Section 3S

1412 pages across all releases.

• cbdsqr(3S) CBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• ccfft(3S) CCFFT, ZZFFT - Applies a complex-to-complex Fast Fourier Transform (FFT)
• ccfft2d(3S) CCFFT2D, ZZFFT2D - Applies a two-dimensional complex-to-complex Fast Fourier Transform (FFT)
• ccfft3d(3S) CCFFT3D, ZZFFT3D - Applies a three-dimensional complex-to-complex Fast Fourier Transform (FFT)
• ccfftf(3S) CCFFTF, CCFFTMF, CCFFTMRF, CCFFT2DF, CCFFT3DF, ZZFFTF, ZZFFTMF, ZZFFTMRF, ZZFFT2DF, ZZFFT3DF - Deallocate memory tacked on to the table array during initialization
• ccfftm(3S) CCFFTM, ZZFFTM - Applies multiple complex-to-complex Fast Fourier Transforms (FFTs)
• ccfftmr(3S) CCFFTMR, ZZFFTMR - Applies multiple complex-to-complex Fast Fourier Transforms (FFTs) to the rows of a two-dimensional (2D) array
• ccor1d(3S) CCOR1D, ZCOR1D, SCOR1D, DCOR1D - Compute the one-dimensional (1D) correlation of two sequences.
• ccor2d(3S) CCOR2D, ZCOR2D, SCOR2D, DCOR2D - Compute the two-dimensional (2D) correlation of two two-dimensional (2D) arrays
• ccorm1d(3S) CCORM1D, ZCORM1D, SCORM1D, DCORM1D - Compute multiple 1D correlations
• cfir1d(3S) CFIR1D, ZFIR1D, SFIR1D, DFIR1D - Compute the 1D convolution of a sequence
• cfir2d(3S) CFIR2D, ZFIR2D, SFIR2D, DFIR2D - Compute the two-dimensional (2D) convolution of two 2D arrays
• cfirm1d(3S) CFIRM1D, ZFIRM1D, SFIRM1D, DFIRM1D - Compute multiple 1D convolutions
• cgbbrd(3S) CGBBRD - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
• cgbcon(3S) CGBCON - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
• cgbequ(3S) CGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
• cgbrfs(3S) CGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
• cgbsv(3S) 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(3S) 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(3S) CGBTF2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
• cgbtrf(3S) CGBTRF - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
• cgbtrs(3S) 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(3S) 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(3S) CGEBAL - balance a general complex matrix A
• cgebd2(3S) CGEBD2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
• cgebrd(3S) CGEBRD - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
• cgecon(3S) CGECON - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF
• cgeequ(3S) CGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
• cgees(3S) 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(3S) 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(3S) CGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• cgeevx(3S) CGEEVX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• cgegs(3S) CGEGS - routine is deprecated and has been replaced by routine CGGES
• cgegv(3S) CGEGV - routine is deprecated and has been replaced by routine CGGEV
• cgehd2(3S) CGEHD2 - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
• cgehrd(3S) CGEHRD - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
• cgelq2(3S) CGELQ2 - compute an LQ factorization of a complex m by n matrix A
• cgelqf(3S) CGELQF - compute an LQ factorization of a complex M-by-N matrix A
• cgels(3S) 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(3S) CGELSD - compute the minimum-norm solution to a real linear least squares problem
• cgelss(3S) CGELSS - compute the minimum norm solution to a complex linear least squares problem
• cgelsx(3S) CGELSX - routine is deprecated and has been replaced by routine CGELSY
• cgelsy(3S) CGELSY - compute the minimum-norm solution to a complex linear least squares problem
• cgemm3m(3S) CGEMM3M, ZGEMM3M - Multiplies a complex general matrix by a complex general matrix
• cgeql2(3S) CGEQL2 - compute a QL factorization of a complex m by n matrix A
• cgeqlf(3S) CGEQLF - compute a QL factorization of a complex M-by-N matrix A
• cgeqp3(3S) CGEQP3 - compute a QR factorization with column pivoting of a matrix A
• cgeqpf(3S) CGEQPF - routine is deprecated and has been replaced by routine CGEQP3
• cgeqr2(3S) CGEQR2 - compute a QR factorization of a complex m by n matrix A
• cgeqrf(3S) CGEQRF - compute a QR factorization of a complex M-by-N matrix A
• cgerfs(3S) CGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
• cgerq2(3S) CGERQ2 - compute an RQ factorization of a complex m by n matrix A
• cgerqf(3S) CGERQF - compute an RQ factorization of a complex M-by-N matrix A
• cgesc2(3S) CGESC2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by CGETC2
• cgesdd(3S) CGESDD - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method
• cgesv(3S) CGESV - compute the solution to a complex system of linear equations A * X = B,
• cgesvd(3S) 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(3S) CGESVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
• cgetc2(3S) CGETC2 - compute an LU factorization, using complete pivoting, of the n- by-n matrix A
• cgetf2(3S) CGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
• cgetrf(3S) CGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
• cgetri(3S) CGETRI - compute the inverse of a matrix using the LU factorization computed by CGETRF
• cgetrs(3S) 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(3S) 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(3S) CGGBAL - balance a pair of general complex matrices (A,B)
• cgges(3S) 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(3S) CGGESX - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),
• cggev(3S) 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(3S) 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(3S) CGGGLM - solve a general Gauss-Markov linear model (GLM) problem
• cgghrd(3S) 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(3S) CGGLSE - solve the linear equality-constrained least squares (LSE) problem
• cggqrf(3S) CGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
• cggrqf(3S) CGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
• cggsvd(3S) CGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
• cggsvp(3S) 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(3S) CGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF
• cgtrfs(3S) CGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
• cgtsv(3S) CGTSV - solve the equation A*X = B,
• cgtsvx(3S) 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(3S) CGTTRF - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
• cgttrs(3S) CGTTRS - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
• cgtts2(3S) CGTTS2 - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
• chbev(3S) CHBEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• chbevd(3S) CHBEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• chbevx(3S) CHBEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• chbgst(3S) CHBGST - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
• chbgv(3S) 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(3S) 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(3S) 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(3S) CHBMV, ZHBMV - Multiplies a complex vector by a complex Hermitian band matrix
• chbtrd(3S) CHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• checon(3S) 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(3S) CHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• cheevd(3S) CHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• cheevr(3S) CHEEVR - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T
• cheevx(3S) CHEEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• chegs2(3S) CHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
• chegst(3S) CHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form
• chegv(3S) 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(3S) 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(3S) 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(3S) CHEMM, ZHEMM - Multiplies a complex general matrix by a complex Hermitian matrix
• chemv(3S) CHEMV, ZHEMV - Multiplies a complex vector by a complex Hermitian matrix
• cher(3S) CHER, ZHER - Performs Hermitian rank 1 update of a complex Hermitian matrix
• cher2(3S) CHER2, ZHER2 - Performs Hermitian rank 2 update of a complex Hermitian matrix
• cher2k(3S) CHER2K, ZHER2K - Performs Hermitian rank 2k update of a complex Hermitian matrix
• cherfs(3S) 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(3S) CHERK, ZHERK - Performs Hermitian rank k update of a complex Hermitian matrix
• chesv(3S) CHESV - compute the solution to a complex system of linear equations A * X = B,
• chesvx(3S) CHESVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
• chetd2(3S) CHETD2 - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• chetf2(3S) CHETF2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• chetrd(3S) CHETRD - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• chetrf(3S) CHETRF - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• chetri(3S) 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(3S) 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(3S) CHGEQZ - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
• chpcon(3S) CHPCON - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF
• chpev(3S) CHPEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
• chpevd(3S) CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
• chpevx(3S) CHPEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
• chpgst(3S) CHPGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
• chpgv(3S) 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(3S) 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(3S) 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(3S) CHPMV, ZHPMV - Multiplies a complex vector by a packed complex Hermitian matrix
• chpr(3S) CHPR, ZHPR - Performs Hermitian rank 1 update of a packed complex Hermitian matrix
• chpr2(3S) CHPR2, ZHPR2 - Performs Hermitian rank 2 update of a packed complex Hermitian matrix
• chprfs(3S) CHPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
• chpsv(3S) CHPSV - compute the solution to a complex system of linear equations A * X = B,
• chpsvx(3S) 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(3S) CHPTRD - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
• chptrf(3S) CHPTRF - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
• chptri(3S) 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(3S) 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(3S) CHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
• chseqr(3S) 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
• clabrd(3S) CLABRD - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
• clacgv(3S) CLACGV - conjugate a complex vector of length N
• clacon(3S) CLACON - estimate the 1-norm of a square, complex matrix A
• clacp2(3S) CLACP2 - copie all or part of a real two-dimensional matrix A to a complex matrix B
• clacpy(3S) CLACPY - copie all or part of a two-dimensional matrix A to another matrix B
• clacrm(3S) CLACRM - perform a very simple matrix-matrix multiplication
• clacrt(3S) CLACRT - perform the operation ( c s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vectors x and y are complex
• cladiv(3S) CLADIV - := X / Y, where X and Y are complex
• claed0(3S) CLAED0 - the divide and conquer method, CLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
• claed7(3S) CLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• claed8(3S) CLAED8 - merge the two sets of eigenvalues together into a single sorted set
• claein(3S) CLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
• claesy(3S) CLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
• claev2(3S) CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
• clags2(3S) CLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
• clagtm(3S) CLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
• clahef(3S) CLAHEF - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• clahqr(3S) CLAHQR - i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
• clahrd(3S) CLAHRD - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
• claic1(3S) CLAIC1 - applie one step of incremental condition estimation in its simplest version
• clals0(3S) CLALS0 - applie back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach
• clalsa(3S) CLALSA - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
• clalsd(3S) CLALSD - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N- by-NRHS
• clangb(3S) CLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
• clange(3S) CLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
• clangt(3S) CLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
• clanhb(3S) CLANHB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
• clanhe(3S) CLANHE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
• clanhp(3S) CLANHP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
• clanhs(3S) CLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
• clanht(3S) CLANHT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
• clansb(3S) CLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
• clansp(3S) CLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
• clansy(3S) CLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
• clantb(3S) CLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
• clantp(3S) CLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
• clantr(3S) CLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
• clapll(3S) CLAPLL - two column vectors X and Y, let A = ( X Y )
• clapmt(3S) CLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
• claqgb(3S) CLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
• claqge(3S) CLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
• claqhb(3S) CLAQHB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• claqhe(3S) CLAQHE - equilibrate a Hermitian matrix A using the scaling factors in the vector S
• claqhp(3S) CLAQHP - equilibrate a Hermitian matrix A using the scaling factors in the vector S
• claqp2(3S) CLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
• claqps(3S) CLAQPS - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3
• claqsb(3S) CLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• claqsp(3S) CLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
• claqsy(3S) CLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
• clar1v(3S) CLAR1V - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
• clar2v(3S) CLAR2V - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
• clarcm(3S) CLARCM - perform a very simple matrix-matrix multiplication
• clarf(3S) CLARF - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
• clarfb(3S) CLARFB - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right
• clarfg(3S) CLARFG - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
• clarft(3S) CLARFT - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
• clarfx(3S) CLARFX - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
• clargv(3S) CLARGV - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
• clarnv(3S) CLARNV - return a vector of n random complex numbers from a uniform or normal distribution
• clarrv(3S) CLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
• clartg(3S) CLARTG - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
• clartv(3S) CLARTV - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
• clarz(3S) CLARZ - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
• clarzb(3S) 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(3S) 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
• clascl(3S) CLASCL - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
• claset(3S) CLASET - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
• clasr(3S) CLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
• classq(3S) CLASSQ - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
• claswp(3S) CLASWP - perform a series of row interchanges on the matrix A
• clasyf(3S) CLASYF - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• clatbs(3S) CLATBS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• clatdf(3S) CLATDF - compute the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible
• clatps(3S) CLATPS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• clatrd(3S) CLATRD - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
• clatrs(3S) CLATRS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• clatrz(3S) CLATRZ - factor the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices
• clatzm(3S) CLATZM - routine is deprecated and has been replaced by routine CUNMRZ
• clauu2(3S) CLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• clauum(3S) CLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• confstr(3S) confstr - get configurable variables
• cpbcon(3S) CPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
• cpbequ(3S) CPBEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
• cpbrfs(3S) CPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
• cpbstf(3S) CPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
• cpbsv(3S) CPBSV - compute the solution to a complex system of linear equations A * X = B,
• cpbsvx(3S) 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(3S) CPBTF2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
• cpbtrf(3S) CPBTRF - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
• cpbtrs(3S) CPBTRS - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF
• cpocon(3S) CPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
• cpoequ(3S) CPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
• cporfs(3S) CPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
• cposv(3S) CPOSV - compute the solution to a complex system of linear equations A * X = B,
• cposvx(3S) 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(3S) CPOTF2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
• cpotrf(3S) CPOTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
• cpotri(3S) 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(3S) CPOTRS - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF
• cppcon(3S) CPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF
• cppequ(3S) CPPEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
• cpprfs(3S) CPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
• cppsv(3S) CPPSV - compute the solution to a complex system of linear equations A * X = B,
• cppsvx(3S) 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(3S) CPPTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
• cpptri(3S) 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(3S) 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(3S) 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(3S) 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(3S) CPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
• cptsv(3S) 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(3S) 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(3S) CPTTRF - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A
• cpttrs(3S) 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(3S) 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
• cspcon(3S) CSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF
• csprfs(3S) CSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
• cspsv(3S) CSPSV - compute the solution to a complex system of linear equations A * X = B,
• cspsvx(3S) 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(3S) CSPTRF - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
• csptri(3S) 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(3S) 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(3S) CSROT, ZDROT - Applies a real plane rotation to a pair of complex vectors
• csrscl(3S) CSRSCL - multiplie an n-element complex vector x by the real scalar 1/a
• cstedc(3S) CSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• cstegr(3S) CSTEGR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• cstein(3S) CSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
• csteqr(3S) CSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
• csycon(3S) 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
• csyrfs(3S) 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
• csysv(3S) CSYSV - compute the solution to a complex system of linear equations A * X = B,
• csysvx(3S) CSYSVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
• csytf2(3S) CSYTF2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• csytrf(3S) CSYTRF - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• csytri(3S) 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(3S) 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(3S) CTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
• ctbrfs(3S) CTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
• ctbtrs(3S) CTBTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ctermid(3S) ctermid, ctermid_r - generate file name for terminal
• ctgevc(3S) CTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
• ctgex2(3S) CTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
• ctgexc(3S) 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(3S) 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(3S) CTGSJA - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
• ctgsna(3S) CTGSNA - estimate reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B)
• ctgsy2(3S) CTGSY2 - solve the generalized Sylvester equation A * R - L * B = scale * C (1) D * R - L * E = scale * F using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
• ctgsyl(3S) CTGSYL - solve the generalized Sylvester equation
• ctpcon(3S) CTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
• ctprfs(3S) CTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
• ctptri(3S) CTPTRI - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
• ctptrs(3S) CTPTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ctrcon(3S) CTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
• ctrevc(3S) CTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
• ctrexc(3S) 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
• ctrid(3S) CTRID - compute the solution to a complex system of linear equations A*x = b, where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N
• ctrrfs(3S) CTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
• ctrsen(3S) 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
• ctrsna(3S) 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)
• ctrsyl(3S) CTRSYL - solve the complex Sylvester matrix equation
• ctrti2(3S) CTRTI2 - compute the inverse of a complex upper or lower triangular matrix
• ctrtri(3S) CTRTRI - compute the inverse of a complex upper or lower triangular matrix A
• ctrtrs(3S) CTRTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ctzrqf(3S) CTZRQF - routine is deprecated and has been replaced by routine CTZRZF
• ctzrzf(3S) CTZRZF - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
• cung2l(3S) CUNG2L - generate an m by n complex matrix Q with orthonormal columns,
• cung2r(3S) CUNG2R - generate an m by n complex matrix Q with orthonormal columns,
• cungbr(3S) 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(3S) 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(3S) CUNGL2 - generate an m-by-n complex matrix Q with orthonormal rows,
• cunglq(3S) CUNGLQ - generate an M-by-N complex matrix Q with orthonormal rows,
• cungql(3S) CUNGQL - generate an M-by-N complex matrix Q with orthonormal columns,
• cungqr(3S) CUNGQR - generate an M-by-N complex matrix Q with orthonormal columns,
• cungr2(3S) CUNGR2 - generate an m by n complex matrix Q with orthonormal rows,
• cungrq(3S) CUNGRQ - generate an M-by-N complex matrix Q with orthonormal rows,
• cungtr(3S) 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
• cunm2l(3S) CUNM2L - 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',
• cunm2r(3S) 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(3S) CUNMBR - VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmhr(3S) CUNMHR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunml2(3S) 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(3S) CUNMLQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmql(3S) CUNMQL - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmqr(3S) CUNMQR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmr2(3S) 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',
• cunmr3(3S) CUNMR3 - 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(3S) CUNMRQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmrz(3S) CUNMRZ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cunmtr(3S) CUNMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cupgtr(3S) 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(3S) CUPMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• cuserid(3S) cuserid - get character login name of the user
• dbdsdc(3S) DBDSDC - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• dbdsqr(3S) DBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• ddisna(3S) 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
• dgbbrd(3S) DGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
• dgbcon(3S) DGBCON - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
• dgbequ(3S) DGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
• dgbrfs(3S) DGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
• dgbsv(3S) 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(3S) 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(3S) DGBTF2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
• dgbtrf(3S) DGBTRF - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
• dgbtrs(3S) 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(3S) 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(3S) DGEBAL - balance a general real matrix A
• dgebd2(3S) DGEBD2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
• dgebrd(3S) DGEBRD - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
• dgecon(3S) 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
• dgeequ(3S) DGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
• dgees(3S) 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(3S) 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(3S) DGEEV - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• dgeevx(3S) DGEEVX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• dgegs(3S) DGEGS - routine is deprecated and has been replaced by routine DGGES
• dgegv(3S) DGEGV - routine is deprecated and has been replaced by routine DGGEV
• dgehd2(3S) DGEHD2 - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
• dgehrd(3S) DGEHRD - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
• dgelq2(3S) DGELQ2 - compute an LQ factorization of a real m by n matrix A
• dgelqf(3S) DGELQF - compute an LQ factorization of a real M-by-N matrix A
• dgels(3S) 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(3S) DGELSD - compute the minimum-norm solution to a real linear least squares problem
• dgelss(3S) DGELSS - compute the minimum norm solution to a real linear least squares problem
• dgelsx(3S) DGELSX - routine is deprecated and has been replaced by routine DGELSY
• dgelsy(3S) DGELSY - compute the minimum-norm solution to a real linear least squares problem
• dgemms(3S) DGEMMS - Multiplies a real general matrix by a real general matrix, using Strassen's algorithm
• dgeql2(3S) DGEQL2 - compute a QL factorization of a real m by n matrix A
• dgeqlf(3S) DGEQLF - compute a QL factorization of a real M-by-N matrix A
• dgeqp3(3S) DGEQP3 - compute a QR factorization with column pivoting of a matrix A
• dgeqpf(3S) DGEQPF - routine is deprecated and has been replaced by routine DGEQP3
• dgeqr2(3S) DGEQR2 - compute a QR factorization of a real m by n matrix A
• dgeqrf(3S) DGEQRF - compute a QR factorization of a real M-by-N matrix A
• dgerfs(3S) DGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
• dgerq2(3S) DGERQ2 - compute an RQ factorization of a real m by n matrix A
• dgerqf(3S) DGERQF - compute an RQ factorization of a real M-by-N matrix A
• dgesc2(3S) DGESC2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by DGETC2
• dgesdd(3S) DGESDD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors
• dgesv(3S) DGESV - compute the solution to a real system of linear equations A * X = B,
• dgesvd(3S) 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(3S) DGESVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
• dgetc2(3S) DGETC2 - compute an LU factorization with complete pivoting of the n-by-n matrix A
• dgetf2(3S) DGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
• dgetrf(3S) DGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
• dgetri(3S) DGETRI - compute the inverse of a matrix using the LU factorization computed by DGETRF
• dgetrs(3S) 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(3S) 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(3S) DGGBAL - balance a pair of general real matrices (A,B)
• dgges(3S) DGGES - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
• dggesx(3S) 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(3S) DGGEV - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
• dggevx(3S) DGGEVX - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
• dggglm(3S) DGGGLM - solve a general Gauss-Markov linear model (GLM) problem
• dgghrd(3S) 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(3S) DGGLSE - solve the linear equality-constrained least squares (LSE) problem
• dggqrf(3S) DGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
• dggrqf(3S) DGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
• dggsvd(3S) DGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
• dggsvp(3S) 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
• dgtcon(3S) DGTCON - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF
• dgtrfs(3S) DGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
• dgtsv(3S) DGTSV - solve the equation A*X = B,
• dgtsvx(3S) 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(3S) DGTTRF - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
• dgttrs(3S) DGTTRS - solve one of the systems of equations A*X = B or A'*X = B,
• dgtts2(3S) DGTTS2 - solve one of the systems of equations A*X = B or A'*X = B,
• dhgeqz(3S) 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(3S) DHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
• dhseqr(3S) 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
• dlabad(3S) DLABAD - take as input the values computed by DLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
• dlabrd(3S) DLABRD - reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
• dlacon(3S) DLACON - estimate the 1-norm of a square, real matrix A
• dlacpy(3S) DLACPY - copie all or part of a two-dimensional matrix A to another matrix B
• dladiv(3S) DLADIV - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
• dlae2(3S) DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
• dlaebz(3S) DLAEBZ - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
• dlaed0(3S) DLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• dlaed1(3S) DLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• dlaed2(3S) DLAED2 - merge the two sets of eigenvalues together into a single sorted set
• dlaed3(3S) DLAED3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
• dlaed4(3S) DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
• dlaed5(3S) DLAED5 - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z)
• dlaed6(3S) DLAED6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
• dlaed7(3S) DLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• dlaed8(3S) DLAED8 - merge the two sets of eigenvalues together into a single sorted set
• dlaed9(3S) DLAED9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
• dlaeda(3S) DLAEDA - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
• dlaein(3S) DLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
• dlaev2(3S) DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
• dlaexc(3S) DLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
• dlag2(3S) DLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
• dlags2(3S) DLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
• dlagtf(3S) 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,
• dlagtm(3S) DLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
• dlagts(3S) DLAGTS - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
• dlagv2(3S) DLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
• dlahqr(3S) DLAHQR - i an auxiliary routine called by DHSEQR to update the eigenvalues and Schur decomposition already computed by DHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
• dlahrd(3S) DLAHRD - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
• dlaic1(3S) DLAIC1 - applie one step of incremental condition estimation in its simplest version
• dlaln2(3S) DLALN2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
• dlals0(3S) DLALS0 - applie back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach
• dlalsa(3S) DLALSA - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
• dlalsd(3S) DLALSD - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N- by-NRHS
• dlamch(3S) DLAMCH - determine double precision machine parameters
• dlamrg(3S) 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
• dlangb(3S) DLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
• dlange(3S) DLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
• dlangt(3S) DLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
• dlanhs(3S) DLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
• dlansb(3S) DLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
• dlansp(3S) DLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
• dlanst(3S) DLANST - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
• dlansy(3S) DLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
• dlantb(3S) DLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
• dlantp(3S) DLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
• dlantr(3S) DLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
• dlanv2(3S) DLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
• dlapll(3S) DLAPLL - two column vectors X and Y, let A = ( X Y )
• dlapmt(3S) DLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
• dlapy2(3S) DLAPY2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
• dlapy3(3S) DLAPY3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
• dlaqgb(3S) DLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
• dlaqge(3S) DLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
• dlaqp2(3S) DLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
• dlaqps(3S) DLAQPS - compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
• dlaqsb(3S) DLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• dlaqsp(3S) DLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
• dlaqsy(3S) DLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
• dlaqtr(3S) DLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
• dlar1v(3S) DLAR1V - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
• dlar2v(3S) DLAR2V - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
• dlarf(3S) DLARF - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
• dlarfb(3S) DLARFB - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right
• dlarfg(3S) DLARFG - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
• dlarft(3S) DLARFT - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
• dlarfx(3S) DLARFX - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
• dlargv(3S) DLARGV - generate a vector of real plane rotations, determined by elements of the real vectors x and y
• dlarnv(3S) DLARNV - return a vector of n random real numbers from a uniform or normal distribution
• dlarrb(3S) DLARRB - the relatively robust representation(RRR) L D L^T, DLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
• dlarre(3S) DLARRE - the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T
• dlarrf(3S) DLARRF - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..
