Sun Performance Library(TM) Reference Manual

Sun WorkShop(TM) 6 update 2

This reference manual is an HTML version of the section 3P man pages. 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 - returns information about current thread usage

bcomm - bcomm, sbcomm, dbcomm - block coordinate matrix-matrix multiply

bdimm - bdimm, sbdimm, dbdimm - block diagonal format matrix-matrix multiply

bdism - bdism, sbdism, dbdism - block diagonal format triangular solve

belmm - belmm, sbelmm, dbelmm - block Ellpack format matrix-matrix multiply

belsm - belsm, sbelsm, dbelsm - block Ellpack format triangular solve

bscmm - bscmm, sbscmm, dbscmm - block sparse column matrix-matrix multiply

bscsm - bscsm, sbscsm, dbscsm - block sparse column format triangular solve

bsrmm - bsrmm, sbsrmm, dbsrmm - block sparse row format matrix-matrix multiply

bsrsm - bsrsm, sbsrsm, dbsrsm - block sparse row format triangular solve

coomm - coomm, scoomm, dcoomm - coordinate matrix-matrix multiply

cscmm - cscmm, scscmm, dcscmm - compressed sparse column format matrix-matrix multiply

cscsm - cscsm, scscsm, dcscsm - compressed sparse column format triangular solve

csrmm - csrmm, scsrmm, dcsrmm - compressed sparse row format matrix-matrix multiply

csrsm - csrsm, scsrsm, dcsrsm - compressed sparse row format triangular solve

caxpy - compute y := alpha * x + y

caxpyi - caxpyi, daxpyi, saxpyi, zaxpyi - Compute y := alpha * x + y

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

cchdc (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

cchdd (obsolete)- downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

cchex (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

cchud (obsolete)- update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

ccnvcor - compute the convolution or correlation of complex vectors

ccnvcor2 - compute the convolution or correlation of complex matrices

ccopy - Copy x to y

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

cdotci - cdotci, cdotui, ddoti, sdoti, zdotci, zdotui - Compute the dot product of two vectors x and y

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

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

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

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.

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

cfftopt - compute the length of the closest fast FFT

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

cgbco (obsolete)- compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.

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

cgbdi (obsolete)- compute the determinant of a general matrix A in banded storage, which has been LU-factored by CGBCO or CGBFA.

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

cgbfa (obsolete)- compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to CGBFA with a call to CGBSL to solve Ax = b or to CGBDI to compute the determinant of A.

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 - 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

cgbsl (obsolete)- solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by CGBCO or CGBFA, and vectors b and x.

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

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

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 - 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 - balance a general complex matrix A

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

cgeco (obsolete)- compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then CGEFA is slightly faster. It is typical to follow a call to CGECO with a call to CGESL to solve Ax = b or to CGEDI to compute the determinant and inverse of A.

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

cgedi (obsolete)- compute the determinant and inverse of a general matrix A, which has been LU-factored by CGECO or CGEFA.

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

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

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

cgefa (obsolete)- compute the LU factorization of a general matrix A. It is typical to follow a call to CGEFA with a call to CGESL to solve Ax = b or to CGEDI to compute the determinant of A.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cgesl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been LU- factored by CGECO or CGEFA, and vectors b and x.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cgthr - cgthr, dgthr, sgthr, zgthr - Gathers specified elements from y into x

cgthrz - cgthrz, dgthrz, sgthrz, zgthrz - Gathers specified elements from y into x and sets gathered elements in y to zero

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

cgtsl (obsolete)- solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.

cgtsv - solve the equation A*X = B,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 - 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 - 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

chico (obsolete)- compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.

chidi (obsolete)- compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by CHICO or CHIFA.

chifa (obsolete)- compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to CHIFA with a call to CHISL to solve Ax = b or to CHIDI to compute the determinant, inverse, and inertia of A.

chisl (obsolete)- solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by CHICO or CHIFA, and vectors b and x.

chpco (obsolete)- compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.

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

chpdi (obsolete)- compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by CHPCO or CHPFA.

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

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

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

chpfa (obsolete)- compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to CHPFA with a call to CHPSL to solve Ax = b or to CHPDI to compute the determinant, inverse, and inertia of A.

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

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

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

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

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

chpsl (obsolete)- solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by CHPCO or CHPFA, and vectors b and x.

