Section 3: library functions
NAME dlasdq.f – SYNOPSIS Functions/Subroutines subroutine dlasdq (UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO) DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. Function/Subroutine Documentation subroutine dlasdq (characterUPLO, integerSQRE, integerN, integerNCVT, integerNRU, integerNCC, double precision, dimension( *…
NAME dlasda.f – SYNOPSIS Functions/Subroutines subroutine dlasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO) DLASDA 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 dlasd8.f – SYNOPSIS Functions/Subroutines subroutine dlasd8 (ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO) DLASD8 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 dlasd8 (integerICOMPQ, integerK, double…
NAME dlasd7.f – SYNOPSIS Functions/Subroutines subroutine dlasd7 (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) DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size…
NAME dlasd6.f – SYNOPSIS Functions/Subroutines subroutine dlasd6 (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) DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by…
NAME dlasd5.f – SYNOPSIS Functions/Subroutines subroutine dlasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK) DLASD5 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 dlasd5 (integerI, double precision, dimension( 2 )D, double precision, dimension( 2 )Z, double precision, dimension(…
NAME dlasd4.f – SYNOPSIS Functions/Subroutines subroutine dlasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc. Function/Subroutine Documentation subroutine dlasd4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( *…
NAME dlasd3.f – SYNOPSIS Functions/Subroutines subroutine dlasd3 (NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO) DLASD3 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 dlasd2.f – SYNOPSIS Functions/Subroutines subroutine dlasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO) DLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc. Function/Subroutine Documentation subroutine dlasd2 (integerNL, integerNR, integerSQRE, integerK,…
NAME dlasd1.f – SYNOPSIS Functions/Subroutines subroutine dlasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO) DLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc. Function/Subroutine Documentation subroutine dlasd1 (integerNL, integerNR, integerSQRE, double precision, dimension( * )D, double precisionALPHA, double precisionBETA, double…
NAME dlasd0.f – SYNOPSIS Functions/Subroutines subroutine dlasd0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO) DLASD0 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 dlasd0 (integerN, integerSQRE, double precision, dimension( * )D, double precision, dimension(…
NAME dlascl2.f – SYNOPSIS Functions/Subroutines subroutine dlascl2 (M, N, D, X, LDX) DLASCL2 performs diagonal scaling on a vector. Function/Subroutine Documentation subroutine dlascl2 (integerM, integerN, double precision, dimension( * )D, double precision, dimension( ldx, * )X, integerLDX) DLASCL2 performs diagonal scaling on a vector. Purpose: DLASCL2 performs a diagonal scaling on a vector: x <–…
NAME dlascl.f – SYNOPSIS Functions/Subroutines subroutine dlascl (TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO) DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. Function/Subroutine Documentation subroutine dlascl (characterTYPE, integerKL, integerKU, double precisionCFROM, double precisionCTO, integerM, integerN, double precision, dimension( lda, * )A, integerLDA, integerINFO) DLASCL multiplies a general…
NAME dlas2.f – SYNOPSIS Functions/Subroutines subroutine dlas2 (F, G, H, SSMIN, SSMAX) DLAS2 computes singular values of a 2-by-2 triangular matrix. Function/Subroutine Documentation subroutine dlas2 (double precisionF, double precisionG, double precisionH, double precisionSSMIN, double precisionSSMAX) DLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: DLAS2 computes the singular values of the 2 – by…
NAME dlarzt.f – SYNOPSIS Functions/Subroutines subroutine dlarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT) DLARZT forms the triangular factor T of a block reflector H = I – vtvH. Function/Subroutine Documentation subroutine dlarzt (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt,…
NAME dlarzb.f – SYNOPSIS Functions/Subroutines subroutine dlarzb (SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK) DLARZB applies a block reflector or its transpose to a general matrix. Function/Subroutine Documentation subroutine dlarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, double precision, dimension( ldv, * )V, integerLDV, double…
NAME dlarz.f – SYNOPSIS Functions/Subroutines subroutine dlarz (SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK) DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Function/Subroutine Documentation subroutine dlarz (characterSIDE, integerM, integerN, integerL, double precision, dimension( * )V, integerINCV, double precisionTAU, double precision, dimension( ldc, * )C, integerLDC, double precision,…
NAME dlaruv.f – SYNOPSIS Functions/Subroutines subroutine dlaruv (ISEED, N, X) DLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentation subroutine dlaruv (integer, dimension( 4 )ISEED, integerN, double precision, dimension( n )X) DLARUV returns a vector of n random real numbers from a uniform distribution. Purpose: DLARUV returns a vector…
NAME dlartv.f – SYNOPSIS Functions/Subroutines subroutine dlartv (N, X, INCX, Y, INCY, C, S, INCC) DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors. Function/Subroutine Documentation subroutine dlartv (integerN, double precision, dimension( * )X, integerINCX, double precision, dimension( * )Y, integerINCY, double precision,…
NAME dlartgs.f – SYNOPSIS Functions/Subroutines subroutine dlartgs (X, Y, SIGMA, CS, SN) DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem. Function/Subroutine Documentation subroutine dlartgs (double precisionX, double precisionY, double precisionSIGMA, double precisionCS, double precisionSN) DLARTGS generates a plane rotation designed to introduce a bulge…