPEVD`	Computes all the eigenvalues and eigenvectors of a Hermitian matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.
`CHPGST` or `ZHPGST`	Reduces a Hermitian-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by `CPPTRF` or `ZPPTRF`.
`CHPGV` or `ZHPGV`	(Replacement with newer version `CHPGVD` or `ZHPGVD` suggested) Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).
`CHPGVX` or `ZHPGVX`	Computes selected eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).
`CHPGVD` or `ZHPGVD`	Computes all the eigenvalues and eigenvectors of a generalized Hermitian-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.
`CHPRFS` or `ZHPRFS`	Improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite in packed storage.
`CHPSV` or `ZHPSV`	Computes the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (simple driver).
`CHPSVX` or `ZHPSVX`	Uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations where the coefficient matrix is Hermitian in packed storage (expert driver).
`CHPTRD` or `ZHPTRD`	Reduces a complex Hermitian matrix stored in packed form to real symmetric tridiagonal form.
`CHPTRF` or `ZHPTRF`	Computes the factorization of a complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method.
`CHPTRI` or `ZHPTRI`	Computes the inverse of a complex Hermitian indefinite matrix in packed storage using the factorization computed by `CHPTRF` or `ZHPTRF`.
`CHPTRS` or `ZHPTRS`	Solves a complex Hermitian indefinite matrix in packed storage, using the factorization computed by `CHPTRF` or `ZHPTRF`.
Upper Hessenberg Matrix
x`HSEIN`	Computes right and/or left eigenvectors of upper Hessenberg matrix using inverse iteration.
x`HSEQR`	Computes eigenvectors and Shur factorization of upper Hessenberg matrix using multishift QR algorithm.
Upper Hessenberg Matrix-Generalized Problem (Hessenberg and Triangular Matrix)
x`HGEQZ`	Implements single-/double-shift version of QZ method for finding the generalized eigenvalues of the equation det(A - w(i) * B) = 0.
Real Orthogonal Matrix in Packed Storage
`SOPGTR` or `DOPGTR`	Generates an orthogonal transformation matrix from a tridiagonal matrix determined by `SSPTRD` or `DSPTRD`.
`SOPMTR` or `DOPMTR`	Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by `SSPTRD` or `DSPTRD`.
Real Orthogonal Matrix
`SORGBR` or `DORGBR`	Generates the orthogonal transformation matrices from reduction to bidiagonal form, as determined by `SGEBRD` or `DGEBRD`.
`SORGHR` or `DORGHR`	Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by `SGEHRD` or `DGEHRD`.
`SORGLQ` or `DORGLQ`	Generates an orthogonal matrix Q from an LQ factorization, as returned by `SGELQF` or `DGELQF`.
`SORGQL` or `DORGQL`	Generates an orthogonal matrix Q from a QL factorization, as returned by `SGEQLF` or `DGEQLF`.
`SORGQR` or `DORGQR`	Generates an orthogonal matrix Q from a QR factorization, as returned by `SGEQRF` or `DGEQRF`.
`SORGRQ` or `DORGRQ`	Generates orthogonal matrix Q from an RQ factorization, as returned by `SGERQF` or `DGERQF`.
`SORGTR` or `DORGTR`	Generates an orthogonal matrix reduced to tridiagonal form by `SSYTRD` or `DSYTRD`.
`SORMBR` or `DORMBR`	Multiplies a general matrix with the orthogonal matrix reduced to bidiagonal form, as determined by `SGEBRD` or `DGEBRD`.
`SORMHR` or `DORMHR`	Multiplies a general matrix by the orthogonal matrix reduced to Hessenberg form by `SGEHRD` or `DGEHRD`.
`SORMLQ` or `DORMLQ`	Multiplies a general matrix by the orthogonal matrix from an LQ factorization, as returned by `SGELQF` or `DGELQF`.
`SORMQL` or `DORMQL`	Multiplies a general matrix by the orthogonal matrix from a QL factorization, as returned by `SGEQLF` or `DGEQLF`.
`SORMQR` or `DORMQR`	Multiplies a general matrix by the orthogonal matrix from a QR factorization, as returned by `SGEQRF` or `DGEQRF`.
`SORMR3` or `DORMR3`	Multiplies a general matrix by the orthogonal matrix returned by `STZRZF` or `DTZRZF`.
`SORMRQ` or `DORMRQ`	Multiplies a general matrix by the orthogonal matrix from an RQ factorization returned by `SGERQF` or `DGERQF`.
`SORMRZ` or `DORMRZ`	Multiplies a general matrix by the orthogonal matrix from an RZ factorization, as returned by `STZRZF` or `DTZRZF`.
`SORMTR` or `DORMTR`	Multiplies a general matrix by the orthogonal transformation matrix reduced to tridiagonal form by `SSYTRD` or `DSYTRD`.
Symmetric or Hermitian Positive Definite Band Matrix
x`PBCON`	Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite band matrix, using the Cholesky factorization returned by x`PBTRF`.
x`PBEQU`	Computes equilibration scale factors for a symmetric or Hermitian positive definite band matrix.
x`PBRFS`	Refines solution to a symmetric or Hermitian positive definite banded system of linear equations.
x`PBSTF`	Computes a split Cholesky factorization of a real symmetric positive definite band matrix.
x`PBSV`	Solves a symmetric or Hermitian positive definite banded system of linear equations (simple driver).
x`PBSVX`	Solves a symmetric or Hermitian positive definite banded system of linear equations (expert driver).
x`PBTRF`	Computes Cholesky factorization of a symmetric or Hermitian positive definite band matrix.
x`PBTRS`	Solves symmetric positive definite banded matrix, using the Cholesky factorization computed by x`PBTRF`.
Symmetric or Hermitian Positive Definite Matrix
x`POCON`	Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite matrix, using the Cholesky factorization returned by x`POTRF`.
x`POEQU`	Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix.
x`PORFS`	Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix.
x`POSV`	Solves a symmetric or Hermitian positive definite system of linear equations (simple driver).
x`POSVX`	Solves a symmetric or Hermitian positive definite system of linear equations (expert driver).
x`POTRF`	Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix.
x`POTRI`	Computes the inverse of a symmetric or Hermitian positive definite matrix using the Cholesky-factorization returned by x`POTRF`.
x`POTRS`	Solves a symmetric or Hermitian positive definite system of linear equations, using the Cholesky factorization returned by x`POTRF`.
Symmetric or Hermitian Positive Definite Matrix in Packed Storage
x`PPCON`	Reciprocal condition number of a Cholesky-factored symmetric positive definite matrix in packed storage.
x`PPEQU`	Computes equilibration scale factors for a symmetric or Hermitian positive definite matrix in packed storage.
x`PPRFS`	Refines solution to a linear system in a Cholesky-factored symmetric or Hermitian positive definite matrix in packed storage.
