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LAPACK

Introduction

LAPACK (Linear Algebra PACKage) provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.

LAPACK supersedes LINPACK and EISPACK. The algorithms in LINPACK and EISPACK operate on rows and columns of matrices, and data reuse is low. This makes them inefficient, spending too much time moving data instead of doing useful floating-point calculations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. Whenever possible, LAPACK calls BLAS (usually Level 2 & Level 3) for maximum data reuse.

How to use LAPACK

• The LAPACK Routine List contains one-line summaries for LAPACK driver, computational, an auxiliary subprograms.
• There is also user interface information in the LAPACK User's Guide [1] and LAPACK Quick Reference [2].
• Compiling and Linking tells how to compile and link with the LAPACK library.

Parallelism

Shared memory parallelism can be obtained on Vector Engine by linking to the OpenMP version of BLAS.

LAPACK Routine List

Simple Driver and Divide and Conquer Driver Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
?GESV SGESV DGESV CGESV ZGESV DSGESV ZCGESV	S D C Z DS ZC	Solves a general system of linear equations AX=B.
?GBSV SGBSV DGBSV CGBSV ZGBSV	S D C Z	Solves a general banded system of linear equations AX=B.
?GTSV SGTSV DGTSV CGTSV ZGTSV	S D C Z	Solves a general tridiagonal system of linear equations AX=B.
?POSV SPOSV DPOSV CPOSV ZPOSV DSPOSV ZCPOSV	S D C Z DS ZC	Solves a symmetric/Hermitian positive definite system of linear equations AX=B.
?PPSV SPPSV DPPSV CPPSV ZPPSV	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage.
?PBSV SPBSV DPBSV CPBSV ZPBSV	S D C Z	Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B.
?PTSV SPTSV DPTSV CPTSV ZPTSV	S D C Z	Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B.
?SYSV SSYSV DSYSV CSYSV ZSYSV	S D C Z	Solves a symmetric indefinite system of linear equations AX=B.
?SPSV SSPSV DSPSV CSPSV ZSPSV	S D C Z	Solves a symmetric indefinite system of linear equations AX=B, where A is held in packed storage.
?GELS SGELS DGELS CGELS ZGELS	S D C Z	Computes the least squares solution to an over-determined system of linear equations, AX=B or AHX=B, or the minimum norm solution of an under-determined system, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A.
?GELSD SGELSD DGELSD CGELSD ZGELSD	S D C Z	Computes the least squares solution to an over-determined system of linear equations, AX=B or AHX=B, or the minimum norm solution of an under-determined system, using a divide and conquer method, where A is a general rectangular matrix of full rank, using a QR or LQ factorization of A.
?GGLSE SGGLSE DGGLSE CGGLSE ZGGLSE	S D C Z	Solves the LSE (Constrained Linear Least Squares Problem) using the GRQ (Generalized RQ) factorization.
?GGGLM SGGGLM DGGGLM CGGGLM ZGGGLM	S D C Z	Solves the GLM (Generalized Linear Regression Model) using the GQR (Generalized QR) factorization.
?SYEV SSYEV DSYEV	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix.
?SYEVD SSYEVD DSYEVD	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
?SPEV SSPEV DSPEV	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix in packed storage.
?SPEVD SSPEVD DSPEVD	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.
?SBEV SSBEV DSBEV	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric band matrix.
?SBEVD SSBEVD DSBEVD	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
?STEV SSTEV DSTEV	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix.
?STEVD SSTEVD DSTEVD	S D	Computes all eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
?GEES SGEES DGEES CGEES ZGEES	S D C Z	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.
?GEEV SGEEV DGEEV CGEEV ZGEEV	S D C Z	Computes the eigenvalues and left and right eigenvectors of a general matrix.
?GESVD SGESVD DGESVD CGESVD ZGESVD	S D C Z	Computes the singular value decomposition (SVD) of a general rectangular matrix.
?GESDD SGESDD DGESDD CGESDD ZGESDD	S D C Z	Computes the singular value decomposition (SVD) of a general rectangular matrix using divide-and-conquer.
?GETRF SGETRF DGETRF CGETRF ZGETRF	S D C Z	Computes an LU factorization of a general tridiagonal matrix, using partial pivoting with row interchanges.
?SYGV SSYGV DSYGV	S D	Computes all eigenvalues and the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax = λBx, ABx = λx, or BAx = λx.
?SYGVD SSYGVD DSYGVD	S D	Computes all eigenvalues and the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx. If eigenvectors are desired, it uses a divide and conquer algorithm.
?SPGV SSPGV DSPGV	S D	Computes all eigenvalues and eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage.
?SPGVD SSPGVD DSPGVD	S D	Computes all eigenvalues and eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.
?SBGV SSBGV DSBGV	S D	Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form Ax=λBx. A and B are assumed to be symmetric and banded, and B is also positive definite.
?SBGVD SSBGVD DSBGVD	S D	Computes all the eigenvalues and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form Ax=λBx. A and B are assumed to be symmetric and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.
?GEGS SGEGS DGEGS CGEGS ZGEGS	S D C Z	Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for a pair of non-symmetric matrices.
?GGES SGGES DGGES CGGES ZGGES	S D C Z	Computes the generalized eigenvalues, Schur form, and left and/or right Schur vectors for a pair of non-symmetric matrices.
?GEGV SGEGV DGEGV CGEGV ZGEGV	S D C Z	Computes the generalized eigenvalues, and left and/or right generalized eigenvectors for a pair of non-symmetric matrices.
?GGEV SGGEV DGGEV CGGEV ZGGEV	S D C Z	Computes the generalized eigenvalues, and left and/or right generalized eigenvectors for a pair of non-symmetric matrices.
?GGSVD SGGSVD DGGSVD CGGSVD ZGGSVD	S D C Z	Computes the Generalized Singular Value Decomposition.
?HESV CHESV ZHESV	C Z	Solves a Hermitian indefinite system of linear equations AX=B.
?HPSV CHPSV ZHPSV	C Z	Solves a Hermitian indefinite system of linear equations AX=B, where A is held in packed storage.
?HEEV CHEEV ZHEEV	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix.
?HEEVD CHEEVD ZHEEVD	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
?HPEV CHPEV ZHPEV	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix in packed storage.
?HPEVD CHPEVD ZHPEVD	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.
?HBEV CHBEV ZHBEV	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian band matrix.
?HBEVD CHBEVD ZHBEVD	C Z	Computes all eigenvalues and, optionally, eigenvectors of a Hermitian band matrix. If eigenvectors are desired, it uses a divide and conquer algorithm.
?HEGV CHEGV ZHEGV	C Z	Computes all eigenvalues and the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx.
?HEGVD CHEGVD ZHEGVD	C Z	Computes all eigenvalues and the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx. If eigenvectors are desired, it uses a divide and conquer algorithm.
?HPGV CHPGV ZHPGV	C Z	Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage.
?HPGVD CHPGVD ZHPGVD	C Z	Computes all eigenvalues and eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm.
?HBGV CHBGV ZHBGV	C Z	Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form Ax=λBx. A and B are assumed to be Hermitian and banded, and B is also positive definite.
?HBGVD CHBGVD ZHBGVD	C Z	Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form Ax=λBx. A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm.A

