INTRO_BLAS1 - Introduction to vector-vector linear algebra subprograms

INTRO_BLAS2 - Introduction to matrix-vector linear algebra subprograms

INTRO_BLAS3 - Introduction to matrix-matrix linear algebra subprograms

INTRO_BLAS - Introduction to SCSL Basic Linear Algebra Subprograms

INTRO_CBLAS - Introduction to the C interface to Fortran 77 Basic Linear Algebra Subprograms (legacy BLAS)

INTRO_FFT - Introduction to signal processing routines

INTRO_LAPACK - Introduction to LAPACK solvers for dense linear systems

INTRO_SCSL - Introduction to Scientific Computing Software Library (SCSL) routines

INTRO_SOLVERS - Introduction to SGI-developed linear equation solvers

CGEMM3M, ZGEMM3M - Multiplies a complex general matrix by a complex general matrix

CHBMV, ZHBMV - Multiplies a complex vector by a complex Hermitian band matrix

CHEMM, ZHEMM - Multiplies a complex general matrix by a complex Hermitian matrix

CHEMV, ZHEMV - Multiplies a complex vector by a complex Hermitian matrix

CHER2, ZHER2 - Performs Hermitian rank 2 update of a complex Hermitian matrix

CHER2K, ZHER2K - Performs Hermitian rank 2k update of a complex Hermitian matrix

CHER, ZHER - Performs Hermitian rank 1 update of a complex Hermitian matrix

CHERK, ZHERK - Performs Hermitian rank k update of a complex Hermitian matrix

CHPMV, ZHPMV - Multiplies a complex vector by a packed complex Hermitian matrix

CHPR2, ZHPR2 - Performs Hermitian rank 2 update of a packed complex Hermitian matrix

CHPR, ZHPR - Performs Hermitian rank 1 update of a packed complex Hermitian matrix

CSROT, ZDROT - applies a real plane rotation to a pair of complex vectors

DGEMMS - Multiplies a real general matrix by a real general matrix, using Strassen's algorithm

ISAMAX, IDAMAX, ICAMAX, IZAMAX - Searches a vector for the first occurrence of the maximum absolute value

ISAMIN, IDAMIN - Searches a vector for the first occurrence of the minimum absolute value

ISMAX, IDMAX - Searches a real vector for the first occurrence of the maximum value

ISMIN, IDMIN - Searches a real vector for the first occurrence of the minimum value

SASUM, DASUM, SCASUM, DZASUM - Sums the absolute value of elements in a real or complex vector

SAXPBY, DAXPBY, CAXPBY, ZAXPBY - Adds a scalar multiple of a Single precision or complex vector x to a scalar multiple of another Single precision or complex vector y

SAXPY, CAXPY, DAXPY, ZAXPY - Adds a scalar multiple of a real or complex vector to another real or complex vector

SCOPY, DCOPY, CCOPY, ZCOPY - Copies a real or complex vector into another real or complex vector

SDOT, DDOT, CDOTC, ZDOTC, CDOTU, ZDOTU - Computes a dot product (inner product) of two real or complex vectors

SGBMV, DGBMV, CGBMV, ZGMBV - Multiplies a real or complex vector by a real or complex general band matrix

SGEMM, DGEMM, CGEMM, ZGEMM - Multiplies a real or complex general matrix by a real or complex general matrix

SGEMV, DGEMV, CGEMV, ZGEMV - Multiplies a real or complex vector by a real or complex general matrix

SGER, DGER, CGERC, ZGERC, CGERU, ZGERU - Performs rank 1 update of a real or complex general matrix

SGESUM, DGESUM, CGESUM, ZGESUM - Adds a scalar multiple of a real or complex matrix to a scalar multiple of another real or complex matrix

SHAD, DHAD, CHAD, ZHAD - Computes the Hadamard product of two vectors

SNRM2, DNRM2, SCNRM2, DZNRM2 - Computes the Euclidean norm of a vector

SROT, DROT, CROT, ZROT - applies a real plane rotation or complex coordinate rotation

SROTG, DROTG, CROTG, ZROTG - Constructs a Givens plane rotation

SROTM, DROTM - applies a modified Givens plane rotation

SROTMG, DROTMG - Constructs a modified Givens plane rotation

SSBMV, DSBMV - Multiplies a real vector by a real symmetric band matrix

SSCAL, DSCAL, CSSCAL, ZDSCAL, CSCAL, ZSCAL - Scales a real or complex vector

SSPMV, DSPMV, CSPMV, ZSPMV - Multiplies a real or complex symmetric packed matrix by a real or complex vector

SSPR2, DSPR2 - Performs symmetric rank 2 update of a real symmetric packed matrix

SSPR, DSPR, CSPR, ZSPR - Performs symmetric rank 1 update of a real or complex symmetric packed matrix

SSUM, DSUM, CSUM, ZSUM - Sums the elements of a real or complex vector

SSWAP, DSWAP, CSWAP, ZSWAP - Swaps two real or complex vectors

SSYMM, DSYMM, CSYMM, ZSYMM - Multiplies a real or complex general matrix by a real or complex symmetric matrix

SSYMV, DSYMV, CSYMV, ZSYMV - Multiplies a real or complex vector by a real or complex symmetric matrix

SSYR2, DSYR2 - Performs symmetric rank 2 update of a real symmetric matrix

SSYR2K, DSYR2K, CSYR2K, ZSYR2K - Performs symmetric rank 2k update of a real or complex symmetric matrix

SSYR, DSYR, CSYR, ZSYR - Performs symmetric rank 1 update of a real or complex symmetric matrix

SSYRK, DSYRK, CSYRK, ZSYRK - Performs symmetric rank k update of a real or complex symmetric matrix

STBMV, DTBMV, CTBMV, ZTBMV - Multiplies a real or complex vector by a real or complex triangular band matrix

STBSV, DTBSV, CTBSV, ZTBSV - Solves a real or complex triangular banded system of equations

STPMV, DTPMV, CTPMV, ZTPMV - Multiplies a real or complex vector by a real or complex triangular packed matrix

STPSV, DTPSV, CTPSV, ZTPSV - Solves a real or complex triangular packed system of equations

STRMM, DTRMM, CTRMM, ZTRMM - Multiplies a real or complex general matrix by a real or complex triangular matrix

STRMV, DTRMV, CTRMV, ZTRMV - Multiplies a real or complex vector by a real or complex triangular matrix

STRSM, DTRSM, CTRSM, ZTRSM - Solves a real or complex triangular system of equations with multiple right-hand sides

STRSV, DTRSV, CTRSV, ZTRSV - Solves a real or complex triangular system of equations

CCFFT2D, ZZFFT2D - applies a two-dimensional complex-to-complex Fast Fourier Transform (FFT)

CCFFT3D, ZZFFT3D - applies a three-dimensional complex-to-complex Fast Fourier Transform (FFT)

CCFFT, ZZFFT - applies a complex-to-complex Fast Fourier Transform (FFT)

CCFFTF, CCFFTMF, CCFFTMRF, CCFFT2DF, CCFFT3DF, ZZFFTF, ZZFFTMF, ZZFFTMRF, ZZFFT2DF, ZZFFT3DF - deallocates memory tacked on to the table array during initialization

CCFFTM, ZZFFTM - applies multiple complex-to-complex Fast Fourier Transforms (FFTs)

CCFFTMR, ZZFFTMR - applies multiple complex-to-complex Fast Fourier Transforms (FFTs) to the rows of a two-dimensional (2D) array

CCOR1D, ZCOR1D, SCOR1D, DCOR1D - computes the one-dimensional (1D) correlation of two sequences.

CCOR2D, ZCOR2D, SCOR2D, DCOR2D - computes the two-dimensional (2D) correlation of two two-dimensional (2D) arrays

CCORM1D, ZCORM1D, SCORM1D, DCORM1D - computes multiple 1D correlations

CFIR1D, ZFIR1D, SFIR1D, DFIR1D -computes the 1D convolution of a sequence

CFIR2D, ZFIR2D, SFIR2D, DFIR2D - computes the two-dimensional (2D) convolution of two 2D arrays

CFIRM1D, ZFIRM1D, SFIRM1D, DFIRM1D - computes multiple 1D convolutions

SCFFT2D, DZFFT2D, CSFFT2D, ZDFFT2D - applies a two-dimensional real-to-complex or complex-to-real Fast Fourier Transform (FFT)

SCFFT3D, DZFFT3D, CSFFT3D, ZDFFT3D - applies a three-dimensional real-to-complex Fast Fourier Transform (FFT)

SCFFT, DZFFT, CSFFT, ZDFFT - computers a real-to-complex or complex-to-real Fast Fourier Transform (FFT)

SCFFTF, SCFFTMF, SCFFT2DF, SCFFT3DF, DZFFTF, DZFFTMF, DZFFT2DF, DZFFT3DF - Deallocate memory tacked on to the table array during initialization

SCFFTM, DZFFTM, CSFFTM, ZDFFTM - applies multiple real-to-complex or complex-to-real Fast Fourier Transforms (FFTs)

CBDSQR - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

CGBBRD - reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation

CGBCON - estimates the reciprocal of the condition number of a complex general band matrix A

CGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

CGBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is banded

CGBSV - computes the solution to a complex system of linear equations

CGBSVX - uses the LU factorization to compute the solution to a complex system of linear equations

