This reference manual is the Sun Performance Library section
3P man pages, available in HTML and PDF formats. For additional information,
see the *Sun Performance Library User's Guide*, available on
`docs.sun.com`, or the *LAPACK Users' Guide*, available
from the Society for Industrial and Applied Mathematics (SIAM).

- available_threads - available_threads - returns information about current thread usage

- blas_dpermute - blas_dpermute - permutes a real (double precision) array in terms of the permutation vector P, output by dsortv

- blas_dsort - blas_dsort - sorts a real (double precision) vector X in increasing or decreasing order using quick sort algorithm

- blas_dsortv - blas_dsortv - sorts a real (double precision) vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permutation vector

- blas_ipermute - blas_ipermute - permutes an integer array in terms of the permutation vector P, output by dsortv

- blas_isort - blas_isort - sorts an integer vector X in increasing or decreasing order using quick sort algorithm

- blas_isortv - blas_isortv - sorts a real vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permutation vector

- blas_spermute - blas_spermute - permutes a real array in terms of the permutation vector P, output by dsortv

- blas_ssort - blas_ssort - sorts a real vector X in increasing or decreasing order using quick sort algorithm

- blas_ssortv - blas_ssortv - sorts a real vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permutation vector

- caxpy - caxpy - compute y := alpha * x + y

- caxpyi - caxpyi - Compute y := alpha * x + y

- cbcomm - cbcomm - block coordinate matrix-matrix multiply

- cbdimm - cbdimm - block diagonal format matrix-matrix multiply

- cbdism - cbdism - block diagonal format triangular solve

- cbdsqr - cbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.

- cbelmm - cbelmm - block Ellpack format matrix-matrix multiply

- cbelsm - cbelsm - block Ellpack format triangular solve

- cbscmm - cbscmm - block sparse column matrix-matrix multiply

- cbscsm - cbscsm - block sparse column format triangular solve

- cbsrmm - cbsrmm - block sparse row format matrix-matrix multiply

- cbsrsm - cbsrsm - block sparse row format triangular solve

- ccnvcor - ccnvcor - compute the convolution or correlation of complex vectors

- ccnvcor2 - ccnvcor2 - compute the convolution or correlation of complex matrices

- ccoomm - ccoomm - coordinate matrix-matrix multiply

- ccopy - ccopy - Copy x to y

- ccscmm - ccscmm - compressed sparse column format matrix-matrix multiply

- ccscsm - ccscsm - compressed sparse column format triangular solve

- ccsrmm - ccsrmm - compressed sparse row format matrix-matrix multiply

- ccsrsm - ccsrsm - compressed sparse row format triangular solve

- cdiamm - cdiamm - diagonal format matrix-matrix multiply

- cdiasm - cdiasm - diagonal format triangular solve

- cdotc - cdotc - compute the dot product of two vectors conjg(x) and y.

- cdotci - cdotci - Compute the complex conjugated indexed dot product.

- cdotu - cdotu - compute the dot product of two vectors x and y.

- cdotui - cdotui - Compute the complex unconjugated indexed dot product.

- cellmm - cellmm - Ellpack format matrix-matrix multiply

- cellsm - cellsm - Ellpack format triangular solve

- cfft2b - cfft2b - compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M*N.

- cfft2f - cfft2f - compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M*N.

- cfft2i - cfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms.

- cfft3b - cfft3b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of CFFT3F followed by a call of CFFT3B will multiply the input sequence by M*N*K.

- cfft3f - cfft3f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of CFFT3F followed by a call of CFFT3B will multiply the input sequence by M*N*K.

- cfft3i - cfft3i - initialize the array WSAVE, which is used in both CFFT3F and CFFT3B.

- cfftb - cfftb - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of CFFTF followed by a call of CFFTB will multiply the input sequence by N.

- cfftc - cfftc - initialize the trigonometric weight and factor tables or compute the Fast Fourier transform (forward or inverse) of a complex sequence.

- cfftc2 - cfftc2 - initialize the trigonometric weight and factor tables or compute the two-dimensional Fast Fourier Transform (forward or inverse) of a two-dimensional complex array.

- cfftc3 - cfftc3 - initialize the trigonometric weight and factor tables or compute the three-dimensional Fast Fourier Transform (forward or inverse) of a three-dimensional complex array.

- cfftcm - cfftcm - initialize the trigonometric weight and factor tables or compute the one-dimensional Fast Fourier Transform (forward or inverse) of a set of data sequences stored in a two-dimensional complex array.

- cfftf - cfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of CFFTF followed by a call of CFFTB will multiply the input sequence by N.

- cffti - cffti - initialize the array WSAVE, which is used in both CFFTF and CFFTB.

- cfftopt - cfftopt - compute the length of the closest fast FFT

- cffts - cffts - initialize the trigonometric weight and factor tables or compute the inverse Fast Fourier Transform of a complex sequence as follows.

- cffts2 - cffts2 - initialize the trigonometric weight and factor tables or compute the two-dimensional inverse Fast Fourier Transform of a two-dimensional complex array.

- cffts3 - cffts3 - initialize the trigonometric weight and factor tables or compute the three-dimensional inverse Fast Fourier Transform of a three-dimensional complex array.

- cfftsm - cfftsm - initialize the trigonometric weight and factor tables or compute the one-dimensional inverse Fast Fourier Transform of a set of complex data sequences stored in a two-dimensional array.

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

- cgbcon - cgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,

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

- cgbmv - cgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y

- cgbrfs - cgbrfs - improve 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

- cgbsv - cgbsv - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices

- cgbsvx - cgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

- cgbtf2 - cgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

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

- cgbtrs - cgbtrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF

- cgebak - cgebak - form 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 - cgebal - balance a general complex matrix A

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

- cgecon - cgecon - estimate 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 CGETRF

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

- cgees - cgees - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

- cgeesx - cgeesx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

- cgeev - cgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

- cgeevx - cgeevx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

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

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

- cgehrd - cgehrd - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

- cgelqf - cgelqf - compute an LQ factorization of a complex M-by-N matrix A

- cgels - cgels - solve 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

- cgelsd - cgelsd - compute the minimum-norm solution to a real linear least squares problem

- cgelss - cgelss - compute the minimum norm solution to a complex linear least squares problem

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

- cgelsy - cgelsy - compute the minimum-norm solution to a complex linear least squares problem

- cgemm - cgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C

- cgemv - cgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y

- cgeqlf - cgeqlf - compute a QL factorization of a complex M-by-N matrix A

- cgeqp3 - cgeqp3 - compute a QR factorization with column pivoting of a matrix A

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

- cgeqrf - cgeqrf - compute a QR factorization of a complex M-by-N matrix A

- cgerc - cgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A

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

- cgerqf - cgerqf - compute an RQ factorization of a complex M-by-N matrix A

- cgeru - cgeru - perform the rank 1 operation A := alpha*x*y' + A

- cgesdd - cgesdd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method

- cgesv - cgesv - compute the solution to a complex system of linear equations A * X = B,

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

- cgesvx - cgesvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,

- cgetf2 - cgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

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

- cgetri - cgetri - compute the inverse of a matrix using the LU factorization computed by CGETRF

- cgetrs - cgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF

- cggbak - cggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL

- cggbal - cggbal - balance a pair of general complex matrices (A,B)

- cgges - cgges - compute 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)

- cggesx - cggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),

- cggev - cggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

- cggevx - cggevx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors

- cggglm - cggglm - solve a general Gauss-Markov linear model (GLM) problem

- cgghrd - cgghrd - reduce 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 - cgglse - solve the linear equality-constrained least squares (LSE) problem

- cggqrf - cggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B.

- cggrqf - cggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

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

- cggsvp - cggsvp - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

- cgssco - cgssco - General sparse solver condition number estimate.

- cgssda - cgssda - Deallocate working storage for the general sparse solver.

- cgssfa - cgssfa - General sparse solver numeric factorization.

- cgssfs - cgssfs - General sparse solver one call interface.

- cgssin - cgssin - Initialize the general sparse solver.

- cgssor - cgssor - General sparse solver ordering and symbolic factorization.

- cgssps - cgssps - Print general sparse solver statics.

- cgssrp - cgssrp - Return permutation used by the general sparse solver.

- cgsssl - cgsssl - Solve routine for the general sparse solver.

- cgssuo - cgssuo - User supplied permutation for ordering used in the general sparse solver.

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

- cgthr - cgthr - Gathers specified elements from y into x.