Expert Driver and RRR Driver Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
?GESVX SGESVX DGESVX CGESVX ZGESVX	S D C Z	Solves a general system of linear equations AX=B, ATX=B or AHX=B, and provides an estimate of the condition number and error bounds on the solution.
?GBSVX SGBSVX DGBSVX CGBSVX ZGBSVX	S D C Z	Solves a general banded system of linear equations AX=B, ATX=B or AHX=B, and provides an estimate of the condition number and error bounds on the solution.
?GTSVX SGTSVX DGTSVX CGTSVX ZGTSVX	S D C Z	Solves a general tridiagonal system of linear equations AX=B, ATX=B or AHX=B, and provides an estimate of the condition number and error bounds on the solution.
?POSVX SPOSVX DPOSVX CPOSVX ZPOSVX	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.
?PPSVX SPPSVX DPPSVX CPPSVX ZPPSVX	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.
?PBSVX SPBSVX DPBSVX CPBSVX ZPBSVX	S D C Z	Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.
?PTSVX SPTSVX DPTSVX CPTSVX ZPTSVX	S D C Z	Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.
?SYSVX SSYSVX DSYSVX CSYSVX ZSYSVX	S D C Z	Solves a symmetric indefinite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.
?SPSVX SSPSVX DSPSVX CSPSVX ZSPSVX	S D C Z	Solves a symmetric indefinite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.
?GELSX SGELSX DGELSX CGELSX ZGELSX	S D C Z	Computes the minimum norm least squares solution to an over- or under-determined system of linear equations AX=B, using a complete orthogonal factorization of A.
?GELSY SGELSY DGELSY CGELSY ZGELSY	S D C Z	Computes the minimum norm least squares solution to an over- or under-determined system of linear equations AX=B, using a complete orthogonal factorization of A.
?GELSS SGELSS DGELSS CGELSS ZGELSS	S D C Z	Computes the minimum norm least squares solution to an over- or under-determined system of linear equations AX=B, using the singular value decomposition of A.
?SYEVX SSYEVX DSYEVX	S D	Computes selected eigenvalues and eigenvectors of a symmetric matrix.
?SYEVR SSYEVR DSYEVR	S D	Computes selected eigenvalues, and optionally, eigenvectors of a real symmetric matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDLT, representations (also known as Relatively Robust Representations).
?SYGVX SSYGVX DSYGVX	S D	Computes selected eigenvalues, and optionally, the eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx.
?SPEVX SSPEVX DSPEVX	S D	Computes selected eigenvalues and eigenvectors of a symmetric matrix in packed storage.
?SPGVX SSPGVX DSPGVX	S D	Computes selected eigenvalues, and optionally, eigenvectors of a generalized symmetric-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage.
?SBEVX SSBEVX DSBEVX	S D	Computes selected eigenvalues and eigenvectors of a symmetric band matrix.
?SBGVX SSBGVX DSBGVX	S D	Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of, the form Ax=λBx. A and B are assumed to be symmetric and banded, and B is also positive definite.
?STEVX SSTEVX DSTEVX	S D	Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix.
?STEVR SSTEVR DSTEVR	S D	Computes selected eigenvalues, and optionally, eigenvectors of a real symmetric tridiagonal matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDLT representations (also known as Relatively Robust Representations).
?GEESX SGEESX DGEESX CGEESX ZGEESX	S D C Z	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.
?GGESX SGGESX DGGESX CGGESX ZGGESX	S D C Z	Computes the generalized eigenvalues, the real Schur form, and, optionally, the left and/or right matrices of Schur vectors.
?GEEVX SGEEVX DGEEVX CGEEVX ZGEEVX	S D C Z	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.
?GGEVX SGGEVX DGGEVX CGGEVX ZGGEVX	S D C Z	Computes the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.
?HESVX CHESVX ZHESVX	C Z	Solves a Hermitian indefinite system of linear equations AX=B, and provides an estimate of the condition number and error bounds on the solution.
?HPSVX CHPSVX ZHPSVX	C Z	Solves a Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, and provides an estimate of the condition number and error bounds on the solution.
?HEEVX CHEEVX ZHEEVX	C Z	Computes selected eigenvalues and eigenvectors of a Hermitian matrix.
?HEEVR CHEEVR ZHEEVR	C Z	Computes selected eigenvalues, and optionally, eigenvectors of a Hermitian matrix. Eigenvalues are computed by the dqds algorithm, and eigenvectors are computed from various "good" LDLT representations (also known as Relatively Robust Representations).
?HEGVX CHEGVX ZHEGVX	C Z	Computes selected eigenvalues, and optionally, the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx.
?HPEVX CHPEVX ZHPEVX	C Z	Computes selected eigenvalues and eigenvectors of a Hermitian matrix in packed storage.
?HPGVX CHPGVX ZHPGVX	C Z	Computes selected eigenvalues, and optionally, the eigenvectors of a generalized Hermitian-definite generalized eigenproblem, Ax=λBx, ABx=λx, or BAx=λx, where A and B are in packed storage.
?HBEVX CHBEVX ZHBEVX	C Z	Computes selected eigenvalues and eigenvectors of a Hermitian band matrix.
?HBGVX CHBGVX ZHBGVX	C Z	Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form Ax=λBx. A and B are assumed to be Hermitian and banded, and B is also positive definite.

