- available_threads - returns information about current thread usage

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

- caxpyi - 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 - compute the Cholesky decomposition of a symmetric positive definite matrix A.

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

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

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

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

- cdotui - 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 xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M*N*K.

- cfft3f - compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M*N*K.

- cfft3i - initialize the array WSAVE, which is used in both xFFT3F and xFFT3B.

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

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

- cffti - initialize the array WSAVE, which is used in both xFFTF and xFFTB.

- 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - gathers specified elements from y into x

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

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

- crot - 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 - scatters elements from x into y

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

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

- cspfa - 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 - 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 - (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,

- 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 - 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 - 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 - 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 - 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

- cunm2r - 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',

- 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

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

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

- dbcomm - block coordinate matrix-matrix multiply

- dbdimm - block diagonal matrix-matrix multiply

- dbdism - block diagonal triangular solve

- 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.

- dbelmm - block Ellpack format matrix-matrix multiply

- dbelsm - block Ellpack format triangular solve

- dbscmm - block sparse column matrix-matrix multiply

- dbscsm - block sparse column triangular solve

- dbsrmm - block sparse row format matrix-matrix multiply

- dbsrsm - block sparse row format triangular solve

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

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

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

- dchud - 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

- dcoomm - coordinate matrix-matrix multiply

- dcopy - Copy x to y

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

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

- dcosqi - initialize the array WSAVE, which is used in both DCOSQF and DCOSQB.

- dcost - compute the discrete Fourier cosine transform of an even sequence. The DDDCOST 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 DCOST.

- dcscmm - compressed sparse column format matrix-matrix multiply

- dcscsm - compressed sparse column format triangular solve

- dcsrmm - compressed sparse row format matrix-matrix multiply

- dcsrsm - compressed sparse row format triangular solve

- ddiamm - diagonal format matrix-matrix multiply

- ddiasm - diagonal format triangular solve

- 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.

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

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

- dellmm - Ellpack format matrix-matrix multiply

- dellsm - Ellpack format triangular solve

- dfft2b - 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.

- dfft2f - 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.

- 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 RFFT operations are unnormalized, so a call of RFFT3F followed by a call of RFFT3B will multiply the input sequence by M*N*K.

- dfft3f - 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.

- dfft3i - initialize the array WSAVE, which is used in both RFFT3F and RFFT3B.

- dfftb - compute a periodic sequence from its Fourier coefficients. The RFFT 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 RFFT 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 - compute the LU factorization and condition number of a general matrix A in banded storage. If the condition number is not needed then DGBFA is slightly faster. It is typical to follow a call to DGBCO with a call to DGBSL to solve Ax = b or to DGBDI 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 - compute the determinant of a general matrix A in banded storage, which has been LU-factored by DGBCO or DGBFA.

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

- dgbfa - compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to DGBFA with a call to DGBSL to solve Ax = b or to DGBDI 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 - solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by DGBCO or DGBFA, 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 DGBTRF

- 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 DGEBAL

- 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 - compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then DGEFA is slightly faster. It is typical to follow a call to DGECO with a call to DGESL to solve Ax = b or to DGEDI 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 DGETRF

- dgedi - compute the determinant and inverse of a general matrix A, which has been LU-factored by DGECO or DGEFA.

- 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 - compute the LU factorization of a general matrix A. It is typical to follow a call to DGEFA with a call to DGESL to solve Ax = b or to DGEDI to compute the determinant of A.

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

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

- 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 DGELSY

- 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 - solve the linear system Ax = b for a general matrix A, which has been LU- factored by DGECO or DGEFA, 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 DGETRF

- 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 DGETRF

- 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 DGGBAL

- 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 statistics

- 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 DGTTRF

- dgthr - gathers specified elements from y into x

- dgthr - gathers specified elements from y into x

- dgthrz - gathers specified elements from y into x and sets gathered elements in y to zero

- dgthrz - gathers specified elements from y into x and sets gathered elements in y to zero

- 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 - 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

- djadmm - Jagged diagonal matrix-matrix multiply

- djadrp - right permutation of a jagged diagonal matrix

- djadsm - Jagged diagonal 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 DORMRZ

- 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 DSPTRD 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 DGEBRD 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 DGEHRD

- 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 DSYTRD

- dormbr - VECT = 'Q', DORMBR 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 - 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 DPBFA is slightly faster. It is typical to follow a call to DPBCO with a call to DPBSL to solve Ax = b or to DPBDI 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 DPBTRF