x`PPSV`	Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (simple driver).
x`PPSVX`	Solves a linear system in a symmetric or Hermitian positive definite matrix in packed storage (expert driver).
x`PPTRF`	Computes Cholesky factorization of a symmetric or Hermitian positive definite matrix in packed storage.
x`PPTRI`	Computes the inverse of a symmetric or Hermitian positive definite matrix in packed storage using the Cholesky-factorization returned by x`PPTRF`.
x`PPTRS`	Solves a symmetric or Hermitian positive definite system of linear equations where the coefficient matrix is in packed storage, using the Cholesky factorization returned by x`PPTRF`.
Symmetric or Hermitian Positive Definite Tridiagonal Matrix
x`PTCON`	Estimates the reciprocal of the condition number of a symmetric or Hermitian positive definite tridiagonal matrix using the Cholesky factorization returned by x`PTTRF`.
x`PTEQR`	Computes all eigenvectors and eigenvalues of a real symmetric or Hermitian positive definite system of linear equations.
x`PTRFS`	Refines solution to a symmetric or Hermitian positive definite tridiagonal system of linear equations.
x`PTSV`	Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (simple driver).
x`PTSVX`	Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations (expert driver).
x`PTTRF`	Computes the LDL^H factorization of a symmetric or Hermitian positive definite tridiagonal matrix.
x`PTTRS`	Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations using the LDL^H factorization returned by x`PTTRF`.
Real Symmetric Band Matrix
`SSBEV` or `DSBEV`	(Replacement with newer version `SSBEVD` or `DSBEVD` suggested) Computes all eigenvalues and eigenvectors of a symmetric band matrix.
`SSBEVD` or `DSBEVD`	Computes all eigenvalues and eigenvectors of a symmetric band matrix and uses a divide and conquer method to calculate eigenvectors.
`SSBEVX` or `DSBEVX`	Computes selected eigenvalues and eigenvectors of a symmetric band matrix.
`SSBGST` or `DSBGST`	Reduces symmetric-definite banded generalized eigenproblem to standard form.
`SSBGV` or `DSBGV`	(Replacement with newer version `SSBGVD` or `DSBGVD` suggested) Computes all eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.
`SSBGVD` or `DSBGVD`	Computes all eigenvalues and eigenvectors of generalized symmetric-definite banded eigenproblem and uses a divide and conquer method to calculate eigenvectors.
`SSBGVX` or `DSBGVX`	Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite banded eigenproblem.
`SSBTRD` or `DSBTRD`	Reduces symmetric band matrix to real symmetric tridiagonal form by using an orthogonal similarity transform.
Symmetric Matrix in Packed Storage
x`SPCON`	Estimates the reciprocal of the condition number of a symmetric packed matrix using the factorization computed by x`SPTRF`.
`SSPEV` or `DSPEV`	(Replacement with newer version `SSPEVD` or `DSPEVD` suggested) Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage (simple driver).
`SSPEVX` or `DSPEVX`	Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage (expert driver).
`SSPEVD` or `DSPEVD`	Computes all the eigenvalues and eigenvectors of a symmetric matrix in packed storage and uses a divide and conquer method to calculate eigenvectors.
`SSPGST` or `DSPGST`	Reduces a real symmetric-definite generalized eigenproblem to standard form where the coefficient matrices are in packed storage and uses the factorization computed by `SPPTRF` or `DPPTRF`.
`SSPGVD` or `DSPGVD`	Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage, and uses a divide and conquer method to calculate eigenvectors.
`SSPGV` or `DSPGV`	(Replacement with newer version `SSPGVD` or `DSPGVD` suggested) Computes all the eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (simple driver).
`SSPGVX` or `DSPGVX`	Computes selected eigenvalues and eigenvectors of a real generalized symmetric-definite eigenproblem where the coefficient matrices are in packed storage (expert driver).
x`SPRFS`	Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite in packed storage.
x`SPSV`	Computes the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (simple driver).
x`SPSVX`	Uses the diagonal pivoting factorization to compute the solution to a system of linear equations where the coefficient matrix is a symmetric matrix in packed storage (expert driver).
`SSPTRD` or `DSPTRD`	Reduces a real symmetric matrix stored in packed form to real symmetric tridiagonal form using an orthogonal similarity transform.
x`SPTRF`	Computes the factorization of a symmetric packed matrix using the Bunch-Kaufman diagonal pivoting method.
x`SPTRI`	Computes the inverse of a symmetric indefinite matrix in packed storage using the factorization computed by `xSPTRF`.
x`SPTRS`	Solves a system of linear equations by the symmetric matrix stored in packed format using the factorization computed by `xSPTRF`.
Real Symmetric Tridiagonal Matrix
`SSTEBZ` or `DSTEBZ`	Computes the eigenvalues of a real symmetric tridiagonal matrix.
x`STEDC`	Computes all the eigenvalues and eigenvectors of a symmetric tridiagonal matrix using a divide and conquer method.
x`STEGR`	Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.
x`STEIN`	Computes selected eigenvectors of a real symmetric tridiagonal matrix using inverse iteration.
x`STEQR`	Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using the implicit QL or QR algorithm.
`SSTERF` or `DSTERF`	Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a root-free QL or QR algorithm variant.
`SSTEV` or `DSTEV`	(Replacement with newer version `SSTEVR` or `DSTEVR` suggested) Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (simple driver).
`SSTEVX` or `DSTEVX`	Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix (expert driver).
`SSTEVD` or `DSTEVD`	(Replacement with newer version `SSTEVR` or `DSTEVR` suggested) Computes all the eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using a divide and conquer method.
`SSTEVR` or `DSTEVR`	Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix using Relatively Robust Representations.
x`STSV`	Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.
x`STTRF`	Computes the factorization of a symmetric tridiagonal matrix.
x`STTRS`	Computes the solution to a system of linear equations where the coefficient matrix is a symmetric tridiagonal matrix.
Symmetric Matrix
x`SYCON`	Estimates the reciprocal of the condition number of a symmetric matrix using the factorization computed by `SSYTRF` or `DSYTRF`.