CGBTF2 - computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

CGBTRF - computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

CGBTRS - solves a system of linear equations with a general band matrix A using the LU factorization computed by CGBTRF

CGEBAK - forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by CGEBAL

CGEBAL - balances a general complex matrix A

CGEBD2 - reduces a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation

CGEBRD - reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation

CGECON - estimates the reciprocal of the condition number of a general complex matrix A using the LU factorization computed by CGETRF

CGEEQU - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

CGEES - computes the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

CGEESX - computes the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

CGEEV - computes the eigenvalues and, optionally, the left and/or right eigenvectors

CGEEVX - computes the eigenvalues and, optionally, the left and/or right eigenvectors

CGEGS - routine is deprecated and has been replaced by routine CGGES

CGEGV - routine is deprecated and has been replaced by routine CGGEV

CGEHD2 - reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

CGEHRD - reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

CGELQ2 - computes an LQ factorization of a complex m by n matrix A

CGELQF - computes an LQ factorization of a complex M-by-N matrix A

CGELS - solves overdetermined or underdetermined complex linear systems

CGELSD - computes the minimum-norm solution to a real linear least squares problem

CGELSS - computes the minimum norm solution to a complex linear least squares problem

CGELSX - routine is deprecated and has been replaced by routine CGELSY

CGELSY - computes the minimum-norm solution to a complex linear least squares problem

CGEQL2 - computes a QL factorization of a complex m by n matrix A

CGEQLF - computes a QL factorization of a complex M-by-N matrix A

CGEQP3 - computes a QR factorization with column pivoting of a matrix A

CGEQPF - routine is deprecated and has been replaced by routine CGEQP3

CGEQR2 - computes a QR factorization of a complex m by n matrix A

CGEQRF - computes a QR factorization of a complex M-by-N matrix A

CGERFS - improves the computed solution to a system of linear equations

CGERQ2 - computes an RQ factorization of a complex m by n matrix A

CGERQF - computes an RQ factorization of a complex M-by-N matrix A

CGESC2 - solves a system of linear equations with a general N-by-N matrix A using the LU factorization with complete pivoting computed by CGETC2

CGESDD - computes the singular value decomposition (SVD) of a complex M-by-N matrix A

CGESV - computes the solution to a complex system of linear equations

CGESVD - computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors

CGESVX - uses the LU factorization to compute the solution to a complex system of linear equations

CGETC2 - computes an LU factorization, using complete pivoting, of the n-by-n matrix A

CGETF2 - computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

CGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

CGETRI - computes the inverse of a matrix using the LU factorization computed by CGETRF

CGETRS - solves a system of linear equations with a general N-by-N matrix A using the LU factorization computed by CGETRF

CGGBAK - forms the right or left eigenvectors of a complex generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL

CGGBAL - balances a pair of general complex matrices (A,B)

CGGES - computes the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)

CGGESX - computes the generalized eigenvalues, the complex Schur form (S,T),

CGGEV - computes the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

CGGEVX - computes the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

CGGGLM - solves a general Gauss-Markov linear model (GLM) problem

CGGHRD - reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular

CGGLSE - solves the linear equality-constrained least squares (LSE) problem

CGGQRF - computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B

CGGRQF - computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

CGGSVD - computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B

CGGSVP - computes unitary matrices

CGTCON - estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF

CGTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal

CGTSV - solves the equation AX = B,

CGTSVX - uses the LU factorization to compute the solution to a complex system of linear equations

CGTTRF - computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges

CGTTRS - solves systems of equations

CGTTS2 - solves systems of equations

CHBEV - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

CHBEVD - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

CHBEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

CHBGST - reduces a complex Hermitian-definite banded generalized eigenproblem

CHBGV - computes all the eigenvalues and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

CHBGVD - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

CHBGVX - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

CHBTRD - reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

CHECON - estimates the reciprocal of the condition number of a complex Hermitian matrix A

CHEEV - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

CHEEVD - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

CHEEVR - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T

CHEEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

CHEGS2 - reduces a complex Hermitian-definite generalized eigenproblem to standard form

CHEGST - reduces a complex Hermitian-definite generalized eigenproblem to standard form

CHEGV - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHEGVD - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHEGVX - computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHERFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite

CHESV - computes the solution to a complex system of linear equations

CHESVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

CHETD2 - reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

CHETF2 - computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

CHETRD - reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

CHETRF - computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

CHETRI - computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by CHETRF

CHETRS - solves a system of linear equations with a complex Hermitian matrix A using the factorization computed by CHETRF

CHGEQZ - implements a single-shift version of the QZ method for finding the generalized eigenvalues

CHPCON - estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization computed by CHPTRF

CHPEV - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

CHPEVD - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

CHPEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

CHPGST - reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

CHPGV - computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHPGVD - computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHPGVX - computes selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem

CHPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed

CHPSV - computes the solution to a complex system of linear equations

CHPSVX - uses diagonal pivoting factorization to compute the solution to a complex system of linear equations

CHPTRD - reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation

CHPTRF - computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method

CHPTRI - computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization computed by CHPTRF

CHPTRS - solves a system of linear equations with a complex Hermitian matrix A stored in packed format using the factorization computed by CHPTRF

CHSEIN - uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H

CHSEQR - computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition

CLABRD - reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form

CLACGV - conjugates a complex vector of length N

CLACON - estimates the 1-norm of a square, complex matrix A

CLACP2 - copies all or part of a real two-dimensional matrix A to a complex matrix B

CLACPY - copies all or part of a two-dimensional matrix A to another matrix B

CLACRM - performs a very simple matrix-matrix multiplication

CLACRT - perform the operation ( c s )( x ) >= ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vectors x and y are complex

CLADIV - := X / Y, where X and Y are complex

CLAED0 - computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block

CLAED7 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

CLAED8 - merges the two sets of eigenvalues together into a single sorted set

CLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

CLAESY - computes the eigendecomposition of a 2-by-2 symmetric matrix

CLAEV2 - computes the eigendecomposition of a 2-by-2 Hermitian matrix

CLAGS2 - computes 2-by-2 unitary matrices U, V and Q

CLAGTM - performs a matrix-vector product

CLAHEF - computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

CLAHQR - an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR

CLAHRD - reduces the first NB columns of a complex general matrix so that elements below the k-th subdiagonal are zero

CLAIC1 - applies one step of incremental condition estimation in its simplest version

CLALS0 - applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix

CLALSA - an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form

CLALSD - 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

CLANGB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A

CLANGE - 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 matrix A

CLANGT - 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 tridiagonal matrix A

CLANHB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals

CLANHE - 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

CLANHP - 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, supplied in packed form

CLANHS - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A

CLANHT - 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 tridiagonal matrix A

CLANSB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals

CLANSP - 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 symmetric matrix A, supplied in packed form

CLANSY - 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 symmetric matrix A

CLANTB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals

CLANTP - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form

CLANTR - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

CLAPLL - computes the QR factorization of A=QR

CLAPMT - rearranges the columns of the M by N matrix X

CLAQGB - equilibrates a general M by N band matrix A

CLAQGE - equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C

CLAQHB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

CLAQHE - equilibrates a Hermitian matrix A using the scaling factors in the vector S

CLAQHP - equilibrates a Hermitian matrix A using the scaling factors in the vector S

CLAQP2 - computes a QR factorization with column pivoting

CLAQPS - computes a step of QR factorization with column pivoting of a complex M-by-N matrix A

CLAQSB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

CLAQSP - equilibrates a symmetric matrix A using the scaling factors in the vector S

CLAQSY - equilibrates a symmetric matrix A using the scaling factors in the vector S

CLAR1V - computes the (scaled) r ^th column of the inverse of the sumbmatrix in rows B1 through BN of a tridiagonal matrix

CLAR2V - applies a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,

CLARCM - performs a very simple matrix-matrix multiplication

CLARF - applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

CLARFB - applies a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right

CLARFG - generates a complex elementary reflector H of order n

CLARFT - forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors

CLARFX - applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right

CLARGV - generates a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y

CLARNV - returns a vector of n random complex numbers from a uniform or normal distribution

CLARRV - computes the eigenvectors of a tridiagonal matrix

CLARTG - generates a plane rotation

CLARTV - applies a vector of complex plane rotations with real cosines to elements of the complex vectors x and y

CLARZ - applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

CLARZB - applies a complex block reflector H or its transpose to a complex distributed M-by-N C from the left or the right

CLARZT - forms the triangular factor T of a complex block reflector H

CLASCL - multiplies the M by N complex matrix A by the real scalar CTO/CFROM

CLASET - initializes a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals

CLASR - performs a transformation A := PA

CLASSQ - returns the values scl and ssq

CLASWP - performs a series of row interchanges on the matrix A

CLASYF - computes a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

CLATBS - solves a triangular system

CLATDF - computes the contribution to the reciprocal Dif-estimate

CLATPS - solves a triangular system

CLATRD - reduces NB rows and columns of a complex Hermitian matrix A

CLATRS - solves a triangular system

CLATRZ - factors a M-by-(M+L) complex upper trapezoidal matrix

CLATZM - routine is deprecated and has been replaced by routine CUNMRZ

CLAUU2 - computes the product U × U' or L' × L

CLAUUM - computes the product U × U' or L' × L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A

CPBCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization computed by CPBTRF

CPBEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)

CPBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded

CPBSTF - computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A

CPBSV - computes the solution to a complex system of linear equations

CPBSVX - uses the Cholesky factorization to compute the solution to a complex system of linear equations

CPBTF2 - computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

CPBTRF - computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

CPBTRS - solves a system of linear equations with a Hermitian positive definite band matrix A

CPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix

CPOEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)

CPORFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite

CPOSV - computes the solution to a complex system of linear equations

CPOSVX - uses the Cholesky factorization to compute the solution to a complex system of linear equations

CPOTF2 - computes the Cholesky factorization of a complex Hermitian positive definite matrix A

CPOTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A

CPOTRI - computes the inverse of a complex Hermitian positive definite matrix A

CPOTRS - solves a system of linear equations with a Hermitian positive definite matrix A

CPPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix

CPPEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

CPPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution

CPPSV - computes the solution to a complex system of linear equations

CPPSVX - uses the Cholesky factorization to compute the solution to a complex system of linear equations

CPPTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format

CPPTRI - computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization computed by CPPTRF

CPPTRS - solves a system of linear equations with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization computed by CPPTRF

CPTCON - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization computed by CPTTRF

CPTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix

CPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal

CPTSV - computes the solution to a complex system of linear equations

CPTSVX - computes the solution to a complex system of linear equations

CPTTRF - computes the factorization of a complex Hermitian positive definite tridiagonal matrix A

CPTTRS - solves a tridiagonal system using the factorization computed by CPTTRF

CPTTS2 - solves a tridiagonal system using the factorization computed by CPTTRF

CSPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A

CSPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed

CSPSV - computes the solution to a complex system of linear equations

CSPSVX - uses diagonal pivoting factorization to compute the solution to a complex system of linear equations

CSPTRF - computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

CSPTRI - computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization computed by CSPTRF

CSPTRS - solves a system of linear equations with a complex symmetric matrix A stored in packed format using the factorization computed by CSPTRF

CSRSCL - multiplies an n-element complex vector x by the real scalar 1/a

CSTEDC - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

CSTEGR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

CSTEIN - computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

CSTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

CSYCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by CSYTRF

CSYRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution

CSYSV - computes the solution to a complex system of linear equations

CSYSVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

CSYTF2 - computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

CSYTRF - computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

CSYTRI - computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by CSYTRF

CSYTRS - solves a system of linear equations with a complex symmetric matrix A using the factorization computed by CSYTRF

CTBCON - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

CTBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

CTBTRS - solves a triangular system

CTGEVC - computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)

CTGEX2 - swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

CTGEXC - reorders the generalized Schur decomposition of a complex matrix pair (A,B), using a unitary equivalence transformation

CTGSEN - reorders the generalized Schur decomposition of a complex matrix pair (A, B)

CTGSJA - computes the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B

CTGSNA - estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B)

CTGSY2 - solves the generalized Sylvester equation using Level 1 and 2 BLAS

CTGSYL - solves the generalized Sylvester equation

CTPCON - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm

CTPRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

CTPTRI - computes the inverse of a complex upper or lower triangular matrix A stored in packed format

CTPTRS - solves a triangular system

CTRCON - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

CTREVC - computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T

CTREXC - reorders the Schur factorization of a complex matrix so that the diagonal element of T with row index IFST is moved to row ILST

CTRID - computes the solution to a complex system of linear equations

CTRRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix

CTRSEN - reorders the Schur factorization of a complex matrix

CTRSNA - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T

CTRSYL - solves the complex Sylvester matrix equation

CTRTI2 - computes the inverse of a complex upper or lower triangular matrix

CTRTRI - computes the inverse of a complex upper or lower triangular matrix A

CTRTRS - solves a triangular system

CTZRQF - routine is deprecated and has been replaced by routine CTZRZF

CTZRZF - reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations

CUNG2L - generates an m by n complex matrix Q with orthonormal columns,

CUNG2R - generates an m by n complex matrix Q with orthonormal columns,

CUNGBR - generates one of the complex unitary matrices Q or P^H determined by CGEBRD when reducing a complex matrix A to bidiagonal form

CUNGHR - generates a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD

CUNGL2 - generates an m-by-n complex matrix Q with orthonormal rows,

CUNGLQ - generates an M-by-N complex matrix Q with orthonormal rows,

CUNGQL - generates an M-by-N complex matrix Q with orthonormal columns,

CUNGQR - generates an M-by-N complex matrix Q with orthonormal columns,

CUNGR2 - generates an m by n complex matrix Q with orthonormal rows,

CUNGRQ - generates an M-by-N complex matrix Q with orthonormal rows,

CUNGTR - generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD

CUNM2L - overwrites the general complex m-by-n matrix C

CUNM2R - overwrites the general complex m-by-n matrix C

CUNMBR - overwrites the general complex M-by-N matrix C

CUNMHR - overwrites the general complex M-by-N matrix C

CUNML2 - overwrites the general complex m-by-n matrix C

CUNMLQ - overwrites the general complex M-by-N matrix C

CUNMQL - overwrites the general complex M-by-N matrix C

CUNMQR - overwrites the general complex M-by-N matrix C

CUNMR2 - overwrites the general complex m-by-n matrix C

CUNMR3 - overwrites the general complex m by n matrix C

CUNMRQ - overwrites the general complex M-by-N matrix C

CUNMRZ - overwrites the general complex M-by-N matrix C

CUNMTR - overwrites the general complex M-by-N matrix C

CUPGTR - generates a complex unitary matrix Q

CUPMTR - overwrites the general complex M-by-N matrix C

DBDSDC - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

DBDSQR - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

DDISNA - computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix

DGBBRD - reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

DGBCON - estimates the reciprocal of the condition number of a real general band matrix A

DGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

DGBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is banded

DGBSV - computes the solution to a real system of linear equations

DGBSVX - uses the LU factorization to compute the solution to a real system of linear equations

DGBTF2 - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

DGBTRF - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

DGBTRS - solves a system of linear equations with a general band matrix A using the LU factorization computed by DGBTRF

DGEBAK - forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL

DGEBAL - balances a general real matrix A

DGEBD2 - reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation

DGEBRD - reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation

DGECON - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF

DGEEQU - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

DGEES - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z

DGEESX - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z

DGEEV - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

DGEEVX - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

DGEGS - routine is deprecated and has been replaced by routine DGGES

DGEGV - routine is deprecated and has been replaced by routine DGGEV

DGEHD2 - reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation

DGEHRD - reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation

DGELQ2 - computes an LQ factorization of a real m by n matrix A

DGELQF - computes an LQ factorization of a real M-by-N matrix A

DGELS - solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A

DGELSD - computes the minimum-norm solution to a real linear least squares problem

DGELSS - computes the minimum norm solution to a real linear least squares problem

DGELSX - routine is deprecated and has been replaced by routine DGELSY

DGELSY - computes the minimum-norm solution to a real linear least squares problem

DGEQL2 - computes a QL factorization of a real m by n matrix A

DGEQLF - computes a QL factorization of a real M-by-N matrix A

DGEQP3 - computes a QR factorization with column pivoting of a matrix A

DGEQPF - routine is deprecated and has been replaced by routine DGEQP3

DGEQR2 - computes a QR factorization of a real m by n matrix A

DGEQRF - computes a QR factorization of a real M-by-N matrix A

DGERFS - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

DGERQ2 - computes an RQ factorization of a real m by n matrix A

DGERQF - computes an RQ factorization of a real M-by-N matrix A

DGESC2 - solves a system of linear equations with a general N-by-N matrix A using the LU factorization with complete pivoting computed by DGETC2

DGESDD - computes the singular value decomposition (SVD) of a real M-by-N matrix A

DGESV - computes the solution to a real system of linear equations

DGESVD - computes the singular value decomposition (SVD) of a real M-by-N matrix A

DGESVX - uses the LU factorization to compute the solution to a real system of linear equations

DGETC2 - computes an LU factorization with complete pivoting of the n-by-n matrix A

DGETF2 - computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

DGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

DGETRI - computes the inverse of a matrix using the LU factorization computed by DGETRF

DGETRS - solves a system of linear equations with a general N-by-N matrix A using the LU factorization computed by DGETRF

DGGBAK - forms the right or left eigenvectors of a real generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL

DGGBAL - balances a pair of general real matrices (A,B)

DGGES - computes for a pair of N-by-N real nonsymmetric matrices (A,B),

DGGESX - computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues and the real Schur form (S,T)

DGGEV - computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues

DGGEVX - computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues

DGGGLM - solves a general Gauss-Markov linear model (GLM) problem

DGGHRD - reduces a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular

DGGLSE - solves the linear equality-constrained least squares (LSE) problem

DGGQRF - computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B

DGGRQF - computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

DGGSVD - computes the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B

DGGSVP - computes orthogonal matrices U, V and Q

DGTCON - estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF

DGTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal

DGTSV - solves the equation AX = B

DGTSVX - uses the LU factorization to compute the solution to a real system of linear equations

DGTTRF - computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges

DGTTRS - solves one of the systems of equations AX = B or A'X = B

DGTTS2 - solves one of the systems of equations AX = B or A'X = B

DHGEQZ - implements a single-/double-shift version of the QZ method for finding generalized eigenvalues