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

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

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

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

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

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

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

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

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

cpbco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.

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

cpbdi (obsolete)- compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by CPBCO or CPBFA.

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)

cpbfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to CPBFA with a call to CPBSL to solve Ax = b or to CPBDI to compute the determinant of A.

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

cpbsl (obsolete)- section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by CPBCO or CPBFA, and vectors b and x.

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

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

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

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

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

cpoco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.

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

cpodi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by CPOCO, CPOFA, or CQRDC.

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)

cpofa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to CPOFA with a call to CPOSL to solve Ax = b or to CPODI to compute the determinant and inverse of A.

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

cposl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by CPOCO or CPOFA, and vectors b and x.

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

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

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

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 - 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

cppco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then CPPFA is slightly faster. It is typical to follow a call to CPPCO with a call to CPPSL to solve Ax = b or to CPPDI to compute the determinant and inverse of A.

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

cppdi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by CPPCO or CPPFA.

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)

cppfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to CPPFA with a call to CPPSL to solve Ax = b or to CPPDI to compute the determinant and inverse of A.

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

cppsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by CPPCO or CPPFA, and vectors b and x.

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

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

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 - 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 - 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 - 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 - 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

cptsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.

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

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 - 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

cqrdc (obsolete)- compute the QR factorization of a general matrix A. It is typical to follow a call to CQRDC with a call to CQRSL to solve Ax = b or to CPODI to compute the determinant of A.

cqrsl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been QR- factored by CQRDC, and vectors b and x.

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

crotg - Construct a Given's plane rotation

cscal - Compute y := alpha * y

csctr - csctr, dsctr, ssctr, zsctr - Scatters elements from x into y

csico (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then CSIFA is slightly faster. It is typical to follow a call to CSICO with a call to CSISL to solve Ax = b or to CSIDI to compute the determinant, inverse, and inertia of A.

csidi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by CSICO or CSIFA.

csifa (obsolete)- compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to CSIFA with a call to CSISL to solve Ax = b or to CSIDI to compute the determinant, inverse, and inertia of A.

csisl (obsolete)- solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by CSICO or CSIFA, and vectors b and x.

cspco (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then CSPFA is slightly faster. It is typical to follow a call to CSPCO with a call to CSPSL to solve Ax = b or to CSPDI to compute the determinant, inverse, and inertia of A.

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

cspdi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by CSPCO or CSPFA.

cspfa (obsolete)- compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to CSPFA with a call to CSPSL to solve Ax = b or to CSPDI to compute the determinant, inverse, and inertia of A.

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

cspsl (obsolete)- solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by CSPCO or CSPFA, and vectors b and x.

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

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

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 - 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 - Apply a plane rotation.

csscal - Compute y := alpha * y

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

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

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

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

csttrf - compute the factorization of a complex Hermitian tridiagonal matrix A

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

csvdc (obsolete)- compute the singular value decomposition of a general matrix A.

cswap - Exchange vectors x and y.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ctgsyl - solve the generalized Sylvester equation

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

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

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

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

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

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

ctrans - transpose and scale source matrix

ctrco (obsolete)- estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.

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

ctrdi (obsolete)- compute the determinant and inverse of a triangular matrix A.

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

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

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

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

ctrsl (obsolete)- solve the linear system Ax = b for a triangular matrix A and vectors b and x.

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

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

ctrsyl - solve the complex Sylvester matrix equation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cvmul - compute the scaled product of complex vectors

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

daxpy - compute y := alpha * x + y

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

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

dchdc (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

dchdd (obsolete)- downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

dchex (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

dchud (obsolete)- update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

dcnvcor - compute the convolution or correlation of real vectors

dcnvcor2 - compute the convolution or correlation of real matrices

dcopy - Copy x to y

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

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

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

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

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

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

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

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

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

dfftopt - compute the length of the closest fast FFT

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

dgbco (obsolete)- compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then SGBFA is slightly faster. It is typical to follow a call to SGBCO with a call to SGBSL to solve Ax = b or to SGBDI to compute the determinant of A.

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

dgbdi (obsolete)- compute the determinant of a general matrix A in banded storage, which has been LU-factored by SGBCO or SGBFA.

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

dgbfa (obsolete)- compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to SGBFA with a call to SGBSL to solve Ax = b or to SGBDI to compute the determinant of A.