`SSYEV` or `DSYEV`	(Replacement with newer version `SSYEVR` or `DSYEVR` suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix.
`SSYEVX` or `DSYEVX`	Computes eigenvalues and eigenvectors of a symmetric matrix (expert driver).
`SSYEVD` or `DSYEVD`	(Replacement with newer version `SSYEVR` or `DSYEVR` suggested) Computes all eigenvalues and eigenvectors of a symmetric matrix and uses a divide and conquer method to calculate eigenvectors.
`SSYEVR` or `DSYEVR`	Computes selected eigenvalues and eigenvectors of a symmetric tridiagonal matrix.
`SSYGST` or `DSYGST`	Reduces a symmetric-definite generalized eigenproblem to standard form using the factorization computed by `SPOTRF` or `DPOTRF`.
`SSYGV` or `DSYGV`	(Replacement with newer version `SSYGVD` or `DSYGVD` suggested) Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.
`SSYGVX` or `DSYGVX`	Computes selected eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem.
`SSYGVD` or `DSYGVD`	Computes all the eigenvalues and eigenvectors of a generalized symmetric-definite eigenproblem and uses a divide and conquer method to calculate eigenvectors.
x`SYRFS`	Improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite.
x`SYSV`	Solves a real symmetric indefinite system of linear equations (simple driver).
x`SYSVX`	Solves a real symmetric indefinite system of linear equations (expert driver).
`SSYTRD` or `DSYTRD`	Reduces a symmetric matrix to real symmetric tridiagonal form by using a orthogonal similarity transformation.
x`SYTRF`	Computes the factorization of a real symmetric indefinite matrix using the diagonal pivoting method.
x`SYTRI`	Computes the inverse of a symmetric indefinite matrix using the factorization computed by x`SYTRF`.
x`SYTRS`	Solves a system of linear equations by the symmetric matrix using the factorization computed by x`SYTRF`.
Triangular Band Matrix
x`TBCON`	Estimates the reciprocal condition number of a triangular band matrix.
x`TBRFS`	Determines error bounds and estimates for solving a triangular banded system of linear equations.
x`TBTRS`	Solves a triangular banded system of linear equations.
Triangular Matrix-Generalized Problem (Pair of Triangular Matrices)
x`TGEVC`	Computes right and/or left generalized eigenvectors of two upper triangular matrices.
x`TGEXC`	Reorders the generalized Schur decomposition of a real or complex matrix pair using an orthogonal or unitary equivalence transformation.
x`TGSEN`	Reorders the generalized real-Schur or Schur decomposition of two matrixes and computes the generalized eigenvalues.
x`TGSJA`	Computes the generalized SVD from two upper triangular matrices obtained from x`GGSVP`.
x`TGSNA`	Estimates reciprocal condition numbers for specified eigenvalues and eigenvectors of two matrices in real-Schur or Schur canonical form.
x`TGSYL`	Solves the generalized Sylvester equation.
Triangular Matrix in Packed Storage
x`TPCON`	Estimates the reciprocal or the condition number of a triangular matrix in packed storage.
x`TPRFS`	Determines error bounds and estimates for solving a triangular system of linear equations where the coefficient matrix is in packed storage.
x`TPTRI`	Computes the inverse of a triangular matrix in packed storage.
x`TPTRS`	Solves a triangular system of linear equations where the coefficient matrix is in packed storage.
Triangular Matrix
x`TRCON`	Estimates the reciprocal or the condition number of a triangular matrix.
x`TREVC`	Computes right and/or left eigenvectors of an upper triangular matrix.
x`TREXC`	Reorders Schur factorization of matrix using an orthogonal or unitary similarity transformation.
x`TRRFS`	Determines error bounds and estimates for triangular system of a linear equations.
x`TRSEN`	Reorders Schur factorization of matrix to group selected cluster of eigenvalues in the leading positions on the diagonal of the upper triangular matrix T and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace.
x`TRSNA`	Estimates the reciprocal condition numbers of selected eigenvalues and eigenvectors of an upper quasi-triangular matrix.
x`TRSYL`	Solves Sylvester matrix equation.
x`TRTRI`	Computes the inverse of a triangular matrix.
x`TRTRS`	Solves a triangular system of linear equations.
Trapezoidal Matrix
x`TZRQF`	Depreciated routine replaced by routine x`TZRZF`.
x`TZRZF`	Reduces a rectangular upper trapezoidal matrix to upper triangular form by means of orthogonal transformations.
Unitary Matrix
`CUNGBR` or `ZUNGBR`	Generates the unitary transformation matrices from reduction to bidiagonal form, as determined by `CGEBRD` or `ZGEBRD`.
`CUNGHR` or `ZUNGHR`	Generates the orthogonal transformation matrix reduced to Hessenberg form, as determined by `CGEHRD` or `ZGEHRD`.
`CUNGLQ` or `ZUNGLQ`	Generates a unitary matrix Q from an LQ factorization, as returned by `CGELQF` or `ZGELQF`.
`CUNGQL` or `ZUNGQL`	Generates a unitary matrix Q from a QL factorization, as returned by `CGEQLF` or `ZGEQLF`.
`CUNGQR` or `ZUNGQR`	Generates a unitary matrix Q from a QR factorization, as returned by `CGEQRF` or `ZGEQRF`.
`CUNGRQ` or `ZUNGRQ`	Generates a unitary matrix Q from an RQ factorization, as returned by `CGERQF` or `ZGERQF`.
`CUNGTR` or `ZUNGTR`	Generates a unitary matrix reduced to tridiagonal form, by `CHETRD` or `ZHETRD`.
`CUNMBR` or `ZUNMBR`	Multiplies a general matrix with the unitary transformation matrix reduced to bidiagonal form, as determined by `CGEBRD` or `ZGEBRD`.
`CUNMHR` or `ZUNMHR`	Multiplies a general matrix by the unitary matrix reduced to Hessenberg form by `CGEHRD` or `ZGEHRD`.
`CUNMLQ` or `ZUNMLQ`	Multiplies a general matrix by the unitary matrix from an LQ factorization, as returned by `CGELQF` or `ZGELQF`.
`CUNMQL` or `ZUNMQL`	Multiplies a general matrix by the unitary matrix from a QL factorization, as returned by `CGEQLF` or `ZGEQLF`.
`CUNMQR` or `ZUNMQR`	Multiplies a general matrix by the unitary matrix from a QR factorization, as returned by `CGEQRF` or `ZGEQRF`.
`CUNMRQ` or `ZUNMRQ`	Multiplies a general matrix by the unitary matrix from an RQ factorization, as returned by `CGERQF` or `ZGERQF`.
`CUNMRZ` or `ZUNMRZ`	Multiplies a general matrix by the unitary matrix from an RZ factorization, as returned by `CTZRZF` or `ZTZRZF`.
`CUNMTR` or `ZUNMTR`	Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by `CHETRD` or `ZHETRD`.
Unitary Matrix in Packed Storage
`CUPGTR` or `ZUPGTR`	Generates the unitary transformation matrix from a tridiagonal matrix determined by `CHPTRD` or `ZHPTRD`.
`CUPMTR` or `ZUPMTR`	Multiplies a general matrix by the unitary transformation matrix reduced to tridiagonal form by `CHPTRD` or `ZHPTRD`.

