Section 3: library functions
NAME slasq3.f – SYNOPSIS Functions/Subroutines subroutine slasq3 (I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, DN2, G, TAU) SLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. Function/Subroutine Documentation subroutine slasq3 (integerI0, integerN0, real, dimension( * )Z, integerPP, realDMIN, realSIGMA, realDESIG, realQMAX,…
NAME slasq2.f – SYNOPSIS Functions/Subroutines subroutine slasq2 (N, Z, INFO) SLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. Function/Subroutine Documentation subroutine slasq2 (integerN, real, dimension( * )Z, integerINFO) SLASQ2 computes all the eigenvalues of the symmetric…
NAME slasq1.f – SYNOPSIS Functions/Subroutines subroutine slasq1 (N, D, E, WORK, INFO) SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. Function/Subroutine Documentation subroutine slasq1 (integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( * )WORK, integerINFO) SLASQ1 computes the singular values of a real square bidiagonal matrix….
NAME 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…
NAME 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…
NAME slasdq.f – SYNOPSIS Functions/Subroutines subroutine 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 Documentation subroutine slasdq (characterUPLO, integerSQRE, integerN, integerNCVT, integerNRU, integerNCC, real, dimension( * )D,…
NAME slasda.f – SYNOPSIS Functions/Subroutines subroutine 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 Documentation…
NAME slasd8.f – SYNOPSIS Functions/Subroutines subroutine 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 Documentation subroutine slasd8 (integerICOMPQ, integerK, real,…
NAME 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…
NAME 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…
NAME 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,…
NAME 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,…
NAME 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…
NAME 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,…
NAME 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, *…
NAME 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,…
NAME 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 *…
NAME 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…
NAME 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].On…
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…