Computational Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Name†	Prefixes	Description
?BBCSD SBBCSD DBBCSD CBBCSD ZBBCSD	S D C Z	Computes the CS decomposition of a orthogonal/unitary matrix in bidiagonal-block form.
?BDSDC SBDSDC DBDSDC	S D	Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using a divide and conquer method.
?BDSQR SBDSQR DBDSQR CBDSQR ZBDSQR	S D C Z	Computes the singular value decomposition (SVD) of a real bidiagonal matrix, using the bidiagonal QR algorithm.
?DISNA SDISNA DDISNA	S D	Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or Hermitian matrix or for the left or right singular vectors of a general matrix.
?GBBRD SGBBRD DGBBRD CGBBRD ZGBBRD	S D C Z	Reduces a general band matrix to real upper bidiagonal form by an orthogonal/unitary transformation.
?GBCON SGBCON DGBCON CGBCON ZGBCON	S D C Z	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 ?GBTRF.
?GBEQU SGBEQU DGBEQU CGBEQU ZGBEQU	S D C Z	Computes row and column scalings to equilibrate a general band matrix and reduce its condition number.
?GBEQUB SGBEQUB DGBEQUB CGBEQUB ZGBEQUB	S D C Z	Computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number.
?GBRFS SGBRFS DGBRFS CGBRFS ZGBRFS	S D C Z	Improves the computed solution to a general banded system of linear equations AX=B, ATX=B or AHX=B, and provides forward and backward error bounds for the solution.
?GBTF2 SGBTF2 DGBTF2 CGBTF2 ZGBTF2	S D C Z	Computes an LU factorization of a general m-by-n band matrix A using partial pivoting with row interchanges.
?GBTRF SGBTRF DGBTRF CGBTRF ZGBTRF	S D C Z	Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges.
?GBTRS SGBTRS DGBTRS CGBTRS ZGBTRS	S D C Z	Solves a general banded system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by ?GBTRF.
?GEBAK SGEBAK DGEBAK CGEBAK ZGEBAK	S D C Z	Transforms eigenvectors of a balanced matrix to those of the original matrix supplied to ?GEBAL.
?GEBAL SGEBAL DGEBAL CGEBAL ZGEBAL	S D C Z	Balances a general matrix in order to improve the accuracy of computed eigenvalues.
?GEBD2 SGEBD2 DGEBD2 CGEBD2 ZGEBD2	S D C Z	Reduces a general m by n matrix A to upper or lower bidiagonal form B by a orthogonal/unitary transformation: QHAP=B.
?GEBRD SGEBRD DGEBRD CGEBRD ZGEBRD	S D C Z	Reduces a general rectangular matrix to real bidiagonal form by an orthogonal/unitary transformation.
?GECON SGECON DGECON CGECON ZGECON	S D C Z	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 ?GETRF.
?GEEQU SGEEQU DGEEQU CGEEQU ZGEEQU	S D C Z	Computes row and column scalings to equilibrate a general rectangular matrix and reduce its condition number.
?GEEQUB SGEEQUB DGEEQUB CGEEQUB ZGEEQUB	S D C Z	Computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number.
?GEHD2 SGEHD2 DGEHD2 CGEHD2 ZGEHD2	S D C Z	Reduces a general matrix A to upper Hessenberg form H by a orthogonal/unitary similarity transformation: QHAQ=H .
?GEHRD SGEHRD DGEHRD CGEHRD ZGEHRD	S D C Z	Reduces a general matrix to upper Hessenberg form by an orthogonal/unitary similarity transformation.
?GEJSV SGEJSV DGEJSV	S D	Computes the singular value decomposition (SVD) of a real M-by-N matrix A, where M>=N.
?GELQ2 SGELQ2 DGELQ2 CGELQ2 ZGELQ2	S D C Z	Computes an LQ factorization of a general m by n matrix A: A=LQ.
?GELQF SGELQF DGELQF CGELQF ZGELQF	S D C Z	Computes an LQ factorization of a general rectangular matrix.
?GEMQRT SGEMQRT DGEMQRT CGEMQRT ZGEMQRT	S D C Z	Overwrites the general M-by-N matrix C with QC, CQ, QHC, CQH where Q is a orthogonal matrix defined as the product of K elementary reflectors: Q=H(1) H(2) ...H(K)=I-VTVH generated using the compact WY representation as returned by ?GEQRT.
?GEQL2 SGEQL2 DGEQL2 CGEQL2 ZGEQL2	S D C Z	Computes a QL factorization of a general m by n matrix A: A=QL.
?GEQLF SGEQLF DGEQLF CGEQLF ZGEQLF	S D C Z	Computes a QL factorization of a general rectangular matrix.
?GEQP3 SGEQP3 DGEQP3 CGEQP3 ZGEQP3	S D C Z	Computes a QR factorization with column pivoting of a general rectangular matrix using Level 3 BLAS.
?GEQPF SGEQPF DGEQPF CGEQPF ZGEQPF	S D C Z	Computes a QR factorization with column pivoting of a general rectangular matrix.
?GEQR2 SGEQR2 DGEQR2 CGEQR2 ZGEQR2	S D C Z	Computes a QR factorization of a general m by n matrix A: A=QR.
?GEQR2P SGEQR2P DGEQR2P CGEQR2P ZGEQR2P	S D C Z	Computes a QR factorization of a general m by n matrix A: A=QR.
?GEQRF SGEQRF DGEQRF CGEQRF ZGEQRF	S D C Z	Computes a QR factorization of a general rectangular matrix.
?GEQRFP SGEQRFP DGEQRFP CGEQRFP ZGEQRFP	S D C Z	Computes a QR factorization of a general M-by-N matrix A: A=QR.
?GEQRT SGEQRT DGEQRT CGEQRT ZGEQRT	S D C Z	Computes a blocked QR factorization of a general M-by-N matrix A using the compact WY representation of Q.
?GEQRT2 SGEQRT2 DGEQRT2 CGEQRT2 ZGEQRT2	S D C Z	Computes a QR factorization of a general M-by-N matrix A, using the compact WY representation of Q.
?GEQRT3 SGEQRT3 DGEQRT3 CGEQRT3 ZGEQRT3	S D C Z	Computes a QR factorization of a general M-by-N matrix A recursively, using the compact WY representation of Q.
?GERFS SGERFS DGERFS CGERFS ZGERFS	S D C Z	Improves the computed solution to a general system of linear equations AX=B, ATX=B or AHX=B, and provides forward and backward error bounds for the solution.
?GERQ2 SGERQ2 DGERQ2 CGERQ2 ZGERQ2	S D C Z	Computes an RQ factorization of a general m by n matrix A: A=RQ.
?GERQF SGERQF DGERQF CGERQF ZGERQF	S D C Z	Computes an RQ factorization of a general rectangular matrix.
?GESVJ SGESVJ DGESVJ	S D	Computes the singular value decomposition (SVD) of a real M-by-N matrix A, where M>=N.
?GETF2 SGETF2 DGETF2 CGETF2 ZGETF2	S D C Z	Computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges.
?GETRI SGETRI DGETRI CGETRI ZGETRI	S D C Z	Computes the inverse of a general matrix, using the LU factorization computed by ?GETRF.
?GETRS SGETRS DGETRS CGETRS ZGETRS	S D C Z	Solves a general system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by ?GETRF.
?GGBAK SGGBAK DGGBAK CGGBAK ZGGBAK	S D C Z	Forms the right or left eigenvectors of the generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ?GGBAL.
?GGBAL SGGBAL DGGBAL CGGBAL ZGGBAL	S D C Z	Balances a pair of general matrices for the generalized eigenvalue problem Ax=λBx.
?GGHRD SGGHRD DGGHRD CGGHRD ZGGHRD	S D C Z	Reduces a pair of matrices to generalized upper Hessenberg form using orthogonal/unitary similarity transformations.
?GGQRF SGGQRF DGGQRF CGGQRF ZGGQRF	S D C Z	Computes a generalized QR factorization of a pair of matrices.
?GGRQF SGGRQF DGGRQF CGGRQF ZGGRQF	S D C Z	Computes a generalized RQ factorization of a pair of matrices.
?GGSVP SGGSVP DGGSVP CGGSVP ZGGSVP	S D C Z	Computes orthogonal/unitary matrices as a preprocessing step for computing the generalized singular value decomposition.
?GSVJ0 SGSVJ0 DGSVJ0	S D	Applies Jacobi rotations in the same way as [DS]GESVJ does, but it does not check convergence (stopping criterion).
?GSVJ1 SGSVJ1 DGSVJ1	S D	Applies Jacobi rotations in the same way as [DS]GESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion).
?GTCON SGTCON DGTCON CGTCON ZGTCON	S D C Z	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 ?GTTRF.
?GTRFS SGTRFS DGTRFS CGTRFS ZGTRFS	S D C Z	Improves the computed solution to a general tridiagonal system of linear equations AX=B, ATX=B or AHX=B, and provides forward and backward error bounds for the solution.
?GTTRF SGTTRF DGTTRF CGTTRF ZGTTRF	S D C Z	Computes an LU factorization of a general tridiagonal matrix, using partial pivoting with row interchanges.
?GTTRS SGTTRS DGTTRS CGTTRS ZGTTRS	S D C Z	Solves a general tridiagonal system of linear equations AX=B, ATX=B or AHX=B, using the LU factorization computed by ?GTTRF.
?GTTS2 SGTTS2 DGTTS2 CGTTS2 ZGTTS2	S D C Z	Solves one of the systems of equations AX=B, ATX=B, or AHX=B, with a tridiagonal matrix A using the LU factorization computed by ?GTTRF.
?HBGST CHBGST ZHBGST	C Z	Reduces a Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form, where B has been factorized by ?PBSTF (Crawford's algorithm).
