# Sun WorkShop 6 Performance Library Reference Manual

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