DHSEIN - uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H

DHSEQR - computes the eigenvalues of a real upper Hessenberg matrix H

DLABAD - returns the square root of values

DLABRD - reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation

DLACON - estimates the 1-norm of a square, real matrix A

DLACPY - copies all or part of a two-dimensional matrix A to another matrix B

DLADIV - performs complex division in real arithmetic

DLAE2 - computes the eigenvalues of a 2-by-2 symmetric matrix

DLAEBZ - contains the iteration loops which compute and use the function N(w)

DLAED0 - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

DLAED1 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

DLAED2 - merges the two sets of eigenvalues together into a single sorted set

DLAED3 - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K

DLAED4 - computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix

DLAED5 - computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix

DLAED6 - computes the positive or negative root (closest to the origin)

DLAED7 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

DLAED8 - merges the two sets of eigenvalues together into a single sorted set

DLAED9 - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP

DLAEDA - computes the Z vector corresponding to the merge step in the CURLVL^th step of the merge process with TLVLS steps for the CURPBMth problem

DLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H

DLAEV2 - computes the eigendecomposition of a 2-by-2 symmetric matrix

DLAEXC - swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

DLAG2 - computes the eigenvalues of a 2 x 2 generalized eigenvalue problem with scaling as necessary to avoid over-/underflow

DLAGS2 - computes 2-by-2 orthogonal matrices U, V and Q

DLAGTF - factorizes a matrix

DLAGTM - performs a matrix-vector product

DLAGTS - solves one of two systems of equations

DLAGV2 - computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

DLAHQR - updates the eigenvalues and Schur decomposition already computed by DHSEQR

DLAHRD - reduces the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k ^th subdiagonal are zero

DLAIC1 - applies one step of incremental condition estimation in its simplest version

DLALN2 - solves a system with possible scaling and perturbation of A

DLALS0 - applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal 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

DLALSA - an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form

DLALSD - uses the singular value decomposition of A to solve the least squares problem

DLAMCH - determines double precision machine parameters

DLAMRG - creates a permutation list which merges the elements of A

DLANGB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A

DLANGE - 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 matrix A

DLANGT - 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 tridiagonal matrix A

DLANHS - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A

DLANSB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals

DLANSP - 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, supplied in packed form

DLANST - 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 tridiagonal matrix A

DLANSY - 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

DLANTB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals

DLANTP - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form

DLANTR - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

DLANV2 - computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form

DLAPLL - computers the QR factorization of A=QR

DLAPMT - rearranges the columns of the M by N matrix X

DLAPY2 - returns sqrt(x ²2+y²) without causing unnecessary overflow

DLAPY3 - returns sqrt(x ²+y²+z²) without causing unnecessary overflow

DLAQGB - equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C

DLAQGE - equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C

DLAQP2 - computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

DLAQPS - computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3

DLAQSB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

DLAQSP - equilibrates a symmetric matrix A using the scaling factors in the vector S

DLAQSY - equilibrates a symmetric matrix A using the scaling factors in the vector S

DLAQTR - solves a real quasi-triangular system

DLAR1V - computes the (scaled) r ^th column of the inverse of a sumbmatrix

DLAR2V - applies a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z

DLARF - applies a real elementary reflector H to a real m by n matrix C, from either the left or the right

DLARFB - applies a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right

DLARFG - generates a real elementary reflector H of order n

DLARFT - forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors

DLARFX - applies a real elementary reflector H to a real m by n matrix C, from either the left or the right

DLARGV - generates a vector of real plane rotations, determined by elements of the real vectors x and y

DLARNV - returns a vector of n random real numbers from a uniform or normal distribution

DLARRB - does limited bisection to locate eigenvalues

DLARRE - sets "small" off-diagonal elements to zero

DLARRF - finds a robust representation of input values

DLARRV - computes the eigenvectors of the tridiagonal matrix

DLARTG - generates a plane rotation

DLARTV - applies a vector of real plane rotations to elements of the real vectors x and y

DLARUV - returns a vector of n random real numbers from a uniform (0,1)

DLARZ - applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right

DLARZB - applies a real block reflector H or its transpose to a real distributed M-by-N C from the left or the right

DLARZT - forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors

DLAS2 - computes the singular values of the 2-by-2 matrix

DLASCL - multiplies the M by N real matrix A by the real scalar CTO/CFROM

DLASD0 - computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B

DLASD1 - computes the SVD of an upper bidiagonal N-by-M matrix B

DLASD2 - merges the two sets of singular values together into a single sorted set

DLASD3 - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z

DLASD4 - computes the square root of the I^th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix

DLASD5 - computes the square root of the I^th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix

DLASD6 - computes the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row

DLASD7 - merges the two sets of singular values together into a single sorted set

DLASD8 - finds the square roots of the roots of the secular equation,

DLASD9 - finds the square roots of the roots of the secular equation,

DLASDA - computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E

DLASDQ - computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired

DLASDT - creates a tree of subproblems for bidiagonal divide and conquer

DLASET - initializes an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals

DLASQ1 - computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E

DLASQ2 - computes all the eigenvalues of the symmetric positive definite tridiagonal matrix

DLASQ3 - computes a shift (TAU)

DLASQ4 - computes an approximation TAU to the smallest eigenvalue using values of d from the previous transform

DLASQ5 - computes one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines

DLASQ6 - computes one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow

DLASR - perform a transformation where A is an m by n real matrix and P is an orthogonal matrix,

DLASRT - sorts numbers

DLASSQ - returns the values scl and smsq

DLASV2 - computes the singular value decomposition of a 2-by-2 triangular matrix

DLASWP - performs a series of row interchanges on the matrix A

DLASY2 - solves for the N1 by N2 matrix X

DLASYF - computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

DLATBS - solves one of two triangular systems with scaling to prevent overflow, where A is an upper or lower triangular band matrix

DLATDF - uses the LU factorization of the n-by-n matrix Z computed by DGETC2

DLATPS - solves a triangular system with scaling to prevent overflow

DLATRD - reduces NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form

DLATRS - solves a triangular system with scaling to prevent overflow

DLATRZ - factors the M-by-(M+L) real upper trapezoidal matrix by means of orthogonal transformations

DLATZM - routine is deprecated and has been replaced by routine DORMRZ

DLAUU2 - computes the product U × U' or L' × L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A

DLAUUM - computes the product U × U' or L' × L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A

DOPGTR - generates a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage

DOPMTR - overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

DORG2L - generates an m by n real matrix Q with orthonormal columns

DORG2R - generates an m by n real matrix Q with orthonormal columns

DORGBR - generates one of the real orthogonal matrices Q or P^T determined by DGEBRD when reducing a real matrix A to bidiagonal form

DORGHR - generates a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

DORGL2 - generates an m by n real matrix Q with orthonormal rows

DORGLQ - generates an M-by-N real matrix Q with orthonormal rows

DORGQL - generates an M-by-N real matrix Q with orthonormal columns

DORGQR - generates an M-by-N real matrix Q with orthonormal columns

DORGR2 - generates an m by n real matrix Q with orthonormal rows

DORGRQ - generates an M-by-N real matrix Q with orthonormal rows

DORGTR - generates a real orthogonal matrix Q as returned by DSYTRD

DORM2L - overwrites the general real m by n matrix C

DORM2R - overwrites the general real m by n matrix C

DORMBR - overwrites the general real M-by-N matrix C

DORMHR - overwrites the general real M-by-N matrix C

DORML2 - overwrites the general real m by n matrix C

DORMLQ - overwrites the general real M-by-N matrix C

DORMQL - overwrites the general real M-by-N matrix C

DORMQR - overwrites the general real M-by-N matrix C

DORMR2 - overwrites the general real m by n matrix C

DORMR3 - overwrites the general real m by n matrix C

DORMRQ - overwrites the general real M-by-N matrix C

DORMRZ - overwrites the general real M-by-N matrix C

DORMTR - overwrites the general real M-by-N matrix C

DPBCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization computed by DPBTRF

DPBEQU - computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)

DPBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution

DPBSTF - computes a split Cholesky factorization of a real symmetric positive definite band matrix A

DPBSV - computes the solution to a real system of linear equations

DPBSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

DPBTF2 - computes the Cholesky factorization of a real symmetric positive definite band matrix A

DPBTRF - computes the Cholesky factorization of a real symmetric positive definite band matrix A

DPBTRS - solves a system of linear equations with a symmetric positive definite band matrix A using the Cholesky factorization computed by DPBTRF

DPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization computed by DPOTRF

DPOEQU - 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)

DPORFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite

DPOSV - computes the solution to a real system of linear equations

DPOSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

DPOTF2 - computes the Cholesky factorization of a real symmetric positive definite matrix A

DPOTRF - computes the Cholesky factorization of a real symmetric positive definite matrix A

DPOTRI - computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by DPOTRF

DPOTRS - solves a system of linear equations with a symmetric positive definite matrix A using the Cholesky factorization computed by DPOTRF

DPPCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization computed by DPPTRF

DPPEQU - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

DPPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed

DPPSV - computes the solution to a real system of linear equations

DPPSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

DPPTRF - computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format

DPPTRI - computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by DPPTRF

DPPTRS - solves a system of linear equations with a symmetric positive definite matrix A in packed storage using the Cholesky factorization computed by DPPTRF