- cgthrz - cgthrz - Gather and zero.

- cgtrfs - cgtrfs - improve 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

- cgtsv - cgtsv - solve the equation A*X = B,

- cgtsvx - cgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

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

- cgttrs - cgttrs - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,

- chbev - chbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- chbevd - chbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- chbevx - chbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- chbgst - chbgst - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

- chbgv - chbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- chbgvd - chbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- chbgvx - chbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- chbmv - chbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

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

- checon - checon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- cheev - cheev - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- cheevd - cheevd - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- cheevr - cheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian tridiagonal matrix T

- cheevx - cheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- chegs2 - chegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form

- chegst - chegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form

- chegv - chegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chegvd - chegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chegvx - chegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chemm - chemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- chemv - chemv - perform the matrix-vector operation y := alpha*A*x + beta*y

- cher - cher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A

- cher2 - cher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

- cher2k - cher2k - perform one of the Hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C

- cherfs - cherfs - improve 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

- cherk - cherk - perform one of the Hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A + beta*C

- chesv - chesv - compute the solution to a complex system of linear equations A * X = B,

- chesvx - chesvx - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,

- chetf2 - chetf2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

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

- chetrf - chetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

- chetri - chetri - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- chetrs - chetrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- chgeqz - chgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right

- chpcon - chpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

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

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

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

- chpgst - chpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

- chpgv - chpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chpgvd - chpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chpgvx - chpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- chpmv - chpmv - perform the matrix-vector operation y := alpha*A*x + beta*y

- chpr - chpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A

- chpr2 - chpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

- chprfs - chprfs - improve 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

- chpsv - chpsv - compute the solution to a complex system of linear equations A * X = B,

- chpsvx - chpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices

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

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

- chptri - chptri - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

- chptrs - chptrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

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

- chseqr - chseqr - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors

- cjadmm - cjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)

- cjadrp - cjadrp - right permutation of a jagged diagonal matrix

- cjadsm - cjadsm - Jagged-diagonal format triangular solve

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

- clarzb - clarzb - applie a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right

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

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

- cosqb - cosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N.

- cosqf - cosqf - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N.

- cosqi - cosqi - initialize the array WSAVE, which is used in both COSQF and COSQB.

- cost - cost - compute the discrete Fourier cosine transform of an even sequence. The COST transforms are unnormalized inverses of themselves, so a call of COST followed by another call of COST will multiply the input sequence by 2 * (N-1).

- costi - costi - initialize the array WSAVE, which is used in COST.

- cpbcon - cpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

- cpbequ - cpbequ - compute 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 - cpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution

- cpbstf - cpbstf - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A

- cpbsv - cpbsv - compute the solution to a complex system of linear equations A * X = B,

- cpbsvx - cpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

- cpbtf2 - cpbtf2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

- cpbtrf - cpbtrf - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

- cpbtrs - cpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

- cpocon - cpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- cpoequ - cpoequ - compute 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 - cporfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,

- cposv - cposv - compute the solution to a complex system of linear equations A * X = B,

- cposvx - cposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

- cpotf2 - cpotf2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A

- cpotrf - cpotrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A

- cpotri - cpotri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- cpotrs - cpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- cppcon - cppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- cppequ - cppequ - compute 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 - cpprfs - improve 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 - cppsv - compute the solution to a complex system of linear equations A * X = B,

- cppsvx - cppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

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

- cpptri - cpptri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- cpptrs - cpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- cptcon - cptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF

- cpteqr - cpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor

- cptrfs - cptrfs - improve 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

- cptsv - cptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices.

- cptsvx - cptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

- cpttrf - cpttrf - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A

- cpttrs - cpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF

- cptts2 - cptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF

- crot - crot - apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors X and Y are complex

- crotg - crotg - Construct a Given's plane rotation

- cscal - cscal - Compute y := alpha * y

- csctr - csctr - Scatters elements from x into y.

- cskymm - cskymm - Skyline format matrix-matrix multiply

- cskysm - cskysm - Skyline format triangular solve

- cspcon - cspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF

- csprfs - csprfs - improve 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

- cspsv - cspsv - compute the solution to a complex system of linear equations A * X = B,

- cspsvx - cspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices

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

- csptri - csptri - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF

- csptrs - csptrs - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF

- csrot - csrot - Apply a plane rotation.

- csscal - csscal - Compute y := alpha * y

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

- cstegr - cstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation

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

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

- cstsv - cstsv - compute the solution to a complex system of linear equations A * X = B where A is a symmetric tridiagonal matrix

- csttrf - csttrf - compute the factorization of a complex symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method

- csttrs - csttrs - computes the solution to a complex system of linear equations A * X = B

- cswap - cswap - Exchange vectors x and y.

- csycon - csycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

- csymm - csymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- csyr2k - csyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C

- csyrfs - csyrfs - improve 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

- csyrk - csyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C

- csysv - csysv - compute the solution to a complex system of linear equations A * X = B,

- csysvx - csysvx - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,

- csytf2 - csytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- csytrf - csytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- csytri - csytri - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

- csytrs - csytrs - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

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

- ctbmv - ctbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ctbsv - ctbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

- ctbtrs - ctbtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

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

- ctgexc - ctgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

- ctgsen - ctgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B) (in terms of an unitary equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B)

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

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

- ctgsyl - ctgsyl - solve the generalized Sylvester equation

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

- ctpmv - ctpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ctpsv - ctpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

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

- ctptrs - ctptrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

- ctrans - ctrans - transpose and scale source matrix

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

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

- ctrexc - ctrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST

- ctrmm - ctrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )

- ctrmv - ctrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ctrsen - ctrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace

- ctrsm - ctrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B

- ctrsna - ctrsna - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)

- ctrsv - ctrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

- ctrsyl - ctrsyl - solve the complex Sylvester matrix equation

- ctrti2 - ctrti2 - compute the inverse of a complex upper or lower triangular matrix

- ctrtri - ctrtri - compute the inverse of a complex upper or lower triangular matrix A

- ctrtrs - ctrtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

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

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

- cung2l - cung2l - generate an m by n complex matrix Q with orthonormal columns,

- cung2r - cung2r - generate an m by n complex matrix Q with orthonormal columns,

- cungbr - cungbr - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form

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

- cungl2 - cungl2 - generate an m-by-n complex matrix Q with orthonormal rows,

- cunglq - cunglq - generate an M-by-N complex matrix Q with orthonormal rows,

- cungql - cungql - generate an M-by-N complex matrix Q with orthonormal columns,

- cungqr - cungqr - generate an M-by-N complex matrix Q with orthonormal columns,

- cungr2 - cungr2 - generate an m by n complex matrix Q with orthonormal rows,

- cungrq - cungrq - generate an M-by-N complex matrix Q with orthonormal rows,

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

- cunmbr - cunmbr - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmhr - cunmhr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunml2 - cunml2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',

- cunmlq - cunmlq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmql - cunmql - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmqr - cunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmr2 - cunmr2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',

- cunmrq - cunmrq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmrz - cunmrz - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cunmtr - cunmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cupgtr - cupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage

- cupmtr - cupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- cvbrmm - cvbrmm - variable block sparse row format matrix-matrix multiply

- cvbrsm - cvbrsm - variable block sparse row format triangular solve

- cvmul - cvmul - compute the scaled product of complex vectors

- dasum - dasum - Return the sum of the absolute values of a vector x.

- daxpy - daxpy - compute y := alpha * x + y

- daxpyi - daxpyi - Compute y := alpha * x + y

- dbcomm - dbcomm - block coordinate matrix-matrix multiply

- dbdimm - dbdimm - block diagonal format matrix-matrix multiply

- dbdism - dbdism - block diagonal format triangular solve

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

- dbdsqr - dbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.

- dbelmm - dbelmm - block Ellpack format matrix-matrix multiply

- dbelsm - dbelsm - block Ellpack format triangular solve

- dbscmm - dbscmm - block sparse column matrix-matrix multiply

- dbscsm - dbscsm - block sparse column format triangular solve

- dbsrmm - dbsrmm - block sparse row format matrix-matrix multiply

- dbsrsm - dbsrsm - block sparse row format triangular solve

- dcnvcor - dcnvcor - compute the convolution or correlation of real vectors

- dcnvcor2 - dcnvcor2 - compute the convolution or correlation of real matrices

- dcoomm - dcoomm - coordinate matrix-matrix multiply

- dcopy - dcopy - Copy x to y

- dcosqb - dcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N.