- dpbdi - compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by DPBCO or DPBFA.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to DPBFA with a call to DPBSL to solve Ax = b or to DPBDI 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 - section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by DPBCO or DPBFA, 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 DPBTRF

- dpoco - compute a Cholesky factorization and condition number of a symmetric positive definite matrix A. If the condition number is not needed then DPOFA is slightly faster. It is typical to follow a call to DPOCO with a call to DPOSL to solve Ax = b or to DPODI 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 DPOTRF

- dpodi - compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by DPOCO, DPOFA, or DQRDC.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to DPOFA with a call to DPOSL to solve Ax = b or to DPODI 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 - solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by DPOCO or DPOFA, 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 DPOTRF

- 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 DPOTRF

- dppco - 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 DPPFA is slightly faster. It is typical to follow a call to DPPCO with a call to DPPSL to solve Ax = b or to DPPDI 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 DPPTRF

- dppdi - compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by DPPCO or DPPFA.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to DPPFA with a call to DPPSL to solve Ax = b or to DPPDI 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 - solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by DPPCO or DPPFA, 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 DPPTRF

- 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 DPPTRF

- 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 DPTTRF

- dpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF, and then calling DBDSQR 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 - 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 DPTTRF

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

- 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 - compute the QR factorization of a general matrix A. It is typical to follow a call to DQRDC with a call to DQRSL to solve Ax = b or to DPODI to compute the determinant of A.

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

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

- drotg - Construct a Given's plane rotation

- droti - applies a Givens rotation to x and y

- droti - applies a Givens rotation to x and y

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

- 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

- dsctr - scatters elements from x into y

- dsctr - scatters elements from x into y

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

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

- dsico - compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then DSIFA is slightly faster. It is typical to follow a call to DSICO with a call to DSISL to solve Ax = b or to DSIDI to compute the determinant, inverse, and inertia of A.

- dsidi - compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by DSICO or DSIFA.

- dsifa - compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to DSIFA with a call to DSISL to solve Ax = b or to DSIDI 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 DSINQ operations are unnormalized inverses of themselves, so a call to DSINQF followed by a call to DSINQB will multiply the input sequence by 4 * N.

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

- dsinqi - initialize the array xWSAVE, which is used in both DSINQF and DSINQB.

- dsint - compute the discrete Fourier sine transform of an odd sequence. The DDDSINT 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 DSINT.

- dsisl - solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by DSICO or DSIFA, and vectors b and x.

- dskymm - Skyline format matrix-matrix multiply

- dskysm - Skyline format triangular solve

- dspco - compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then DSPFA is slightly faster. It is typical to follow a call to DSPCO with a call to DSPSL to solve Ax = b or to DSPDI 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 DSPTRF

- dspdi - compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by DSPCO or DSPFA.

- 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 - compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to DSPFA with a call to DSPSL to solve Ax = b or to DSPDI 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 - solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by DSPCO or DSPFA, 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 DSPTRF

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

- dstebz - 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 - 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 DSYTRF

- 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 DSYTRF

- 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 DSYTRF

- 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 - estimate the condition number of a triangular matrix A. It is typical to follow a call to DTRCO with a call to DTRSL to solve Ax = b or to DTRDI 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 - 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 - 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 DTZRZF

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

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

- dvbrsm - variable block sparse row format triangular solve

- 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.

- 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.

- lsame - case insensitive single character compare

- 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 RFFT 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

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

- sbcomm - block coordinate matrix-matrix multiply

- sbdimm - block diagonal matrix-matrix multiply

- sbdism - block diagonal triangular solve

- 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.

- sbelmm - block Ellpack format matrix-matrix multiply

- sbelsm - block Ellpack format triangular solve

- sbscmm - block sparse column matrix-matrix multiply

- sbscsm - block sparse column triangular solve

- sbsrmm - block sparse row format matrix-matrix multiply

- sbsrsm - block sparse row format triangular solve

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

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

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

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

- schud - 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

- scoomm - coordinate matrix-matrix multiply

- scopy - Copy x to y

- scscmm - compressed sparse column format matrix-matrix multiply

- scscsm - compressed sparse column format triangular solve

- scsrmm - compressed sparse row format matrix-matrix multiply

- scsrsm - compressed sparse row format triangular solve

- sdiamm - diagonal format matrix-matrix multiply

- sdiasm - diagonal format triangular solve

- 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.

