Section 3: library functions
slaset.f – Synopsis Functions/Subroutines subroutine slaset (UPLO, M, N, ALPHA, BETA, A, LDA) SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. Function/Subroutine Documentation subroutine slaset (characterUPLO, integerM, integerN, realALPHA, realBETA, real, dimension( lda, * )A, integerLDA) SLASET initializes the off-diagonal elements and the diagonal elements of a matrix…
slasdt.f – Synopsis Functions/Subroutines subroutine slasdt (N, LVL, ND, INODE, NDIML, NDIMR, MSUB) SLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. Function/Subroutine Documentation subroutine slasdt (integerN, integerLVL, integerND, integer, dimension( * )INODE, integer, dimension( * )NDIML, integer, dimension( * )NDIMR, integerMSUB) SLASDT creates a tree of subproblems for bidiagonal…
slasdq.f – SynopsisFunctions/Subroutinessubroutine slasdq (UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO) SLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. Function/Subroutine Documentationsubroutine slasdq (characterUPLO, integerSQRE, integerN, integerNCVT, integerNRU, integerNCC, real, dimension( * )D, real, dimension( * )E,…
slasda.f – SynopsisFunctions/Subroutinessubroutine slasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. Function/Subroutine Documentationsubroutine slasda (integerICOMPQ, integerSMLSIZ,…
slasd8.f – SynopsisFunctions/Subroutinessubroutine slasd8 (ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO) SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. Function/Subroutine Documentationsubroutine slasd8 (integerICOMPQ, integerK, real, dimension( * )D, real,…
slasd7.f – Synopsis Functions/Subroutines subroutine slasd7 (ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S, INFO) SLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of…
slasd6.f – Synopsis Functions/Subroutines subroutine slasd6 (ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, IWORK, INFO) SLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc….
slasd5.f – Synopsis Functions/Subroutines subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK) SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA,…
slasd4.f – Synopsis Functions/Subroutines subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension(…
slasd3.f – Synopsis Functions/Subroutines subroutine slasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO) SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix…
slasd2.f – Synopsis Functions/Subroutines subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO) SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real,…
slasd1.f – Synopsis Functions/Subroutines subroutine slasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO) SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd1 (integerNL, integerNR, integerSQRE, real, dimension( * )D, realALPHA, realBETA, real, dimension( ldu, * )U,…
slasd0.f – Synopsis Functions/Subroutines subroutine slasd0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO) SLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd0 (integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real,…
slascl2.f – Synopsis Functions/Subroutines subroutine slascl2 (M, N, D, X, LDX) SLASCL2 performs diagonal scaling on a vector. Function/Subroutine Documentation subroutine slascl2 (integerM, integerN, real, dimension( * )D, real, dimension( ldx, * )X, integerLDX) SLASCL2 performs diagonal scaling on a vector. Purpose: SLASCL2 performs a diagonal scaling on a vector: x <– D * x…
slascl.f – Synopsis Functions/Subroutines subroutine slascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO) SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. Function/Subroutine Documentation subroutine slascl (characterTYPE, integerKL, integerKU, realCFROM, realCTO, integerM, integerN, real, dimension( lda, * )A, integerLDA, integerINFO) SLASCL multiplies a general rectangular matrix by a…
slas2.f – Synopsis Functions/Subroutines subroutine slas2 (F, G, H, SSMIN, SSMAX) SLAS2 computes singular values of a 2-by-2 triangular matrix. Function/Subroutine Documentation subroutine slas2 (realF, realG, realH, realSSMIN, realSSMAX) SLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: SLAS2 computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H…
slarzt.f – Synopsis Functions/Subroutines subroutine slarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) SLARZT forms the triangular factor T of a block reflector H = I – vtvH. Function/Subroutine Documentation subroutine slarzt (characterDIRECT, characterSTOREV, integerN, integerK, real, dimension( ldv, * )V, integerLDV, real, dimension( * )TAU, real, dimension( ldt, * )T, integerLDT) SLARZT…
slarzb.f – Synopsis Functions/Subroutines subroutine slarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) SLARZB applies a block reflector or its transpose to a general matrix. Function/Subroutine Documentation subroutine slarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, real, dimension( ldv, * )V, integerLDV, real, dimension( ldt,…
slarz.f – Synopsis Functions/Subroutines subroutine slarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentation subroutine slarz (characterSIDE, integerM, integerN, integerL, real, dimension( * )V, integerINCV, realTAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK) SLARZ applies…
slaruv.f – Synopsis Functions/Subroutines subroutine slaruv (ISEED, N, X) SLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentation subroutine slaruv (integer, dimension( 4 )ISEED, integerN, real, dimension( n )X) SLARUV returns a vector of n random real numbers from a uniform distribution. Purpose: SLARUV returns a vector of n…