- dcosqf - dcosqf - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N.

- dcosqi - dcosqi - initialize the array WSAVE, which is used in both COSQF and COSQB.

- dcost - dcost - compute the discrete Fourier cosine transform of an even sequence. The COST transforms are unnormalized inverses of themselves, so a call of COST followed by another call of COST will multiply the input sequence by 2 * (N-1).

- dcosti - dcosti - initialize the array WSAVE, which is used in COST.

- dcscmm - dcscmm - compressed sparse column format matrix-matrix multiply

- dcscsm - dcscsm - compressed sparse column format triangular solve

- dcsrmm - dcsrmm - compressed sparse row format matrix-matrix multiply

- dcsrsm - dcsrsm - compressed sparse row format triangular solve

- ddiamm - ddiamm - diagonal format matrix-matrix multiply

- ddiasm - ddiasm - diagonal format triangular solve

- ddisna - ddisna - compute 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

- ddot - ddot - compute the dot product of two vectors x and y.

- ddoti - ddoti - Compute the indexed dot product.

- dellmm - dellmm - Ellpack format matrix-matrix multiply

- dellsm - dellsm - Ellpack format triangular solve

- dezftb - dezftb - computes a periodic sequence from its Fourier coefficients. DEZFTB is a simplified but slower version of DFFTB.

- dezftf - dezftf - computes the Fourier coefficients of a periodic sequence. DEZFTF is a simplified but slower version of DFFTF.

- dezfti - dezfti - initializes the array WSAVE, which is used in both DEZFTF and DEZFTB.

- dfft2b - dfft2b - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFT2F followed by a call of DFFT2B will multiply the input sequence by M*N.

- dfft2f - dfft2f - compute the Fourier coefficients of a periodic sequence. The DFFT operations are unnormalized, so a call of DFFT2F followed by a call of DFFT2B will multiply the input sequence by M*N.

- dfft2i - dfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms.

- dfft3b - dfft3b - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFT3F followed by a call of DFFT3B will multiply the input sequence by M*N*K.

- dfft3f - dfft3f - compute the Fourier coefficients of a real periodic sequence. The DFFT operations are unnormalized, so a call of DFFT3F followed by a call of DFFT3B will multiply the input sequence by M*N*K.

- dfft3i - dfft3i - initialize the array WSAVE, which is used in both DFFT3F and DFFT3B.

- dfftb - dfftb - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFTF followed by a call of DFFTB will multiply the input sequence by N.

- dfftf - dfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of DFFTF followed by a call of DFFTB will multiply the input sequence by N.

- dffti - dffti - initialize the array WSAVE, which is used in both DFFTF and DFFTB.

- dfftopt - dfftopt - compute the length of the closest fast FFT

- dfftz - dfftz - initialize the trigonometric weight and factor tables or compute the forward Fast Fourier Transform of a double precision sequence.

- dfftz2 - dfftz2 - initialize the trigonometric weight and factor tables or compute the two-dimensional forward Fast Fourier Transform of a two-dimensional double precision array.

- dfftz3 - dfftz3 - initialize the trigonometric weight and factor tables or compute the three-dimensional forward Fast Fourier Transform of a three-dimensional double complex array.

- dfftzm - dfftzm - initialize the trigonometric weight and factor tables or compute the one-dimensional forward Fast Fourier Transform of a set of double precision data sequences stored in a two-dimensional array.

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

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

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

- dgbmv - dgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*A'*x + beta*y

- dgbrfs - dgbrfs - improve 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

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

- dgbsvx - dgbsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

- dgbtf2 - dgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

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

- dgbtrs - dgbtrs - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by SGBTRF

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

- dgebal - dgebal - balance a general real matrix A

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

- dgecon - dgecon - estimate 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

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

- dgees - dgees - compute 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 - dgeesx - compute 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 - dgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

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

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

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

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

- dgelqf - dgelqf - compute an LQ factorization of a real M-by-N matrix A

- dgels - dgels - solve 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 - dgelsd - compute the minimum-norm solution to a real linear least squares problem

- dgelss - dgelss - compute the minimum norm solution to a real linear least squares problem

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

- dgelsy - dgelsy - compute the minimum-norm solution to a real linear least squares problem

- dgemm - dgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C

- dgemv - dgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*A'*x + beta*y

- dgeqlf - dgeqlf - compute a QL factorization of a real M-by-N matrix A

- dgeqp3 - dgeqp3 - compute a QR factorization with column pivoting of a matrix A

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

- dgeqrf - dgeqrf - compute a QR factorization of a real M-by-N matrix A

- dger - dger - perform the rank 1 operation A := alpha*x*y' + A

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

- dgerqf - dgerqf - compute an RQ factorization of a real M-by-N matrix A

- dgesdd - dgesdd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors

- dgesv - dgesv - compute the solution to a real system of linear equations A * X = B,

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

- dgesvx - dgesvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B,

- dgetf2 - dgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

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

- dgetri - dgetri - compute the inverse of a matrix using the LU factorization computed by SGETRF

- dgetrs - dgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF

- dggbak - dggbak - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL

- dggbal - dggbal - balance a pair of general real matrices (A,B)

- dgges - dgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),

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

- dggev - dggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)

- dggevx - dggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)

- dggglm - dggglm - solve a general Gauss-Markov linear model (GLM) problem

- dgghrd - dgghrd - reduce 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 - dgglse - solve the linear equality-constrained least squares (LSE) problem

- dggqrf - dggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B.

- dggrqf - dggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

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

- dggsvp - dggsvp - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

- dgssco - dgssco - General sparse solver condition number estimate.

- dgssda - dgssda - Deallocate working storage for the general sparse solver.

- dgssfa - dgssfa - General sparse solver numeric factorization.

- dgssfs - dgssfs - General sparse solver one call interface.

- dgssin - dgssin - Initialize the general sparse solver.

- dgssor - dgssor - General sparse solver ordering and symbolic factorization.

- dgssps - dgssps - Print general sparse solver statics.

- dgssrp - dgssrp - Return permutation used by the general sparse solver.

- dgsssl - dgsssl - Solve routine for the general sparse solver.

- dgssuo - dgssuo - User supplied permutation for ordering used in the general sparse solver.

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

- dgthr - dgthr - Gathers specified elements from y into x.

- dgthrz - dgthrz - Gather and zero.

- dgtrfs - dgtrfs - improve 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

- dgtsv - dgtsv - solve the equation A*X = B,

- dgtsvx - dgtsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,

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

- dgttrs - dgttrs - solve one of the systems of equations A*X = B or A'*X = B,

- dhgeqz - dhgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form

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

- dhseqr - dhseqr - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors

- djadmm - djadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)

- djadrp - djadrp - right permutation of a jagged diagonal matrix

- djadsm - djadsm - Jagged-diagonal format triangular solve

- dlagtf - dlagtf - factorize the matrix (T-lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T-lambda*I = PLU

- dlamrg - dlamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order

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

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

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

- dlasrt - dlasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )

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

- dnrm2 - dnrm2 - Return the Euclidian norm of a vector.

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

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

- dorg2l - dorg2l - generate an m by n real matrix Q with orthonormal columns,

- dorg2r - dorg2r - generate an m by n real matrix Q with orthonormal columns,

- dorgbr - dorgbr - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form

- dorghr - dorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD

- dorgl2 - dorgl2 - generate an m by n real matrix Q with orthonormal rows,

- dorglq - dorglq - generate an M-by-N real matrix Q with orthonormal rows,

- dorgql - dorgql - generate an M-by-N real matrix Q with orthonormal columns,

- dorgqr - dorgqr - generate an M-by-N real matrix Q with orthonormal columns,

- dorgr2 - dorgr2 - generate an m by n real matrix Q with orthonormal rows,

- dorgrq - dorgrq - generate an M-by-N real matrix Q with orthonormal rows,

- dorgtr - dorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD

- dormbr - dormbr - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

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

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

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

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

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

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

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

- dpbcon - dpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF

- dpbequ - dpbequ - compute 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 - dpbrfs - improve 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 - dpbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A

- dpbsv - dpbsv - compute the solution to a real system of linear equations A * X = B,

- dpbsvx - dpbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

- dpbtf2 - dpbtf2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A

- dpbtrf - dpbtrf - compute the Cholesky factorization of a real symmetric positive definite band matrix A

- dpbtrs - dpbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF

- dpocon - dpocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- dpoequ - dpoequ - compute 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 - dporfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

- dposv - dposv - compute the solution to a real system of linear equations A * X = B,

- dposvx - dposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

- dpotf2 - dpotf2 - compute the Cholesky factorization of a real symmetric positive definite matrix A

- dpotrf - dpotrf - compute the Cholesky factorization of a real symmetric positive definite matrix A

- dpotri - dpotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- dpotrs - dpotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- dppcon - dppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- dppequ - dppequ - compute 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 - dpprfs - improve 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

- dppsv - dppsv - compute the solution to a real system of linear equations A * X = B,

- dppsvx - dppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

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

- dpptri - dpptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- dpptrs - dpptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- dptcon - dptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF

- dpteqr - dpteqr - compute 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

- dptrfs - dptrfs - improve 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

- dptsv - dptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices.