DPTCON - computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization computed by DPTTRF

DPTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix

DPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal

DPTSV - computes the solution to a real system of linear equations

DPTSVX - computes the solution to a real system of linear equations where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

DPTTRF - computes the factorization of a real symmetric positive definite tridiagonal matrix A

DPTTRS - solves a tridiagonal system using the factorization of A computed by DPTTRF

DPTTS2 - solves a tridiagonal system using the factorization of A computed by DPTTRF

DRSCL - multiplies an n-element real vector x by the real scalar 1/a

DSBEV - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

DSBEVD - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

DSBEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

DSBGST - reduces a real symmetric-definite banded generalized eigenproblem

DSBGV - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem

DSBGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem

DSBGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem

DSBTRD - reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

DSECND - returns the user time for a process in seconds

DSPCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A

DSPEV - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

DSPEVD - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

DSPEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

DSPGST - reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage

DSPGV - computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

DSPGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

DSPGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem

DSPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed

DSPSV - computes the solution to a real system of linear equations

DSPSVX - uses the diagonal pivoting factorization to compute the solution to a real system of linear equations where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices

DSPTRD - reduces a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation

DSPTRF - computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

DSPTRI - computes the inverse of a real symmetric indefinite matrix A in packed storage using a factorization computed by DSPTRF

DSPTRS - solves a system of linear equations with a real symmetric matrix A stored in packed format using a factorization computed by DSPTRF

DSTEBZ - computes the eigenvalues of a symmetric tridiagonal matrix T

DSTEDC - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

DSTEGR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

DSTEIN - computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

DSTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

DSTERF - computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm

DSTEV - computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

DSTEVD - computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix

DSTEVR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

DSTEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

DSYCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using a factorization computed by DSYTRF

DSYEV - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

DSYEVD - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

DSYEVR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T

DSYEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

DSYGS2 - reduces a real symmetric-definite generalized eigenproblem to standard form

DSYGST - reduces a real symmetric-definite generalized eigenproblem to standard form

DSYGV - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

DSYGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

DSYGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem

DSYRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution

DSYSV - computes the solution to a real system of linear equations

DSYSVX - uses the diagonal pivoting factorization to compute the solution to a real system of linear equations

DSYTD2 - reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

DSYTF2 - computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

DSYTRD - reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation

DSYTRF - computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

DSYTRI - computes the inverse of a real symmetric indefinite matrix A using a factorizationcomputed by DSYTRF

DSYTRS - solves a system of linear equations with a real symmetric matrix A using a factorization computed by DSYTRF

DTBCON - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

DTBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

DTBTRS - solves a triangular system

DTGEVC - computes some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)

DTGEX2 - swaps adjacent diagonal blocks (A11, B11) and (A22, B22)

DTGEXC - reorders the generalized real Schur decomposition of a real matrix pair (A,B)

DTGSEN - reorders the generalized real Schur decomposition of a real matrix pair (A, B)

DTGSJA - computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B

DTGSNA - estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form

DTGSY2 - solves the generalized Sylvester equation

DTGSYL - solves the generalized Sylvester equation

DTPCON - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm

DTPRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

DTPTRI - computes the inverse of a real upper or lower triangular matrix A stored in packed format

DTPTRS - solves a triangular system

DTRCON - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

DTREVC - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T

DTREXC - reorders the real Schur factorization of a real matrix so that the diagonal block of T with row index IFST is moved to row ILST

DTRID - computes the solution to a real system of linear equations where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N

DTRRFS - provide serror bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix

DTRSEN - reorders the real Schur factorization of a real matrix so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T

DTRSNA - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T

DTRSYL - solves the real Sylvester matrix equation

DTRTI2 - computes the inverse of a real upper or lower triangular matrix

DTRTRI - computes the inverse of a real upper or lower triangular matrix A

DTRTRS - solves a triangular system

DTZRQF - routine is deprecated and has been replaced by routine DTZRZF

DTZRZF - reduces the M-by-N real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations

DZSUM1 - takes the sum of the absolute values of a complex vector and returns a double precision result

ICMAX1 - finds the index of the element whose real part has maximum absolute value

ILAENV - called from the LAPACK routines to choose problem-dependent parameters for the local environment

IZMAX1 - finds the index of the element whose real part has maximum absolute value

LSAME - return .TRUE

LSAMEN - tests if the first N letters of CA are the same as the first N letters of CB, regardless of case

SBDSDC - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

SBDSQR - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

SCSUM1 - take the sum of the absolute values of a complex vector and returns a single precision result

SDISNA - computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix

SECOND - returns the user time for a process in seconds

SGBBRD - reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

SGBCON - estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

SGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

SGBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is banded

SGBSV - computes the solution to a real system of linear equations where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices

SGBSVX - uses the LU factorization to compute the solution to a real system of linear equations

SGBTF2 - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

SGBTRF - computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

SGBTRS - solves a system of linear equations with a general band matrix A using the LU factorization computed by SGBTRF

SGEBAK - forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL

SGEBAL - balances a general real matrix A

SGEBD2 - reduces a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation

SGEBRD - reduces a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation

SGECON - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF

SGEEQU - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

SGEES - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z

SGEESX - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z

SGEEV - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

SGEEVX - computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

SGEGS - routine is deprecated and has been replaced by routine SGGES

SGEGV - routine is deprecated and has been replaced by routine SGGEV

SGEHD2 - reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation

SGEHRD - reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation

SGELQ2 - computes an LQ factorization of a real m by n matrix A

SGELQF - computes an LQ factorization of a real M-by-N matrix A

SGELS - solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A

SGELSD - computes the minimum-norm solution to a real linear least squares problem

SGELSS - computes the minimum norm solution to a real linear least squares problem

SGELSX - routine is deprecated and has been replaced by routine SGELSY

SGELSY - computes the minimum-norm solution to a real linear least squares problem

SGEQL2 - computes a QL factorization of a real m by n matrix A

SGEQLF - computes a QL factorization of a real M-by-N matrix A

SGEQP3 - computes a QR factorization with column pivoting of a matrix A

SGEQPF - routine is deprecated and has been replaced by routine SGEQP3

SGEQR2 - computes a QR factorization of a real m by n matrix A

SGEQRF - computes a QR factorization of a real M-by-N matrix A

SGERFS - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

SGERQ2 - computes an RQ factorization of a real m by n matrix A

SGERQF - computes an RQ factorization of a real M-by-N matrix A

SGESC2 - solves a system of linear equations with a general N-by-N matrix A using the LU factorization with complete pivoting computed by SGETC2

SGESDD - computes the singular value decomposition (SVD) of a real M-by-N matrix A

SGESV - computes the solution to a real system of linear equations

SGESVD - computes the singular value decomposition (SVD) of a real M-by-N matrix A

SGESVX - uses the LU factorization to compute the solution to a real system of linear equations

SGETC2 - computes an LU factorization with complete pivoting of the n-by-n matrix A

SGETF2 - computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

SGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

SGETRI - computes the inverse of a matrix using the LU factorization computed by SGETRF

SGETRS - solves a system of linear equations with a general N-by-N matrix A using the LU factorization computed by SGETRF

SGGBAK - forms the right or left eigenvectors of a real generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL

SGGBAL - balances a pair of general real matrices (A,B)

SGGES - computes for a pair of N-by-N real nonsymmetric matrices (A,B),

SGGESX - computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and,

SGGEV - computes for a pair of N-by-N real nonsymmetric matrices (A,B)

SGGEVX - computes for a pair of N-by-N real nonsymmetric matrices (A,B)

SGGGLM - solves a general Gauss-Markov linear model (GLM) problem

SGGHRD - reduces a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, where A is a general matrix and B is upper triangular

SGGLSE - solves the linear equality-constrained least squares (LSE) problem

SGGQRF - computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B

SGGRQF - computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

SGGSVD - computes the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B

SGGSVP - computes orthogonal matrices U, V and Q

SGTCON - estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF

SGTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal

SGTSV - solves the equation AX = B,

SGTSVX - uses the LU factorization to compute the solution to a real system of linear equations

SGTTRF - computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges

SGTTRS - solves one of two systems of equations

SGTTS2 - solves one of two systems of equations

SHGEQZ - implements a single-/double-shift version of the QZ method for finding generalized eigenvalues

SHSEIN - uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H

SHSEQR - computes the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition

SLABAD - takes as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large

SLABRD - reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation

SLACON - estimates the 1-norm of a square, real matrix A

SLACPY - copies all or part of a two-dimensional matrix A to another matrix B

SLADIV - performs complex division in real arithmetic

SLAE2 - computes the eigenvalues of a 2-by-2 symmetric matrix

SLAEBZ - contains the iteration loops which compute and use the function N(w)

SLAED0 - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SLAED1 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

SLAED2 - merges the two sets of eigenvalues together into a single sorted set

SLAED3 - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K

SLAED4 - computes the I ^th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix

SLAED5 - computes the I ^th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix

SLAED6 - computes the positive or negative root (closest to the origin)

SLAED7 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

SLAED8 - merges the two sets of eigenvalues together into a single sorted set

SLAED9 - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP

SLAEDA - computes the Z vector corresponding to the merge step in the CURLVL^th step of the merge process with TLVLS steps for the CURPBMth problem

SLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H

SLAEV2 - computes the eigendecomposition of a 2-by-2 symmetric matrix

SLAEXC - swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation

SLAG2 - computes the eigenvalues of a 2 x 2 generalized eigenvalue problem with scaling as necessary

SLAGS2 - computes 2-by-2 orthogonal matrices

SLAGTF - factorizes the matrix where T is an n by n tridiagonal matrix and lambda is a scalar

SLAGTM - performs a matrix-vector product

SLAGTS - solves one of twi systems of equations

SLAGV2 - computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular

SLAHQR - an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR

SLAHRD - reduces the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k ^th subdiagonal are zero

SLAIC1 - applies one step of incremental condition estimation in its simplest version

SLALN2 - solves a system with possible scaling ("s") and perturbation of A

SLALS0 - applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix

SLALSA - an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form

SLALSD - uses the singular value decomposition of A to solve the least squares problem

SLAMCH - determines single precision machine parameters

SLAMRG - creates a permutation list that merges the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order

SLANGB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A

SLANGE - 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 matrix A

SLANGT - 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 tridiagonal matrix A

SLANHS - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A

SLANSB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals

SLANSP - 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, supplied in packed form

SLANST - 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 tridiagonal matrix A

SLANSY - 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

SLANTB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A

SLANTP - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A

SLANTR - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

SLANV2 - computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form

SLAPLL - computes the QR factorization of A=QR

SLAPMT - rearranges the columns of the M by N matrix X

SLAPY2 - returns sqrt(x ²+y²) without causing unnecessary overflow

SLAPY3 - returns sqrt(x ²+y²+z²) without causing unnecessary overflow

SLAQGB - equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals

SLAQGE - equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C

SLAQP2 - computes a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)

SLAQPS - computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas3

SLAQSB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

SLAQSP - equilibrates a symmetric matrix A using the scaling factors in the vector S

SLAQSY - equilibrates a symmetric matrix A using the scaling factors in the vector S

SLAQTR - solves a real quasi-triangular system

SLAR1V - computes the (scaled) r ^th column of the inverse of the sumbmatrix of a tridiagonal matrix

SLAR2V - applies a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z

SLARF - applies a real elementary reflector H to a real m by n matrix C, from either the left or the right

SLARFB - applies a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right

SLARFG - generates a real elementary reflector H of order n

SLARFT - forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors

SLARFX - applies a real elementary reflector H to a real m by n matrix C, from either the left or the right

SLARGV - generates a vector of real plane rotations, determined by elements of the real vectors x and y

SLARNV - returns a vector of n random real numbers from a uniform or normal distribution

SLARRB - does limited bisection to locate eigenvalues

SLARRE - sets "small" off-diagonal elements to zero

SLARRF - finds a robust representation of input values.

SLARRV - computes the eigenvectors of the tridiagonal matrix

SLARTG - generates a plane rotation

SLARTV - applies a vector of real plane rotations to elements of the real vectors x and y

SLARUV - returns a vector of n random real numbers from a uniform (0,1)

SLARZ - applies a real elementary reflector H to a real M-by-N matrix C, from either the left or the right

SLARZB - applies a real block reflector H or its transpose to a real distributed M-by-N C from the left or the right

SLARZT - forms the triangular factor T of a real block reflector H

SLAS2 - computes the singular values of the 2-by-2 matrix

SLASCL - multiplie the M by N real matrix A by the real scalar CTO/CFROM

SLASD0 - computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B

SLASD1 - computes the SVD of an upper bidiagonal N-by-M matrix B,

SLASD2 - merges the two sets of singular values together into a single sorted set

SLASD3 - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z

SLASD4 - computes the square root of the I^th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix

SLASD5 -computes the square root of the I^th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix

SLASD6 - computes the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row

SLASD7 - merges the two sets of singular values together into a single sorted set

SLASD8 - finds the square roots of the roots of the secular equation,

SLASD9 - finds the square roots of the roots of the secular equation,

SLASDA - computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E

SLASDQ - computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired

SLASDT - creates a tree of subproblems for bidiagonal divide and conquer

SLASET - initializes an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals

SLASQ1 - computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E

SLASQ2 - computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z

SLASQ3 - checks for deflation, computes a shift (TAU) and calls dqds

SLASQ4 - computes an approximation TAU to the smallest eigenvalue using values of d from the previous transform

SLASQ5 - computes sone dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines

SLASQ6 - computes one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow

SLASR - performs a transformation

SLASRT - sorts numbers

SLASSQ - returns the values scl and smsq

SLASV2 - computes the singular value decomposition of a 2-by-2 triangular matrix

SLASWP - performs a series of row interchanges on the matrix A

SLASY2 - solves for the N1 by N2 matrix X

SLASYF - computes a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

SLATBS - solves one of two triangular systems with scaling to prevent overflow

SLATDF - computes a contribution to the reciprocal Dif-estimate

SLATPS - solves one of two triangular systems with scaling to prevent overflow

SLATRD - reduces NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form

SLATRS - solves one of two triangular systems with scaling to prevent overflow

SLATRZ - factors the M-by-(M+L) real upper trapezoidal matrix by means of orthogonal transformations

SLATZM - routine is deprecated and has been replaced by routine SORMRZ

SLAUU2 - computes the product U × U' or L' × L

SLAUUM - computes the product U × U' or L' × L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A

SOPGTR - generates a real orthogonal matrix Q as returned by SSPTRD using packed storage

SOPMTR - overwrites the general real M-by-N matrix C

SORG2L - generates an m by n real matrix Q with orthonormal columns,

SORG2R - generates an m by n real matrix Q with orthonormal columns,

SORGBR - generates one of the real orthogonal matrices determined by SGEBRD when reducing a real matrix A to bidiagonal form

SORGHR - generates a real orthogonal matrix Q as returned by SGEHRD

SORGL2 - generates an m by n real matrix Q with orthonormal rows

SORGLQ - generates an M-by-N real matrix Q with orthonormal rows

SORGQL - generates an M-by-N real matrix Q with orthonormal columns

SORGQR - generates an M-by-N real matrix Q with orthonormal columns

SORGR2 - generates an m by n real matrix Q with orthonormal rows

SORGRQ - generates an M-by-N real matrix Q with orthonormal rows

SORGTR - generates a real orthogonal matrix Q as returned by SSYTRD

SORM2L - overwrites the general real m by n matrix C

SORM2R - overwrites the general real m by n matrix C with Q

SORMBR - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SORMHR - overwrites the general real M-by-N matrix C

SORML2 - overwrites the general real m by n matrix C

SORMLQ - overwrites the general real M-by-N matrix C

SORMQL - overwrites the general real M-by-N matrix C

SORMQR - overwrites the general real M-by-N matrix C

SORMR2 - overwrites the general real m by n matrix C

SORMR3 - overwrites the general real m by n matrix C

SORMRQ - overwrites the general real M-by-N matrix C

SORMRZ - overwrites the general real M-by-N matrix C

SORMTR - overwrites the general real M-by-N matrix C

SPBCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization computed by SPBTRF

SPBEQU - computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)

SPBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded

SPBSTF - computes a split Cholesky factorization of a real symmetric positive definite band matrix A

SPBSV - computes the solution to a real system of linear equations

SPBSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

SPBTF2 - computes the Cholesky factorization of a real symmetric positive definite band matrix A

SPBTRF - computes the Cholesky factorization of a real symmetric positive definite band matrix A

SPBTRS - solves a system of linear equations with a symmetric positive definite band matrix A using the Cholesky factorization computed by SPBTRF

SPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization computed by SPOTRF

SPOEQU - 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)

SPORFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite

SPOSV - computes the solution to a real system of linear equations

SPOSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

SPOTF2 - computes the Cholesky factorization of a real symmetric positive definite matrix A

SPOTRF - computes the Cholesky factorization of a real symmetric positive definite matrix A

SPOTRI - computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by SPOTRF

SPOTRS - solves a system of linear equations with a symmetric positive definite matrix A using the Cholesky factorization computed by SPOTRF

SPPCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization computed by SPPTRF

SPPEQU - computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

SPPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution

SPPSV - computes the solution to a real system of linear equations

SPPSVX - uses the Cholesky factorization to compute the solution to a real system of linear equations

SPPTRF - computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format

SPPTRI - computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by SPPTRF

SPPTRS - solves a system of linear equations with a symmetric positive definite matrix A in packed storage using the Cholesky factorization computed by SPPTRF

SPTCON - computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization computed by SPTTRF

SPTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor

SPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SPTSV - computes the solution to a real system of linear equations

SPTSVX - uses a factorization to compute the solution to a real system of linear equations

SPTTRF - computes the factorization of a real symmetric positive definite tridiagonal matrix A

SPTTRS - solves a tridiagonal system

SPTTS2 - solves a tridiagonal system using the factorization of A computed by SPTTRF

SRSCL - multiplies an n-element real vector x by the real scalar 1/a

SSBEV - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

SSBEVD - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

SSBEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

SSBGST - reduces a real symmetric-definite banded generalized eigenproblem

SSBGV - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem

SSBGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem

SSBGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem

SSBTRD - reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

SSPCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A

SSPEV - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

SSPEVD - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

SSPEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage

SSPGST - reduces a real symmetric-definite generalized eigenproblem to standard form, using packed storage