?HBTRD CHBTRD ZHBTRD	C Z	Reduces a Hermitian band matrix to real symmetric tridiagonal form by a unitary similarity transformation.
?HECON CHECON ZHECON	C Z	Estimates the reciprocal of the condition number of a Hermitian indefinite matrix, using the factorization computed by ?HETRF.
?HEEQUB CHEEQUB ZHEEQUB	C Z	Computes row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the two-norm).
?HEGS2 CHEGS2 ZHEGS2	C Z	Reduces a complex Hermitian-definite generalized eigenproblem to standard form.
?HEGST CHEGST ZHEGST	C Z	Reduces a Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx, or BAx=λx, to standard form, where B has been factorized by ?POTRF.
?HERFS CHERFS ZHERFS	C Z	Improves the computed solution to a Hermitian indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution.
?HETD2 CHETD2 ZHETD2	C Z	Reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: QHAQ=T.
?HETF2 CHETF2 ZHETF2	C Z	Computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method: A=UDUH or A=LDLH where U (or L) is a product of permutation and unit upper (lower) triangular matrices, UH is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
?HETRD CHETRD ZHETRD	C Z	Reduces a Hermitian matrix to real symmetric tridiagonal form by an orthogonal/unitary similarity transformation.
?HETRF CHETRF ZHETRF	C Z	Computes the factorization of a Hermitian-indefinite matrix, using the diagonal pivoting method.
?HETRI CHETRI ZHETRI	C Z	Computes the inverse of a Hermitian indefinite matrix, using the factorization computed by ?HETRF.
?HETRI2 CHETRI2 ZHETRI2	C Z	Computes the inverse of a complex hermitian indefinite matrix A using the factorization A=UDUT or A=LDLT computed by ?HETRF.
?HETRI2X CHETRI2X ZHETRI2X	C Z	Computes the inverse of a complex Hermitian indefinite matrix A using the factorization A=UDUH or A=LDLH computed by ?HETRF.
?HETRS CHETRS ZHETRS	C Z	Solves a Hermitian indefinite system of linear equations AX=B, using the factorization computed by ?HPTRF.
?HETRS2 CHETRS2 ZHETRS2	C Z	Solves a system of linear equations AX=B with a complex Hermitian matrix A using the factorization A=UDUH or A=LDLH computed by ?HETRF and converted by ?SYCONV.
?HFRK CHFRK ZHFRK	C Z	Performs one of the Hermitian rank--k operations C:=αAAH+βC, or C:=αAHA+βC, where α and β are real scalars, C is an n--by--n Hermitian matrix and A is an n--by--k matrix in the first case and a k--by--n matrix in the second case.
?HGEQZ SHGEQZ DHGEQZ CHGEQZ ZHGEQZ	S D C Z	Implements a single/double-shift version of the QZ method for finding the generalized eigenvalues of the equation det(A - w(i) B) = 0.
?HPCON CHPCON ZHPCON	C Z	Estimates the reciprocal of the condition number of a Hermitian indefinite matrix in packed storage, using the factorization computed by ?HPTRF.
?HPGST CHPGST ZHPGST	C Z	Reduces a Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx, or BAx=λx, to standard form, where A and B are held in packed storage, and B has been factorized by ?PPTRF.
?HPRFS CHPRFS ZHPRFS	C Z	Improves the computed solution to a Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.
?HPTRD CHPTRD ZHPTRD	C Z	Reduces a Hermitian matrix in packed storage to real symmetric tridiagonal form by a unitary similarity transformation.
?HPTRF CHPTRF ZHPTRF	C Z	Computes the factorization of a Hermitian-indefinite matrix in packed storage, using the diagonal pivoting method.
?HPTRI CHPTRI ZHPTRI	C Z	Computes the inverse of a Hermitian indefinite matrix in packed storage, using the factorization computed by ?HPTRF.
?HPTRS CHPTRS ZHPTRS	C Z	Solves a Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by ?HPTRF.
?HSEIN SHSEIN DHSEIN CHSEIN ZHSEIN	S D C Z	Computes specified right and/or left eigenvectors of an upper Hessenberg matrix by inverse iteration.
?HSEQR SHSEQR DHSEQR CHSEQR ZHSEQR	S D C Z	Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the multishift QR algorithm.
?LAED0 SLAED0 DLAED0 CLAED0 ZLAED0	S D C Z	Computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.
?LAED1 SLAED1 DLAED1	S D	Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix.
?LAED2 SLAED2 DLAED2	S D	Merges the two sets of eigenvalues together into a single sorted set.
?LAED3 SLAED3 DLAED3	S D	Finds the roots of the secular equation, as defined by the values in D, W, and ρ, between 1 and K.
?LAED4 SLAED4 DLAED4	S D	Computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array D, and that D(i)<D(j) for i<j and that ρ>0.
?LAED5 SLAED5 DLAED5	S D	Computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix.
?LAED6 SLAED6 DLAED6	S D	Computes the positive or negative root (closest to the origin) of the secular equation, as defined by the values in D, Z, and ρ.
?LAED7 SLAED7 DLAED7 CLAED7 ZLAED7	S D C Z	Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix.
?LAED8 SLAED8 DLAED8 CLAED8 ZLAED8	S D C Z	Merges the two sets of eigenvalues together into a single sorted set.
?LAED9 SLAED9 DLAED9	S D	Finds the roots of the secular equation, as defined by the values in D, Z, and ρ, between KSTART and KSTOP.
?LAEDA SLAEDA DLAEDA	S D	Computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem.
?LAGTF SLAGTF DLAGTF	S D	Factorizes the matrix (T-λI), where T is an n by n tridiagonal matrix and λ is a scalar, as T-λI=PLU, where P is a permutation matrix, L is a unit lower tridiagonal matrix with at most one non-zero sub-diagonal elements per column and U is an upper triangular matrix with at most two non-zero super-diagonal elements per column.
?LAHEF CLAHEF ZLAHEF	C Z	Computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method.
?LALS0 SLALS0 DLALS0 CLALS0 ZLALS0	S D C Z	Applies back the multiplying factors of either the left or the right singular vector matrix of a bidiagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach.
?LALSA SLALSA DLALSA CLALSA ZLALSA	S D C Z	Applies the singular vector matrix of an upper bidiagonal matrix or its inverse matrix to the right hand side.
?LALSD SLALSD DLALSD CLALSD ZLALSD	S D C Z	Uses the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of AX-B, where A is N-by-N upper bidiagonal, and X and B are N-by-NRHS.
?LAMRG SLAMRG DLAMRG	S D	Creates a permutation list which merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order.
?LANHF CLANHF ZLANHF	C Z	Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A in RFP format.
?LANSF SLANSF DLANSF	S D	Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format.
?LARTGS SLARTGS DLARTGS	S D	Generates a plane rotation designed to introduce a bulge in Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD problem.
?LARZ SLARZ DLARZ CLARZ ZLARZ	S D C Z	Applies a general elementary reflector H to a general M-by-N matrix C, from either the left or the right.
?LARZB SLARZB DLARZB CLARZB ZLARZB	S D C Z	Applies a general block reflector H or its transpose HH to a general distributed M-by-N C from the left or the right.
?LARZT SLARZT DLARZT CLARZT ZLARZT	S D C Z	Forms the triangular factor T of a general block reflector H of order>n, which is defined as a product of k elementary reflectors.
?LASQ1 SLASQ1 DLASQ1	S D	Computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E.
?LASQ2 SLASQ2 DLASQ2	S D	Computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow.
?LASQ3 SLASQ3 DLASQ3	S D	Checks for deflation, computes a shift (TAU) and calls dqds.
?LASQ4 SLASQ4 DLASQ4	S D	Computes an approximation TAU to the smallest eigenvalue using values of d from the previous transform.
?LASQ5 SLASQ5 DLASQ5	S D	Computes one dqds transform, one version for IEEE machines another for non IEEE machines.
?LASQ6 SLASQ6 DLASQ6	S D	Computes one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow.
?LASRT SLASRT DLASRT	S D	Sort the numbers in D in increasing order (if ID='I') or in decreasing order (if ID='D' ).
?LASYF SLASYF DLASYF CLASYF ZLASYF	S D C Z	Computes a partial factorization of a general symmetric matrix A using the Bunch-Kaufman diagonal pivoting method.