• dlarrv(3S) DLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
• dlartg(3S) DLARTG - generate a plane rotation so that [ CS SN ]
• dlartv(3S) DLARTV - applie a vector of real plane rotations to elements of the real vectors x and y
• dlaruv(3S) DLARUV - return a vector of n random real numbers from a uniform (0,1)
• dlarz(3S) DLARZ - applie a real elementary reflector H to a real M-by-N matrix C, from either the left or the right
• dlarzb(3S) DLARZB - applie 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(3S) 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
• dlas2(3S) DLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
• dlascl(3S) DLASCL - multiplie the M by N real matrix A by the real scalar CTO/CFROM
• dlasd0(3S) DLASD0 - a divide and conquer approach, DLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
• dlasd1(3S) DLASD1 - compute the SVD of an upper bidiagonal N-by-M matrix B,
• dlasd2(3S) DLASD2 - merge the two sets of singular values together into a single sorted set
• dlasd3(3S) DLASD3 - find all the square roots of the roots of the secular equation, as defined by the values in D and Z
• dlasd4(3S) DLASD4 - subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0
• dlasd5(3S) DLASD5 - subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z)
• dlasd6(3S) DLASD6 - compute the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
• dlasd7(3S) DLASD7 - merge the two sets of singular values together into a single sorted set
• dlasd8(3S) DLASD8 - find the square roots of the roots of the secular equation,
• dlasd9(3S) DLASD9 - find the square roots of the roots of the secular equation,
• dlasda(3S) DLASDA - a divide and conquer approach, DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
• dlasdq(3S) DLASDQ - compute the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired
• dlasdt(3S) DLASDT - create a tree of subproblems for bidiagonal divide and conquer
• dlaset(3S) DLASET - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
• dlasq1(3S) DLASQ1 - compute the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
• dlasq2(3S) DLASQ2 - compute all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow
• dlasq3(3S) DLASQ3 - check for deflation, computes a shift (TAU) and calls dqds
• dlasq4(3S) DLASQ4 - compute an approximation TAU to the smallest eigenvalue using values of d from the previous transform
• dlasq5(3S) DLASQ5 - compute one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines
• dlasq6(3S) DLASQ6 - compute one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow
• dlasr(3S) DLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
• dlasrt(3S) DLASRT - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
• dlassq(3S) DLASSQ - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
• dlasv2(3S) DLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
• dlaswp(3S) DLASWP - perform a series of row interchanges on the matrix A
• dlasy2(3S) DLASY2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
• dlasyf(3S) DLASYF - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• dlatbs(3S) DLATBS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
• dlatdf(3S) DLATDF - use the LU factorization of the n-by-n matrix Z computed by DGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s
• dlatps(3S) DLATPS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
• dlatrd(3S) DLATRD - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
• dlatrs(3S) DLATRS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
• dlatrz(3S) DLATRZ - factor the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations
• dlatzm(3S) DLATZM - routine is deprecated and has been replaced by routine DORMRZ
• dlauu2(3S) DLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• dlauum(3S) DLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• dopgtr(3S) 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(3S) DOPMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dorg2l(3S) DORG2L - generate an m by n real matrix Q with orthonormal columns,
• dorg2r(3S) DORG2R - generate an m by n real matrix Q with orthonormal columns,
• dorgbr(3S) 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(3S) 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(3S) DORGL2 - generate an m by n real matrix Q with orthonormal rows,
• dorglq(3S) DORGLQ - generate an M-by-N real matrix Q with orthonormal rows,
• dorgql(3S) DORGQL - generate an M-by-N real matrix Q with orthonormal columns,
• dorgqr(3S) DORGQR - generate an M-by-N real matrix Q with orthonormal columns,
• dorgr2(3S) DORGR2 - generate an m by n real matrix Q with orthonormal rows,
• dorgrq(3S) DORGRQ - generate an M-by-N real matrix Q with orthonormal rows,
• dorgtr(3S) 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
• dorm2l(3S) DORM2L - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• dorm2r(3S) DORM2R - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• dormbr(3S) DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormhr(3S) DORMHR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dorml2(3S) DORML2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• dormlq(3S) DORMLQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormql(3S) DORMQL - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormqr(3S) DORMQR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormr2(3S) DORMR2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• dormr3(3S) DORMR3 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• dormrq(3S) DORMRQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormrz(3S) DORMRZ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dormtr(3S) DORMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• dpbcon(3S) 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
• dpbequ(3S) DPBEQU - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
• dpbrfs(3S) DPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
• dpbstf(3S) DPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
• dpbsv(3S) DPBSV - compute the solution to a real system of linear equations A * X = B,
• dpbsvx(3S) 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(3S) DPBTF2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A
• dpbtrf(3S) DPBTRF - compute the Cholesky factorization of a real symmetric positive definite band matrix A
• dpbtrs(3S) 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
• dpocon(3S) 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
• dpoequ(3S) DPOEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
• dporfs(3S) DPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
• dposv(3S) DPOSV - compute the solution to a real system of linear equations A * X = B,
• dposvx(3S) 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(3S) DPOTF2 - compute the Cholesky factorization of a real symmetric positive definite matrix A
• dpotrf(3S) DPOTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A
• dpotri(3S) 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(3S) 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
• dppcon(3S) 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
• dppequ(3S) DPPEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
• dpprfs(3S) DPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
• dppsv(3S) DPPSV - compute the solution to a real system of linear equations A * X = B,
• dppsvx(3S) 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(3S) DPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
• dpptri(3S) 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(3S) 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
• dpsldlt(3S) DPSLDLT_Destroy, DPSLDLT_ExtractPerm, DPSLDLT_Factor, DPSLDLT_FactorOOC, DPSLDLT_OOCLimit, DPSLDLT_OOCPath, DPSLDLT_Ordering, DPSLDLT_Preprocess, DPSLDLT_PreprocessZ, DPSLDLT_Solve, DPSLDLT_SolveM, DPSLDLT_Storage - Parallel sparse symmetric solver for linear systems of real equations
• dpsldu(3S) DPSLDU_Destroy, DPSLDU_ExtractPerm, DPSLDU_Factor, DPSLDU_FactorOOC, DPSLDU_OOCLimit, DPSLDU_OOCPath, DPSLDU_Ordering, DPSLDU_Preprocess, DPSLDU_PreprocessZ, DPSLDU_Solve, DPSLDU_SolveM, DPSLDU_Storage - Parallel sparse unsymmetric solver for linear systems of real equations
• dptcon(3S) 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(3S) 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(3S) DPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
• dptsv(3S) 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(3S) 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(3S) DPTTRF - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A
• dpttrs(3S) DPTTRS - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF
• dptts2(3S) DPTTS2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF
• drscl(3S) DRSCL - multiplie an n-element real vector x by the real scalar 1/a
• dsbev(3S) DSBEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• dsbevd(3S) DSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• dsbevx(3S) DSBEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• dsbgst(3S) DSBGST - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
• dsbgv(3S) 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(3S) 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(3S) DSBGVX - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
• dsbtrd(3S) DSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
• dsecnd(3S) DSECND - return the user time for a process in seconds
• dspcon(3S) DSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF
• dspev(3S) DSPEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• dspevd(3S) DSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• dspevx(3S) DSPEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• dspgst(3S) DSPGST - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
• dspgv(3S) 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(3S) 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(3S) 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
• dsprfs(3S) DSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
• dspsv(3S) DSPSV - compute the solution to a real system of linear equations A * X = B,
• dspsvx(3S) 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(3S) DSPTRD - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
• dsptrf(3S) DSPTRF - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
• dsptri(3S) 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(3S) 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(3S) DSTEBZ - compute the eigenvalues of a symmetric tridiagonal matrix T
• dstedc(3S) DSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• dstegr(3S) DSTEGR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• dstein(3S) DSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
• dsteqr(3S) DSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
• dsterf(3S) DSTERF - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
• dstev(3S) DSTEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
• dstevd(3S) DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
