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488 lines
16 KiB
488 lines
16 KiB
/* dlasda.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__0 = 0; |
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static doublereal c_b11 = 0.; |
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static doublereal c_b12 = 1.; |
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static integer c__1 = 1; |
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static integer c__2 = 2; |
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|
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/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, |
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integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer |
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*ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, |
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doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, |
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integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, |
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doublereal *s, doublereal *work, integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, |
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difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, |
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poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, |
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z_dim1, z_offset, i__1, i__2; |
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/* Builtin functions */ |
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integer pow_ii(integer *, integer *); |
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/* Local variables */ |
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integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, |
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vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; |
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doublereal beta; |
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integer idxq, nlvl; |
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doublereal alpha; |
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integer inode, ndiml, ndimr, idxqi, itemp; |
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, |
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doublereal *, integer *); |
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integer sqrei; |
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extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, |
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integer *, doublereal *, doublereal *, doublereal *, doublereal *, |
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doublereal *, integer *, integer *, integer *, integer *, |
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integer *, doublereal *, integer *, doublereal *, doublereal *, |
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doublereal *, doublereal *, integer *, doublereal *, doublereal *, |
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doublereal *, integer *, integer *); |
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integer nwork1, nwork2; |
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extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer |
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*, integer *, integer *, doublereal *, doublereal *, doublereal *, |
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integer *, doublereal *, integer *, doublereal *, integer *, |
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doublereal *, integer *), dlasdt_(integer *, integer *, |
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integer *, integer *, integer *, integer *, integer *), dlaset_( |
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char *, integer *, integer *, doublereal *, doublereal *, |
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doublereal *, integer *), xerbla_(char *, integer *); |
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integer smlszp; |
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/* -- LAPACK auxiliary routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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|
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/* Purpose */ |
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/* ======= */ |
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/* Using a divide and conquer approach, DLASDA computes the singular */ |
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/* value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */ |
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/* B with diagonal D and offdiagonal E, where M = N + SQRE. The */ |
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/* algorithm computes the singular values in the SVD B = U * S * VT. */ |
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/* The orthogonal matrices U and VT are optionally computed in */ |
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/* compact form. */ |
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/* A related subroutine, DLASD0, computes the singular values and */ |
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/* the singular vectors in explicit form. */ |
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/* Arguments */ |
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/* ========= */ |
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/* ICOMPQ (input) INTEGER */ |
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/* Specifies whether singular vectors are to be computed */ |
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/* in compact form, as follows */ |
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/* = 0: Compute singular values only. */ |
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/* = 1: Compute singular vectors of upper bidiagonal */ |
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/* matrix in compact form. */ |
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/* SMLSIZ (input) INTEGER */ |
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/* The maximum size of the subproblems at the bottom of the */ |
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/* computation tree. */ |
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/* N (input) INTEGER */ |
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/* The row dimension of the upper bidiagonal matrix. This is */ |
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/* also the dimension of the main diagonal array D. */ |
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/* SQRE (input) INTEGER */ |
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/* Specifies the column dimension of the bidiagonal matrix. */ |
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/* = 0: The bidiagonal matrix has column dimension M = N; */ |
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/* = 1: The bidiagonal matrix has column dimension M = N + 1. */ |
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/* D (input/output) DOUBLE PRECISION array, dimension ( N ) */ |
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/* On entry D contains the main diagonal of the bidiagonal */ |
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/* matrix. On exit D, if INFO = 0, contains its singular values. */ |
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/* E (input) DOUBLE PRECISION array, dimension ( M-1 ) */ |
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/* Contains the subdiagonal entries of the bidiagonal matrix. */ |
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/* On exit, E has been destroyed. */ |
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/* U (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */ |
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */ |
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/* singular vector matrices of all subproblems at the bottom */ |
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/* level. */ |
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/* LDU (input) INTEGER, LDU = > N. */ |
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/* The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */ |
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/* GIVNUM, and Z. */ |
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/* VT (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */ |
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right */ |
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/* singular vector matrices of all subproblems at the bottom */ |
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/* level. */ |
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/* K (output) INTEGER array, */ |
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/* dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */ |
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/* If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */ |
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/* secular equation on the computation tree. */ |
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/* DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ), */ |
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/* where NLVL = floor(log_2 (N/SMLSIZ))). */ |
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/* DIFR (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */ |
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/* dimension ( N ) if ICOMPQ = 0. */ |
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/* If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */ |
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/* record distances between singular values on the I-th */ |
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/* level and singular values on the (I -1)-th level, and */ |
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/* DIFR(1:N, 2 * I ) contains the normalizing factors for */ |
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/* the right singular vector matrix. See DLASD8 for details. */ |
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/* Z (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, NLVL ) if ICOMPQ = 1 and */ |
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/* dimension ( N ) if ICOMPQ = 0. */ |
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/* The first K elements of Z(1, I) contain the components of */ |
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/* the deflation-adjusted updating row vector for subproblems */ |
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/* on the I-th level. */ |
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/* POLES (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */ |
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */ |
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/* POLES(1, 2*I) contain the new and old singular values */ |