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

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

dgbsl (obsolete)- solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by SGBCO or SGBFA, and vectors b and x.

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

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

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 - 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 - balance a general real matrix A

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

dgeco (obsolete)- compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then SGEFA is slightly faster. It is typical to follow a call to SGECO with a call to SGESL to solve Ax = b or to SGEDI to compute the determinant and inverse of A.

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

dgedi (obsolete)- compute the determinant and inverse of a general matrix A, which has been LU-factored by SGECO or SGEFA.

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

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

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

dgefa (obsolete)- compute the LU factorization of a general matrix A. It is typical to follow a call to SGEFA with a call to SGESL to solve Ax = b or to SGEDI to compute the determinant of A.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

dgesl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been LU- factored by SGECO or SGEFA, and vectors b and x.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 - Condition number estimate

dgssda - Deallocate working storage

dgssfa - Numeric factorization

dgssfs - One call interface

dgssin - Initialize the sparse solver

dgssor - Orders and symbolically factors

dgssps - Print solver statics

dgssrp - Return permutation

dgsssl - Solve

dgssuo - User supplied permutation for ordering

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

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

dgtsl (obsolete)- solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.

dgtsv - solve the equation A*X = B,

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

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

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

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

diamm - diamm, sdiamm, ddiamm - diagonal format matrix-matrix multiply

diasm - diasm, sdiasm, ddiasm - diagonal format triangular solve

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

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

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

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

dnrm2 - Return the Euclidian norm of a vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

dpbco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then SPBFA is slightly faster. It is typical to follow a call to SPBCO with a call to SPBSL to solve Ax = b or to SPBDI to compute the determinant of A.

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

dpbdi (obsolete)- compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by SPBCO or SPBFA.

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)

dpbfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to SPBFA with a call to SPBSL to solve Ax = b or to SPBDI to compute the determinant of A.

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

dpbsl (obsolete)- section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by SPBCO or SPBFA, and vectors b and x.

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

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

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

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

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

dpoco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then SPOFA is slightly faster. It is typical to follow a call to SPOCO with a call to SPOSL to solve Ax = b or to SPODI to compute the determinant and inverse of A.

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

dpodi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by SPOCO, SPOFA, or SQRDC.

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)

dpofa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to SPOFA with a call to SPOSL to solve Ax = b or to SPODI to compute the determinant and inverse of A.

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

dposl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by SPOCO or SPOFA, and vectors b and x.

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

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

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

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 - 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

dppco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then SPPFA is slightly faster. It is typical to follow a call to SPPCO with a call to SPPSL to solve Ax = b or to SPPDI to compute the determinant and inverse of A.

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

dppdi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by SPPCO or SPPFA.

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)

dppfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to SPPFA with a call to SPPSL to solve Ax = b or to SPPDI to compute the determinant and inverse of A.

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

dppsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by SPPCO or SPPFA, and vectors b and x.

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

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

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 - 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 - 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 - 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 - 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

dptsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.

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

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

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

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

dqrdc (obsolete)- compute the QR factorization of a general matrix A. It is typical to follow a call to SQRDC with a call to SQRSL to solve Ax = b or to SPODI to compute the determinant of A.

dqrsl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been QR- factored by SQRDC, and vectors b and x.

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

drotg - Construct a Given's plane rotation

droti - droti, sroti - Apply a Givens rotation to x and y

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

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

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

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

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

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

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

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

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

dscal - Compute y := alpha * y

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

dsecnd - return the user time for a process in seconds

dsico (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then SSIFA is slightly faster. It is typical to follow a call to SSICO with a call to SSISL to solve Ax = b or to SSIDI to compute the determinant, inverse, and inertia of A.

dsidi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by SSICO or SSIFA.

dsifa (obsolete)- compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to SSIFA with a call to SSISL to solve Ax = b or to SSIDI to compute the determinant, inverse, and inertia of A.

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

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

dsisl (obsolete)- solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by SSICO or SSIFA, and vectors b and x.

dspco (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then SSPFA is slightly faster. It is typical to follow a call to SSPCO with a call to SSPSL to solve Ax = b or to SSPDI to compute the determinant, inverse, and inertia of A.

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 SSPTRF

dspdi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by SSPCO or SSPFA.