?LATRZ SLATRZ DLATRZ CLATRZ ZLATRZ	S D C Z	Factors the M-by-(M+L) general upper trapezoidal matrix [A1 A2]=[A(1:M,1:M) A(1:M,N-L+1:N)] as ( R 0 )*Z by means of orthogonal/unitary transformations, where Z is an (M+L)-by-(M+L) orthogonal/unitary matrix and, R and A1 are M-by-M upper triangular matrices.
?LATZM SLATZM DLATZM CLATZM ZLATZM	S D C Z	Applies a Householder matrix generated by ?TZRQF to a matrix. This routine is deprecated and has been replaced by routine [DS]ORMRZ/[ZC]UNMRZ.
?OPGTR SOPGTR DOPGTR	S D	Generates the orthogonal transformation matrix from a reduction to tridiagonal form determined by ?SPTRD.
?OPMTR SOPMTR DOPMTR	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form, determined by ?SPTRD.
?ORBDB SORBDB DORBDB	S D	Simultaneously bidiagonalizes the blocks of an M-by-M partitioned orthogonal matrix X.
?ORCSD SORCSD DORCSD	S D	Computes the CS decomposition of an M-by-M partitioned orthogonal matrix X.
?ORG2L SORG2L DORG2L	S D	Generates an m by n real matrix Q with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order m Q=H(k) ...H(2) H(1) as returned by ?GEQLF.
?ORG2R SORG2R DORG2R	S D	Generates an m by n real matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m Q=H(1) H(2) ...H(k) as returned by ?GEQRF.
?ORGBR SORGBR DORGBR	S D	Generates the orthogonal transformation matrices from a reduction to bidiagonal form determined by ?GEBRD.
?ORGHR SORGHR DORGHR	S D	Generates the orthogonal transformation matrix from a reduction to Hessenberg form determined by ?GEHRD.
?ORGL2 SORGL2 DORGL2	S D	Generates an m by n real matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n Q=H(k) ...H(2) H(1) as returned by ?GELQF.
?ORGLQ SORGLQ DORGLQ	S D	Generates all or part of the orthogonal matrix Q from an LQ factorization determined by ?GELQF.
?ORGQL SORGQL DORGQL	S D	Generates all or part of the orthogonal matrix Q from a QL factorization determined by ?GEQLF.
?ORGQR SORGQR DORGQR	S D	Generates all or part of the orthogonal matrix Q from a QR factorization determined by ?GEQRF.
?ORGR2 SORGR2 DORGR2	S D	Generates an m by n real matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n Q=H(1) H(2) ...H(k) as returned by ?GERQF.
?ORGRQ SORGRQ DORGRQ	S D	Generates all or part of the orthogonal matrix Q from an RQ factorization determined by ?GERQF.
?ORGTR SORGTR DORGTR	S D	Generates the orthogonal transformation matrix from a reduction to tridiagonal form determined by ?SYTRD.
?ORM2L SORM2L DORM2L	S D	Overwrites the general real m by n matrix C with QC, QTC, CQ, CQT, where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q=H(k) ...H(2) H(1) as returned by ?GEQLF.
?ORM2R SORM2R DORM2R	S D	Overwrites the general real m by n matrix C with QC, QTC, CQ, CQT, where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q=H(1) H(2) ...H(k) as returned by ?GEQRF.
?ORMBR SORMBR DORMBR	S D	Multiplies a general matrix by one of the orthogonal transformation matrices from a reduction to bidiagonal form determined by ?GEBRD.
?ORMHR SORMHR DORMHR	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to Hessenberg form determined by ?GEHRD.
?ORML2 SORML2 DORML2	S D	Overwrites the general real m by n matrix C with QC, QTC, CQ, CQT, where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q=H(k) ...H(2) H(1) as returned by ?GELQF.
?ORMLQ SORMLQ DORMLQ	S D	Multiplies a general matrix by the orthogonal matrix from an LQ factorization determined by ?GELQF.
?ORMQL SORMQL DORMQL	S D	Multiplies a general matrix by the orthogonal matrix from a QL factorization determined by ?GEQLF.
?ORMQR SORMQR DORMQR	S D	Multiplies a general matrix by the orthogonal matrix from a QR factorization determined by ?GEQRF.
?ORMR2 SORMR2 DORMR2	S D	Overwrites the general real m by n matrix C with QC, QTC, CQ,CQT, where Q is a real orthogonal matrix defined as the product of k elementary reflectors Q=H(1) H(2) ...H(k) as returned by ?GERQF.
?ORMR3 SORMR3 DORMR3	S D	Multiples a general matrix by the orthogonal matrix from an RZ factorization determined by ?TZRZF.
?ORMRQ SORMRQ DORMRQ	S D	Multiplies a general matrix by the orthogonal matrix from an RQ factorization determined by ?GERQF.
?ORMRZ SORMRZ DORMRZ	S D	Multiples a general matrix by the orthogonal matrix from an RZ factorization determined by ?TZRZF.
?ORMTR SORMTR DORMTR	S D	Multiplies a general matrix by the orthogonal transformation matrix from a reduction to tridiagonal form determined by ?SYTRD.
?PBCON SPBCON DPBCON CPBCON ZPBCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite band matrix, using the Cholesky factorization computed by ?PBTRF.
?PBEQU SPBEQU DPBEQU CPBEQU ZPBEQU	S D C Z	Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite band matrix and reduce its condition number.
?PBRFS SPBRFS DPBRFS CPBRFS ZPBRFS	S D C Z	Improves the computed solution to a symmetric/Hermitian positive definite banded system of linear equations AX=B, and provides forward and backward error bounds for the solution.
?PBSTF SPBSTF DPBSTF CPBSTF ZPBSTF	S D C Z	Computes a split Cholesky factorization of a symmetric/Hermitian positive definite band matrix.
?PBTF2 SPBTF2 DPBTF2 CPBTF2 ZPBTF2	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix A.
?PBTRF SPBTRF DPBTRF CPBTRF ZPBTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix.
?PBTRS SPBTRS DPBTRS CPBTRS ZPBTRS	S D C Z	Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B, using the Cholesky factorization computed by ?PBTRF.
?PFTRF SPFTRF DPFTRF CPFTRF ZPFTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix A.
?PFTRI SPFTRI DPFTRI CPFTRI ZPFTRI	S D C Z	Computes the inverse of a symmetric/Hermitian positive definite matrix A using the Cholesky factorization A=UHU or A=LLH computed by ?PFTRF.
?PFTRS SPFTRS DPFTRS CPFTRS ZPFTRS	S D C Z	Solves a system of linear equations AX=B with a symmetric/Hermitian positive definite matrix A using the Cholesky factorization A=UHU or A=LLH computed by ?PFTRF.
?POCON SPOCON DPOCON CPOCON ZPOCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by ?POTRF.
?POEQU SPOEQU DPOEQU CPOEQU ZPOEQU	S D C Z	Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix and reduce its condition number.
?POEQUB SPOEQUB DPOEQUB CPOEQUB ZPOEQUB	S D C Z	Computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm).
?PORFS SPORFS DPORFS CPORFS ZPORFS	S D C Z	Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations AX=B, and provides forward and backward error bounds for the solution.
?POTF2 SPOTF2 DPOTF2 CPOTF2 ZPOTF2	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix A.
?POTRF SPOTRF DPOTRF CPOTRF ZPOTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix.
?POTRI SPOTRI DPOTRI CPOTRI ZPOTRI	S D C Z	Computes the inverse of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by ?POTRF.
?POTRS SPOTRS DPOTRS CPOTRS ZPOTRS	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, using the Cholesky factorization computed by ?POTRF.
?PPCON SPPCON DPPCON CPPCON ZPPCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by ?PPTRF.
?PPEQU SPPEQU DPPEQU CPPEQU ZPPEQU	S D C Z	Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix in packed storage and reduce its condition number.
?PPRFS SPPRFS DPPRFS CPPRFS ZPPRFS	S D C Z	Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.
?PPTRF SPPTRF DPPTRF CPPTRF ZPPTRF	S D C Z	Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix in packed storage.
?PPTRI SPPTRI DPPTRI CPPTRI ZPPTRI	S D C Z	Computes the inverse of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by ?PPTRF.
?PPTRS SPPTRS DPPTRS CPPTRS ZPPTRS	S D C Z	Solves a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage, using the Cholesky factorization computed by ?PPTRF.
?PSTF2 SPSTF2 DPSTF2 CPSTF2 ZPSTF2	S D C Z	Computes the Cholesky factorization with complete pivoting of a symmetric/Hermitian positive semidefinite matrix A.
?PSTRF SPSTRF DPSTRF CPSTRF ZPSTRF	S D C Z	Computes the Cholesky factorization with complete pivoting of a symmetric/Hermitian positive semidefinite matrix A.