• dstevr(3S) DSTEVR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• dstevx(3S) DSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
• dsycon(3S) 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(3S) DSYEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• dsyevd(3S) DSYEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• dsyevr(3S) DSYEVR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T
• dsyevx(3S) DSYEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• dsygs2(3S) DSYGS2 - reduce a real symmetric-definite generalized eigenproblem to standard form
• dsygst(3S) DSYGST - reduce a real symmetric-definite generalized eigenproblem to standard form
• dsygv(3S) 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(3S) 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(3S) 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
• dsyrfs(3S) 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
• dsysv(3S) DSYSV - compute the solution to a real system of linear equations A * X = B,
• dsysvx(3S) DSYSVX - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,
• dsytd2(3S) DSYTD2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
• dsytf2(3S) DSYTF2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• dsytrd(3S) DSYTRD - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
• dsytrf(3S) DSYTRF - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• dsytri(3S) 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(3S) 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(3S) DTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
• dtbrfs(3S) DTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
• dtbtrs(3S) DTBTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• dtgevc(3S) DTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
• dtgex2(3S) DTGEX2 - swap adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation
• dtgexc(3S) 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(3S) 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(3S) DTGSJA - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
• dtgsna(3S) 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
• dtgsy2(3S) DTGSY2 - solve the generalized Sylvester equation
• dtgsyl(3S) DTGSYL - solve the generalized Sylvester equation
• dtpcon(3S) DTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
• dtprfs(3S) DTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
• dtptri(3S) DTPTRI - compute the inverse of a real upper or lower triangular matrix A stored in packed format
• dtptrs(3S) DTPTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• dtrcon(3S) DTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
• dtrevc(3S) DTREVC - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
• dtrexc(3S) 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
• dtrid(3S) DTRID - compute the solution to a real system of linear equations A*x = b, where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N
• dtrrfs(3S) DTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
• dtrsen(3S) 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,
• dtrsna(3S) 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)
• dtrsyl(3S) DTRSYL - solve the real Sylvester matrix equation
• dtrti2(3S) DTRTI2 - compute the inverse of a real upper or lower triangular matrix
• dtrtri(3S) DTRTRI - compute the inverse of a real upper or lower triangular matrix A
• dtrtrs(3S) DTRTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• dtzrqf(3S) DTZRQF - routine is deprecated and has been replaced by routine DTZRZF
• dtzrzf(3S) DTZRZF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
• dzsum1(3S) DZSUM1 - take the sum of the absolute values of a complex vector and returns a double precision result
• fclose(3S) fclose, fflush - close or flush a stream
• ferror(3S) ferror, feof, clearerr, fileno - stream status inquiries
• flockfile(3S) flockfile, ftrylockfile, funlockfile - stdio synchronization functions
• fopen(3S) fopen, freopen, fdopen - open a stream
• fread(3S) fread, fwrite - binary input/output
• fseek(3S) fseek, fseek64, rewind, ftell, ftell64 - reposition a file pointer in a stream
• fsetpos(3S) fsetpos, fsetpos64, fgetpos, fgetpos64 - reposition a file pointer in a stream
• fwprintf(3S) fwprintf: fwprintf, wprintf, swprintf - print formatted wide-character output
• fwscanf(3S) fwscanf: fwscanf, wscanf, swscanf - convert formatted wide-character input
• getc(3S) getc, getchar, fgetc, getw, getc_unlocked, getchar_unlocked - get character or word from a stream
• gets(3S) gets, fgets - get a string from a stream
• getwc(3S) getwc, getwchar, fgetwc - get wchar_t character or word from a stream
• getws(3S) getws, fgetws - get a wchar_t string from a stream
• icmax1(3S) ICMAX1 - find the index of the element whose real part has maximum absolute value
• ilaenv(3S) ILAENV - i called from the LAPACK routines to choose problem-dependent parameters for the local environment
• intro_blas(3S) INTRO_BLAS - Introduction to SCSL Basic Linear Algebra Subprograms
• intro_blas1(3S) INTRO_BLAS1 - Introduction to vector-vector linear algebra subprograms
• intro_blas2(3S) INTRO_BLAS2 - Introduction to matrix-vector linear algebra subprograms
• intro_blas3(3S) INTRO_BLAS3 - Introduction to matrix-matrix linear algebra subprograms
• intro_cblas(3S) INTRO_CBLAS - Introduction to the C interface to Fortran 77 Basic Linear Algebra Subprograms (legacy BLAS)
• intro_fft(3S) INTRO_FFT - Introduction to signal processing routines
• intro_lapack(3S) INTRO_LAPACK - Introduction to LAPACK solvers for dense linear systems
• intro_scsl(3S) INTRO_SCSL - Introduction to Scientific Computing Software Library (SCSL) routines
• intro_solvers(3S) INTRO_SOLVERS - Introduction to SGI-developed linear equation solvers
• isamax(3S) ISAMAX, IDAMAX, ICAMAX, IZAMAX - Searches a vector for the first occurrence of the maximum absolute value
• isamin(3S) ISAMIN, IDAMIN - Searches a vector for the first occurrence of the minimum absolute value
• ismax(3S) ISMAX, IDMAX - Searches a real vector for the first occurrence of the maximum value
• ismin(3S) ISMIN, IDMIN - Searches a real vector for the first occurrence of the minimum value
• iterative(3S) DIterative, DIterative_DropTol, DIterative_DropStorage - Parallel sparse iterative linear system solver
• izmax1(3S) IZMAX1 - find the index of the element whose real part has maximum absolute value
• lsame(3S) LSAME - return .TRUE
• lsamen(3S) LSAMEN - test if the first N letters of CA are the same as the first N letters of CB, regardless of case
• mbrchar(3S) mbrchar: mbrlen, mbrtowc, wcrtomb, btowc, wctob, mbsinit - multibyte character handling (restartable)
• mbrstring(3S) mbrstring: mbsrtowcs, wcsrtombs - multibyte string functions (restartable)
• popen(3S) popen, pclose - initiate pipe to/from a process
• printf(3S) printf, fprintf, snprintf, sprintf - print formatted output
• psldlt(3S) PSLDLT_Destroy, PSLDLT_ExtractPerm, PSLDLT_Factor, PSLDLT_FactorOOC, PSLDLT_OOCLimit, PSLDLT_OOCPath, PSLDLT_Ordering, PSLDLT_Preprocess, PSLDLT_PreprocessZ, PSLDLT_Solve, PSLDLT_SolveM, PSLDLT_Storage - Parallel sparse symmetric linear system solver
• psldu(3S) PSLDU_Destroy, PSLDU_ExtractPerm, PSLDU_Factor, PSLDU_FactorOOC, PSLDU_OOCLimit, PSLDU_OOCPath, PSLDU_Ordering, PSLDU_Preprocess, PSLDU_PreprocessZ, PSLDU_Solve, PSLDU_SolveM, PSLDU_Storage - Parallel sparse unsymmetric linear system solver
• putc(3S) putc, putchar, fputc, putw, putc_unlocked, putchar_unlocked - put character or word on a stream
• puts(3S) puts, fputs - put a string on a stream
• putwc(3S) putwc, putwchar, fputwc - put wchar_t character on a stream
• putws(3S) putws, fputws - put a wchar_t string on a stream
• sasum(3S) SASUM, DASUM, SCASUM, DZASUM - Sums the absolute value of elements in a real or complex vector
• saxpby(3S) SAXPBY, DAXPBY, CAXPBY, ZAXPBY - Adds a scalar multiple of a Single precision or complex vector x to a scalar multiple of another Single precision or complex vector y
• saxpy(3S) SAXPY, CAXPY, DAXPY, ZAXPY - Adds a scalar multiple of a real or complex vector to another real or complex vector
• sbdsdc(3S) SBDSDC - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• sbdsqr(3S) SBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• scanf(3S) scanf, fscanf, sscanf - convert formatted input
• scfft(3S) SCFFT, DZFFT, CSFFT, ZDFFT - Computes a real-to-complex or complex-to- real Fast Fourier Transform (FFT)
• scfft2d(3S) SCFFT2D, DZFFT2D, CSFFT2D, ZDFFT2D - Applies a two-dimensional real-to- complex or complex-to-real Fast Fourier Transform (FFT)
• scfft3d(3S) SCFFT3D, DZFFT3D, CSFFT3D, ZDFFT3D - Applies a three-dimensional real- to-complex Fast Fourier Transform (FFT)
• scfftf(3S) SCFFTF, SCFFTMF, SCFFT2DF, SCFFT3DF, DZFFTF, DZFFTMF, DZFFT2DF, DZFFT3DF - Deallocate memory tacked on to the table array during initialization
• scfftm(3S) SCFFTM, DZFFTM, CSFFTM, ZDFFTM - Applies multiple real-to-complex or complex-to-real Fast Fourier Transforms (FFTs)
• scopy(3S) SCOPY, DCOPY, CCOPY, ZCOPY - Copies a real or complex vector into another real or complex vector
• scsum1(3S) SCSUM1 - take the sum of the absolute values of a complex vector and returns a single precision result
• sdisna(3S) 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(3S) SDOT, DDOT, CDOTC, ZDOTC, CDOTU, ZDOTU - Computes a dot product (inner product) of two real or complex vectors
• second(3S) SECOND - return the user time for a process in seconds
• sgbbrd(3S) SGBBRD - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation
• sgbcon(3S) SGBCON - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,
• sgbequ(3S) SGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
• sgbmv(3S) SGBMV, DGBMV, CGBMV, ZGMBV - Multiplies a real or complex vector by a real or complex general band matrix
• sgbrfs(3S) SGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
• sgbsv(3S) 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(3S) 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(3S) SGBTF2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
• sgbtrf(3S) SGBTRF - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges
• sgbtrs(3S) 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(3S) 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(3S) SGEBAL - balance a general real matrix A
• sgebd2(3S) SGEBD2 - reduce a real general m by n matrix A to upper or lower bidiagonal form B by an orthogonal transformation
• sgebrd(3S) SGEBRD - reduce a general real M-by-N matrix A to upper or lower bidiagonal form B by an orthogonal transformation
• sgecon(3S) SGECON - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF
• sgeequ(3S) SGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
• sgees(3S) 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(3S) 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(3S) SGEEV - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• sgeevx(3S) SGEEVX - compute for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• sgegs(3S) SGEGS - routine is deprecated and has been replaced by routine SGGES
• sgegv(3S) SGEGV - routine is deprecated and has been replaced by routine SGGEV