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

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

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

dspfa (obsolete)- compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to SSPFA with a call to SSPSL to solve Ax = b or to SSPDI to compute the determinant, inverse, and inertia of A.

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

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

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

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

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

dspsl (obsolete)- solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by SSPCO or SSPFA, and vectors b and x.

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

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

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

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 - 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

dstebz - compute the eigenvalues of a symmetric tridiagonal matrix T

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

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

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

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

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

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

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

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

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

dsttrf - compute the factorization of a symmetric tridiagonal matrix A

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

dsvdc (obsolete)- compute the singular value decomposition of a general matrix A.

dswap - Exchange vectors x and y.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 - solve the generalized Sylvester equation

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

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

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

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

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

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

dtrans - transpose and scale source matrix

dtrco (obsolete)- estimate the condition number of a triangular matrix A. It is typical to follow a call to STRCO with a call to STRSL to solve Ax = b or to STRDI to compute the determinant and inverse of A.

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

dtrdi (obsolete)- compute the determinant and inverse of a triangular matrix A.

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

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

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

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

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,

dtrsl (obsolete)- solve the linear system Ax = b for a triangular matrix A and vectors b and x.

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

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

dtrsyl - solve the real Sylvester matrix equation

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

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

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

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

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

dwiener - perform Wiener deconvolution of two signals

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

dznrm2 - Return the Euclidian norm of a vector.

ellmm - ellmm, sellmm, dellmm - Ellpack format matrix-matrix multiply

ellsm - ellsm, sellsm, dellsm - Ellpack format triangular solve

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

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

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

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

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

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

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

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

jadmm - jadmm, sjadmm, djadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack)

jadrp - jadrp, sjadrp, djadrp - right permutation of a jagged diagonal matrix

jadsm - jadsm, sjadsm, djadsm - Jagged diagonal format triangular solve

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

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

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

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

rfftopt - compute the length of the closest fast FFT

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

saxpy - compute y := alpha * x + y

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

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

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

schdc (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

schdd (obsolete)- downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

schex (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

schud (obsolete)- update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

scnrm2 - Return the Euclidian norm of a vector.

scnvcor - compute the convolution or correlation of real vectors

scnvcor2 - compute the convolution or correlation of real matrices

scopy - Copy x to y

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

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

second - return the user time for a process in seconds

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

sgbco (obsolete)- compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then SGBFA is slightly faster. It is typical to follow a call to SGBCO with a call to SGBSL to solve Ax = b or to SGBDI to compute the determinant of A.

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

sgbdi (obsolete)- compute the determinant of a general matrix A in banded storage, which has been LU-factored by SGBCO or SGBFA.

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

sgbfa (obsolete)- compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to SGBFA with a call to SGBSL to solve Ax = b or to SGBDI to compute the determinant of A.

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

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

sgbsl (obsolete)- solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by SGBCO or SGBFA, and vectors b and x.

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

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

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 - 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 - balance a general real matrix A

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

sgeco (obsolete)- compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then SGEFA is slightly faster. It is typical to follow a call to SGECO with a call to SGESL to solve Ax = b or to SGEDI to compute the determinant and inverse of A.

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

sgedi (obsolete)- compute the determinant and inverse of a general matrix A, which has been LU-factored by SGECO or SGEFA.

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

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

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

sgefa (obsolete)- compute the LU factorization of a general matrix A. It is typical to follow a call to SGEFA with a call to SGESL to solve Ax = b or to SGEDI to compute the determinant of A.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sgesl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been LU- factored by SGECO or SGEFA, and vectors b and x.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sgtsl (obsolete)- solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.

sgtsv - solve the equation A*X = B,

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

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

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

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

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

skymm - skymm, sskymm, dskymm - Skyline format matrix-matrix multiply

skysm - skysm, sskysm, dskysm - Skyline format triangular solve

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

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

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

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

snrm2 - Return the Euclidian norm of a vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

spbco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then SPBFA is slightly faster. It is typical to follow a call to SPBCO with a call to SPBSL to solve Ax = b or to SPBDI to compute the determinant of A.

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

spbdi (obsolete)- compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by SPBCO or SPBFA.

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)

spbfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to SPBFA with a call to SPBSL to solve Ax = b or to SPBDI to compute the determinant of A.

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

spbsl (obsolete)- section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by SPBCO or SPBFA, and vectors b and x.