**TABLE A-2** BLAS1 (Basic Linear Algebra Subprograms, Level 1) Routines
Routine	Function
`SASUM,` `DASUM,` `SCASUM,` `DZASUM`	Sum of the absolute values of a vector
`xAXPY`	Product of a scalar and vector plus a vector
`xCOPY`	Copy a vector
`SDOT,` `DDOT,` `DSDOT,` `SDSDOT, CDOTU,` `ZDOTU,` `DQDOTA,` `DQDOTI`	Dot product (inner product)
`CDOTC,` `ZDOTC`	Dot product conjugating first vector
`SNRM2,` `DNRM2, SCNRM2,` `DCNRM2,` `DZNRM2`	Euclidean norm of a vector
`xROTG`	Set up Givens plane rotation
`xROT,` `CSROT, ZDROT`	Apply Given's plane rotation
`SROTMG,` `DROTMG`	Set up modified Given's plane rotation
`SROTM,` `DROTM`	Apply modified Given's rotation
`ISAMAX,` `DAMAX, ICAMAX,` `IZAMAX`	Index of element with maximum absolute value
`xSCAL,` `CSSCAL,` `ZDSCAL`	Scale a vector
`xSWAP`	Swap two vectors
`CVMUL`, `ZVMUL`	Compute scaled product of complex vectors

