Section 3: library functions
slalsd.f – Synopsis Functions/Subroutines subroutine slalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, IWORK, INFO) SLALSD uses the singular value decomposition of A to solve the least squares problem. Function/Subroutine Documentation subroutine slalsd (characterUPLO, integerSMLSIZ, integerN, integerNRHS, real, dimension( * )D, real, dimension( * )E, real, dimension( ldb, * )B, integerLDB,…
slalsa.f – Synopsis Functions/Subroutines subroutine slalsa (ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) SLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. Function/Subroutine Documentation subroutine slalsa (integerICOMPQ, integerSMLSIZ, integerN, integerNRHS, real,…
slals0.f – Synopsis Functions/Subroutines subroutine slals0 (ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO) SLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. Function/Subroutine Documentation subroutine slals0 (integerICOMPQ,…
slaln2.f – Synopsis Functions/Subroutines subroutine slaln2 (LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, LDB, WR, WI, X, LDX, SCALE, XNORM, INFO) SLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. Function/Subroutine Documentation subroutine slaln2 (logicalLTRANS, integerNA, integerNW, realSMIN, realCA, real, dimension( lda, * )A, integerLDA, realD1, realD2,…
slaisnan.f – Synopsis Functions/Subroutines LOGICAL function slaisnan (SIN1, SIN2) SLAISNAN tests input for NaN by comparing two arguments for inequality. Function/Subroutine Documentation LOGICAL function slaisnan (realSIN1, realSIN2) SLAISNAN tests input for NaN by comparing two arguments for inequality. Purpose: This routine is not for general use. It exists solely to avoid over-optimization in SISNAN. SLAISNAN…
slaic1.f – Synopsis Functions/Subroutines subroutine slaic1 (JOB, J, X, SEST, W, GAMMA, SESTPR, S, C) SLAIC1 applies one step of incremental condition estimation. Function/Subroutine Documentation subroutine slaic1 (integerJOB, integerJ, real, dimension( j )X, realSEST, real, dimension( j )W, realGAMMA, realSESTPR, realS, realC) SLAIC1 applies one step of incremental condition estimation. Purpose: SLAIC1 applies one step…
slahrd.f – Synopsis Functions/Subroutines subroutine slahrd (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) SLAHRD reduces the first nb columns of a general rectangular matrix A so that elements below the k-th subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. Function/Subroutine…
slahr2.f – Synopsis Functions/Subroutines subroutine slahr2 (N, K, NB, A, LDA, TAU, T, LDT, Y, LDY) SLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of…
slahqr.f – Synopsis Functions/Subroutines subroutine slahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ, Z, LDZ, INFO) SLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. Function/Subroutine Documentation subroutine slahqr (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, real, dimension( ldh, * )H, integerLDH, real, dimension( *…
slagv2.f – Synopsis Functions/Subroutines subroutine slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. Function/Subroutine Documentation subroutine slagv2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( 2 )ALPHAR,…
slagts.f – Synopsis Functions/Subroutines subroutine slagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO) SLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf. Function/Subroutine Documentation subroutine slagts (integerJOB, integerN, real, dimension( *…
slagtm.f – Synopsis Functions/Subroutines subroutine slagtm (TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB) SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. Function/Subroutine…
slagtf.f – Synopsis Functions/Subroutines subroutine slagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO) SLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges. Function/Subroutine Documentation subroutine slagtf (integerN, real, dimension( * )A, realLAMBDA, real, dimension( * )B,…
slags2.f – Synopsis Functions/Subroutines subroutine slags2 (UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ) SLAGS2 computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel. Function/Subroutine Documentation subroutine slags2 (logicalUPPER, realA1, realA2,…
slag2d.f – Synopsis Functions/Subroutines subroutine slag2d (M, N, SA, LDSA, A, LDA, INFO) SLAG2D converts a single precision matrix to a double precision matrix. Function/Subroutine Documentation subroutine slag2d (integerM, integerN, real, dimension( ldsa, * )SA, integerLDSA, double precision, dimension( lda, * )A, integerLDA, integerINFO) SLAG2D converts a single precision matrix to a double precision matrix….
slag2.f – Synopsis Functions/Subroutines subroutine slag2 (A, LDA, B, LDB, SAFMIN, SCALE1, SCALE2, WR1, WR2, WI) SLAG2 computes the eigenvalues of a 2-by-2 generalized eigenvalue problem, with scaling as necessary to avoid over-/underflow. Function/Subroutine Documentation subroutine slag2 (real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realSAFMIN, realSCALE1, realSCALE2, realWR1, realWR2, realWI)…
slaexc.f – Synopsis Functions/Subroutines subroutine slaexc (WANTQ, N, T, LDT, Q, LDQ, J1, N1, N2, WORK, INFO) SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. Function/Subroutine Documentation subroutine slaexc (logicalWANTQ, integerN, real, dimension( ldt, * )T, integerLDT, real, dimension( ldq, * )Q, integerLDQ,…
slaev2.f – Synopsis Functions/Subroutines subroutine slaev2 (A, B, C, RT1, RT2, CS1, SN1) SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1) SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric…
slaein.f – Synopsis Functions/Subroutines subroutine slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO) SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Function/Subroutine Documentation subroutine slaein (logicalRIGHTV, logicalNOINIT, integerN, real, dimension( ldh, * )H, integerLDH, realWR, realWI, real, dimension(…
slaeda.f – Synopsis Functions/Subroutines subroutine slaeda (N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO) SLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. Function/Subroutine Documentation subroutine slaeda (integerN, integerTLVLS, integerCURLVL, integerCURPBM, integer, dimension( * )PRMPTR,…