?PTCON SPTCON DPTCON CPTCON ZPTCON	S D C Z	Computes the reciprocal of the condition number of a symmetric/Hermitian positive definite tridiagonal matrix, using the LDLH factorization computed by ?PTTRF.
?PTEQR SPTEQR DPTEQR CPTEQR ZPTEQR	S D C Z	Computes all eigenvalues and eigenvectors of a symmetric positive definite tridiagonal matrix, by computing the SVD of its bidiagonal Cholesky factor.
?PTRFS SPTRFS DPTRFS CPTRFS ZPTRFS	S D C Z	Improves the computed solution to a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B, and provides forward and backward error bounds for the solution.
?PTTRF SPTTRF DPTTRF CPTTRF ZPTTRF	S D C Z	Computes the LDLH factorization of a symmetric/Hermitian positive definite tridiagonal matrix.
?PTTRS SPTTRS DPTTRS CPTTRS ZPTTRS	S D C Z	Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations, using the LDLH factorization computed by ?PTTRF.
?PTTS2 SPTTS2 DPTTS2 CPTTS2 ZPTTS2	S D C Z	Solves a tridiagonal system of the form AX=B using the factorization A=UHDU or A=LDLH computed by ?PTTRF.
?SBGST SSBGST DSBGST	S D	Reduces a real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form, where B has been factorized by ?PBSTF (Crawford's algorithm).
?SBTRD SSBTRD DSBTRD	S D	Reduces a symmetric band matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.
?SFRK SSFRK DSFRK	S D	Performs one of the symmetric rank--k operations C:=αAAT+βC, or C:=αATA+βC, where alpha and beta are real scalars, C is an n--by--n symmetric matrix and A is an n--by--k matrix in the first case and a k--by--n matrix in the second case.
?SPCON SSPCON DSPCON CSPCON ZSPCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric indefinite matrix in packed storage, using the factorization computed by ?SPTRF.
?SPGST SSPGST DSPGST	S D	Reduces a symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx, or BAx=λx, to standard form, where A and B are held in packed storage, and B has been factorized by ?PPTRF.
?SPRFS SSPRFS DSPRFS CSPRFS ZSPRFS	S D C Z	Improves the computed solution to a symmetric indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution.
?SPTRD SSPTRD DSPTRD	S D	Reduces a symmetric matrix in packed storage to real symmetric tridiagonal form by an orthogonal similarity transformation.
?SPTRF SSPTRF DSPTRF CSPTRF ZSPTRF	S D C Z	Computes the factorization of a symmetric-indefinite matrix in packed storage, using the diagonal pivoting method.
?SPTRI SSPTRI DSPTRI CSPTRI ZSPTRI	S D C Z	Computes the inverse of a symmetric indefinite matrix in packed storage, using the factorization computed by ?SPTRF.
?SPTRS SSPTRS DSPTRS CSPTRS ZSPTRS	S D C Z	Solves a symmetric indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by ?SPTRF.
?STEBZ SSTEBZ DSTEBZ	S D	Computes selected eigenvalues of a real symmetric tridiagonal matrix by bisection.
?STEDC SSTEDC DSTEDC CSTEDC ZSTEDC	S D C Z	Computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer algorithm.
?STEGR SSTEGR DSTEGR CSTEGR ZSTEGR	S D C Z	Computes selected eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix. The eigenvalues are computed by the dqds algorithm, while eigenvectors are computed from various "good" LDLT representations (also known as Relatively Robust Representations).
?STEIN SSTEIN DSTEIN CSTEIN ZSTEIN	S D C Z	Computes selected eigenvectors of a real symmetric tridiagonal matrix by inverse iteration.
?STEMR SSTEMR DSTEMR CSTEMR ZSTEMR	S D C Z	Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T.
?STEQR SSTEQR DSTEQR CSTEQR ZSTEQR	S D C Z	Computes all eigenvalues and eigenvectors of a real symmetric tridiagonal matrix, using the implicit QL or QR algorithm.
?STERF SSTERF DSTERF	S D	Computes all eigenvalues of a real symmetric tridiagonal matrix, using a root-free variant of the QL or QR algorithm.
?SYCON SSYCON DSYCON CSYCON ZSYCON	S D C Z	Estimates the reciprocal of the condition number of a symmetric indefinite matrix, using the factorization computed by ?SYTRF.
?SYCONV SSYCONV DSYCONV CSYCONV ZSYCONV	S D C Z	Converts A given by [DS]SYTRF/[ZC]HETRF into L and D and vice-versa.
?SYEQUB SSYEQUB DSYEQUB CSYEQUB ZSYEQUB	S D C Z	Computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm).
?SYGS2 SSYGS2 DSYGS2	S D	Reduces a real symmetric-definite generalized eigenproblem to standard form.
?SYGST SSYGST DSYGST	S D	Reduces a symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx, or BAx=λx, to standard form, where B has been factorized by ?POTRF.
?SYRFS SSYRFS DSYRFS CSYRFS ZSYRFS	S D C Z	Improves the computed solution to a symmetric indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution.
?SYTD2 SSYTD2 DSYTD2	S D	Reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation: QTAQ=T.
?SYTF2 SSYTF2 DSYTF2 CSYTF2 ZSYTF2	S D C Z	Computes the factorization of a general symmetric matrix A using the Bunch-Kaufman diagonal pivoting method: A=UDUT or A=LDLT where U (or L) is a product of permutation and unit upper (lower) triangular matrices, UT is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
?SYTRD SSYTRD DSYTRD	S D	Reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation.
?SYTRF SSYTRF DSYTRF CSYTRF ZSYTRF	S D C Z	Computes the factorization of a symmetric-indefinite matrix, using the diagonal pivoting method.
?SYTRI SSYTRI DSYTRI CSYTRI ZSYTRI	S D C Z	Computes the inverse of a symmetric indefinite matrix, using the factorization computed by ?SYTRF.
?SYTRI2 SSYTRI2 DSYTRI2 CSYTRI2 ZSYTRI2	S D C Z	Computes the inverse of a general symmetric indefinite matrix A using the factorization A=UDUT or A=LDLT computed by ?SYTRF.
?SYTRI2X SSYTRI2X DSYTRI2X CSYTRI2X ZSYTRI2X	S D C Z	Computes the inverse of a general symmetric indefinite matrix A using the factorization A=UDUT or A=LDLT computed by ?SYTRF.
?SYTRS SSYTRS DSYTRS CSYTRS ZSYTRS	S D C Z	Solves a symmetric indefinite system of linear equations AX=B, using the factorization computed by ?SPTRF.
?SYTRS2 SSYTRS2 DSYTRS2 CSYTRS2 ZSYTRS2	S D C Z	Solves a system of linear equations AX=B with a general symmetric matrix A using the factorization A=UDUT or A=LDLT computed by ?SYTRF and converted by ?SYCONV.
?TBCON STBCON DTBCON CTBCON ZTBCON	S D C Z	Estimates the reciprocal of the condition number of a triangular band matrix, in either the 1-norm or the Infinity-norm.
?TBRFS STBRFS DTBRFS CTBRFS ZTBRFS	S D C Z	Provides forward and backward error bounds for the solution of a triangular banded system of linear equations AX=B, ATX=B or AHX=B.
?TBTRS STBTRS DTBTRS CTBTRS ZTBTRS	S D C Z	Solves a triangular banded system of linear equations AX=B, ATX=B or AHX=B.
?TFSM STFSM DTFSM CTFSM ZTFSM	S D C Z	Solves the matrix equation op(A)*X=αB or X*op(A)=βB where α is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op(A)=A or op(A)=AH.
?TFTRI STFTRI DTFTRI CTFTRI ZTFTRI	S D C Z	Computes the inverse of a triangular matrix A stored in RFP format.
?TFTTP STFTTP DTFTTP CTFTTP ZTFTTP	S D C Z	Copies a triangular matrix A from rectangular full packed format (TF) to standard packed format (TP).
?TFTTR STFTTR DTFTTR CTFTTR ZTFTTR	S D C Z	Copies a triangular matrix A from rectangular full packed format (TF) to standard full format (TR).
?TGEVC STGEVC DTGEVC CTGEVC ZTGEVC	S D C Z	Computes some or all of the right and/or left generalized eigenvectors of a pair of upper triangular matrices.
?TGEXC STGEXC DTGEXC CTGEXC ZTGEXC	S D C Z	Reorders the generalized 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.
?TGSEN STGSEN DTGSEN CTGSEN ZTGSEN	S D C Z	Reorders the generalized Schur decomposition of a matrix pair (A,B) so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B).
?TGSJA STGSJA DTGSJA CTGSJA ZTGSJA	S D C Z	Computes the generalized singular value decomposition of two upper triangular (or trapezoidal) matrices as output by ?GGSVP.
?TGSNA STGSNA DTGSNA CTGSNA ZTGSNA	S D C Z	Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A,B) in generalized Schur canonical form, as returned by ?GGES.
?TGSYL STGSYL DTGSYL CTGSYL ZTGSYL	S D C Z	Solves the generalized Sylvester equation.