- sdoti - 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

- sellmm - Ellpack format matrix-matrix multiply

- sellsm - Ellpack format triangular solve

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

- sgbco - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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

- sgthr - gathers specified elements from y into x

- sgthrz - gathers specified elements from y into x and sets gathered elements in y to zero

- 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 - 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.

- sjadmm - Jagged diagonal matrix-matrix multiply

- sjadrp - right permutation of a jagged diagonal matrix

- sjadsm - Jagged diagonal 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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

- sroti - applies a Givens rotation to x and y

- 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

- ssctr - scatters elements from x into y

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

- ssifa - 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 - 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.

- sskymm - Skyline format matrix-matrix multiply

- sskysm - Skyline format triangular solve

- sspco - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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

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

- svbrsm - variable block sparse row format triangular solve

- 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

- 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 VDCOSQF followed by a call of VDCOSQB 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 VDCOSQF followed by a call of VDCOSQB will return the original sequence.

- vdcosqi - initialize the array WSAVE, which is used in both VDCOSQF and VDCOSQB.

- vdcost - compute the discrete Fourier cosine transform of an even sequence. The VDCOST transform is normalized, so a call of VDCOST followed by a call of VDCOST will return the original sequence.

- vdcosti - initialize the array WSAVE, which is used in VDCOST.

- vdfftb - compute a periodic sequence from its Fourier coefficients. The VRFFT operations are normalized, so a call of VDFFTF followed by a call of VDFFTB will return the original sequence.

- vdfftf - compute the Fourier coefficients of a periodic sequence. The VRFFT operations are normalized, so a call of VDFFTF followed by a call of VDFFTB will return the original sequence.

- vdffti - initialize the array WSAVE, which is used in both VDFFTF and VDFFTB.

- 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 VDSINQF followed by a call of VDSINQB 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 VDSINQF followed by a call of VDSINQB will return the original sequence.

- vdsinqi - initialize the array WSAVE, which is used in both VDSINQF and VDSINQB.

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

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

- 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 VCFFT 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 VCFFT 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.

- xerbla - i an error handler for the LAPACK routines

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

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

- zaxpyi - 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 - compute the Cholesky decomposition of a symmetric positive definite matrix A.

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

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

- zchud - 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).

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

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

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

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

- zdotui - 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 xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M*N.

- zfft2f - 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.

- 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 xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M*N*K.

- zfft3f - compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M*N*K.

- zfft3i - initialize the array WSAVE, which is used in both xFFT3F and xFFT3B.

- zfftb - compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N.

- zfftf - compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFTF followed by a call of xFFTB will multiply the input sequence by N.

- zffti - initialize the array WSAVE, which is used in both xFFTF and xFFTB.

- 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 - 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 - compute the determinant of a general matrix A in banded storage, which has been LU-factored by ZGBCO or ZGBFA.

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

- zgbfa - compute the LU factorization of a matrix A in banded storage. It is typical to follow a call to ZGBFA with a call to ZGBSL to solve Ax = b or to ZGBDI 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 - solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by ZGBCO or ZGBFA, 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 ZGBTRF

- 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 ZGEBAL

- 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 - compute the LU factorization and estimate the condition number of a general matrix A. If the condition number is not needed then ZGEFA is slightly faster. It is typical to follow a call to ZGECO with a call to ZGESL to solve Ax = b or to ZGEDI 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 ZGETRF

- zgedi - compute the determinant and inverse of a general matrix A, which has been LU-factored by ZGECO or ZGEFA.

- 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 - compute the LU factorization of a general matrix A. It is typical to follow a call to ZGEFA with a call to ZGESL to solve Ax = b or to ZGEDI to compute the determinant of A.

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

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

- 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 ZGELSY

- 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 - solve the linear system Ax = b for a general matrix A, which has been LU- factored by ZGECO or ZGEFA, 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 ZGETRF

- 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 ZGETRF

- 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 ZGGBAL

- 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 ZGTTRF

- zgthr - gathers specified elements from y into x

- zgthr - gathers specified elements from y into x

- zgthrz - gathers specified elements from y into x and sets gathered elements in y to zero

- zgthrz - gathers specified elements from y into x and sets gathered elements in y to zero

- 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 - 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 ZHETRF

- 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 ZHETRF

- 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 ZHETRF

- 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 - 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 - compute the determinant, inertia, and inverse of a Hermitian matrix A, which has been UDU-factored by ZHICO or ZHIFA.