- dptsvx - dptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

- dpttrf - dpttrf - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A

- dpttrs - dpttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF

- dptts2 - dptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF

- dqdota - dqdota - compute a double precision constant plus an extended precision constant plus the extended precision dot product of two double precision vectors x and y.

- dqdoti - dqdoti - compute a constant plus the extended precision dot product of two double precision vectors x and y.

- drot - drot - Apply a Given's rotation constructed by SROTG.

- drotg - drotg - Construct a Given's plane rotation

- droti - droti - Apply an indexed Givens rotation.

- drotm - drotm - Apply a Gentleman's modified Given's rotation constructed by SROTMG.

- drotmg - drotmg - Construct a Gentleman's modified Given's plane rotation

- dsbev - dsbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- dsbevd - dsbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- dsbevx - dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- dsbgst - dsbgst - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

- dsbgv - dsbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- dsbgvd - dsbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- dsbgvx - dsbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- dsbmv - dsbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

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

- dscal - dscal - Compute y := alpha * y

- dsctr - dsctr - Scatters elements from x into y.

- dsdot - dsdot - compute the double precision dot product of two single precision vectors x and y.

- dsecnd - dsecnd - return the user time for a process in seconds

- dsinqb - dsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N.

- dsinqf - dsinqf - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N.

- dsinqi - dsinqi - initialize the array xWSAVE, which is used in both SINQF and SINQB.

- dsint - dsint - compute the discrete Fourier sine transform of an odd sequence. The SINT transforms are unnormalized inverses of themselves, so a call of SINT followed by another call of SINT will multiply the input sequence by 2 * (N+1).

- dsinti - dsinti - initialize the array WSAVE, which is used in subroutine SINT.

- dskymm - dskymm - Skyline format matrix-matrix multiply

- dskysm - dskysm - Skyline format triangular solve

- dspcon - dspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF

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

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

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

- dspgst - dspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage

- dspgv - dspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dspgvd - dspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dspgvx - dspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dspmv - dspmv - perform the matrix-vector operation y := alpha*A*x + beta*y

- dspr - dspr - perform the symmetric rank 1 operation A := alpha*x*x' + A

- dspr2 - dspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A

- dsprfs - dsprfs - improve 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

- dspsv - dspsv - compute the solution to a real system of linear equations A * X = B,

- dspsvx - dspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices

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

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

- dsptri - dsptri - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF

- dsptrs - dsptrs - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF

- dstebz - dstebz - compute the eigenvalues of a symmetric tridiagonal matrix T

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

- dstegr - dstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation

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

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

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

- dstev - dstev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

- dstevd - dstevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix

- dstevr - dstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

- dstevx - dstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

- dstsv - dstsv - compute the solution to a system of linear equations A * X = B where A is a symmetric tridiagonal matrix

- dsttrf - dsttrf - compute the factorization of a symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method

- dsttrs - dsttrs - computes the solution to a real system of linear equations A * X = B

- dswap - dswap - Exchange vectors x and y.

- dsycon - dsycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

- dsyev - dsyev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- dsyevd - dsyevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- dsyevr - dsyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

- dsyevx - dsyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- dsygs2 - dsygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form

- dsygst - dsygst - reduce a real symmetric-definite generalized eigenproblem to standard form

- dsygv - dsygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dsygvd - dsygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dsygvx - dsygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- dsymm - dsymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- dsymv - dsymv - perform the matrix-vector operation y := alpha*A*x + beta*y

- dsyr - dsyr - perform the symmetric rank 1 operation A := alpha*x*x' + A

- dsyr2 - dsyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A

- dsyr2k - dsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C

- dsyrfs - dsyrfs - improve 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

- dsyrk - dsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C

- dsysv - dsysv - compute the solution to a real system of linear equations A * X = B,

- dsysvx - dsysvx - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,

- dsytd2 - dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

- dsytf2 - dsytf2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- dsytrd - dsytrd - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation

- dsytrf - dsytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- dsytri - dsytri - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

- dsytrs - dsytrs - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

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

- dtbmv - dtbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- dtbsv - dtbsv - solve one of the systems of equations A*x = b, or A'*x = b

- dtbtrs - dtbtrs - solve a triangular system of the form A * X = B or A**T * X = B,

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

- dtgexc - dtgexc - reorder the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation (A, B) = Q * (A, B) * Z',

- dtgsen - dtgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B) (in terms of an orthonormal equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and the upper triangular B

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

- dtgsna - dtgsna - estimate reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z

- dtgsyl - dtgsyl - solve the generalized Sylvester equation

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

- dtpmv - dtpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- dtpsv - dtpsv - solve one of the systems of equations A*x = b, or A'*x = b

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

- dtptrs - dtptrs - solve a triangular system of the form A * X = B or A**T * X = B,

- dtrans - dtrans - transpose and scale source matrix

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

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

- dtrexc - dtrexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST

- dtrmm - dtrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A )

- dtrmv - dtrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- dtrsen - dtrsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,

- dtrsm - dtrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B

- dtrsna - dtrsna - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)

- dtrsv - dtrsv - solve one of the systems of equations A*x = b, or A'*x = b

- dtrsyl - dtrsyl - solve the real Sylvester matrix equation

- dtrti2 - dtrti2 - compute the inverse of a real upper or lower triangular matrix

- dtrtri - dtrtri - compute the inverse of a real upper or lower triangular matrix A

- dtrtrs - dtrtrs - solve a triangular system of the form A * X = B or A**T * X = B,

- dtzrqf - dtzrqf - routine is deprecated and has been replaced by routine STZRZF

- dtzrzf - dtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations

- dvbrmm - dvbrmm - variable block sparse row format matrix-matrix multiply

- dvbrsm - dvbrsm - variable block sparse row format triangular solve

- dwiener - dwiener - perform Wiener deconvolution of two signals

- dzasum - dzasum - Return the sum of the absolute values of a vector x.

- dznrm2 - dznrm2 - Return the Euclidian norm of a vector.

- ezfftb - ezfftb - computes a periodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB.

- ezfftf - ezfftf - computes the Fourier coefficients of a periodic sequence. EZFFTF is a simplified but slower version of RFFTF.

- ezffti - ezffti - initializes the array WSAVE, which is used in both EZFFTF and EZFFTB.

- fft - fft - Fast Fourier transform subroutines

- icamax - icamax - return the index of the element with largest absolute value.

- idamax - idamax - return the index of the element with largest absolute value.

- ilaenv - ilaenv - The name of the calling subroutine, in either upper case or lower case.

- isamax - isamax - return the index of the element with largest absolute value.

- izamax - izamax - return the index of the element with largest absolute value.

- lsame - lsame - returns .TRUE. if CA is the same letter as CB regardless of case

- rfft2b - rfft2b - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFT2F followed by a call of RFFT2B will multiply the input sequence by M*N.

- rfft2f - rfft2f - compute the Fourier coefficients of a periodic sequence. The RFFT operations are unnormalized, so a call of RFFT2F followed by a call of RFFT2B will multiply the input sequence by M*N.

- rfft2i - rfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms.

- rfft3b - rfft3b - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFT3F followed by a call of RFFT3B will multiply the input sequence by M*N*K.

- rfft3f - rfft3f - compute the Fourier coefficients of a real periodic sequence. The RFFT operations are unnormalized, so a call of RFFT3F followed by a call of RFFT3B will multiply the input sequence by M*N*K.

- rfft3i - rfft3i - initialize the array WSAVE, which is used in both RFFT3F and RFFT3B.

- rfftb - rfftb - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFTF followed by a call of RFFTB will multiply the input sequence by N.

- rfftf - rfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of RFFTF followed by a call of RFFTB will multiply the input sequence by N.