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/* involved in the secular equations on the I-th level. */ |
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/* GIVPTR (output) INTEGER array, */ |
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/* dimension ( N ) if ICOMPQ = 1, and not referenced if */ |
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/* ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */ |
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/* the number of Givens rotations performed on the I-th */ |
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/* problem on the computation tree. */ |
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/* GIVCOL (output) INTEGER array, */ |
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/* dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */ |
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/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ |
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/* GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */ |
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/* of Givens rotations performed on the I-th level on the */ |
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/* computation tree. */ |
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/* LDGCOL (input) INTEGER, LDGCOL = > N. */ |
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/* The leading dimension of arrays GIVCOL and PERM. */ |
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/* PERM (output) INTEGER array, */ |
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/* dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */ |
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/* if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */ |
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/* permutations done on the I-th level of the computation tree. */ |
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/* GIVNUM (output) DOUBLE PRECISION array, */ |
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/* dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */ |
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/* referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ |
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/* GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */ |
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/* values of Givens rotations performed on the I-th level on */ |
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/* the computation tree. */ |
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/* C (output) DOUBLE PRECISION array, */ |
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/* dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */ |
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/* If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */ |
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/* C( I ) contains the C-value of a Givens rotation related to */ |
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/* the right null space of the I-th subproblem. */ |
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/* S (output) DOUBLE PRECISION array, dimension ( N ) if */ |
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/* ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */ |
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/* and the I-th subproblem is not square, on exit, S( I ) */ |
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/* contains the S-value of a Givens rotation related to */ |
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/* the right null space of the I-th subproblem. */ |
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/* WORK (workspace) DOUBLE PRECISION array, dimension */ |
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/* (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */ |
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/* IWORK (workspace) INTEGER array. */ |
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/* Dimension must be at least (7 * N). */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit. */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
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/* > 0: if INFO = 1, an singular value did not converge */ |
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/* Further Details */ |
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/* =============== */ |
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/* Based on contributions by */ |
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/* Ming Gu and Huan Ren, Computer Science Division, University of */ |
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/* California at Berkeley, USA */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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--d__; |
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--e; |
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givnum_dim1 = *ldu; |
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givnum_offset = 1 + givnum_dim1; |
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givnum -= givnum_offset; |
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poles_dim1 = *ldu; |
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poles_offset = 1 + poles_dim1; |
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poles -= poles_offset; |
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z_dim1 = *ldu; |
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z_offset = 1 + z_dim1; |
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z__ -= z_offset; |
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difr_dim1 = *ldu; |
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difr_offset = 1 + difr_dim1; |
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difr -= difr_offset; |
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difl_dim1 = *ldu; |
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difl_offset = 1 + difl_dim1; |
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difl -= difl_offset; |
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vt_dim1 = *ldu; |
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vt_offset = 1 + vt_dim1; |
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vt -= vt_offset; |
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u_dim1 = *ldu; |
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u_offset = 1 + u_dim1; |
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u -= u_offset; |
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--k; |
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--givptr; |
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perm_dim1 = *ldgcol; |
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perm_offset = 1 + perm_dim1; |
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perm -= perm_offset; |
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givcol_dim1 = *ldgcol; |
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givcol_offset = 1 + givcol_dim1; |
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givcol -= givcol_offset; |
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--c__; |
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--s; |
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--work; |
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--iwork; |
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/* Function Body */ |
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*info = 0; |
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if (*icompq < 0 || *icompq > 1) { |
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*info = -1; |
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} else if (*smlsiz < 3) { |
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*info = -2; |
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} else if (*n < 0) { |
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*info = -3; |
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} else if (*sqre < 0 || *sqre > 1) { |
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*info = -4; |
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} else if (*ldu < *n + *sqre) { |
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*info = -8; |
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} else if (*ldgcol < *n) { |
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*info = -17; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DLASDA", &i__1); |
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return 0; |
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} |
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m = *n + *sqre; |
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/* If the input matrix is too small, call DLASDQ to find the SVD. */ |
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if (*n <= *smlsiz) { |
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if (*icompq == 0) { |
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dlasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ |
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vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & |
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work[1], info); |
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} else { |
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dlasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] |
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, ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], |
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info); |
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} |
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return 0; |
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} |
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/* Book-keeping and set up the computation tree. */ |
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inode = 1; |
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ndiml = inode + *n; |
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ndimr = ndiml + *n; |
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idxq = ndimr + *n; |
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iwk = idxq + *n; |
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ncc = 0; |
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nru = 0; |
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smlszp = *smlsiz + 1; |
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vf = 1; |
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vl = vf + m; |
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nwork1 = vl + m; |
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nwork2 = nwork1 + smlszp * smlszp; |
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dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], |
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smlsiz); |
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/* for the nodes on bottom level of the tree, solve */ |