SSPGV - computes all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

SSPGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

SSPGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem

SSPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed

SSPSV - computes the solution to a real system of linear equations

SSPSVX - uses the diagonal pivoting factorization to compute the solution to a real system of linear equations

SSPTRD - reduces a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation

SSPTRF - computes the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

SSPTRI - computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization computed by SSPTRF

SSPTRS - solves a system of linear equations with a real symmetric matrix A stored in packed format using the factorization computed by SSPTRF

SSTEBZ - computes the eigenvalues of a symmetric tridiagonal matrix T

SSTEDC - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SSTEGR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

SSTEIN - computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

SSTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

SSTERF - computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm

SSTEV - computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

SSTEVD - computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix

SSTEVR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

SSTEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

SSYCON - estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization computed by SSYTRF

SSYEV - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

SSYEVD - computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

SSYEVR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T

SSYEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

SSYGS2 - reduces a real symmetric-definite generalized eigenproblem to standard form

SSYGST - reduces a real symmetric-definite generalized eigenproblem to standard form

SSYGV - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

SSYGVD - computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem

SSYGVX - computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem

SSYRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite

SSYSV - computes the solution to a real system of linear equations

SSYSVX - uses the diagonal pivoting factorization to compute the solution to a real system of linear equations

SSYTD2 - reduces a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

SSYTF2 - computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

SSYTRD - reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation

SSYTRF - computes the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

SSYTRI - computes the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF

SSYTRS - solves a system of linear equations with a real symmetric matrix A using the factorization computed by SSYTRF

STBCON - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

STBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

STBTRS - solves a triangular system of the form

STGEVC - computes some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)

STGEX2 - swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation

STGEXC - reorders the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation

STGSEN - reorders the generalized real Schur decomposition of a real matrix pair (A, B)

STGSJA - computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B

STGSNA - estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair

STGSY2 - solves the generalized Sylvester equation

STGSYL - solves the generalized Sylvester equation

STPCON - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm

STPRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

STPTRI - computes the inverse of a real upper or lower triangular matrix A stored in packed format

STPTRS - solves a triangular system

STRCON - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

STREVC - computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T

STREXC - reorders the real Schur factorization of a real matrix

STRID - computes the solution to a real system of linear equations

STRRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix

STRSEN - reorders the real Schur factorization of a real matrix

STRSNA - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T

STRSYL - solves the real Sylvester matrix equation

STRTI2 - computes the inverse of a real upper or lower triangular matrix

STRTRI - computes the inverse of a real upper or lower triangular matrix A

STRTRS - solves a triangular system

STZRQF - routine is deprecated and has been replaced by routine STZRZF

STZRZF - reduces the M-by-N real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations

XERBLA - error handler for the LAPACK routines

ZBDSQR - computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B

ZDRSCL - multiplies an n-element complex vector x by the real scalar 1/a

ZGBBRD - reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation

ZGBCON - estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,

ZGBEQU - computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number

ZGBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution

ZGBSV - computes the solution to a complex system of linear equations where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices

ZGBSVX - uses the LU factorization to compute the solution to a complex system of linear equations

ZGBTF2 - computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

ZGBTRF - computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

ZGBTRS - solves a system of linear equations with a general band matrix A using the LU factorization computed by ZGBTRF

ZGEBAK - forms the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by ZGEBAL

ZGEBAL - balances a general complex matrix A

ZGEBD2 - reduces a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation

ZGEBRD - reduces a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation

ZGECON - estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF

ZGEEQU - computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

ZGEES - computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

ZGEESX - computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

ZGEEV - computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

ZGEEVX - computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

ZGEGS - routine is deprecated and has been replaced by routine ZGGES

ZGEGV - routine is deprecated and has been replaced by routine ZGGEV

ZGEHD2 - reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

ZGEHRD - reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

ZGELQ2 - computes an LQ factorization of a complex m by n matrix A

ZGELQF - computes an LQ factorization of a complex M-by-N matrix A

ZGELS - solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A

ZGELSD - computes the minimum-norm solution to a real linear least squares problem

ZGELSS - computes the minimum norm solution to a complex linear least squares problem

ZGELSX - routine is deprecated and has been replaced by routine ZGELSY

ZGELSY - computes the minimum-norm solution to a complex linear least squares problem

ZGEQL2 - computes a QL factorization of a complex m by n matrix A

ZGEQLF - computes a QL factorization of a complex M-by-N matrix A

ZGEQP3 - computes a QR factorization with column pivoting of a matrix A

ZGEQPF - routine is deprecated and has been replaced by routine ZGEQP3

ZGEQR2 - computes a QR factorization of a complex m by n matrix A

ZGEQRF - computes a QR factorization of a complex M-by-N matrix A

ZGERFS - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution

ZGERQ2 - computes an RQ factorization of a complex m by n matrix A

ZGERQF - computes an RQ factorization of a complex M-by-N matrix A

ZGESC2 - solves a system of linear equations with a general N-by-N matrix A using the LU factorization with complete pivoting computed by ZGETC2

ZGESDD - computes the singular value decomposition (SVD) of a complex M-by-N matrix A

ZGESV - computes the solution to a complex system of linear equations

ZGESVD - computes the singular value decomposition (SVD) of a complex M-by-N matrix A

ZGESVX - uses the LU factorization to compute the solution to a complex system of linear equations

ZGETC2 - computes an LU factorization, using complete pivoting, of the n-by-n matrix A

ZGETF2 - computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

ZGETRF - computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges

ZGETRI - computes the inverse of a matrix using the LU factorization computed by ZGETRF

ZGETRS - solves a system of linear equations with a general N-by-N matrix A using the LU factorization computed by ZGETRF

ZGGBAK - forms the right or left eigenvectors of a complex generalized eigenvalue problem by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL

ZGGBAL - balances a pair of general complex matrices (A,B)

ZGGES - computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR)

ZGGESX - computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),

ZGGEV - computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

ZGGEVX - computes for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

ZGGGLM - solves a general Gauss-Markov linear model (GLM) problem

ZGGHRD - reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular

ZGGLSE - solves the linear equality-constrained least squares (LSE) problem

ZGGQRF - computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B

ZGGRQF - computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

ZGGSVD - computes the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B

ZGGSVP - computes unitary matrices U, V and Q

ZGTCON - estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF

ZGTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution

ZGTSV - solves the equation AX = B

ZGTSVX - uses the LU factorization to compute the solution to a complex system of linear equations

ZGTTRF - computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges

ZGTTRS - solves one of the systems of equations

ZGTTS2 - solves one of the systems of equations

ZHBEV - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

ZHBEVD - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

ZHBEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

ZHBGST - reduces a complex Hermitian-definite banded generalized eigenproblem to standard form

ZHBGV - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

ZHBGVD - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

ZHBGVX - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem

ZHBTRD - reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

ZHECON - estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization computed by ZHETRF

ZHEEV - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

ZHEEVD - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

ZHEEVR - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T

ZHEEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

ZHEGS2 - reduces a complex Hermitian-definite generalized eigenproblem to standard form

ZHEGST - reduces a complex Hermitian-definite generalized eigenproblem to standard form

ZHEGV - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHEGVD - computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHEGVX - computes selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHERFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution

ZHESV - computes the solution to a complex system of linear equations

ZHESVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

ZHETD2 - reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

ZHETF2 - computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

ZHETRD - reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

ZHETRF - computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

ZHETRI - computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by ZHETRF

ZHETRS - solves a system of linear equations with a complex Hermitian matrix A using the factorization computed by ZHETRF

ZHGEQZ - implements a single-shift version of the QZ method for finding generalized eigenvalues

ZHPCON - estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization computed by ZHPTRF

ZHPEV - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

ZHPEVD - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

ZHPEVX - computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage

ZHPGST - reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

ZHPGV - computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHPGVD - computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHPGVX - computes selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem

ZHPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution

ZHPSV - computes the solution to a complex system of linear equations

ZHPSVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

ZHPTRD - reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation

ZHPTRF - computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method

ZHPTRI - computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization computed by ZHPTRF

ZHPTRS - solves a system of linear equations with a complex Hermitian matrix A stored in packed format using the factorization computed by ZHPTRF

ZHSEIN - uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H

ZHSEQR - computes the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition

ZLABRD - reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation

ZLACGV - conjugates a complex vector of length N

ZLACON - estimatse the 1-norm of a square, complex matrix A

ZLACP2 - copies all or part of a real two-dimensional matrix A to a complex matrix B

ZLACPY - copies all or part of a two-dimensional matrix A to another matrix B

ZLACRM - performs a very simple matrix-matrix multiplication

ZLACRT - performs the operation ( c s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vectors x and y are complex

ZLADIV - := X / Y, where X and Y are complex

ZLAED0 - computes all eigenvalues of a symmetric tridiagonal matrix

ZLAED7 - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix

ZLAED8 - merges the two sets of eigenvalues together into a single sorted set

ZLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

ZLAESY - computes the eigendecomposition of a 2-by-2 symmetric matrix

ZLAEV2 - computes the eigendecomposition of a 2-by-2 Hermitian matrix

ZLAGS2 - computes 2-by-2 unitary matrices U, V and Q

ZLAGTM - performs a matrix-vector product

ZLAHEF - computes a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

ZLAHQR - called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR

ZLAHRD - reduces the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k^th subdiagonal are zero