• sgehd2(3S) SGEHD2 - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
• sgehrd(3S) SGEHRD - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
• sgelq2(3S) SGELQ2 - compute an LQ factorization of a real m by n matrix A
• sgelqf(3S) SGELQF - compute an LQ factorization of a real M-by-N matrix A
• sgels(3S) 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(3S) SGELSD - compute the minimum-norm solution to a real linear least squares problem
• sgelss(3S) SGELSS - compute the minimum norm solution to a real linear least squares problem
• sgelsx(3S) SGELSX - routine is deprecated and has been replaced by routine SGELSY
• sgelsy(3S) SGELSY - compute the minimum-norm solution to a real linear least squares problem
• sgemm(3S) SGEMM, DGEMM, CGEMM, ZGEMM - Multiplies a real or complex general matrix by a real or complex general matrix
• sgemv(3S) SGEMV, DGEMV, CGEMV, ZGEMV - Multiplies a real or complex vector by a real or complex general matrix
• sgeql2(3S) SGEQL2 - compute a QL factorization of a real m by n matrix A
• sgeqlf(3S) SGEQLF - compute a QL factorization of a real M-by-N matrix A
• sgeqp3(3S) SGEQP3 - compute a QR factorization with column pivoting of a matrix A
• sgeqpf(3S) SGEQPF - routine is deprecated and has been replaced by routine SGEQP3
• sgeqr2(3S) SGEQR2 - compute a QR factorization of a real m by n matrix A
• sgeqrf(3S) SGEQRF - compute a QR factorization of a real M-by-N matrix A
• sger(3S) SGER, DGER, CGERC, ZGERC, CGERU, ZGERU - Performs rank 1 update of a real or complex general matrix
• sgerfs(3S) SGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
• sgerq2(3S) SGERQ2 - compute an RQ factorization of a real m by n matrix A
• sgerqf(3S) SGERQF - compute an RQ factorization of a real M-by-N matrix A
• sgesc2(3S) SGESC2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by SGETC2
• sgesdd(3S) SGESDD - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors
• sgesum(3S) SGESUM, DGESUM, CGESUM, ZGESUM - Adds a scalar multiple of a real or complex matrix to a scalar multiple of another real or complex matrix
• sgesv(3S) SGESV - compute the solution to a real system of linear equations A * X = B,
• sgesvd(3S) 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(3S) SGESVX - use the LU factorization to compute the solution to a real system of linear equations A * X = B,
• sgetc2(3S) SGETC2 - compute an LU factorization with complete pivoting of the n-by-n matrix A
• sgetf2(3S) SGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
• sgetrf(3S) SGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
• sgetri(3S) SGETRI - compute the inverse of a matrix using the LU factorization computed by SGETRF
• sgetrs(3S) 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(3S) 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(3S) SGGBAL - balance a pair of general real matrices (A,B)
• sgges(3S) SGGES - compute for a pair of N-by-N real nonsymmetric matrices (A,B),
• sggesx(3S) 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(3S) SGGEV - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
• sggevx(3S) SGGEVX - compute for a pair of N-by-N real nonsymmetric matrices (A,B)
• sggglm(3S) SGGGLM - solve a general Gauss-Markov linear model (GLM) problem
• sgghrd(3S) 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(3S) SGGLSE - solve the linear equality-constrained least squares (LSE) problem
• sggqrf(3S) SGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
• sggrqf(3S) SGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
• sggsvd(3S) SGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B
• sggsvp(3S) 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(3S) SGTCON - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF
• sgtrfs(3S) SGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
• sgtsv(3S) SGTSV - solve the equation A*X = B,
• sgtsvx(3S) 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(3S) SGTTRF - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges
• sgttrs(3S) SGTTRS - solve one of the systems of equations A*X = B or A'*X = B,
• sgtts2(3S) SGTTS2 - solve one of the systems of equations A*X = B or A'*X = B,
• shad(3S) SHAD, DHAD, CHAD, ZHAD - Computes the Hadamard product of two vectors
• shgeqz(3S) 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(3S) SHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
• shseqr(3S) 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
• slabad(3S) SLABAD - take as input the values computed by SLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large
• slabrd(3S) SLABRD - reduce the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
• slacon(3S) SLACON - estimate the 1-norm of a square, real matrix A
• slacpy(3S) SLACPY - copie all or part of a two-dimensional matrix A to another matrix B
• sladiv(3S) SLADIV - perform complex division in real arithmetic a + i*b p + i*q = --------- c + i*d The algorithm is due to Robert L
• slae2(3S) SLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
• slaebz(3S) SLAEBZ - contain the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
• slaed0(3S) SLAED0 - compute all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• slaed1(3S) SLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• slaed2(3S) SLAED2 - merge the two sets of eigenvalues together into a single sorted set
• slaed3(3S) SLAED3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
• slaed4(3S) SLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
• slaed5(3S) SLAED5 - subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z * transpose(Z)
• slaed6(3S) SLAED6 - compute the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
• slaed7(3S) SLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• slaed8(3S) SLAED8 - merge the two sets of eigenvalues together into a single sorted set
• slaed9(3S) SLAED9 - find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
• slaeda(3S) SLAEDA - compute the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem
• slaein(3S) SLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
• slaev2(3S) SLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
• slaexc(3S) SLAEXC - swap adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation
• slag2(3S) SLAG2 - compute the eigenvalues of a 2 x 2 generalized eigenvalue problem A - w B, with scaling as necessary to avoid over-/underflow
• slags2(3S) SLAGS2 - compute 2-by-2 orthogonal matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) The rows of the transformed A and B are parallel, where U = ( CSU SNU ), V = ( CSV SNV ), Q = ( CSQ SNQ ) ( -SNU CSU ) ( -SNV CSV ) ( -SNQ CSQ ) Z' denotes the transpose of Z
• slagtf(3S) 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,
• slagtm(3S) SLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
• slagts(3S) SLAGTS - may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*x = y,
• slagv2(3S) SLAGV2 - compute the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular
• slahqr(3S) SLAHQR - i an auxiliary routine called by SHSEQR to update the eigenvalues and Schur decomposition already computed by SHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
• slahrd(3S) SLAHRD - reduce the first NB columns of a real general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
• slaic1(3S) SLAIC1 - applie one step of incremental condition estimation in its simplest version
• slaln2(3S) SLALN2 - solve a system of the form (ca A - w D ) X = s B or (ca A' - w D) X = s B with possible scaling ("s") and perturbation of A
• slals0(3S) SLALS0 - applie back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach
• slalsa(3S) SLALSA - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
• slalsd(3S) SLALSD - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N- by-NRHS
• slamch(3S) SLAMCH - determine single precision machine parameters
• slamrg(3S) 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
• slangb(3S) SLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
• slange(3S) SLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
• slangt(3S) SLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
• slanhs(3S) SLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
• slansb(3S) SLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
• slansp(3S) SLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
• slanst(3S) SLANST - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
• slansy(3S) SLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A
• slantb(3S) SLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
• slantp(3S) SLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
• slantr(3S) SLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
• slanv2(3S) SLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
• slapll(3S) SLAPLL - two column vectors X and Y, let A = ( X Y )
• slapmt(3S) SLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
• slapy2(3S) SLAPY2 - return sqrt(x**2+y**2), taking care not to cause unnecessary overflow
• slapy3(3S) SLAPY3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
• slaqgb(3S) SLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
• slaqge(3S) SLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
• slaqp2(3S) SLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
• slaqps(3S) SLAQPS - compute a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3
• slaqsb(3S) SLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• slaqsp(3S) SLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
• slaqsy(3S) SLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
• slaqtr(3S) SLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE
• slar1v(3S) SLAR1V - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
• slar2v(3S) SLAR2V - applie a vector of real plane rotations from both sides to a sequence of 2-by-2 real symmetric matrices, defined by the elements of the vectors x, y and z
• slarf(3S) SLARF - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
• slarfb(3S) SLARFB - applie a real block reflector H or its transpose H' to a real m by n matrix C, from either the left or the right
• slarfg(3S) SLARFG - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I
• slarft(3S) SLARFT - form the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors
• slarfx(3S) SLARFX - applie a real elementary reflector H to a real m by n matrix C, from either the left or the right
• slargv(3S) SLARGV - generate a vector of real plane rotations, determined by elements of the real vectors x and y
• slarnv(3S) SLARNV - return a vector of n random real numbers from a uniform or normal distribution
• slarrb(3S) SLARRB - the relatively robust representation(RRR) L D L^T, SLARRB does ``limited'' bisection to locate the eigenvalues of L D L^T,
• slarre(3S) SLARRE - the tridiagonal matrix T, SLARRE sets "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (i) the numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and (iii) eigenvalues of each L_i D_i L_i^T
• slarrf(3S) SLARRF - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( IFIRST ), W( IFIRST+1 ), ..