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/* their subproblems by DLASDQ. */ |
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ndb1 = (nd + 1) / 2; |
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i__1 = nd; |
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for (i__ = ndb1; i__ <= i__1; ++i__) { |
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/* IC : center row of each node */ |
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/* NL : number of rows of left subproblem */ |
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/* NR : number of rows of right subproblem */ |
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/* NLF: starting row of the left subproblem */ |
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/* NRF: starting row of the right subproblem */ |
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i1 = i__ - 1; |
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ic = iwork[inode + i1]; |
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nl = iwork[ndiml + i1]; |
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nlp1 = nl + 1; |
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nr = iwork[ndimr + i1]; |
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nlf = ic - nl; |
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nrf = ic + 1; |
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idxqi = idxq + nlf - 2; |
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vfi = vf + nlf - 1; |
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vli = vl + nlf - 1; |
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sqrei = 1; |
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if (*icompq == 0) { |
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dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp); |
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dlasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & |
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work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], |
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&nl, &work[nwork2], info); |
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itemp = nwork1 + nl * smlszp; |
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dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); |
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dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); |
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} else { |
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dlaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu); |
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dlaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], |
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ldu); |
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dlasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & |
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vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + |
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u_dim1], ldu, &work[nwork1], info); |
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dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); |
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dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) |
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; |
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} |
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if (*info != 0) { |
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return 0; |
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} |
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i__2 = nl; |
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for (j = 1; j <= i__2; ++j) { |
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iwork[idxqi + j] = j; |
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/* L10: */ |
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} |
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if (i__ == nd && *sqre == 0) { |
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sqrei = 0; |
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} else { |
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sqrei = 1; |
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} |
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idxqi += nlp1; |
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vfi += nlp1; |
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vli += nlp1; |
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nrp1 = nr + sqrei; |
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if (*icompq == 0) { |
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dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp); |
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dlasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & |
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work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], |
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&nr, &work[nwork2], info); |
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itemp = nwork1 + (nrp1 - 1) * smlszp; |
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dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); |
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dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); |
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} else { |
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dlaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu); |
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dlaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], |
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ldu); |
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dlasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & |
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vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + |
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u_dim1], ldu, &work[nwork1], info); |
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dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); |
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dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) |
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; |
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} |
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if (*info != 0) { |
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return 0; |
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} |
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i__2 = nr; |
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for (j = 1; j <= i__2; ++j) { |
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iwork[idxqi + j] = j; |
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/* L20: */ |
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} |
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/* L30: */ |
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} |
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/* Now conquer each subproblem bottom-up. */ |
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j = pow_ii(&c__2, &nlvl); |
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for (lvl = nlvl; lvl >= 1; --lvl) { |
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lvl2 = (lvl << 1) - 1; |
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|
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/* Find the first node LF and last node LL on */ |
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/* the current level LVL. */ |
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if (lvl == 1) { |
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lf = 1; |
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ll = 1; |
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} else { |
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i__1 = lvl - 1; |
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lf = pow_ii(&c__2, &i__1); |
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ll = (lf << 1) - 1; |
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} |
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i__1 = ll; |
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for (i__ = lf; i__ <= i__1; ++i__) { |
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im1 = i__ - 1; |
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ic = iwork[inode + im1]; |
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nl = iwork[ndiml + im1]; |
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nr = iwork[ndimr + im1]; |
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nlf = ic - nl; |
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nrf = ic + 1; |
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if (i__ == ll) { |
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sqrei = *sqre; |
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} else { |
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sqrei = 1; |
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} |
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vfi = vf + nlf - 1; |
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vli = vl + nlf - 1; |
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idxqi = idxq + nlf - 1; |
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alpha = d__[ic]; |
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beta = e[ic]; |
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if (*icompq == 0) { |
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dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & |
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work[vli], &alpha, &beta, &iwork[idxqi], &perm[ |
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perm_offset], &givptr[1], &givcol[givcol_offset], |
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ldgcol, &givnum[givnum_offset], ldu, &poles[ |
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poles_offset], &difl[difl_offset], &difr[difr_offset], |
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&z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], |
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&iwork[iwk], info); |
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} else { |
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--j; |
|
dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & |
|
work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + |
|
lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * |
|
givcol_dim1], ldgcol, &givnum[nlf + lvl2 * |
|
givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & |
|
difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * |
|
difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], |
|
&s[j], &work[nwork1], &iwork[iwk], info); |
|
} |
|
if (*info != 0) { |
|
return 0; |
|
} |
|
/* L40: */ |
|
} |
|
/* L50: */ |
|
} |
|
|
|
return 0; |
|
|
|
/* End of DLASDA */ |
|
|
|
} /* dlasda_ */
|
|
|