- zhifa - compute the UDU factorization of a Hermitian matrix A. It is typical to follow a call to ZHIFA with a call to ZHISL to solve Ax = b or to ZHIDI to compute the determinant, inverse, and inertia of A.

- zhisl - solve the linear system Ax = b for a Hermitian matrix A, which has been UDU-factored by ZHICO or ZHIFA, and vectors b and x.

- zhpco - 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 ZHPTRF

- zhpdi - compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by ZHPCO or ZHPFA.

- 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 - compute the UDU factorization of a Hermitian matrix A in packed storage. It is typical to follow a call to ZHPFA with a call to ZHPSL to solve Ax = b or to ZHPDI 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 - solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by ZHPCO or ZHPFA, 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 ZHPTRF

- 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 ZHPTRF

- 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 ZUNMRZ

- zpbco - 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 ZPBTRF

- zpbdi - compute the determinant of a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by ZPBCO or ZPBFA.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A in banded storage. It is typical to follow a call to ZPBFA with a call to ZPBSL to solve Ax = b or to ZPBDI 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 - section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by ZPBCO or ZPBFA, 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 ZPBTRF

- zpoco - 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 ZPOTRF

- zpodi - compute the determinant and inverse of a symmetric positive definite matrix A, which has been Cholesky-factored by ZPOCO, ZPOFA, or ZQRDC.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A. It is typical to follow a call to ZPOFA with a call to ZPOSL to solve Ax = b or to ZPODI 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 - solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by ZPOCO or ZPOFA, 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 ZPOTRF

- 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 ZPOTRF

- zppco - 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 ZPPFA is slightly faster. It is typical to follow a call to ZPPCO with a call to ZPPSL to solve Ax = b or to ZPPDI 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 ZPPTRF

- zppdi - compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by ZPPCO or ZPPFA.

- 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 - compute a Cholesky factorization of a symmetric positive definite matrix A in packed storage. It is typical to follow a call to ZPPFA with a call to ZPPSL to solve Ax = b or to ZPPDI 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 - solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by ZPPCO or ZPPFA, 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 ZPPTRF

- 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 ZPPTRF

- 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 ZPTTRF

- zpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using DPTTRF and then calling ZBDSQR 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 - 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 ZPTTRF

- 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 ZPTTRF

- zqrdc - compute the QR factorization of a general matrix A. It is typical to follow a call to ZQRDC with a call to ZQRSL to solve Ax = b or to ZPODI to compute the determinant of A.

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

- zrot - 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

- zsctr - scatters elements from x into y

- zsctr - scatters elements from x into y

- zsico - compute the UDU factorization and condition number of a symmetric matrix A. If the condition number is not needed then ZSIFA is slightly faster. It is typical to follow a call to ZSICO with a call to ZSISL to solve Ax = b or to ZSIDI to compute the determinant, inverse, and inertia of A.

- zsidi - compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by ZSICO or ZSIFA.

- zsifa - compute the UDU factorization of a symmetric matrix A. It is typical to follow a call to ZSIFA with a call to ZSISL to solve Ax = b or to ZSIDI to compute the determinant, inverse, and inertia of A.

- zsisl - solve the linear system Ax = b for a symmetric matrix A, which has been UDU-factored by ZSICO or ZSIFA, and vectors b and x.

- zspco - compute the UDU factorization and condition number of a symmetric matrix A in packed storage. If the condition number is not needed then ZSPFA is slightly faster. It is typical to follow a call to ZSPCO with a call to ZSPSL to solve Ax = b or to ZSPDI 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 ZSPTRF

- zspdi - compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by ZSPCO or ZSPFA.

- zspfa - compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to ZSPFA with a call to ZSPSL to solve Ax = b or to ZSPDI 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 - solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by ZSPCO or ZSPFA, 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 ZSPTRF

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

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

- zstegr - (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,

- 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 - 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 ZSYTRF

- 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 ZSYTRF

- 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 ZSYTRF

- 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 - 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 - 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 - 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 ZTZRZF

- 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 ZGEBRD 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 ZGEHRD

- 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 ZHETRD

- zunm2r - 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',

- zunmbr - VECT = 'Q', ZUNMBR 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 ZHPTRD 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

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