- rffti - rffti - initialize the array WSAVE, which is used in both RFFTF and RFFTB.

- rfftopt - rfftopt - compute the length of the closest fast FFT

- sasum - sasum - Return the sum of the absolute values of a vector x.

- saxpy - saxpy - compute y := alpha * x + y

- saxpyi - saxpyi - Compute y := alpha * x + y

- sbcomm - sbcomm - block coordinate matrix-matrix multiply

- sbdimm - sbdimm - block diagonal format matrix-matrix multiply

- sbdism - sbdism - block diagonal format triangular solve

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

- sbdsqr - sbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.

- sbelmm - sbelmm - block Ellpack format matrix-matrix multiply

- sbelsm - sbelsm - block Ellpack format triangular solve

- sbscmm - sbscmm - block sparse column matrix-matrix multiply

- sbscsm - sbscsm - block sparse column format triangular solve

- sbsrmm - sbsrmm - block sparse row format matrix-matrix multiply

- sbsrsm - sbsrsm - block sparse row format triangular solve

- scasum - scasum - Return the sum of the absolute values of a vector x.

- scnrm2 - scnrm2 - Return the Euclidian norm of a vector.

- scnvcor - scnvcor - compute the convolution or correlation of real vectors

- scnvcor2 - scnvcor2 - compute the convolution or correlation of real matrices

- scoomm - scoomm - coordinate matrix-matrix multiply

- scopy - scopy - Copy x to y

- scscmm - scscmm - compressed sparse column format matrix-matrix multiply

- scscsm - scscsm - compressed sparse column format triangular solve

- scsrmm - scsrmm - compressed sparse row format matrix-matrix multiply

- scsrsm - scsrsm - compressed sparse row format triangular solve

- sdiamm - sdiamm - diagonal format matrix-matrix multiply

- sdiasm - sdiasm - diagonal format triangular solve

- sdisna - sdisna - compute 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

- sdot - sdot - compute the dot product of two vectors x and y.

- sdoti - sdoti - Compute the indexed dot product.

- sdsdot - sdsdot - compute a constant plus the double precision dot product of two single precision vectors x and y

- second - second - return the user time for a process in seconds

- sellmm - sellmm - Ellpack format matrix-matrix multiply

- sellsm - sellsm - Ellpack format triangular solve

- sfftc - sfftc - initialize the trigonometric weight and factor tables or compute the forward Fast Fourier Transform of a real sequence.

- sfftc2 - sfftc2 - initialize the trigonometric weight and factor tables or compute the two-dimensional forward Fast Fourier Transform of a two-dimensional real array.

- sfftc3 - sfftc3 - initialize the trigonometric weight and factor tables or compute the three-dimensional forward Fast Fourier Transform of a three-dimensional complex array.

- sfftcm - sfftcm - initialize the trigonometric weight and factor tables or compute the one-dimensional forward Fast Fourier Transform of a set of real data sequences stored in a two-dimensional array.

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

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

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

- sgbmv - sgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*A'*x + beta*y

- sgbrfs - sgbrfs - improve 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

- sgbsv - sgbsv - compute the solution to a real system of linear equations A * X = B, 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 - sgbsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

- sgbtf2 - sgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

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

- sgbtrs - sgbtrs - solve a system of linear equations A * X = B or A' * X = B with a general band matrix A using the LU factorization computed by SGBTRF

- sgebak - sgebak - form 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 - sgebal - balance a general real matrix A

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

- sgecon - sgecon - estimate 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 - sgeequ - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

- sgees - sgees - compute 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 - sgeesx - compute 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 - sgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

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

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

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

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

- sgelqf - sgelqf - compute an LQ factorization of a real M-by-N matrix A

- sgels - sgels - solve 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 - sgelsd - compute the minimum-norm solution to a real linear least squares problem

- sgelss - sgelss - compute the minimum norm solution to a real linear least squares problem

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

- sgelsy - sgelsy - compute the minimum-norm solution to a real linear least squares problem

- sgemm - sgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C

- sgemv - sgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*A'*x + beta*y

- sgeqlf - sgeqlf - compute a QL factorization of a real M-by-N matrix A

- sgeqp3 - sgeqp3 - compute a QR factorization with column pivoting of a matrix A

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

- sgeqrf - sgeqrf - compute a QR factorization of a real M-by-N matrix A

- sger - sger - perform the rank 1 operation A := alpha*x*y' + A

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

- sgerqf - sgerqf - compute an RQ factorization of a real M-by-N matrix A

- sgesdd - sgesdd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors

- sgesv - sgesv - compute the solution to a real system of linear equations A * X = B,

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

- sgesvx - sgesvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B,

- sgetf2 - sgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

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

- sgetri - sgetri - compute the inverse of a matrix using the LU factorization computed by SGETRF

- sgetrs - sgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF

- sggbak - sggbak - form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL

- sggbal - sggbal - balance a pair of general real matrices (A,B)

- sgges - sgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B),

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

- sggev - sggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B)

- sggevx - sggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B)

- sggglm - sggglm - solve a general Gauss-Markov linear model (GLM) problem

- sgghrd - sgghrd - reduce 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 - sgglse - solve the linear equality-constrained least squares (LSE) problem

- sggqrf - sggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B.

- sggrqf - sggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

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

- sggsvp - sggsvp - compute orthogonal matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

- sgssco - sgssco - General sparse solver condition number estimate.

- sgssda - sgssda - Deallocate working storage for the general sparse solver.

- sgssfa - sgssfa - General sparse solver numeric factorization.

- sgssfs - sgssfs - General sparse solver one call interface.

- sgssin - sgssin - Initialize the general sparse solver.

- sgssor - sgssor - General sparse solver ordering and symbolic factorization.

- sgssps - sgssps - Print general sparse solver statics.

- sgssrp - sgssrp - Return permutation used by the general sparse solver.

- sgsssl - sgsssl - Solve routine for the general sparse solver.

- sgssuo - sgssuo - User supplied permutation for ordering used in the general sparse solver.

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

- sgthr - sgthr - Gathers specified elements from y into x.

- sgthrz - sgthrz - Gather and zero.

- sgtrfs - sgtrfs - improve 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

- sgtsv - sgtsv - solve the equation A*X = B,

- sgtsvx - sgtsvx - use the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B,

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

- sgttrs - sgttrs - solve one of the systems of equations A*X = B or A'*X = B,

- shgeqz - shgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form

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

- shseqr - shseqr - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors

- sinqb - sinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N.

- sinqf - sinqf - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N.

- sinqi - sinqi - initialize the array xWSAVE, which is used in both SINQF and SINQB.

- sint - sint - compute the discrete Fourier sine transform of an odd sequence. The SINT transforms are unnormalized inverses of themselves, so a call of SINT followed by another call of SINT will multiply the input sequence by 2 * (N+1).

- sinti - sinti - initialize the array WSAVE, which is used in subroutine SINT.

- sjadmm - sjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)

- sjadrp - sjadrp - right permutation of a jagged diagonal matrix

- sjadsm - sjadsm - Jagged-diagonal format triangular solve

- slagtf - slagtf - factorize the matrix (T-lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T-lambda*I = PLU

- slamrg - slamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order

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

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

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

- slasrt - slasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )

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

- snrm2 - snrm2 - Return the Euclidian norm of a vector.

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

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

- sorg2l - sorg2l - generate an m by n real matrix Q with orthonormal columns,

- sorg2r - sorg2r - generate an m by n real matrix Q with orthonormal columns,

- sorgbr - sorgbr - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal form

- sorghr - sorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD

- sorgl2 - sorgl2 - generate an m by n real matrix Q with orthonormal rows,

- sorglq - sorglq - generate an M-by-N real matrix Q with orthonormal rows,

- sorgql - sorgql - generate an M-by-N real matrix Q with orthonormal columns,

- sorgqr - sorgqr - generate an M-by-N real matrix Q with orthonormal columns,

- sorgr2 - sorgr2 - generate an m by n real matrix Q with orthonormal rows,

- sorgrq - sorgrq - generate an M-by-N real matrix Q with orthonormal rows,

- sorgtr - sorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD

- sormbr - sormbr - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

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

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

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

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

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

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

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

- spbcon - spbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF

- spbequ - spbequ - compute 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 - spbrfs - improve 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

- spbstf - spbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A

- spbsv - spbsv - compute the solution to a real system of linear equations A * X = B,

- spbsvx - spbsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

- spbtf2 - spbtf2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A

- spbtrf - spbtrf - compute the Cholesky factorization of a real symmetric positive definite band matrix A

- spbtrs - spbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF

- spocon - spocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- spoequ - spoequ - compute 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 - sporfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,

- sposv - sposv - compute the solution to a real system of linear equations A * X = B,

- sposvx - sposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

- spotf2 - spotf2 - compute the Cholesky factorization of a real symmetric positive definite matrix A

- spotrf - spotrf - compute the Cholesky factorization of a real symmetric positive definite matrix A

- spotri - spotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- spotrs - spotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF

- sppcon - sppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- sppequ - sppequ - compute 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 - spprfs - improve 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 - sppsv - compute the solution to a real system of linear equations A * X = B,

- sppsvx - sppsvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A * X = B,

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

- spptri - spptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- spptrs - spptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF

- sptcon - sptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF

- spteqr - spteqr - compute 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 - sptrfs - improve 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 - sptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices.

