NAME slassq.f – SYNOPSIS Functions/Subroutines subroutine slassq (N, X, INCX, SCALE, SUMSQ) SLASSQ updates a sum of squares represented in scaled form. Function/Subroutine Documentation subroutine slassq (integerN, real, dimension( * )X, integerINCX, realSCALE, realSUMSQ) SLASSQ updates a sum of squares represented in scaled form. Purpose: SLASSQ returns the values scl and smsq such that (…
NAME slasrt.f – SYNOPSIS Functions/Subroutines subroutine slasrt (ID, N, D, INFO) SLASRT sorts numbers in increasing or decreasing order. Function/Subroutine Documentation subroutine slasrt (characterID, integerN, real, dimension( * )D, integerINFO) SLASRT sorts numbers in increasing or decreasing order. Purpose: Sort the numbers in D in increasing order (if ID = ‘I’) or in decreasing order…
NAME slasr.f – SYNOPSIS Functions/Subroutines subroutine slasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA) SLASR applies a sequence of plane rotations to a general rectangular matrix. Function/Subroutine Documentation subroutine slasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, real, dimension( * )C, real, dimension( * )S, real, dimension( lda, * )A, integerLDA) SLASR applies a sequence…
NAME slasq6.f – SYNOPSIS Functions/Subroutines subroutine slasq6 (I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DNM1, DNM2) SLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. Function/Subroutine Documentation subroutine slasq6 (integerI0, integerN0, real, dimension( * )Z, integerPP, realDMIN, realDMIN1, realDMIN2, realDN, realDNM1, realDNM2) SLASQ6 computes one dqd transform in ping-pong form….
NAME slasq5.f – SYNOPSIS Functions/Subroutines subroutine slasq5 (I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, IEEE, EPS) SLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. Function/Subroutine Documentation subroutine slasq5 (integerI0, integerN0, real, dimension( * )Z, integerPP, realTAU, realSIGMA, realDMIN, realDMIN1, realDMIN2, realDN, realDNM1, realDNM2, logicalIEEE, realEPS)…
NAME slasq4.f – SYNOPSIS Functions/Subroutines subroutine slasq4 (I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1, DN2, TAU, TTYPE, G) SLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr. Function/Subroutine Documentation subroutine slasq4 (integerI0, integerN0, real, dimension( * )Z, integerPP, integerN0IN, realDMIN, realDMIN1, realDMIN2,…
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,…