**TABLE A-3** BLAS2 (Basic Linear Algebra Subprograms, Level 2) Routines
Routine	Function
x`GBMV`	Product of a matrix in banded storage and a vector
x`GEMV`	Product of a general matrix and a vector
`SGER,` `DGER, CGERC,` `ZGERC, CGERU,` `ZGERU`	Rank-1 update to a general matrix
`CHBMV,` `ZHBMV`	Product of a Hermitian matrix in banded storage and a vector
`CHEMV,` `ZHEMV`	Product of a Hermitian matrix and a vector
`CHER,` `ZHER`	Rank-1 update to a Hermitian matrix
`CHER2,` `ZHER2`	Rank-2 update to a Hermitian matrix
`CHPMV,` `ZHPMV`	Product of a Hermitian matrix in packed storage and a vector
`CHPR,` `ZHPR`	Rank-1 update to a Hermitian matrix in packed storage
`CHPR2,` `ZHPR2`	Rank-2 update to a Hermitian matrix in packed storage
`SSBMV,` `DSBMV`	Product of a symmetric matrix in banded storage and a vector
x`SPMV`	Product of a Symmetric matrix in packed storage and a vector
`SSPR,` `DSPR`	Rank-1 update to a real symmetric matrix in packed storage
`SSPR2,` `DSPR2`	Rank-2 update to a real symmetric matrix in packed storage
`SSYMV,` `DSYMV`	Product of a symmetric matrix and a vector
`SSYR,` `DSYR`	Rank-1 update to a real symmetric matrix
`SSYR2,` `DSYR2`	Rank-2 update to a real symmetric matrix
x`TBMV`	Product of a triangular matrix in banded storage and a vector
x`TBSV`	Solution to a triangular system in banded storage of linear equations
x`TPMV`	Product of a triangular matrix in packed storage and a vector
x`TPSV`	Solution to a triangular system of linear equations in packed storage
x`TRMV`	Product of a triangular matrix and a vector
x`TRSV`	Solution to a triangular system of linear equations