- sptsvx - sptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

- spttrf - spttrf - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A

- spttrs - spttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF

- sptts2 - sptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF

- srot - srot - Apply a Given's rotation constructed by SROTG.

- srotg - srotg - Construct a Given's plane rotation

- sroti - sroti - Apply an indexed Givens rotation.

- srotm - srotm - Apply a Gentleman's modified Given's rotation constructed by SROTMG.

- srotmg - srotmg - Construct a Gentleman's modified Given's plane rotation

- ssbev - ssbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- ssbevd - ssbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- ssbevx - ssbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

- ssbgst - ssbgst - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

- ssbgv - ssbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- ssbgvd - ssbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- ssbgvx - ssbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- ssbmv - ssbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

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

- sscal - sscal - Compute y := alpha * y

- ssctr - ssctr - Scatters elements from x into y.

- sskymm - sskymm - Skyline format matrix-matrix multiply

- sskysm - sskysm - Skyline format triangular solve

- sspcon - sspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF

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

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

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

- sspgst - sspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage

- sspgv - sspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- sspgvd - sspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- sspgvx - sspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- sspmv - sspmv - perform the matrix-vector operation y := alpha*A*x + beta*y

- sspr - sspr - perform the symmetric rank 1 operation A := alpha*x*x' + A

- sspr2 - sspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A

- ssprfs - ssprfs - improve 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

- sspsv - sspsv - compute the solution to a real system of linear equations A * X = B,

- sspsvx - sspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices

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

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

- ssptri - ssptri - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF

- ssptrs - ssptrs - solve a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF

- sstebz - sstebz - compute the eigenvalues of a symmetric tridiagonal matrix T

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

- sstegr - sstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation

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

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

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

- sstev - sstev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

- sstevd - sstevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix

- sstevr - sstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

- sstevx - sstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A

- sstsv - sstsv - compute the solution to a system of linear equations A * X = B where A is a symmetric tridiagonal matrix

- ssttrf - ssttrf - compute the factorization of a symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method

- ssttrs - ssttrs - computes the solution to a real system of linear equations A * X = B

- sswap - sswap - Exchange vectors x and y.

- ssycon - ssycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

- ssyev - ssyev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- ssyevd - ssyevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- ssyevr - ssyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T

- ssyevx - ssyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A

- ssygs2 - ssygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form

- ssygst - ssygst - reduce a real symmetric-definite generalized eigenproblem to standard form

- ssygv - ssygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- ssygvd - ssygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- ssygvx - ssygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- ssymm - ssymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- ssymv - ssymv - perform the matrix-vector operation y := alpha*A*x + beta*y

- ssyr - ssyr - perform the symmetric rank 1 operation A := alpha*x*x' + A

- ssyr2 - ssyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A

- ssyr2k - ssyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C

- ssyrfs - ssyrfs - improve 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

- ssyrk - ssyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C

- ssysv - ssysv - compute the solution to a real system of linear equations A * X = B,

- ssysvx - ssysvx - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,

- ssytd2 - ssytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation

- ssytf2 - ssytf2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- ssytrd - ssytrd - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation

- ssytrf - ssytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- ssytri - ssytri - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

- ssytrs - ssytrs - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF

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

- stbmv - stbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- stbsv - stbsv - solve one of the systems of equations A*x = b, or A'*x = b

- stbtrs - stbtrs - solve a triangular system of the form A * X = B or A**T * X = B,

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

- stgexc - stgexc - reorder the generalized real Schur decomposition of a real matrix pair (A,B) using an orthogonal equivalence transformation (A, B) = Q * (A, B) * Z',

- stgsen - stgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B) (in terms of an orthonormal equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix A and the upper triangular B

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

- stgsna - stgsna - estimate reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B) in generalized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z

- stgsyl - stgsyl - solve the generalized Sylvester equation

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

- stpmv - stpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- stpsv - stpsv - solve one of the systems of equations A*x = b, or A'*x = b

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

- stptrs - stptrs - solve a triangular system of the form A * X = B or A**T * X = B,

- strans - strans - transpose and scale source matrix

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

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

- strexc - strexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST

- strmm - strmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A )

- strmv - strmv - perform one of the matrix-vector operations x := A*x, or x := A'*x

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

- strsen - strsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,

- strsm - strsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B

- strsna - strsna - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a real upper quasi-triangular matrix T (or of any matrix Q*T*Q**T with Q orthogonal)

- strsv - strsv - solve one of the systems of equations A*x = b, or A'*x = b

- strsyl - strsyl - solve the real Sylvester matrix equation

- strti2 - strti2 - compute the inverse of a real upper or lower triangular matrix

- strtri - strtri - compute the inverse of a real upper or lower triangular matrix A

- strtrs - strtrs - solve a triangular system of the form A * X = B or A**T * X = B,

- stzrqf - stzrqf - routine is deprecated and has been replaced by routine STZRZF

- stzrzf - stzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations

- sunperf_version - sunperf_version - gets library information 1i SUBROUTINE SUNPERF_VERSION(VERSION, PATCH, UPDATE) 1i INTEGER VERSION, PATCH, UPDATE 1i

- svbrmm - svbrmm - variable block sparse row format matrix-matrix multiply

- svbrsm - svbrsm - variable block sparse row format triangular solve

- swiener - swiener - perform Wiener deconvolution of two signals

- use_threads - use_threads - Sets the number of threads to use for subsequent parallel regions

- using_threads - using_threads - In a parallel environment, if called from a serial region of the master thread it returns the number of threads available for execution (determined by function OMP_GET_NUM_THREADS). Else, if it is called from a thread in the team executing the parallel region it returns a 1. USING_THREADS subroutine

- vcfftb - vcfftb - compute a periodic sequence from its Fourier coefficients. The VCFFT operations are normalized, so a call of VCFFTF followed by a call of VCFFTB will return the original sequence.

- vcfftf - vcfftf - compute the Fourier coefficients of a periodic sequence. The VCFFT operations are normalized, so a call of VCFFTF followed by a call of VCFFTB will return the original sequence.

- vcffti - vcffti - initialize the array WSAVE, which is used in both VCFFTF and VCFFTB.

- vcosqb - vcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence.

- vcosqf - vcosqf - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence.

- vcosqi - vcosqi - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB.

- vcost - vcost - compute the discrete Fourier cosine transform of an even sequence. The VCOST transform is normalized, so a call of VCOST followed by a call of VCOST will return the original sequence.

- vcosti - vcosti - initialize the array WSAVE, which is used in VCOST.

- vdcosqb - vdcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence.

- vdcosqf - vdcosqf - compute the Fourier coefficients in a cosine series representation with only odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence.

- vdcosqi - vdcosqi - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB.

- vdcost - vdcost - compute the discrete Fourier cosine transform of an even sequence. The VCOST transform is normalized, so a call of VCOST followed by a call of VCOST will return the original sequence.

- vdcosti - vdcosti - initialize the array WSAVE, which is used in VCOST.

- vdfftb - vdfftb - compute a periodic sequence from its Fourier coefficients. The VRFFT operations are normalized, so a call of VRFFTF followed by a call of VRFFTB will return the original sequence.

- vdfftf - vdfftf - compute the Fourier coefficients of a periodic sequence. The VRFFT operations are normalized, so a call of VRFFTF followed by a call of VRFFTB will return the original sequence.

- vdffti - vdffti - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB.

- vdsinqb - vdsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence.

- vdsinqf - vdsinqf - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence.

- vdsinqi - vdsinqi - initialize the array WSAVE, which is used in both VSINQF and VSINQB.