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

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

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

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

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

spoco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then SPOFA is slightly faster. It is typical to follow a call to SPOCO with a call to SPOSL to solve Ax = b or to SPODI to compute the determinant and inverse of A.

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

spodi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by SPOCO, SPOFA, or SQRDC.

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)

spofa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to SPOFA with a call to SPOSL to solve Ax = b or to SPODI to compute the determinant and inverse of A.

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

sposl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by SPOCO or SPOFA, and vectors b and x.

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

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

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

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 - 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

sppco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then SPPFA is slightly faster. It is typical to follow a call to SPPCO with a call to SPPSL to solve Ax = b or to SPPDI to compute the determinant and inverse of A.

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

sppdi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by SPPCO or SPPFA.

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)

sppfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to SPPFA with a call to SPPSL to solve Ax = b or to SPPDI to compute the determinant and inverse of A.

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

sppsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by SPPCO or SPPFA, and vectors b and x.

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

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

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 - 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 - 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 - 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 - 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

sptsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.

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

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

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

sqrdc (obsolete)- compute the QR factorization of a general matrix A. It is typical to follow a call to SQRDC with a call to SQRSL to solve Ax = b or to SPODI to compute the determinant of A.

sqrsl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been QR- factored by SQRDC, and vectors b and x.

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

srotg - Construct a Given's plane rotation

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

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

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

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

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

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

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

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

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

sscal - Compute y := alpha * y

ssico (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then SSIFA is slightly faster. It is typical to follow a call to SSICO with a call to SSISL to solve Ax = b or to SSIDI to compute the determinant, inverse, and inertia of A.

ssidi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by SSICO or SSIFA.

ssifa (obsolete)- compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to SSIFA with a call to SSISL to solve Ax = b or to SSIDI to compute the determinant, inverse, and inertia of A.

ssisl (obsolete)- solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by SSICO or SSIFA, and vectors b and x.

sspco (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then SSPFA is slightly faster. It is typical to follow a call to SSPCO with a call to SSPSL to solve Ax = b or to SSPDI to compute the determinant, inverse, and inertia of A.

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

sspdi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by SSPCO or SSPFA.

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

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

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

sspfa (obsolete)- compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to SSPFA with a call to SSPSL to solve Ax = b or to SSPDI to compute the determinant, inverse, and inertia of A.

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

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

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

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

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

sspsl (obsolete)- solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by SSPCO or SSPFA, and vectors b and x.

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

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

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

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 - 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 - compute the eigenvalues of a symmetric tridiagonal matrix T

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

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

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

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

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

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

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

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

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

ssttrf - compute the factorization of a symmetric tridiagonal matrix A

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

ssvdc (obsolete)- compute the singular value decomposition of a general matrix A.

sswap - Exchange vectors x and y.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 - solve the generalized Sylvester equation

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

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

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

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

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

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

strans - transpose and scale source matrix

strco (obsolete)- estimate the condition number of a triangular matrix A. It is typical to follow a call to STRCO with a call to STRSL to solve Ax = b or to STRDI to compute the determinant and inverse of A.

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

strdi (obsolete)- compute the determinant and inverse of a triangular matrix A.

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

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

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

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

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,

strsl (obsolete)- solve the linear system Ax = b for a triangular matrix A and vectors b and x.

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

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

strsyl - solve the real Sylvester matrix equation

strti2 - compute the inverse of a real upper or lower triangular matrix

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

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

stzrqf - routine is deprecated and has been replaced by routine 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 - gets library information .HP 1i SUBROUTINE SUNPERF_VERSION(VERSION, PATCH, UPDATE) .HP 1i INTEGER VERSION, PATCH, UPDATE .HP 1i

swiener - perform Wiener deconvolution of two signals

use_threads - set the upper bound on the number of threads that the calling thread wants used

using_threads - returns the current Use number set by the USE_THREADS subroutine

vbrmm - vbrmm, svbrmm, dvbrmm - variable block sparse row format matrix-matrix multiply

vbrsm - vbrsm, svbrsm, dvbrsm - variable block sparse row format triangular solve

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 - 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 - initialize the array WSAVE, which is used in both VCFFTF and VCFFTB.

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 - 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 - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB.

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 - initialize the array WSAVE, which is used in VCOST.

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 - 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 - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB.