• slarrv(3S) SLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
• slartg(3S) SLARTG - generate a plane rotation so that [ CS SN ]
• slartv(3S) SLARTV - applie a vector of real plane rotations to elements of the real vectors x and y
• slaruv(3S) SLARUV - return a vector of n random real numbers from a uniform (0,1)
• slarz(3S) SLARZ - applie a real elementary reflector H to a real M-by-N matrix C, from either the left or the right
• slarzb(3S) SLARZB - applie 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(3S) 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
• slas2(3S) SLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
• slascl(3S) SLASCL - multiplie the M by N real matrix A by the real scalar CTO/CFROM
• slasd0(3S) SLASD0 - a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
• slasd1(3S) SLASD1 - compute the SVD of an upper bidiagonal N-by-M matrix B,
• slasd2(3S) SLASD2 - merge the two sets of singular values together into a single sorted set
• slasd3(3S) SLASD3 - find all the square roots of the roots of the secular equation, as defined by the values in D and Z
• slasd4(3S) SLASD4 - subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0
• slasd5(3S) SLASD5 - subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z)
• slasd6(3S) SLASD6 - compute the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
• slasd7(3S) SLASD7 - merge the two sets of singular values together into a single sorted set
• slasd8(3S) SLASD8 - find the square roots of the roots of the secular equation,
• slasd9(3S) SLASD9 - find the square roots of the roots of the secular equation,
• slasda(3S) SLASDA - a divide and conquer approach, SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
• slasdq(3S) SLASDQ - compute the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired
• slasdt(3S) SLASDT - create a tree of subproblems for bidiagonal divide and conquer
• slaset(3S) SLASET - initialize an m-by-n matrix A to BETA on the diagonal and ALPHA on the offdiagonals
• slasq1(3S) SLASQ1 - compute the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E
• slasq2(3S) SLASQ2 - compute all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd array Z to high relative accuracy are computed to high relative accuracy, in the absence of denormalization, underflow and overflow
• slasq3(3S) SLASQ3 - check for deflation, computes a shift (TAU) and calls dqds
• slasq4(3S) SLASQ4 - compute an approximation TAU to the smallest eigenvalue using values of d from the previous transform
• slasq5(3S) SLASQ5 - compute one dqds transform in ping-pong form, one version for IEEE machines another for non IEEE machines
• slasq6(3S) SLASQ6 - compute one dqd (shift equal to zero) transform in ping-pong form, with protection against underflow and overflow
• slasr(3S) SLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n real matrix and P is an orthogonal matrix,
• slasrt(3S) SLASRT - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' )
• slassq(3S) SLASSQ - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
• slasv2(3S) SLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]
• slaswp(3S) SLASWP - perform a series of row interchanges on the matrix A
• slasy2(3S) SLASY2 - solve for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in op(TL)*X + ISGN*X*op(TR) = SCALE*B,
• slasyf(3S) SLASYF - compute a partial factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• slatbs(3S) SLATBS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular band matrix
• slatdf(3S) SLATDF - use the LU factorization of the n-by-n matrix Z computed by SGETC2 and computes a contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and choosing the r.h.s
• slatps(3S) SLATPS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow, where A is an upper or lower triangular matrix stored in packed form
• slatrd(3S) SLATRD - reduce NB rows and columns of a real symmetric matrix A to symmetric tridiagonal form by an orthogonal similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
• slatrs(3S) SLATRS - solve one of the triangular systems A *x = s*b or A'*x = s*b with scaling to prevent overflow
• slatrz(3S) SLATRZ - factor the M-by-(M+L) real upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means of orthogonal transformations
• slatzm(3S) SLATZM - routine is deprecated and has been replaced by routine SORMRZ
• slauu2(3S) SLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• slauum(3S) SLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• snrm2(3S) SNRM2, DNRM2, SCNRM2, DZNRM2 - Computes the Euclidean norm of a vector
• sopgtr(3S) 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(3S) SOPMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sorg2l(3S) SORG2L - generate an m by n real matrix Q with orthonormal columns,
• sorg2r(3S) SORG2R - generate an m by n real matrix Q with orthonormal columns,
• sorgbr(3S) 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(3S) 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(3S) SORGL2 - generate an m by n real matrix Q with orthonormal rows,
• sorglq(3S) SORGLQ - generate an M-by-N real matrix Q with orthonormal rows,
• sorgql(3S) SORGQL - generate an M-by-N real matrix Q with orthonormal columns,
• sorgqr(3S) SORGQR - generate an M-by-N real matrix Q with orthonormal columns,
• sorgr2(3S) SORGR2 - generate an m by n real matrix Q with orthonormal rows,
• sorgrq(3S) SORGRQ - generate an M-by-N real matrix Q with orthonormal rows,
• sorgtr(3S) 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
• sorm2l(3S) SORM2L - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• sorm2r(3S) SORM2R - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• sormbr(3S) SORMBR - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormhr(3S) SORMHR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sorml2(3S) SORML2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• sormlq(3S) SORMLQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormql(3S) SORMQL - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormqr(3S) SORMQR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormr2(3S) SORMR2 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• sormr3(3S) SORMR3 - overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',
• sormrq(3S) SORMRQ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormrz(3S) SORMRZ - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• sormtr(3S) SORMTR - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• spbcon(3S) SPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
• spbequ(3S) SPBEQU - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition number (with respect to the two-norm)
• spbrfs(3S) SPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and provides error bounds and backward error estimates for the solution
• spbstf(3S) SPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
• spbsv(3S) SPBSV - compute the solution to a real system of linear equations A * X = B,
• spbsvx(3S) 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(3S) SPBTF2 - compute the Cholesky factorization of a real symmetric positive definite band matrix A
• spbtrf(3S) SPBTRF - compute the Cholesky factorization of a real symmetric positive definite band matrix A
• spbtrs(3S) SPBTRS - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF
• spocon(3S) SPOCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
• spoequ(3S) SPOEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
• sporfs(3S) SPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite,
• sposv(3S) SPOSV - compute the solution to a real system of linear equations A * X = B,
• sposvx(3S) 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(3S) SPOTF2 - compute the Cholesky factorization of a real symmetric positive definite matrix A
• spotrf(3S) SPOTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A
• spotri(3S) 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(3S) SPOTRS - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF
• sppcon(3S) SPPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF
• sppequ(3S) SPPEQU - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
• spprfs(3S) SPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
• sppsv(3S) SPPSV - compute the solution to a real system of linear equations A * X = B,
• sppsvx(3S) 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(3S) SPPTRF - compute the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format
• spptri(3S) 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(3S) 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(3S) 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(3S) 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(3S) SPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
• sptsv(3S) 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(3S) 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(3S) SPTTRF - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A
• spttrs(3S) SPTTRS - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF
• sptts2(3S) SPTTS2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF
• srand64(3S) srand64, drand64, drand64_advance, drand64_get, drand64_getv, drand64_maxthreads, drand64_set, drand64_setv, drand64_thread - Thread- safe parallel 64-bit random number generator
• srot(3S) SROT, DROT, CROT, ZROT - Applies a real plane rotation or complex coordinate rotation
• srotg(3S) SROTG, DROTG, CROTG, ZROTG - Constructs a Givens plane rotation
• srotm(3S) SROTM, DROTM - Applies a modified Givens plane rotation
• srotmg(3S) SROTMG, DROTMG - Constructs a modified Givens plane rotation
• srscl(3S) SRSCL - multiplie an n-element real vector x by the real scalar 1/a
• ssbev(3S) SSBEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• ssbevd(3S) SSBEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• ssbevx(3S) SSBEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
• ssbgst(3S) SSBGST - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
• ssbgv(3S) 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(3S) 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(3S) SSBGVX - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
• ssbmv(3S) SSBMV, DSBMV - Multiplies a real vector by a real symmetric band matrix
• ssbtrd(3S) SSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
• sscal(3S) SSCAL, DSCAL, CSSCAL, ZDSCAL, CSCAL, ZSCAL - Scales a real or complex vector
• sspcon(3S) SSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF
• sspev(3S) SSPEV - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• sspevd(3S) SSPEVD - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• sspevx(3S) SSPEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage
• sspgst(3S) SSPGST - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage
• sspgv(3S) 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(3S) 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(3S) 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(3S) SSPMV, DSPMV, CSPMV, ZSPMV - Multiplies a real or complex symmetric packed matrix by a real or complex vector
• sspr(3S) SSPR, DSPR, CSPR, ZSPR - Performs symmetric rank 1 update of a real or complex symmetric packed matrix
• sspr2(3S) SSPR2, DSPR2 - Performs symmetric rank 2 update of a real symmetric packed matrix
• ssprfs(3S) SSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
• sspsv(3S) SSPSV - compute the solution to a real system of linear equations A * X = B,
• sspsvx(3S) 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(3S) SSPTRD - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation
• ssptrf(3S) SSPTRF - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
• ssptri(3S) 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(3S) 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(3S) SSTEBZ - compute the eigenvalues of a symmetric tridiagonal matrix T
• sstedc(3S) SSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• sstegr(3S) SSTEGR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• sstein(3S) SSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
• ssteqr(3S) SSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
• ssterf(3S) SSTERF - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm
• sstev(3S) SSTEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
• sstevd(3S) SSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
• sstevr(3S) SSTEVR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• sstevx(3S) SSTEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
• ssum(3S) SSUM, DSUM, CSUM, ZSUM - Sums the elements of a real or complex vector
• sswap(3S) SSWAP, DSWAP, CSWAP, ZSWAP - Swaps two real or complex vectors
• ssycon(3S) 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(3S) SSYEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• ssyevd(3S) SSYEVD - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• ssyevr(3S) SSYEVR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix T
• ssyevx(3S) SSYEVX - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A
• ssygs2(3S) SSYGS2 - reduce a real symmetric-definite generalized eigenproblem to standard form
• ssygst(3S) SSYGST - reduce a real symmetric-definite generalized eigenproblem to standard form
• ssygv(3S) 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(3S) 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(3S) 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(3S) SSYMM, DSYMM, CSYMM, ZSYMM - Multiplies a real or complex general matrix by a real or complex symmetric matrix
• ssymv(3S) SSYMV, DSYMV, CSYMV, ZSYMV - Multiplies a real or complex vector by a real or complex symmetric matrix
• ssyr(3S) SSYR, DSYR, CSYR, ZSYR - Performs symmetric rank 1 update of a real or complex symmetric matrix
• ssyr2(3S) SSYR2, DSYR2 - Performs symmetric rank 2 update of a real symmetric matrix
• ssyr2k(3S) SSYR2K, DSYR2K, CSYR2K, ZSYR2K - Performs symmetric rank 2k update of a real or complex symmetric matrix
• ssyrfs(3S) 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(3S) SSYRK, DSYRK, CSYRK, ZSYRK - Performs symmetric rank k update of a real or complex symmetric matrix
• ssysv(3S) SSYSV - compute the solution to a real system of linear equations A * X = B,
• ssysvx(3S) SSYSVX - use the diagonal pivoting factorization to compute the solution to a real system of linear equations A * X = B,
• ssytd2(3S) SSYTD2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation
• ssytf2(3S) SSYTF2 - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• ssytrd(3S) SSYTRD - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation
• ssytrf(3S) SSYTRF - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• ssytri(3S) 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(3S) 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(3S) STBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
• stbmv(3S) STBMV, DTBMV, CTBMV, ZTBMV - Multiplies a real or complex vector by a real or complex triangular band matrix
• stbrfs(3S) STBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
• stbsv(3S) STBSV, DTBSV, CTBSV, ZTBSV - Solves a real or complex triangular banded system of equations
• stbtrs(3S) STBTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• stdio(3S) stdio - standard buffered input/output package
• stgevc(3S) STGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B)
• stgex2(3S) STGEX2 - swap adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation
• stgexc(3S) 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(3S) 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(3S) STGSJA - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
• stgsna(3S) 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
• stgsy2(3S) STGSY2 - solve the generalized Sylvester equation
• stgsyl(3S) STGSYL - solve the generalized Sylvester equation
• stpcon(3S) STPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
• stpmv(3S) STPMV, DTPMV, CTPMV, ZTPMV - Multiplies a real or complex vector by a real or complex triangular packed matrix
• stprfs(3S) STPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
• stpsv(3S) STPSV, DTPSV, CTPSV, ZTPSV - Solves a real or complex triangular packed system of equations
• stptri(3S) STPTRI - compute the inverse of a real upper or lower triangular matrix A stored in packed format
• stptrs(3S) STPTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• strcon(3S) STRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
• strevc(3S) STREVC - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
• strexc(3S) 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
• strfmon(3S) strfmon - convert monetary value to string
• strid(3S) STRID - compute the solution to a real system of linear equations A*x = b, where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N
• strmm(3S) STRMM, DTRMM, CTRMM, ZTRMM - Multiplies a real or complex general matrix by a real or complex triangular matrix
• strmv(3S) STRMV, DTRMV, CTRMV, ZTRMV - Multiplies a real or complex vector by a real or complex triangular matrix
• strrfs(3S) STRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
• strsen(3S) STRSEN - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T,
• strsm(3S) STRSM, DTRSM, CTRSM, ZTRSM - Solves a real or complex triangular system of equations with multiple right-hand sides
• strsna(3S) 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(3S) STRSV, DTRSV, CTRSV, ZTRSV - Solves a real or complex triangular system of equations
• strsyl(3S) STRSYL - solve the real Sylvester matrix equation
• strti2(3S) STRTI2 - compute the inverse of a real upper or lower triangular matrix
• strtri(3S) STRTRI - compute the inverse of a real upper or lower triangular matrix A
• strtrs(3S) STRTRS - solve a triangular system of the form A * X = B or A**T * X = B,
• stzrqf(3S) STZRQF - routine is deprecated and has been replaced by routine STZRZF
• stzrzf(3S) STZRZF - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations
• system(3S) system - issue a shell command
• tmpfile(3S) tmpfile - create a temporary file
• tmpnam(3S) tmpnam, tempnam - create a name for a temporary file
• ungetc(3S) ungetc - push character back into input stream
• ungetwc(3S) ungetwc - push wchar_t character back into input stream
• vfwprintf(3S) vfwprintf: vfwprintf, vwprintf, vswprintf - wide-character formatted output of a stdarg argument list
• vfwscanf(3S) vfwscanf: vfwscanf, vwscanf, vswscanf - convert formatted wide-character input
• vprintf(3S) vprintf, vfprintf, vsnprintf, vsprintf - print formatted output of a variable argument list
• wconv(3S) wconv: towupper, towlower, wctrans, towctrans - translation character functions and extensible translation functions
• wcstod(3S) wcstod: wcstod, wcstof, wcstold - convert wide-character string to floating-point number
• wcstol(3S) wcstol, wcstoul, wcstoll, wcstoull - convert wide character string to long integer, unsigned long integer, long long integer, unsigned long long integer, respectively
• wcstring(3S) wcstring: wcscat, wscat, wcsncat, wsncat, wcscmp, wscmp, wcsncmp, wsncmp, wcscoll, wcscpy, wscpy, wcsncpy, wsncpy, wcslen, wslen, wcschr, wschr, wcsrchr, wsrchr, wcspbrk, wspbrk, wcsspn, wsspn, wscspn, wcstok, wstostr, wcswcs, wcswidth, wcwidth - wchar_t string operations and type transformation
• wctype(3S) wctype: iswalpha, iswupper, iswlower, iswdigit, iswxdigit, iswalnum, iswspace, iswpunct, iswprint, iswgraph, iswcntrl, iswascii, isphonogram, isideogram, isenglish, isnumber, isspecial, wctype, iswctype - classification functions for ASCII and supplementary code set characters, and extensible wide character classification functions
• widec(3S) widec - multibyte character I/O routines
• wmemstring(3S) wmemstring: wmemchr, wmemcmp, wmemcpy, wmemmove, wmemset - wide character array functions
• xerbla(3S) XERBLA - i an error handler for the LAPACK routines
• zbdsqr(3S) ZBDSQR - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
• zdrscl(3S) ZDRSCL - multiplie an n-element complex vector x by the real scalar 1/a
• zgbbrd(3S) ZGBBRD - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation
• zgbcon(3S) ZGBCON - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm,
• zgbequ(3S) ZGBEQU - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number
• zgbrfs(3S) ZGBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
• zgbsv(3S) 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(3S) 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(3S) ZGBTF2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
• zgbtrf(3S) ZGBTRF - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges
• zgbtrs(3S) 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(3S) 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(3S) ZGEBAL - balance a general complex matrix A
• zgebd2(3S) ZGEBD2 - reduce a complex general m by n matrix A to upper or lower real bidiagonal form B by a unitary transformation
• zgebrd(3S) ZGEBRD - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation
• zgecon(3S) 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
• zgeequ(3S) ZGEEQU - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number
• zgees(3S) 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(3S) 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(3S) ZGEEV - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• zgeevx(3S) ZGEEVX - compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors
• zgegs(3S) ZGEGS - routine is deprecated and has been replaced by routine ZGGES
• zgegv(3S) ZGEGV - routine is deprecated and has been replaced by routine ZGGEV
• zgehd2(3S) ZGEHD2 - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
• zgehrd(3S) ZGEHRD - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
• zgelq2(3S) ZGELQ2 - compute an LQ factorization of a complex m by n matrix A
• zgelqf(3S) ZGELQF - compute an LQ factorization of a complex M-by-N matrix A
• zgels(3S) 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(3S) ZGELSD - compute the minimum-norm solution to a real linear least squares problem
• zgelss(3S) ZGELSS - compute the minimum norm solution to a complex linear least squares problem
• zgelsx(3S) ZGELSX - routine is deprecated and has been replaced by routine ZGELSY
• zgelsy(3S) ZGELSY - compute the minimum-norm solution to a complex linear least squares problem
• zgeql2(3S) ZGEQL2 - compute a QL factorization of a complex m by n matrix A
• zgeqlf(3S) ZGEQLF - compute a QL factorization of a complex M-by-N matrix A
• zgeqp3(3S) ZGEQP3 - compute a QR factorization with column pivoting of a matrix A
• zgeqpf(3S) ZGEQPF - routine is deprecated and has been replaced by routine ZGEQP3
• zgeqr2(3S) ZGEQR2 - compute a QR factorization of a complex m by n matrix A
• zgeqrf(3S) ZGEQRF - compute a QR factorization of a complex M-by-N matrix A
• zgerfs(3S) ZGERFS - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
• zgerq2(3S) ZGERQ2 - compute an RQ factorization of a complex m by n matrix A
• zgerqf(3S) ZGERQF - compute an RQ factorization of a complex M-by-N matrix A
• zgesc2(3S) ZGESC2 - solve a system of linear equations A * X = scale* RHS with a general N-by-N matrix A using the LU factorization with complete pivoting computed by ZGETC2
• zgesdd(3S) ZGESDD - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method
• zgesv(3S) ZGESV - compute the solution to a complex system of linear equations A * X = B,
• zgesvd(3S) 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(3S) ZGESVX - use the LU factorization to compute the solution to a complex system of linear equations A * X = B,
• zgetc2(3S) ZGETC2 - compute an LU factorization, using complete pivoting, of the n- by-n matrix A
• zgetf2(3S) ZGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
• zgetrf(3S) ZGETRF - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
• zgetri(3S) ZGETRI - compute the inverse of a matrix using the LU factorization computed by ZGETRF
• zgetrs(3S) 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(3S) 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(3S) ZGGBAL - balance a pair of general complex matrices (A,B)
• zgges(3S) 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(3S) ZGGESX - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T),
• zggev(3S) 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(3S) 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(3S) ZGGGLM - solve a general Gauss-Markov linear model (GLM) problem
• zgghrd(3S) 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(3S) ZGGLSE - solve the linear equality-constrained least squares (LSE) problem
• zggqrf(3S) ZGGQRF - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B
• zggrqf(3S) ZGGRQF - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B
• zggsvd(3S) ZGGSVD - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B
• zggsvp(3S) 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(3S) ZGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF
• zgtrfs(3S) ZGTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution
• zgtsv(3S) ZGTSV - solve the equation A*X = B,
• zgtsvx(3S) 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(3S) ZGTTRF - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges
• zgttrs(3S) ZGTTRS - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
• zgtts2(3S) ZGTTS2 - solve one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B,
• zhbev(3S) ZHBEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• zhbevd(3S) ZHBEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• zhbevx(3S) ZHBEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A
• zhbgst(3S) ZHBGST - reduce a complex Hermitian-definite banded generalized eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,
• zhbgv(3S) 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(3S) 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(3S) 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
• zhbtrd(3S) ZHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• zhecon(3S) 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(3S) ZHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• zheevd(3S) ZHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• zheevr(3S) ZHEEVR - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix T
• zheevx(3S) ZHEEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
• zhegs2(3S) ZHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form
• zhegst(3S) ZHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form
• zhegv(3S) 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(3S) 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(3S) 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
• zherfs(3S) 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
• zhesv(3S) ZHESV - compute the solution to a complex system of linear equations A * X = B,
• zhesvx(3S) ZHESVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
• zhetd2(3S) ZHETD2 - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• zhetf2(3S) ZHETF2 - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• zhetrd(3S) ZHETRD - reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
• zhetrf(3S) ZHETRF - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• zhetri(3S) 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(3S) 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(3S) ZHGEQZ - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A - w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranformation (usually called Q) on the left and another (usually called Z) on the right
• zhpcon(3S) 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
• zhpev(3S) ZHPEV - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
• zhpevd(3S) ZHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
• zhpevx(3S) ZHPEVX - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
• zhpgst(3S) ZHPGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage
• zhpgv(3S) 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(3S) 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(3S) 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
• zhprfs(3S) ZHPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution
• zhpsv(3S) ZHPSV - compute the solution to a complex system of linear equations A * X = B,
• zhpsvx(3S) 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(3S) ZHPTRD - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation
• zhptrf(3S) ZHPTRF - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
• zhptri(3S) 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(3S) 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(3S) ZHSEIN - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H
• zhseqr(3S) 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
• zlabrd(3S) ZLABRD - reduce the first NB rows and columns of a complex general m by n matrix A to upper or lower real bidiagonal form by a unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A
• zlacgv(3S) ZLACGV - conjugate a complex vector of length N
• zlacon(3S) ZLACON - estimate the 1-norm of a square, complex matrix A
• zlacp2(3S) ZLACP2 - copie all or part of a real two-dimensional matrix A to a complex matrix B
• zlacpy(3S) ZLACPY - copie all or part of a two-dimensional matrix A to another matrix B
• zlacrm(3S) ZLACRM - perform a very simple matrix-matrix multiplication
• zlacrt(3S) ZLACRT - perform the operation ( c s )( x ) ==> ( x ) ( -s c )( y ) ( y ) where c and s are complex and the vectors x and y are complex
• zladiv(3S) ZLADIV - := X / Y, where X and Y are complex
• zlaed0(3S) ZLAED0 - the divide and conquer method, ZLAED0 computes all eigenvalues of a symmetric tridiagonal matrix which is one diagonal block of those from reducing a dense or band Hermitian matrix and corresponding eigenvectors of the dense or band matrix
• zlaed7(3S) ZLAED7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
• zlaed8(3S) ZLAED8 - merge the two sets of eigenvalues together into a single sorted set
• zlaein(3S) ZLAEIN - use inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H
• zlaesy(3S) ZLAESY - compute the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
• zlaev2(3S) ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
• zlags2(3S) ZLAGS2 - compute 2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),
• zlagtm(3S) ZLAGTM - perform a matrix-vector product of the form B := alpha * A * X + beta * B where A is a tridiagonal matrix of order N, B and X are N by NRHS matrices, and alpha and beta are real scalars, each of which may be 0., 1., or -1
• zlahef(3S) ZLAHEF - compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
• zlahqr(3S) ZLAHQR - i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
• zlahrd(3S) ZLAHRD - reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
• zlaic1(3S) ZLAIC1 - applie one step of incremental condition estimation in its simplest version
• zlals0(3S) ZLALS0 - applie back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach
• zlalsa(3S) ZLALSA - i an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.)