- vdsint - vdsint - compute the discrete Fourier sine transform of an odd sequence. The VSINT transforms are unnormalized inverses of themselves, so a call of VSINT followed by another call of VSINT will multiply the input sequence by 2 * (N+1). The VSINT transforms are normalized, so a call of VSINT followed by a call of VSINT will return the original sequence.

- vdsinti - vdsinti - initialize the array WSAVE, which is used in subroutine VSINT.

- vrfftb - vrfftb - compute a periodic sequence from its Fourier coefficients. The VRFFT operations are normalized, so a call of VRFFTF followed by a call of VRFFTB will return the original sequence.

- vrfftf - vrfftf - compute the Fourier coefficients of a periodic sequence. The VRFFT operations are normalized, so a call of VRFFTF followed by a call of VRFFTB will return the original sequence.

- vrffti - vrffti - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB.

- vsinqb - vsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence.

- vsinqf - vsinqf - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence.

- vsinqi - vsinqi - initialize the array WSAVE, which is used in both VSINQF and VSINQB.

- vsint - vsint - compute the discrete Fourier sine transform of an odd sequence. The VSINT transforms are unnormalized inverses of themselves, so a call of VSINT followed by another call of VSINT will multiply the input sequence by 2 * (N+1). The VSINT transforms are normalized, so a call of VSINT followed by a call of VSINT will return the original sequence.

- vsinti - vsinti - initialize the array WSAVE, which is used in subroutine VSINT.

- vzfftb - vzfftb - compute a periodic sequence from its Fourier coefficients. The VZFFT operations are normalized, so a call of VZFFTF followed by a call of VZFFTB will return the original sequence.

- vzfftf - vzfftf - compute the Fourier coefficients of a periodic sequence. The VZFFT operations are normalized, so a call of VZFFTF followed by a call of VZFFTB will return the original sequence.

- vzffti - vzffti - initialize the array WSAVE, which is used in both VZFFTF and VZFFTB.

- zaxpy - zaxpy - compute y := alpha * x + y

- zaxpyi - zaxpyi - Compute y := alpha * x + y

- zbcomm - zbcomm - block coordinate matrix-matrix multiply

- zbdimm - zbdimm - block diagonal format matrix-matrix multiply

- zbdism - zbdism - block diagonal format triangular solve

- zbdsqr - zbdsqr - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B.

- zbelmm - zbelmm - block Ellpack format matrix-matrix multiply

- zbelsm - zbelsm - block Ellpack format triangular solve

- zbscmm - zbscmm - block sparse column matrix-matrix multiply

- zbscsm - zbscsm - block sparse column format triangular solve

- zbsrmm - zbsrmm - block sparse row format matrix-matrix multiply

- zbsrsm - zbsrsm - block sparse row format triangular solve

- zcnvcor - zcnvcor - compute the convolution or correlation of complex vectors

- zcnvcor2 - zcnvcor2 - compute the convolution or correlation of complex matrices

- zcoomm - zcoomm - coordinate matrix-matrix multiply

- zcopy - zcopy - Copy x to y

- zcscmm - zcscmm - compressed sparse column format matrix-matrix multiply

- zcscsm - zcscsm - compressed sparse column format triangular solve

- zcsrmm - zcsrmm - compressed sparse row format matrix-matrix multiply

- zcsrsm - zcsrsm - compressed sparse row format triangular solve

- zdiamm - zdiamm - diagonal format matrix-matrix multiply.

- zdiasm - zdiasm - diagonal format triangular solve

- zdotc - zdotc - compute the dot product of two vectors conjg(x) and y.

- zdotci - zdotci - Compute the complex conjugated indexed dot product.

- zdotu - zdotu - compute the dot product of two vectors x and y.

- zdotui - zdotui - Compute the complex unconjugated indexed dot product.

- zdrot - zdrot - Apply a plane rotation.

- zdscal - zdscal - Compute y := alpha * y

- zellmm - zellmm - Ellpack format matrix-matrix multiply

- zellsm - zellsm - Ellpack format triangular solve

- zfft2b - zfft2b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFT2F followed by a call of ZFFT2B will multiply the input sequence by M*N.

- zfft2f - zfft2f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFT2F followed by a call of ZFFT2B will multiply the input sequence by M*N.

- zfft2i - zfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms.

- zfft3b - zfft3b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFT3F followed by a call of ZFFT3B will multiply the input sequence by M*N*K.

- zfft3f - zfft3f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFT3F followed by a call of ZFFT3B will multiply the input sequence by M*N*K.

- zfft3i - zfft3i - initialize the array WSAVE, which is used in both ZFFT3F and ZFFT3B.

- zfftb - zfftb - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFTF followed by a call of ZFFTB will multiply the input sequence by N.

- zfftd - zfftd - initialize the trigonometric weight and factor tables or compute the inverse Fast Fourier Transform of a double complex sequence.

- zfftd2 - zfftd2 - initialize the trigonometric weight and factor tables or compute the two-dimensional inverse Fast Fourier Transform of a two-dimensional double complex array.

- zfftd3 - zfftd3 - initialize the trigonometric weight and factor tables or compute the three-dimensional inverse Fast Fourier Transform of a three-dimensional double complex array.

- zfftdm - zfftdm - initialize the trigonometric weight and factor tables or compute the one-dimensional inverse Fast Fourier Transform of a set of double complex data sequences stored in a two-dimensional array.

- zfftf - zfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFTF followed by a call of ZFFTB will multiply the input sequence by N.

- zffti - zffti - initialize the array WSAVE, which is used in both ZFFTF and ZFFTB.

- zfftopt - zfftopt - compute the length of the closest fast FFT

- zfftz - zfftz - initialize the trigonometric weight and factor tables or compute the Fast Fourier transform (forward or inverse) of a double complex sequence.

- zfftz2 - zfftz2 - initialize the trigonometric weight and factor tables or compute the two-dimensional Fast Fourier Transform (forward or inverse) of a two-dimensional double complex array.

- zfftz3 - zfftz3 - initialize the trigonometric weight and factor tables or compute the three-dimensional Fast Fourier Transform (forward or inverse) of a three-dimensional double complex array.

- zfftzm - zfftzm - initialize the trigonometric weight and factor tables or compute the one-dimensional Fast Fourier Transform (forward or inverse) of a set of data sequences stored in a two-dimensional double complex array.

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

- zgbcon - zgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,

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

- zgbmv - zgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y

- zgbrfs - zgbrfs - improve 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 - zgbsv - compute the solution to a complex system of linear equations A * X = B, 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 - zgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

- zgbtf2 - zgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

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

- zgbtrs - zgbtrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general band matrix A using the LU factorization computed by CGBTRF

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

- zgebal - zgebal - balance a general complex matrix A

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

- zgecon - zgecon - estimate 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 CGETRF

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

- zgees - zgees - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

- zgeesx - zgeesx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z

- zgeev - zgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

- zgeevx - zgeevx - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors

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

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

- zgehrd - zgehrd - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation

- zgelqf - zgelqf - compute an LQ factorization of a complex M-by-N matrix A

- zgels - zgels - solve 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 - zgelsd - compute the minimum-norm solution to a real linear least squares problem

- zgelss - zgelss - compute the minimum norm solution to a complex linear least squares problem

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

- zgelsy - zgelsy - compute the minimum-norm solution to a complex linear least squares problem

- zgemm - zgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C

- zgemv - zgemv - perform one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y

- zgeqlf - zgeqlf - compute a QL factorization of a complex M-by-N matrix A

- zgeqp3 - zgeqp3 - compute a QR factorization with column pivoting of a matrix A

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

- zgeqrf - zgeqrf - compute a QR factorization of a complex M-by-N matrix A

- zgerc - zgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A

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

- zgerqf - zgerqf - compute an RQ factorization of a complex M-by-N matrix A

- zgeru - zgeru - perform the rank 1 operation A := alpha*x*y' + A

- zgesdd - zgesdd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method

- zgesv - zgesv - compute the solution to a complex system of linear equations A * X = B,

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

- zgesvx - zgesvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,

- zgetf2 - zgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

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

- zgetri - zgetri - compute the inverse of a matrix using the LU factorization computed by CGETRF

- zgetrs - zgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF

- zggbak - zggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL

- zggbal - zggbal - balance a pair of general complex matrices (A,B)

- zgges - zgges - compute 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 - zggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),

- zggev - zggev - compute 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 - zggevx - compute 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 - zggglm - solve a general Gauss-Markov linear model (GLM) problem

- zgghrd - zgghrd - reduce 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 - zgglse - solve the linear equality-constrained least squares (LSE) problem

- zggqrf - zggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B.