**TABLE A-4** BLAS3 (Basic Linear Algebra Subprograms, Level 3) Routines
Routine	Function
x`GEMM`	Product of two general matrices
`CHEMM` or `ZHEMM`	Product of a Hermitian matrix and a general matrix
`CHERK` or `ZHERK`	Rank-k update of a Hermitian matrix
`CHER2K` or `ZHER2K`	Rank-2k update of a Hermitian matrix
x`SYMM`	Product of a symmetric matrix and a general matrix
x`SYRK`	Rank-k update of a symmetric matrix
x`SYR2K`	Rank-2k update of a symmetric matrix
x`TRMM`	Product of a triangular matrix and a general matrix
x`TRSM`	Solution for a triangular system of equations

**TABLE A-5** Sparse BLAS Routines
Routines	Function
x`AXPYI`	Adds a scalar multiple of a sparse vector X to a full vector Y.
`SBCOMM` or `DBCOMM`	Block coordinate matrix-matrix multiply.
`SBDIMM` or `DBDIMM`	Block diagonal format matrix-matrix multiply.
`SBDISM` or `DBDISM`	Block Diagonal format triangular solve.
`SBELMM` or `DBELMM`	Block Ellpack format matrix-matrix multiply.
`SBELSM` or `DBELSM`	Block Ellpack format triangular solve.
`SBSCMM` or `DBSCMM`	Block compressed sparse column format matrix-matrix multiply.
`SBSCSM` or `DBSCSM`	Block compressed sparse column format triangular solve.
`SBSRMM` or `DBSRMM`	Block compressed sparse row format matrix-matrix multiply.
`SBSRSM` or `DBSRSM`	Block compressed sparse row format triangular solve.
`SCOOMM` or `DCOOMM`	Coordinate format matrix-matrix multiply.
`SCSCMM` or `DCSCMM`	Compressed sparse column format matrix-matrix multiply
`SCSCSM` or `DCSCSM`	Compressed sparse column format triangular solve
`SCSRMM` or `DCSRMM`	Compressed sparse row format matrix-matrix multiply.
`SCSRSM` or `DCSRSM`	Compressed sparse row format triangular solve.
`SDIAMM` or `DDIAMM`	Diagonal format matrix-matrix multiply.
`SDIASM` or `DDIASM`	Diagonal format triangular solve.
`SDOTI, DDOTI, CDOTUI,` or `ZDOTUI`	Computes the dot product of a sparse vector and a full vector.
`CDOTCI,` or `ZDOTCI,`	Computes the conjugate dot product of a sparse vector and a full vector.
`SELLMM` or `DELLMM`	Ellpack format matrix-matrix multiply.
`SELLSM` or `DELLSM`	Ellpack format triangular solve.
x`CGTHR`	Given a full vector, creates a sparse vector and corresponding index vector.
x`CGTHRZ`	Given a full vector, creates a sparse vector and corresponding index vector and zeros the full vector.
`SJADMM` or `DJADMM`	Jagged diagonal matrix-matrix multiply.
`SJADRP` or `DJADRP`	Right permutation of a jagged diagonal matrix.
`SJADSM` or `DJADSM`	Jagged diagonal triangular solve.
`SROTI` or `DROTI`	Applies a Givens rotation to a sparse vector and a full vector.
x`CSCTR`	Given a sparse vector and corresponding index vector, puts those elements into a full vector.
`SSKYMM` or `DSKYMM`	Skyline format matrix-matrix multiply.
`SSKYSM` or `DSKYSM`	Skyline format triangular solve.
`SVBRMM` or `DVBRMM`	Variable block sparse row format matrix-matrix multiply.
`SVBRSM` or `DVBRSM`	Variable block sparse row format triangular solve.