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 - initialize the array WSAVE, which is used in VCOST.

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 - 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 - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB.

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 - 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 - initialize the array WSAVE, which is used in both VSINQF and VSINQB.

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

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 - 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 - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB.

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 - 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 - initialize the array WSAVE, which is used in both VSINQF and VSINQB.

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

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 - 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 - initialize the array WSAVE, which is used in both VZFFTF and VZFFTB.

zaxpy - compute y := alpha * x + y

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

zchdc (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

zchdd (obsolete)- downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

zchex (obsolete)- compute the Cholesky decomposition of a symmetric positive definite matrix A.

zchud (obsolete)- update an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

zcnvcor - compute the convolution or correlation of complex vectors

zcnvcor2 - compute the convolution or correlation of complex matrices

zcopy - Copy x to y

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

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

zdrot - Apply a plane rotation.

zdscal - Compute y := alpha * y

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

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 - 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 - initialize the array WSAVE, which is used in both ZFFT3F and ZFFT3B.

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.

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 - initialize the array WSAVE, which is used in both ZFFTF and ZFFTB.

zfftopt - compute the length of the closest fast FFT

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

zgbco (obsolete)- compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then xGBFA is slightly faster. It is typical to follow a call to xGBCO with a call to xGBSL to solve Ax = b or to xGBDI to compute the determinant of A.

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

zgbdi (obsolete)- compute the determinant of a general matrix A in banded storage, which has been LU-factored by CGBCO or CGBFA.

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

zgbfa (obsolete)- compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to CGBFA with a call to CGBSL to solve Ax = b or to CGBDI to compute the determinant of A.

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 - 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

zgbsl (obsolete)- solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by CGBCO or CGBFA, and vectors b and x.

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

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

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 - 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 - balance a general complex matrix A

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

zgeco (obsolete)- compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then CGEFA is slightly faster. It is typical to follow a call to CGECO with a call to CGESL to solve Ax = b or to CGEDI to compute the determinant and inverse of A.

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

zgedi (obsolete)- compute the determinant and inverse of a general matrix A, which has been LU-factored by CGECO or CGEFA.

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

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

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

zgefa (obsolete)- compute the LU factorization of a general matrix A. It is typical to follow a call to CGEFA with a call to CGESL to solve Ax = b or to CGEDI to compute the determinant of A.

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

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

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

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

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

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

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

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

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

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

zgeqp3 - compute a QR factorization with column pivoting of a matrix A

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

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

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

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

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

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

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

zgesl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been LU- factored by CGECO or CGEFA, and vectors b and x.

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

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

zgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

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

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

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

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

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

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

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

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

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

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

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

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

zgtsl (obsolete)- solve the linear system Ax = b for a tridiagonal matrix A and vectors b and x.

zgtsv - solve the equation A*X = B,

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

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

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

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

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

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

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

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

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

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

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

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

zhegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form

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

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

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

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

zher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

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

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

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

zhetf2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method

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

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

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 - 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 - 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

zhico (obsolete)- compute the UDU factorization and condition number of a Hermitian matrix A. If the condition number is not needed then xHIFA is slightly faster. It is typical to follow a call to xHICO with a call to xHISL to solve Ax = b or to xHIDI to compute the determinant, inverse, and inertia of A.

zhidi (obsolete)- compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by CHICO or CHIFA.

zhifa (obsolete)- compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to CHIFA with a call to CHISL to solve Ax = b or to CHIDI to compute the determinant, inverse, and inertia of A.

zhisl (obsolete)- solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by CHICO or CHIFA, and vectors b and x.

zhpco (obsolete)- compute the UDU factorization and condition number of a Hermitian matrix A in packed storage. If the condition number is not needed then xHPFA is slightly faster. It is typical to follow a call to xHPCO with a call to xHPSL to solve Ax = b or to xHPDI to compute the determinant, inverse, and inertia of A.

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

zhpdi (obsolete)- compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by CHPCO or CHPFA.

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

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

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

zhpfa (obsolete)- compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to CHPFA with a call to CHPSL to solve Ax = b or to CHPDI to compute the determinant, inverse, and inertia of A.

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

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

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

zhpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A

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

zhpsl (obsolete)- solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by CHPCO or CHPFA, and vectors b and x.

