Section 3: library functions
dlasda.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasda (integerICOMPQ, integerSMLSIZ,…
dlasd8.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd8 (integerICOMPQ, integerK, double precision, dimension( * )D,…
dlasd7.f – SynopsisFunctions/Subroutinessubroutine 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 of the problem….
dlasd6.f – SynopsisFunctions/Subroutinessubroutine 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 sbdsdc. Function/Subroutine Documentationsubroutine…
dlasd5.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd5 (integerI, double precision, dimension( 2 )D, double precision, dimension( 2 )Z, double precision, dimension( 2 )DELTA, double precisionRHO,…
dlasd4.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension(…
dlasd3.f – SynopsisFunctions/Subroutinessubroutine 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 matrix multiplication. Used…
dlasd2.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd2 (integerNL, integerNR, integerSQRE, integerK, double precision, dimension( *…
dlasd1.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd1 (integerNL, integerNR, integerSQRE, double precision, dimension( * )D, double precisionALPHA, double precisionBETA, double precision, dimension( ldu, *…
dlasd0.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlasd0 (integerN, integerSQRE, double precision, dimension( * )D, double precision, dimension( * )E, double precision,…
dlascl2.f – SynopsisFunctions/Subroutinessubroutine dlascl2 (M, N, D, X, LDX) DLASCL2 performs diagonal scaling on a vector. Function/Subroutine Documentationsubroutine 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 <– D * x where the…
dlascl.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlascl (characterTYPE, integerKL, integerKU, double precisionCFROM, double precisionCTO, integerM, integerN, double precision, dimension( lda, * )A, integerLDA, integerINFO)DLASCL multiplies a general rectangular matrix by a real…
dlas2.f – SynopsisFunctions/Subroutinessubroutine dlas2 (F, G, H, SSMIN, SSMAX) DLAS2 computes singular values of a 2-by-2 triangular matrix. Function/Subroutine Documentationsubroutine 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-2 matrix [ F G ] [ 0…
dlarzt.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarzt (characterDIRECT, characterSTOREV, integerN, integerK, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( * )TAU, double precision, dimension( ldt, * )T, integerLDT)DLARZT forms…
dlarzb.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarzb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, integerL, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldt, *…
dlarz.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlarz (characterSIDE, integerM, integerN, integerL, double precision, dimension( * )V, integerINCV, double precisionTAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK)DLARZ applies…
dlaruv.f – SynopsisFunctions/Subroutinessubroutine dlaruv (ISEED, N, X) DLARUV returns a vector of n random real numbers from a uniform distribution. Function/Subroutine Documentationsubroutine 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 of n random real numbers…
dlartv.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlartv (integerN, double precision, dimension( * )X, integerINCX, double precision, dimension( * )Y, integerINCY, double precision, dimension( * )C, double…
dlartgs.f – SynopsisFunctions/Subroutinessubroutine 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 Documentationsubroutine dlartgs (double precisionX, double precisionY, double precisionSIGMA, double precisionCS, double precisionSN)DLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for…
dlartgp.f – SynopsisFunctions/Subroutinessubroutine dlartgp (F, G, CS, SN, R) DLARTGP generates a plane rotation so that the diagonal is nonnegative. Function/Subroutine Documentationsubroutine dlartgp (double precisionF, double precisionG, double precisionCS, double precisionSN, double precisionR)DLARTGP generates a plane rotation so that the diagonal is nonnegative. Purpose: DLARTGP generates a plane rotation so that [ CS SN ]…