**TABLE A-6** Sparse Solver Routines
Routines	Function
`DGSSFS`	One call interface to sparse solver.
`DGSSIN`	Sparse solver initialization.
`DGSSOR`	Fill reducing ordering and symbolic factorization.
`DGSSFA`	Matrix value input and numeric factorization.
`DGSSSL`	Triangular solve.
`DGSSUO`	Sets user-specified ordering permutation.
`DGSSRP`	Returns permutation used by solver.
`DGSSCO`	Returns condition number estimate of coefficient matrix.
`DGSSDA`	De-allocates sparse solver.
`DGSSPS`	Prints solver statistics.

**TABLE A-7** FFTPACK and VFFTPACK (Fast Fourier Transform and Vectorized Fast Fourier Transform) Routines
Routine	Function
`COSQB, DCOSQB, VCOSQB,` `VDCOSQB`	Cosine quarter-wave synthesis
`COSQF, DCOSQF, VCOSQF, VDCOSQF`	Cosine quarter-wave transform
`COSQI, DCOSQI, VCOSQI, VDCOSQI`	Initialize cosine quarter-wave transform and synthesis
`COST, DCOST, VCOST,` `VDCOST`	Cosine even-wave transform
`COSTI, DCOSTI, VCOSTI, VDCOSTI`	Initialize cosine even-wave transform
`EZFFTB`	EZ Fourier synthesis
`EZFFTF`	EZ Fourier transform
`EZFFTI`	Initialize EZ Fourier transform and synthesis
`RFFTB,` `DFFTB, CFFTB,` `ZFFTB, VRFFTB,` `VDFFTB, VCFFTB,` `VZFFTB`	Fourier synthesis
`RFFTF,` `DFFTF, CFFTF,` `ZFFTF, VRFFTF,` `VDFFTF, VCFFTF,` `VZFFTF`	Fourier transform
`RFFTI,` `DFFTI, CFFTI,` `ZFFTI, VRFFTI,` `VDFFTI, VCFFTI,` `VZFFTI`	Initialize Fourier transform and synthesis
`SINQB,` `DSINQB, VSINQB,` `VDSINQB`	Sine quarter-wave synthesis
`SINQF,` `DSINQF, VSINQF,` `VDSINQF`	Sine quarter-wave transform
`SINQI,` `DSINQI, VSINQI,` `VDSINQI`	Initialize sine quarter-wave transform and synthesis
`SINT,` `DSINT, VSINT,` `VDSINT`	Sine odd-wave transform
`SINTI,` `DSINT, VSINTI,` `VDSINTI`	Initialize sine odd-wave transform
`RFFT2B,` `DFFT2B, CFFT2B,` `ZFFT2B`	Two-dimensional Fourier synthesis
`RFFT2F,` `DFFT2F, CFFT2F,` `ZFFT2F`	Two-dimensional Fourier transform
`RFFT2I,` `DFFT2I, CFFT2I,` `ZFFT2I`	Initialize two-dimensional Fourier transform or synthesis
`RFFT3B,` `DFFT3B, CFFT3B,` `ZFFT3B`	Three-dimensional Fourier synthesis
`RFFT3F,` `DFFT3F, CFFT3F,` `DFFT3F`	Three-dimensional Fourier transform
`RFFT3I,` `DFFT3I, CFFT3I,` `DFFT3I`	Initialize three-dimensional Fourier transform or synthesis

**TABLE A-8** Other Routines
Routines	Function
x`CNVCOR`	Computes convolution or correlation
x`CNVCOR2`	Computes two-dimensional convolution or correlation
x`TRANS`	Transposes array
`SWIENER` or `DWEINER`	Performs Wiener deconvolution of two signals