ZLAIC1 - applies one step of incremental condition estimation in its simplest version

ZLALS0 - applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal 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

ZLALSA - an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form

ZLALSD - uses the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm

ZLANGB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A,

ZLANGE - 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 matrix A

ZLANGT - 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 tridiagonal matrix A

ZLANHB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals

ZLANHE - 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

ZLANHP - 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, supplied in packed form

ZLANHS - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A

ZLANHT - 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 tridiagonal matrix A

ZLANSB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals

ZLANSP - 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 symmetric matrix A, supplied in packed form

ZLANSY - 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 symmetric matrix A

ZLANTB - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals

ZLANTP - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form

ZLANTR - returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A

ZLAPLL - computes the QR factorization of A=QR

ZLAPMT - rearranges the columns of the M by N matrix X

ZLAQGB - equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C

ZLAQGE - equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C

ZLAQHB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

ZLAQHE - equilibrates a Hermitian matrix A using the scaling factors in the vector S

ZLAQHP - equilibrates a Hermitian matrix A using the scaling factors in the vector S

ZLAQP2 - computes a QR factorization with column pivoting

ZLAQPS - computes a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3

ZLAQSB - equilibrates a symmetric band matrix A using the scaling factors in the vector S

ZLAQSP - equilibrates a symmetric matrix A using the scaling factors in the vector S

ZLAQSY - equilibrates a symmetric matrix A using the scaling factors in the vector S

ZLAR1V - computes the (scaled) r ^th column of the inverse of the sumbmatrix

ZLAR2V - applies a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,

ZLARCM - performs a very simple matrix-matrix multiplication

ZLARF - applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

ZLARFB - applies a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right

ZLARFG - generates a complex elementary reflector H o

ZLARFT - forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors

ZLARFX - applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right

ZLARGV - generates a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y

ZLARNV - returns a vector of n random complex numbers from a uniform or normal distribution

ZLARRV - computes the eigenvectors of a tridiagonal matrix

ZLARTG - generates a plane rotation

ZLARTV - applies a vector of complex plane rotations with real cosines to elements of the complex vectors x and y

ZLARZ - applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

ZLARZB - applies a complex block reflector H or its transpose to a complex distributed M-by-N C from the left or the right

ZLARZT - forms the triangular factor T of a complex block reflector which is defined as a product of k elementary reflectors

ZLASCL - multiplies the M by N complex matrix A by the real scalar CTO/CFROM

ZLASET - initializes a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals

ZLASR - performs a transformation where A is an m by n complex matrix and P is an orthogonal matrix

ZLASSQ - returns the values scl and ssq

ZLASWP - performs a series of row interchanges on the matrix A

ZLASYF - computes a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

ZLATBS - solves triangular systems

ZLATDF - computes the contribution to the reciprocal Dif-estimate

ZLATPS - solves triangular systems

ZLATRD - reduces NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form

ZLATRS - solves triangular systems

ZLATRZ - factors the M-by-(M+L) complex upper trapezoidal matrix

ZLATZM - routine is deprecated and has been replaced by routine ZUNMRZ

ZLAUU2 - computes the product U × U' or L' × L

ZLAUUM - computes the product U × U' or L' × L

ZPBCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix

ZPBEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A

ZPBRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded

ZPBSTF - computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBSV - computes the solution to a complex system of linear equations

ZPBSVX - uses the Cholesky factorization to compute the solution to a complex system of linear equations

ZPBTF2 - computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBTRF - computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBTRS - solves a system of linear equations with a Hermitian positive definite band matrix A using the Cholesky factorization computed by ZPBTRF

ZPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization computed by ZPOTRF

ZPOEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)

ZPORFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,

ZPOSV - computes the solution to a complex system of linear equations

ZPOSVX - uses the Cholesky factorization to compute the solution to a complex system of linear equations

ZPOTF2 - computes the Cholesky factorization of a complex Hermitian positive definite matrix A

ZPOTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A

ZPOTRI - computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization computed by ZPOTRF

ZPOTRS - solves a system of linear equations with a Hermitian positive definite matrix A using the Cholesky factorization computed by ZPOTRF

ZPPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization computed by ZPPTRF

ZPPEQU - computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

ZPPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution

ZPPSV - computes the solution to a complex system of linear equations

ZPPSVX - use the Cholesky factorization to compute the solution to a complex system of linear equations

ZPPTRF - computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format

ZPPTRI - computes the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization computed by ZPPTRF

ZPPTRS - solves a system of linear equations with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization computed by ZPPTRF

ZPTCON - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization computed by ZPTTRF

ZPTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix

ZPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

ZPTSV - computes the solution to a complex system of linear equations where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

ZPTSVX - uses the factorization to compute the solution to a complex system of linear equations where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

ZPTTRF - computes the factorization of a complex Hermitian positive definite tridiagonal matrix A

ZPTTRS - solves a tridiagonal system of the form using the factorization computed by ZPTTRF

ZPTTS2 - solves a tridiagonal system of the form using the factorization computed by ZPTTRF

ZSPCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization computed by ZSPTRF

ZSPRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution

ZSPSV - computes the solution to a complex system of linear equations

ZSPSVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

ZSPTRF - computes the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method

ZSPTRI - computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization computed by ZSPTRF

ZSPTRS - solves a system of linear equations with a complex symmetric matrix A stored in packed format using the factorization computed by ZSPTRF

ZSTEDC - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

ZSTEGR - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

ZSTEIN - computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration

ZSTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

ZSYCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by ZSYTRF

ZSYRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution

ZSYSV - computes the solution to a complex system of linear equations

ZSYSVX - uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations

ZSYTF2 - computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

ZSYTRF - computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

ZSYTRI - computes the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF

ZSYTRS - solves a system of linear equations with a complex symmetric matrix A using the factorization computed by ZSYTRF

ZTBCON - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

ZTBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

ZTBTRS - solves a triangular system

ZTGEVC - computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)

ZTGEX2 - swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)

ZTGEXC - reorders the generalized Schur decomposition of a complex matrix pair (A,B)

ZTGSEN - reorders the generalized Schur decomposition of a complex matrix pair (A, B)

ZTGSJA - computes the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B

ZTGSNA - estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B)

ZTGSY2 - solves the generalized Sylvester equation

ZTGSYL - solves the generalized Sylvester equation

ZTPCON - estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm

ZTPRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix

ZTPTRI - computes the inverse of a complex upper or lower triangular matrix A stored in packed format

ZTPTRS - solves a triangular system

ZTRCON - estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

ZTREVC - computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T

ZTREXC - reorders the Schur factorization of a complex matrix so that the diagonal element of T with row index IFST is moved to row ILST

ZTRID - computes the solution to a complex system of linear equations where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N

ZTRRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix

ZTRSEN - reorders the Schur factorization of a complex matrix

ZTRSNA - estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T

ZTRSYL - solves the complex Sylvester matrix equation

ZTRTI2 - computes the inverse of a complex upper or lower triangular matrix

ZTRTRI - computes the inverse of a complex upper or lower triangular matrix A

ZTRTRS - solves a triangular system

ZTZRQF - routine is deprecated and has been replaced by routine ZTZRZF

ZTZRZF - reduces the M-by-N complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations

ZUNG2L - generates an m by n complex matrix Q with orthonormal columns,

ZUNG2R - generates an m by n complex matrix Q with orthonormal columns,

ZUNGBR - generates one of the complex unitary matrices determined by ZGEBRD when reducing a complex matrix A to bidiagonal form

ZUNGHR - generates a complex unitary matrix Q

ZUNGL2 - generates an m-by-n complex matrix Q with orthonormal rows,

ZUNGLQ - generates an M-by-N complex matrix Q with orthonormal rows,

ZUNGQL - generates an M-by-N complex matrix Q with orthonormal columns,

ZUNGQR - generates an M-by-N complex matrix Q with orthonormal columns,

ZUNGR2 - generates an m by n complex matrix Q with orthonormal rows,

ZUNGRQ - generates an M-by-N complex matrix Q with orthonormal rows,

ZUNGTR - generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD

ZUNM2L - overwrites the general complex m-by-n matrix C

ZUNM2R - overwrites the general complex m-by-n matrix C

ZUNMBR - overwrites the general complex M-by-N matrix C

ZUNMHR - overwrites the general complex M-by-N matrix C

ZUNML2 - overwrites the general complex m-by-n matrix C

ZUNMLQ - overwrites the general complex M-by-N matrix C

ZUNMQL - overwrites the general complex M-by-N matrix C

ZUNMQR - overwrites the general complex M-by-N matrix C

ZUNMR2 - overwrites the general complex m-by-n matrix C

ZUNMR3 - overwrites the general complex m by n matrix C

ZUNMRQ - overwrites the general complex M-by-N matrix C

ZUNMRZ - overwrites the general complex M-by-N matrix C

ZUPGTR - generates a complex unitary matrix Q

ZUPMTR - overwrites the general complex M-by-N matrix C