- zggrqf - zggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B

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

- zggsvp - zggsvp - compute unitary matrices U, V and Q such that N-K-L K L U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0

- zgssco - zgssco - General sparse solver condition number estimate.

- zgssda - zgssda - Deallocate working storage for the general sparse solver.

- zgssfa - zgssfa - General sparse solver numeric factorization.

- zgssfs - zgssfs - General sparse solver one call interface.

- zgssin - zgssin - Initialize the general sparse solver.

- zgssor - zgssor - General sparse solver ordering and symbolic factorization.

- zgssps - zgssps - Print general sparse solver statics.

- zgssrp - zgssrp - Return permutation used by the general sparse solver.

- zgsssl - zgsssl - Solve routine for the general sparse solver.

- zgssuo - zgssuo - User supplied permutation for ordering used in the general sparse solver.

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

- zgthr - zgthr - Gathers specified elements from y into x.

- zgthrz - zgthrz - Gather and zero.

- zgtrfs - zgtrfs - improve 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 - zgtsv - solve the equation A*X = B,

- zgtsvx - zgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A * X = B, A**T * X = B, or A**H * X = B,

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

- zgttrs - zgttrs - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,

- zhbev - zhbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- zhbevd - zhbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- zhbevx - zhbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A

- zhbgst - zhbgst - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,

- zhbgv - zhbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- zhbgvd - zhbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- zhbgvx - zhbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x

- zhbmv - zhbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

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

- zhecon - zhecon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- zheev - zheev - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- zheevd - zheevd - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- zheevr - zheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian tridiagonal matrix T

- zheevx - zheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

- zhegs2 - zhegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form

- zhegst - zhegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form

- zhegv - zhegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhegvd - zhegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhegvx - zhegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhemm - zhemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- zhemv - zhemv - perform the matrix-vector operation y := alpha*A*x + beta*y

- zher - zher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A

- zher2 - zher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

- zher2k - zher2k - perform one of the Hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C

- zherfs - zherfs - improve 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

- zherk - zherk - perform one of the Hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A + beta*C

- zhesv - zhesv - compute the solution to a complex system of linear equations A * X = B,

- zhesvx - zhesvx - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,

- zhetf2 - zhetf2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

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

- zhetrf - zhetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

- zhetri - zhetri - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- zhetrs - zhetrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF

- zhgeqz - zhgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right

- zhpcon - zhpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

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

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

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

- zhpgst - zhpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

- zhpgv - zhpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhpgvd - zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhpgvx - zhpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

- zhpmv - zhpmv - perform the matrix-vector operation y := alpha*A*x + beta*y

- zhpr - zhpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A

- zhpr2 - zhpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

- zhprfs - zhprfs - improve 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 - zhpsv - compute the solution to a complex system of linear equations A * X = B,

- zhpsvx - zhpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices

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

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

- zhptri - zhptri - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

- zhptrs - zhptrs - solve a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF

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

- zhseqr - zhseqr - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors

- zjadmm - zjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)

- zjadrp - zjadrp - right permutation of a jagged diagonal matrix

- zjadsm - zjadsm - Jagged-diagonal format triangular solve

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

- zlarzb - zlarzb - applie a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right

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

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

- zpbcon - zpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

- zpbequ - zpbequ - compute 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)

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

- zpbstf - zpbstf - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A

- zpbsv - zpbsv - compute the solution to a complex system of linear equations A * X = B,

- zpbsvx - zpbsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

- zpbtf2 - zpbtf2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

- zpbtrf - zpbtrf - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

- zpbtrs - zpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

- zpocon - zpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- zpoequ - zpoequ - compute 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 - zporfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,

- zposv - zposv - compute the solution to a complex system of linear equations A * X = B,

- zposvx - zposvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

- zpotf2 - zpotf2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A

- zpotrf - zpotrf - compute the Cholesky factorization of a complex Hermitian positive definite matrix A

- zpotri - zpotri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- zpotrs - zpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF

- zppcon - zppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- zppequ - zppequ - compute 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 - zpprfs - improve 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 - zppsv - compute the solution to a complex system of linear equations A * X = B,

- zppsvx - zppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,

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

- zpptri - zpptri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- zpptrs - zpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF

- zptcon - zptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF

- zpteqr - zpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor

- zptrfs - zptrfs - improve 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 - zptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices.

- zptsvx - zptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

- zpttrf - zpttrf - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A

- zpttrs - zpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF

- zptts2 - zptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF

- zrot - zrot - apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors X and Y are complex

- zrotg - zrotg - Construct a Given's plane rotation

- zscal - zscal - Compute y := alpha * y

- zsctr - zsctr - Scatters elements from x into y.

- zskymm - zskymm - Skyline format matrix-matrix multiply

- zskysm - zskysm - Skyline format triangular solve

- zspcon - zspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF

- zsprfs - zsprfs - improve 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 - zspsv - compute the solution to a complex system of linear equations A * X = B,

- zspsvx - zspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices

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

- zsptri - zsptri - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF

- zsptrs - zsptrs - solve a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF

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

- zstegr - zstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation

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

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

- zstsv - zstsv - compute the solution to a complex system of linear equations A * X = B where A is a symmetric tridiagonal matrix

- zsttrf - zsttrf - compute the factorization of a complex symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method

- zsttrs - zsttrs - computes the solution to a complex system of linear equations A * X = B

- zswap - zswap - Exchange vectors x and y.

- zsycon - zsycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

- zsymm - zsymm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C

- zsyr2k - zsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C

- zsyrfs - zsyrfs - improve 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

- zsyrk - zsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C

- zsysv - zsysv - compute the solution to a complex system of linear equations A * X = B,

- zsysvx - zsysvx - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,

- zsytf2 - zsytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- zsytrf - zsytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

- zsytri - zsytri - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

- zsytrs - zsytrs - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

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

- ztbmv - ztbmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ztbsv - ztbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

- ztbtrs - ztbtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

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

- ztgexc - ztgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transformation (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST

- ztgsen - ztgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B) (in terms of an unitary equivalence trans- formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B)

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

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

- ztgsyl - ztgsyl - solve the generalized Sylvester equation

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

- ztpmv - ztpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ztpsv - ztpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

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

- ztptrs - ztptrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

- ztrans - ztrans - transpose and scale source matrix

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

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

- ztrexc - ztrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST

- ztrmm - ztrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' )

- ztrmv - ztrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x

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

- ztrsen - ztrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace

- ztrsm - ztrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B

- ztrsna - ztrsna - estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary)

- ztrsv - ztrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b

- ztrsyl - ztrsyl - solve the complex Sylvester matrix equation

- ztrti2 - ztrti2 - compute the inverse of a complex upper or lower triangular matrix

- ztrtri - ztrtri - compute the inverse of a complex upper or lower triangular matrix A

- ztrtrs - ztrtrs - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,

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

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

- zung2l - zung2l - generate an m by n complex matrix Q with orthonormal columns,

- zung2r - zung2r - generate an m by n complex matrix Q with orthonormal columns,

- zungbr - zungbr - generate one of the complex unitary matrices Q or P**H determined by CGEBRD when reducing a complex matrix A to bidiagonal form

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

- zungl2 - zungl2 - generate an m-by-n complex matrix Q with orthonormal rows,

- zunglq - zunglq - generate an M-by-N complex matrix Q with orthonormal rows,

- zungql - zungql - generate an M-by-N complex matrix Q with orthonormal columns,

- zungqr - zungqr - generate an M-by-N complex matrix Q with orthonormal columns,

- zungr2 - zungr2 - generate an m by n complex matrix Q with orthonormal rows,

- zungrq - zungrq - generate an M-by-N complex matrix Q with orthonormal rows,

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

- zunmbr - zunmbr - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmhr - zunmhr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunml2 - zunml2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',

- zunmlq - zunmlq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmql - zunmql - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmqr - zunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmr2 - zunmr2 - overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'C', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'C',

- zunmrq - zunmrq - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmrz - zunmrz - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zunmtr - zunmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zupgtr - zupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage

- zupmtr - zupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

- zvbrmm - zvbrmm - variable block sparse row format matrix-matrix multiply

- zvbrsm - zvbrsm - variable block sparse row format triangular solve

- zvmul - zvmul - compute the scaled product of complex vectors