**TABLE A-9** LINPACK Routines
Routine	Function
x`CHDC`	Cholesky decomposition of a symmetric positive definite matrix
x`CHDD`	Downdate an augmented Cholesky decomposition
x`CHEX`	Update an augmented Cholesky decomposition with permutations
x`CHUD`	Update an augmented Cholesky decomposition
x`GBCO`	LU Factorization and condition number of a general matrix in banded storage
x`GBDI`	Determinant of an LU-factored general matrix in banded storage
x`GBFA`	LU factorization of a general matrix in banded storage
x`GBSL`	Solution to a linear system in an LU-factored matrix in banded storage
x`GECO`	LU factorization and condition number of a general matrix
x`GEDI`	Determinant and inverse of an LU-factored general matrix
x`GEFA`	LU factorization of a general matrix
x`GESL`	Solution to a linear system in an LU-factored general matrix
x`GTSL`	Solution to a linear system in a tridiagonal matrix
`CHICO` or `ZHICO`	UDU factorization and condition number of a Hermitian matrix
`CHIDI` or `ZHIDI`	Determinant, inertia, and inverse of a UDU-factored Hermitian matrix
`CHIFA` or `ZHIFA`	UDU factorization of a Hermitian matrix
`CHISL` or `ZHISL`	Solution to a linear system in a UDU-factored Hermitian matrix
`CHPCO` or `ZHPCO`	UDU factorization and condition number of a Hermitian matrix in packed storage
`CHPDI` or `ZHPDI`	Determinant, inertia, and inverse of a UDU-factored Hermitian matrix in packed storage
`CHPFA` or `ZHPFA`	UDU factorization of a Hermitian matrix in packed storage
`CHPSL` or `ZHPSL`	Solution to a linear system in a UDU-factored Hermitian matrix in packed storage
x`PBCO`	Cholesky factorization and condition number of a symmetric positive definite matrix in banded storage
x`PBDI`	Determinant of a Cholesky-factored symmetric positive definite matrix in banded storage
x`PBFA`	Cholesky factorization of a symmetric positive definite matrix in banded storage
x`PBSL`	Solution to a linear system in a Cholesky-factored symmetric positive definite matrix in banded storage
x`POCO`	Cholesky factorization and condition number of a symmetric positive definite matrix
x`PODI`	Determinant and inverse of a Cholesky-factored symmetric positive definite matrix
x`POFA`	Cholesky factorization of a symmetric positive definite matrix
x`POSL`	Solution to a linear system in a Cholesky-factored symmetric positive definite matrix
x`PPCO`	Cholesky factorization and condition number of a symmetric positive definite matrix in packed storage
x`PPDI`	Determinant and inverse of a Cholesky-factored symmetric positive definite matrix in packed storage
x`PPFA`	Cholesky factorization of a symmetric positive definite matrix in packed storage
x`PPSL`	Solution to a linear system in a Cholesky-factored symmetric positive definite matrix in packed storage
x`PTSL`	Solution to a linear system in a symmetric positive definite tridiagonal matrix
x`QRDC`	QR factorization of a general matrix
x`QRSL`	Solution to a linear system in a QR-factored general matrix
x`SICO`	UDU factorization and condition number of a symmetric matrix
x`SIDI`	Determinant, inertia, and inverse of a UDU-factored symmetric matrix
x`SIFA`	UDU factorization of a symmetric matrix
x`SISL`	Solution to a linear system in a UDU-factored symmetric matrix
x`SPCO`	UDU factorization and condition number of a symmetric matrix in packed storage
x`SPDI`	Determinant, inertia, and inverse of a UDU-factored symmetric matrix in packed storage
x`SPFA`	UDU factorization of a symmetric matrix in packed storage
x`SPSL`	Solution to a linear system in a UDU-factored symmetric matrix in packed storage
x`SVDC`	Singular value decomposition of a general matrix
x`TRCO`	Condition number of a triangular matrix
x`TRDI`	Determinant and inverse of a triangular matrix
x`TRSL`	Solution to a linear system in a triangular matrix

Library | Contents | Previous | Next | Index

Appendix A

Sun Performance Library Routines

FFTPACK and VFFTPACK Routines

Other Routines TABLE A-8 Other Routines Routines Function xCNVCOR Computes convolution or correlation xCNVCOR2 Computes two-dimensional convolution or correlation xTRANS Transposes array SWIENER or DWEINER Performs Wiener deconvolution of two signals

Other Routines

TABLE A-8 Other Routines
Routines Function

x`CNVCOR` Computes convolution or correlation

x`CNVCOR2` Computes two-dimensional convolution or correlation

x`TRANS` Transposes array

`SWIENER` or `DWEINER` Performs Wiener deconvolution of two signals