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

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

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

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

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

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

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

zpbco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage. If the condition number is not needed then xPBFA is slightly faster. It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.

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

zpbdi (obsolete)- compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by CPBCO or CPBFA.

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)

zpbfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to CPBFA with a call to CPBSL to solve Ax = b or to CPBDI to compute the determinant of A.

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

zpbsl (obsolete)- section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by CPBCO or CPBFA, and vectors b and x.

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

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

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

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

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

zpoco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then xPOFA is slightly faster. It is typical to follow a call to xPOCO with a call to xPOSL to solve Ax = b or to xPODI to compute the determinant and inverse of A.

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

zpodi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by CPOCO, CPOFA, or CQRDC.

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)

zpofa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to CPOFA with a call to CPOSL to solve Ax = b or to CPODI to compute the determinant and inverse of A.

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

zposl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by CPOCO or CPOFA, and vectors b and x.

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

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

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

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 - 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

zppco (obsolete)- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in packed storage. If the condition number is not needed then CPPFA is slightly faster. It is typical to follow a call to CPPCO with a call to CPPSL to solve Ax = b or to CPPDI to compute the determinant and inverse of A.

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

zppdi (obsolete)- compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by CPPCO or CPPFA.

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)

zppfa (obsolete)- compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to CPPFA with a call to CPPSL to solve Ax = b or to CPPDI to compute the determinant and inverse of A.

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

zppsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by CPPCO or CPPFA, and vectors b and x.

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

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

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 - 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 - 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 - 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 - 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

zptsl (obsolete)- solve the linear system Ax = b for a symmetric positive definite tridiagonal matrix A and vectors b and x.

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

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 - 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

zqrdc (obsolete)- compute the QR factorization of a general matrix A. It is typical to follow a call to CQRDC with a call to CQRSL to solve Ax = b or to CPODI to compute the determinant of A.

zqrsl (obsolete)- solve the linear system Ax = b for a general matrix A, which has been QR- factored by CQRDC, and vectors b and x.

zrot - apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors CX and CY are complex

zrotg - Construct a Given's plane rotation

zscal - Compute y := alpha * y

zsico (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then CSIFA is slightly faster. It is typical to follow a call to CSICO with a call to CSISL to solve Ax = b or to CSIDI to compute the determinant, inverse, and inertia of A.

zsidi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by CSICO or CSIFA.

zsifa (obsolete)- compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to CSIFA with a call to CSISL to solve Ax = b or to CSIDI to compute the determinant, inverse, and inertia of A.

zsisl (obsolete)- solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by CSICO or CSIFA, and vectors b and x.

zspco (obsolete)- compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then CSPFA is slightly faster. It is typical to follow a call to CSPCO with a call to CSPSL to solve Ax = b or to CSPDI to compute the determinant, inverse, and inertia of A.

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 CSPTRF

zspdi (obsolete)- compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by CSPCO or CSPFA.

zspfa (obsolete)- compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to CSPFA with a call to CSPSL to solve Ax = b or to CSPDI to compute the determinant, inverse, and inertia of A.

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

zspsl (obsolete)- solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by CSPCO or CSPFA, and vectors b and x.

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

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

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 - 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

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

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

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

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

zsttrf - compute the factorization of a complex Hermitian tridiagonal matrix A

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

zsvdc (obsolete)- compute the singular value decomposition of a general matrix A.

zswap - Exchange vectors x and y.

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

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

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

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

zsytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method

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

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

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

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

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

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

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

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

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

ztgsyl - solve the generalized Sylvester equation

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

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

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

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

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

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

ztrans - transpose and scale source matrix

ztrco (obsolete)- estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.

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

ztrdi (obsolete)- compute the determinant and inverse of a triangular matrix A.

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

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

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

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

ztrsl (obsolete)- solve the linear system Ax = b for a triangular matrix A and vectors b and x.

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

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

ztrsyl - solve the complex Sylvester matrix equation

ztrti2 - compute the inverse of a complex upper or lower triangular matrix

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

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

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

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

zung2l - generate an m by n complex matrix Q with orthonormal columns,

zung2r - generate an m by n complex matrix Q with orthonormal columns,

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

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

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

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

zungr2 - generate an m by n complex matrix Q with orthonormal rows,

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

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

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

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

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

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

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

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

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

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

zvmul - compute the scaled product of complex vectors