?TPCON STPCON DTPCON CTPCON ZTPCON	S D C Z	Estimates the reciprocal of the condition number of a triangular matrix in packed storage, in either the 1-norm or the Infinity-norm.
?TPMQRT STPMQRT DTPMQRT CTPMQRT ZTPMQRT	S D C Z	Applies a general orthogonal matrix Q obtained from a "triangular-pentagonal" general block reflector H to a general general matrix C, which consists of two blocks A and B.
?TPQRT STPQRT DTPQRT CTPQRT ZTPQRT	S D C Z	Computes a blocked QR factorization of a general "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.
?TPQRT2 STPQRT2 DTPQRT2 CTPQRT2 ZTPQRT2	S D C Z	Computes a QR factorization of a general "triangular-pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q.
?TPRFS STPRFS DTPRFS CTPRFS ZTPRFS	S D C Z	Provides forward and backward error bounds for the solution of a triangular system of linear equations AX=B, ATX=B or AHX=B, where A is held in packed storage.
?TPTRI STPTRI DTPTRI CTPTRI ZTPTRI	S D C Z	Computes the inverse of a triangular matrix in packed storage.
?TPTRS STPTRS DTPTRS CTPTRS ZTPTRS	S D C Z	Solves a triangular system of linear equations AX=B, ATX=B or AHX=B, where A is held in packed storage.
?TPTTF STPTTF DTPTTF CTPTTF ZTPTTF	S D C Z	Copies a triangular matrix A from standard packed format (TP) to rectangular full packed format (TF).
?TPTTR STPTTR DTPTTR CTPTTR ZTPTTR	S D C Z	Copies a triangular matrix A from standard packed format (TP) to standard full format (TR).
?TRCON STRCON DTRCON CTRCON ZTRCON	S D C Z	Estimates the reciprocal of the condition number of a triangular matrix, in either the 1-norm or the Infinity-norm.
?TREVC STREVC DTREVC CTREVC ZTREVC	S D C Z	Computes left and right eigenvectors of an upper quasi-triangular/triangular matrix.
?TREXC STREXC DTREXC CTREXC ZTREXC	S D C Z	Reorders the Schur factorization of a matrix by an orthogonal/unitary similarity transformation.
?TRRFS STRRFS DTRRFS CTRRFS ZTRRFS	S D C Z	Provides forward and backward error bounds for the solution of a triangular system of linear equations AX=B, ATX=B or AHX=B.
?TRSEN STRSEN DTRSEN CTRSEN ZTRSEN	S D C Z	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.
?TRSNA STRSNA DTRSNA CTRSNA ZTRSNA	S D C Z	Estimates the reciprocal condition numbers (sensitivities) of selected eigenvalues and eigenvectors of an upper quasi-triangular/triangular matrix.
?TRSYL STRSYL DTRSYL CTRSYL ZTRSYL	S D C Z	Solves the Sylvester matrix equation AX ± XB=C, where A and B are upper quasi-triangular/triangular, and may be transposed.
?TRTI2 STRTI2 DTRTI2 CTRTI2 ZTRTI2	S D C Z	Computes the inverse of a general upper or lower triangular matrix.
?TRTRI STRTRI DTRTRI CTRTRI ZTRTRI	S D C Z	Computes the inverse of a triangular matrix.
?TRTRS STRTRS DTRTRS CTRTRS ZTRTRS	S D C Z	Solves a triangular system of linear equations AX=B, ATX=B or AHX=B.
?TRTTF STRTTF DTRTTF CTRTTF ZTRTTF	S D C Z	Copies a triangular matrix A from standard full format (TR) to rectangular full packed format (TF) .
?TRTTP STRTTP DTRTTP CTRTTP ZTRTTP	S D C Z	Copies a triangular matrix A from full format (TR) to standard packed format (TP).
?TZRQF STZRQF DTZRQF CTZRQF ZTZRQF	S D C Z	Computes an RQ factorization of an upper trapezoidal matrix.
?TZRZF STZRZF DTZRZF CTZRZF ZTZRZF	S D C Z	Computes an RZ factorization of an upper trapezoidal matrix (blocked version of ?TZRQF).
?UNBDB CUNBDB ZUNBDB	C Z	Simultaneously bidiagonalizes the blocks of an M-by-M partitioned unitary matrix X.
?UNCSD CUNCSD ZUNCSD	C Z	Computes the CS decomposition of an M-by-M partitioned unitary matrix X.
?UNG2L CUNG2L ZUNG2L	C Z	Generates an m by n complex matrix Q with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order m Q=H(k) ...H(2) H(1) as returned by ?GEQLF.
?UNG2R CUNG2R ZUNG2R	C Z	Generates an m by n complex matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m Q=H(1) H(2) ...H(k) as returned by ?GEQRF.
?UNGBR CUNGBR ZUNGBR	C Z	Generates the unitary transformation matrices from a reduction to bidiagonal form determined by ?GEBRD.
?UNGHR CUNGHR ZUNGHR	C Z	Generates the unitary transformation matrix from a reduction to Hessenberg form determined by ?GEHRD.
?UNGL2 CUNGL2 ZUNGL2	C Z	Generates an m-by-n complex matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n Q=H(k)H ...H(2)H H(1)H as returned by ?GELQF.
?UNGLQ CUNGLQ ZUNGLQ	C Z	Generates all or part of the unitary matrix Q from an LQ factorization determined by ?GELQF.
?UNGQL CUNGQL ZUNGQL	C Z	Generates all or part of the unitary matrix Q from a QL factorization determined by ?GEQLF.
?UNGQR CUNGQR ZUNGQR	C Z	Generates all or part of the unitary matrix Q from a QR factorization determined by ?GEQRF.
?UNGR2 CUNGR2 ZUNGR2	C Z	Generates an m by n complex matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n Q=H(1)H H(2)H ...H(k)H as returned by ?GERQF.
?UNGRQ CUNGRQ ZUNGRQ	C Z	Generates all or part of the unitary matrix Q from an RQ factorization determined by ?GERQF.
?UNGTR CUNGTR ZUNGTR	C Z	Generates the unitary transformation matrix from a reduction to tridiagonal form determined by ?HETRD.
?UNM2L CUNM2L ZUNM2L	C Z	Overwrites the general complex m-by-n matrix C with QC, QHC, CQ , CQH, where Q is a complex unitary matrix defined as the product of k elementary reflectors Q=H(k) ...H(2) H(1) as returned by ?GEQLF.
?UNM2R CUNM2R ZUNM2R	C Z	Overwrites the general complex m-by-n matrix C with QC, QHC,CQ, CQH, where Q is a complex unitary matrix defined as the product of k elementary reflectors Q=H(1) H(2) ...H(k) as returned by ?GEQRF.
?UNMBR CUNMBR ZUNMBR	C Z	Multiplies a general matrix by one of the unitary transformation matrices from a reduction to bidiagonal form determined by ?GEBRD.
?UNMHR CUNMHR ZUNMHR	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to Hessenberg form determined by ?GEHRD.
?UNML2 CUNML2 ZUNML2	C Z	Overwrites the general complex m-by-n matrix C with QC, QHC, CQ, CQH, where Q is a complex unitary matrix defined as the product of k elementary reflectors Q=H(k)H ...H(2)H H(1)H as returned by ?GELQF.
?UNMLQ CUNMLQ ZUNMLQ	C Z	Multiplies a general matrix by the unitary matrix from an LQ factorization determined by ?GELQF.
?UNMQL CUNMQL ZUNMQL	C Z	Multiplies a general matrix by the unitary matrix from a QL factorization determined by ?GEQLF.
?UNMQR CUNMQR ZUNMQR	C Z	Multiplies a general matrix by the unitary matrix from a QR factorization determined by ?GEQRF.
?UNMR2 CUNMR2 ZUNMR2	C Z	Overwrites the general complex m-by-n matrix C with QC, QHC, CQ, CQH, where Q is a complex unitary matrix defined as the product of k elementary reflectors Q=H(1)H H(2)H ...H(k)H as returned by ?GERQF.
?UNMR3 CUNMR3 ZUNMR3	C Z	Multiples a general matrix by the unitary matrix from an RZ factorization determined by ?TZRZF.
?UNMRQ CUNMRQ ZUNMRQ	C Z	Multiplies a general matrix by the unitary matrix from an RQ factorization determined by ?GERQF.
?UNMRZ CUNMRZ ZUNMRZ	C Z	Multiples a general matrix by the unitary matrix from an RZ factorization determined by ?TZRZF.
?UNMTR CUNMTR ZUNMTR	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by ?HETRD.
?UPGTR CUPGTR ZUPGTR	C Z	Generates the unitary transformation matrix from a reduction to tridiagonal form determined by ?HPTRD.
?UPMTR CUPMTR ZUPMTR	C Z	Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by ?HPTRD.
CHLA_TRANSTYPE		Translates from a BLAST-specified integer constant to the character string specifying a transposition operation.
ILADIAG		Translated from a character string specifying if a matrix has unit diagonal or not to the relevant BLAST-specified integer constant.
ILAPREC		Translated from a character string specifying an intermediate precision to the relevant BLAST-specified integer constant.
ILATRANS		Translates from a character string specifying a transposition operation to the relevant BLAST-specified integer constant.
ILAUPLO		Translated from a character string specifying a upper-or lower-triangular matrix to the relevant BLAST-specified integer constant.
ILAVER		Returns the LAPACK version.