• zlalsd(3S) ZLALSD - use the singular value decomposition of A to solve the least squares problem of finding X to minimize the Euclidean norm of each column of A*X-B, where A is N-by-N upper bidiagonal, and X and B are N- by-NRHS
• zlangb(3S) ZLANGB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
• zlange(3S) ZLANGE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
• zlangt(3S) ZLANGT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
• zlanhb(3S) ZLANHB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
• zlanhe(3S) ZLANHE - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
• zlanhp(3S) ZLANHP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
• zlanhs(3S) ZLANHS - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
• zlanht(3S) ZLANHT - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
• zlansb(3S) ZLANSB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
• zlansp(3S) ZLANSP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
• zlansy(3S) ZLANSY - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
• zlantb(3S) ZLANTB - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
• zlantp(3S) ZLANTP - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
• zlantr(3S) ZLANTR - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
• zlapll(3S) ZLAPLL - two column vectors X and Y, let A = ( X Y )
• zlapmt(3S) ZLAPMT - rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
• zlaqgb(3S) ZLAQGB - equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
• zlaqge(3S) ZLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
• zlaqhb(3S) ZLAQHB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• zlaqhe(3S) ZLAQHE - equilibrate a Hermitian matrix A using the scaling factors in the vector S
• zlaqhp(3S) ZLAQHP - equilibrate a Hermitian matrix A using the scaling factors in the vector S
• zlaqp2(3S) ZLAQP2 - compute a QR factorization with column pivoting of the block A(OFFSET+1:M,1:N)
• zlaqps(3S) ZLAQPS - compute a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3
• zlaqsb(3S) ZLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S
• zlaqsp(3S) ZLAQSP - equilibrate a symmetric matrix A using the scaling factors in the vector S
• zlaqsy(3S) ZLAQSY - equilibrate a symmetric matrix A using the scaling factors in the vector S
• zlar1v(3S) ZLAR1V - compute the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I
• zlar2v(3S) ZLAR2V - applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
• zlarcm(3S) ZLARCM - perform a very simple matrix-matrix multiplication
• zlarf(3S) ZLARF - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
• zlarfb(3S) ZLARFB - applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right
• zlarfg(3S) ZLARFG - generate a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I
• zlarft(3S) ZLARFT - form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
• zlarfx(3S) ZLARFX - applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
• zlargv(3S) ZLARGV - generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
• zlarnv(3S) ZLARNV - return a vector of n random complex numbers from a uniform or normal distribution
• zlarrv(3S) ZLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the eigenvalues of L D L^T
• zlartg(3S) ZLARTG - generate a plane rotation so that [ CS SN ] [ F ] [ R ] [ __ ]
• zlartv(3S) ZLARTV - applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
• zlarz(3S) ZLARZ - applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
• zlarzb(3S) 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(3S) 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
• zlascl(3S) ZLASCL - multiplie the M by N complex matrix A by the real scalar CTO/CFROM
• zlaset(3S) ZLASET - initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
• zlasr(3S) ZLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side ) where A is an m by n complex matrix and P is an orthogonal matrix,
• zlassq(3S) ZLASSQ - return the values scl and ssq such that ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
• zlaswp(3S) ZLASWP - perform a series of row interchanges on the matrix A
• zlasyf(3S) ZLASYF - compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• zlatbs(3S) ZLATBS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• zlatdf(3S) ZLATDF - compute the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the norm of x is as large as possible
• zlatps(3S) ZLATPS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• zlatrd(3S) ZLATRD - reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
• zlatrs(3S) ZLATRS - solve one of the triangular systems A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
• zlatrz(3S) ZLATRZ - factor the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices
• zlatzm(3S) ZLATZM - routine is deprecated and has been replaced by routine ZUNMRZ
• zlauu2(3S) ZLAUU2 - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• zlauum(3S) ZLAUUM - compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
• zpbcon(3S) 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
• zpbequ(3S) ZPBEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)
• zpbrfs(3S) ZPBRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
• zpbstf(3S) ZPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
• zpbsv(3S) ZPBSV - compute the solution to a complex system of linear equations A * X = B,
• zpbsvx(3S) 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(3S) ZPBTF2 - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
• zpbtrf(3S) ZPBTRF - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
• zpbtrs(3S) 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
• zpocon(3S) 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
• zpoequ(3S) ZPOEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm)
• zporfs(3S) ZPORFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite,
• zposv(3S) ZPOSV - compute the solution to a complex system of linear equations A * X = B,
• zposvx(3S) 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(3S) ZPOTF2 - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
• zpotrf(3S) ZPOTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A
• zpotri(3S) 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(3S) 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
• zppcon(3S) 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
• zppequ(3S) ZPPEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
• zpprfs(3S) ZPPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution
• zppsv(3S) ZPPSV - compute the solution to a complex system of linear equations A * X = B,
• zppsvx(3S) 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(3S) ZPPTRF - compute the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format
• zpptri(3S) 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(3S) 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
• zpsldlt(3S) ZPSLDLT_Destroy, ZPSLDLT_ExtractPerm, ZPSLDLT_Factor, ZPSLDLT_FactorOOC, ZPSLDLT_OOCLimit, ZPSLDLT_OOCPath, ZPSLDLT_Ordering, ZPSLDLT_Preprocess, ZPSLDLT_PreprocessZ, ZPSLDLT_Solve, ZPSLDLT_SolveM, ZPSLDLT_Storage - Parallel sparse symmetric solver for linear systems of complex equations
• zpsldu(3S) ZPSLDU_Destroy, ZPSLDU_ExtractPerm, ZPSLDU_Factor, ZPSLDU_FactorOOC, ZPSLDU_OOCLimit, ZPSLDU_OOCPath, ZPSLDU_Ordering, ZPSLDU_Preprocess, ZPSLDU_PreprocessZ, ZPSLDU_Solve, ZPSLDU_SolveM, ZPSLDU_Storage - Parallel sparse unsymmetric solver for linear systems of complex equations
• zptcon(3S) 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(3S) 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(3S) ZPTRFS - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution
• zptsv(3S) 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(3S) 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(3S) ZPTTRF - compute the L*D*L' factorization of a complex Hermitian positive definite tridiagonal matrix A
• zpttrs(3S) 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(3S) 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
• zspcon(3S) ZSPCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
• zsprfs(3S) ZSPRFS - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution
• zspsv(3S) ZSPSV - compute the solution to a complex system of linear equations A * X = B,
• zspsvx(3S) 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(3S) ZSPTRF - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method
• zsptri(3S) 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(3S) 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(3S) ZSTEDC - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
• zstegr(3S) ZSTEGR - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T
• zstein(3S) ZSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
• zsteqr(3S) ZSTEQR - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method
• zsycon(3S) 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
• zsyrfs(3S) 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
• zsysv(3S) ZSYSV - compute the solution to a complex system of linear equations A * X = B,
• zsysvx(3S) ZSYSVX - use the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B,
• zsytf2(3S) ZSYTF2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• zsytrf(3S) ZSYTRF - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
• zsytri(3S) 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(3S) 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(3S) ZTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
• ztbrfs(3S) ZTBRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
• ztbtrs(3S) ZTBTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ztgevc(3S) ZTGEVC - compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B)
• ztgex2(3S) ZTGEX2 - swap adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22)
• ztgexc(3S) 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(3S) 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(3S) ZTGSJA - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B
• ztgsna(3S) ZTGSNA - estimate reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a matrix pair (A, B)
• ztgsy2(3S) ZTGSY2 - solve the generalized Sylvester equation A * R - L * B = scale * C (1) D * R - L * E = scale * F using Level 1 and 2 BLAS, where R and L are unknown M-by-N matrices,
• ztgsyl(3S) ZTGSYL - solve the generalized Sylvester equation
• ztpcon(3S) ZTPCON - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm
• ztprfs(3S) ZTPRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
• ztptri(3S) ZTPTRI - compute the inverse of a complex upper or lower triangular matrix A stored in packed format
• ztptrs(3S) ZTPTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ztrcon(3S) ZTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm
• ztrevc(3S) ZTREVC - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
• ztrexc(3S) 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
• ztrid(3S) ZTRID - compute the solution to a complex system of linear equations A*x = b, where A is an N-by-N tridiagonal matrix, and x and b are vectors of length N
• ztrrfs(3S) ZTRRFS - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
• ztrsen(3S) 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
• ztrsna(3S) 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)
• ztrsyl(3S) ZTRSYL - solve the complex Sylvester matrix equation
• ztrti2(3S) ZTRTI2 - compute the inverse of a complex upper or lower triangular matrix
• ztrtri(3S) ZTRTRI - compute the inverse of a complex upper or lower triangular matrix A
• ztrtrs(3S) ZTRTRS - solve a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
• ztzrqf(3S) ZTZRQF - routine is deprecated and has been replaced by routine ZTZRZF
• ztzrzf(3S) ZTZRZF - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations
• zung2l(3S) ZUNG2L - generate an m by n complex matrix Q with orthonormal columns,
• zung2r(3S) ZUNG2R - generate an m by n complex matrix Q with orthonormal columns,
• zungbr(3S) 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(3S) 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(3S) ZUNGL2 - generate an m-by-n complex matrix Q with orthonormal rows,
• zunglq(3S) ZUNGLQ - generate an M-by-N complex matrix Q with orthonormal rows,
• zungql(3S) ZUNGQL - generate an M-by-N complex matrix Q with orthonormal columns,
• zungqr(3S) ZUNGQR - generate an M-by-N complex matrix Q with orthonormal columns,
• zungr2(3S) ZUNGR2 - generate an m by n complex matrix Q with orthonormal rows,
• zungrq(3S) ZUNGRQ - generate an M-by-N complex matrix Q with orthonormal rows,
• zungtr(3S) 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
• zunm2l(3S) ZUNM2L - 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',
• zunm2r(3S) 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(3S) ZUNMBR - VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmhr(3S) ZUNMHR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunml2(3S) 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(3S) ZUNMLQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmql(3S) ZUNMQL - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmqr(3S) ZUNMQR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmr2(3S) 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',
• zunmr3(3S) ZUNMR3 - 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(3S) ZUNMRQ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmrz(3S) ZUNMRZ - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zunmtr(3S) ZUNMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
• zupgtr(3S) 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(3S) ZUPMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'