Auxiliary Subprograms

^† ? indicates prefix which must be filled with a combination of:
S = REAL(kind=4), D = REAL(kind=8), C = COMPLEX(kind=4), Z = COMPLEX(kind=8)

Prefixes	Routine†
S D C Z	?GESC2 SGESC2 DGESC2 CGESC2 ZGESC2 ?GETC2 SGETC2 DGETC2 CGETC2 ZGETC2 ?LABRD SLABRD DLABRD CLABRD ZLABRD ?LACN2 SLACN2 DLACN2 CLACN2 ZLACN2 ?LACON SLACON DLACON CLACON ZLACON ?LACPY SLACPY DLACPY CLACPY ZLACPY ?LADIV SLADIV DLADIV CLADIV ZLADIV ?LAEIN SLAEIN DLAEIN CLAEIN ZLAEIN ?LAEV2 SLAEV2 DLAEV2 CLAEV2 ZLAEV2 ?LAGS2 SLAGS2 DLAGS2 CLAGS2 ZLAGS2 ?LAGTM SLAGTM DLAGTM CLAGTM ZLAGTM ?LAHQR SLAHQR DLAHQR CLAHQR ZLAHQR ?LAHR2 SLAHR2 DLAHR2 CLAHR2 ZLAHR2 ?LAHRD SLAHRD DLAHRD CLAHRD ZLAHRD ?LAIC1 SLAIC1 DLAIC1 CLAIC1 ZLAIC1 ?LANGB SLANGB DLANGB CLANGB ZLANGB ?LANGE SLANGE DLANGE CLANGE ZLANGE ?LANGT SLANGT DLANGT CLANGT ZLANGT ?LANHS SLANHS DLANHS CLANHS ZLANHS ?LANSB SLANSB DLANSB CLANSB ZLANSB ?LANSP SLANSP DLANSP CLANSP ZLANSP ?LANSY SLANSY DLANSY CLANSY ZLANSY ?LANTB SLANTB DLANTB CLANTB ZLANTB ?LANTP SLANTP DLANTP CLANTP ZLANTP ?LANTR SLANTR DLANTR CLANTR ZLANTR ?LAPLL SLAPLL DLAPLL CLAPLL ZLAPLL ?LAPMR SLAPMR DLAPMR CLAPMR ZLAPMR ?LAPMT SLAPMT DLAPMT CLAPMT ZLAPMT ?LAQGB SLAQGB DLAQGB CLAQGB ZLAQGB ?LAQGE SLAQGE DLAQGE CLAQGE ZLAQGE ?LAQP2 SLAQP2 DLAQP2 CLAQP2 ZLAQP2 ?LAQPS SLAQPS DLAQPS CLAQPS ZLAQPS ?LAQR0 SLAQR0 DLAQR0 CLAQR0 ZLAQR0 ?LAQR1 SLAQR1 DLAQR1 CLAQR1 ZLAQR1 ?LAQR2 SLAQR2 DLAQR2 CLAQR2 ZLAQR2 ?LAQR3 SLAQR3 DLAQR3 CLAQR3 ZLAQR3 ?LAQR4 SLAQR4 DLAQR4 CLAQR4 ZLAQR4 ?LAQR5 SLAQR5 DLAQR5 CLAQR5 ZLAQR5 ?LAQSB SLAQSB DLAQSB CLAQSB ZLAQSB ?LAQSP SLAQSP DLAQSP CLAQSP ZLAQSP ?LAQSY SLAQSY DLAQSY CLAQSY ZLAQSY ?LAR1V SLAR1V DLAR1V CLAR1V ZLAR1V ?LAR2V SLAR2V DLAR2V CLAR2V ZLAR2V ?LARF SLARF DLARF CLARF ZLARF ?LARFB SLARFB DLARFB CLARFB ZLARFB ?LARFG SLARFG DLARFG CLARFG ZLARFG ?LARFGP SLARFGP DLARFGP CLARFGP ZLARFGP ?LARFT SLARFT DLARFT CLARFT ZLARFT ?LARFX SLARFX DLARFX CLARFX ZLARFX ?LARGV SLARGV DLARGV CLARGV ZLARGV ?LARNV SLARNV DLARNV CLARNV ZLARNV ?LARRV SLARRV DLARRV CLARRV ZLARRV ?LARTG SLARTG DLARTG CLARTG ZLARTG ?LARTV SLARTV DLARTV CLARTV ZLARTV ?LASCL SLASCL DLASCL CLASCL ZLASCL ?LASET SLASET DLASET CLASET ZLASET ?LASR SLASR DLASR CLASR ZLASR ?LASSQ SLASSQ DLASSQ CLASSQ ZLASSQ ?LASWP SLASWP DLASWP CLASWP ZLASWP ?LATBS SLATBS DLATBS CLATBS ZLATBS ?LATDF SLATDF DLATDF CLATDF ZLATDF ?LATPS SLATPS DLATPS CLATPS ZLATPS ?LATRD SLATRD DLATRD CLATRD ZLATRD ?LATRS SLATRS DLATRS CLATRS ZLATRS ?LAUU2 SLAUU2 DLAUU2 CLAUU2 ZLAUU2 ?LAUUM SLAUUM DLAUUM CLAUUM ZLAUUM ?SYSWAPR SSYSWAPR DSYSWAPR CSYSWAPR ZSYSWAPR ?TGEX2 STGEX2 DTGEX2 CTGEX2 ZTGEX2 ?TGSY2 STGSY2 DTGSY2 CTGSY2 ZTGSY2 ?TPRFB STPRFB DTPRFB CTPRFB ZTPRFB ILA?LC ILASLC ILADLC ILACLC ILAZLC ILA?LR ILASLR ILADLR ILACLR ILAZLR
S D CS ZD	?RSCL SRSCL DRSCL CSRSCL ZDRSCL
S D	?ISNAN SISNAN DISNAN ?LABAD SLABAD DLABAD ?LAE2 SLAE2 DLAE2 ?LAEBZ SLAEBZ DLAEBZ ?LAEXC SLAEXC DLAEXC ?LAG2 SLAG2 DLAG2 ?LAGTS SLAGTS DLAGTS ?LAGV2 SLAGV2 DLAGV2 ?LAISNAN SLAISNAN DLAISNAN ?LALN2 SLALN2 DLALN2 ?LAMCH SLAMCH DLAMCH ?LANEG SLANEG DLANEG ?LANST SLANST DLANST ?LANV2 SLANV2 DLANV2 ?LAPY2 SLAPY2 DLAPY2 ?LAPY3 SLAPY3 DLAPY3 ?LAQTR SLAQTR DLAQTR ?LARRA SLARRA DLARRA ?LARRB SLARRB DLARRB ?LARRC SLARRC DLARRC ?LARRD SLARRD DLARRD ?LARRE SLARRE DLARRE ?LARRF SLARRF DLARRF ?LARRJ SLARRJ DLARRJ ?LARRK SLARRK DLARRK ?LARRR SLARRR DLARRR ?LARTGP SLARTGP DLARTGP ?LARUV SLARUV DLARUV ?LAS2 SLAS2 DLAS2 ?LASD0 SLASD0 DLASD0 ?LASD1 SLASD1 DLASD1 ?LASD2 SLASD2 DLASD2 ?LASD3 SLASD3 DLASD3 ?LASD4 SLASD4 DLASD4 ?LASD5 SLASD5 DLASD5 ?LASD6 SLASD6 DLASD6 ?LASD7 SLASD7 DLASD7 ?LASD8 SLASD8 DLASD8 ?LASDA SLASDA DLASDA ?LASDQ SLASDQ DLASDQ ?LASDT SLASDT DLASDT ?LASV2 SLASV2 DLASV2 ?LASY2 SLASY2 DLASY2
C Z	?HESWAPR CHESWAPR ZHESWAPR ?LACGV CLACGV ZLACGV ?LACP2 CLACP2 ZLACP2 ?LACRM CLACRM ZLACRM ?LACRT CLACRT ZLACRT ?LAESY CLAESY ZLAESY ?LANHB CLANHB ZLANHB ?LANHE CLANHE ZLANHE ?LANHP CLANHP ZLANHP ?LANHT CLANHT ZLANHT ?LAQHB CLAQHB ZLAQHB ?LAQHE CLAQHE ZLAQHE ?LAQHP CLAQHP ZLAQHP ?LARCM CLARCM ZLARCM ?SPMV CSPMV ZSPMV ?SPR CSPR ZSPR ?SYR CSYR ZSYR I?MAX1 ICMAX1 IZMAX1
SC DZ	?SUM1 SCSUM1 DZSUM1
n/a	CLAG2Z DLAG2S DLAT2S DSECND IEEECK ILAENV IPARMQ LSAMEN SECOND SLAG2D XERBLA_ARRAY ZLAG2C ZLAT2C

External Links

1. LAPACK User's Guide
2. A Quick Reference guide for LAPACK (downloading a PostScript format file)
3. A hardcopy LAPACK User's Guide may be ordered from SIAM.

Version Information

• This manual page version: 2.2.0-181019