368 lines
11 KiB
C
368 lines
11 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer *
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ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e,
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doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
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doublereal *c__, integer *ldc, doublereal *work, integer *info)
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{
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/* System generated locals */
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integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1,
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i__2;
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/* Local variables */
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integer i__, j;
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doublereal r__, cs, sn;
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integer np1, isub;
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doublereal smin;
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integer sqre1;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *
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, doublereal *, integer *);
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integer iuplo;
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extern /* Subroutine */ int dlartg_(doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *), xerbla_(char *,
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integer *), dbdsqr_(char *, integer *, integer *, integer
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*, integer *, doublereal *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *);
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logical rotate;
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/* -- LAPACK auxiliary routine (version 3.1) -- */
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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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/* Purpose */
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/* ======= */
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/* DLASDQ computes the singular value decomposition (SVD) of a real */
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/* (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */
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/* E, accumulating the transformations if desired. Letting B denote */
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/* the input bidiagonal matrix, the algorithm computes orthogonal */
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/* matrices Q and P such that B = Q * S * P' (P' denotes the transpose */
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/* of P). The singular values S are overwritten on D. */
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/* The input matrix U is changed to U * Q if desired. */
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/* The input matrix VT is changed to P' * VT if desired. */
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/* The input matrix C is changed to Q' * C if desired. */
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/* See "Computing Small Singular Values of Bidiagonal Matrices With */
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/* Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */
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/* LAPACK Working Note #3, for a detailed description of the algorithm. */
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/* Arguments */
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/* ========= */
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/* UPLO (input) CHARACTER*1 */
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/* On entry, UPLO specifies whether the input bidiagonal matrix */
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/* is upper or lower bidiagonal, and wether it is square are */
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/* not. */
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/* UPLO = 'U' or 'u' B is upper bidiagonal. */
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/* UPLO = 'L' or 'l' B is lower bidiagonal. */
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/* SQRE (input) INTEGER */
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/* = 0: then the input matrix is N-by-N. */
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/* = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */
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/* (N+1)-by-N if UPLU = 'L'. */
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/* The bidiagonal matrix has */
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/* N = NL + NR + 1 rows and */
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/* M = N + SQRE >= N columns. */
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/* N (input) INTEGER */
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/* On entry, N specifies the number of rows and columns */
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/* in the matrix. N must be at least 0. */
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/* NCVT (input) INTEGER */
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/* On entry, NCVT specifies the number of columns of */
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/* the matrix VT. NCVT must be at least 0. */
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/* NRU (input) INTEGER */
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/* On entry, NRU specifies the number of rows of */
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/* the matrix U. NRU must be at least 0. */
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/* NCC (input) INTEGER */
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/* On entry, NCC specifies the number of columns of */
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/* the matrix C. NCC must be at least 0. */
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/* D (input/output) DOUBLE PRECISION array, dimension (N) */
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/* On entry, D contains the diagonal entries of the */
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/* bidiagonal matrix whose SVD is desired. On normal exit, */
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/* D contains the singular values in ascending order. */
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/* E (input/output) DOUBLE PRECISION array. */
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/* dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */
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/* On entry, the entries of E contain the offdiagonal entries */
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/* of the bidiagonal matrix whose SVD is desired. On normal */
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/* exit, E will contain 0. If the algorithm does not converge, */
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/* D and E will contain the diagonal and superdiagonal entries */
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/* of a bidiagonal matrix orthogonally equivalent to the one */
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/* given as input. */
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/* VT (input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT) */
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/* On entry, contains a matrix which on exit has been */
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/* premultiplied by P', dimension N-by-NCVT if SQRE = 0 */
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/* and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */
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/* LDVT (input) INTEGER */
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/* On entry, LDVT specifies the leading dimension of VT as */
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/* declared in the calling (sub) program. LDVT must be at */
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/* least 1. If NCVT is nonzero LDVT must also be at least N. */
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/* U (input/output) DOUBLE PRECISION array, dimension (LDU, N) */
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/* On entry, contains a matrix which on exit has been */
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/* postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */
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/* and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */
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/* LDU (input) INTEGER */
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/* On entry, LDU specifies the leading dimension of U as */
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/* declared in the calling (sub) program. LDU must be at */
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/* least max( 1, NRU ) . */
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/* C (input/output) DOUBLE PRECISION array, dimension (LDC, NCC) */
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/* On entry, contains an N-by-NCC matrix which on exit */
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/* has been premultiplied by Q' dimension N-by-NCC if SQRE = 0 */
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/* and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */
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/* LDC (input) INTEGER */
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/* On entry, LDC specifies the leading dimension of C as */
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/* declared in the calling (sub) program. LDC must be at */
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/* least 1. If NCC is nonzero, LDC must also be at least N. */
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/* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */
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/* Workspace. Only referenced if one of NCVT, NRU, or NCC is */
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/* nonzero, and if N is at least 2. */
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/* INFO (output) INTEGER */
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/* On exit, a value of 0 indicates a successful exit. */
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/* If INFO < 0, argument number -INFO is illegal. */
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/* If INFO > 0, the algorithm did not converge, and INFO */
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/* specifies how many superdiagonals 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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/* .. External Functions .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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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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vt_dim1 = *ldvt;
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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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c_dim1 = *ldc;
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c_offset = 1 + c_dim1;
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c__ -= c_offset;
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--work;
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/* Function Body */
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*info = 0;
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iuplo = 0;
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if (lsame_(uplo, "U")) {
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iuplo = 1;
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}
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if (lsame_(uplo, "L")) {
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iuplo = 2;
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}
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if (iuplo == 0) {
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*info = -1;
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} else if (*sqre < 0 || *sqre > 1) {
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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 (*ncvt < 0) {
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*info = -4;
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} else if (*nru < 0) {
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*info = -5;
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} else if (*ncc < 0) {
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*info = -6;
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} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) {
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*info = -10;
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} else if (*ldu < max(1,*nru)) {
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*info = -12;
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} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) {
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*info = -14;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DLASDQ", &i__1);
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return 0;
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}
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if (*n == 0) {
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return 0;
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}
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/* ROTATE is true if any singular vectors desired, false otherwise */
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rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
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np1 = *n + 1;
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sqre1 = *sqre;
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/* If matrix non-square upper bidiagonal, rotate to be lower */
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/* bidiagonal. The rotations are on the right. */
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if (iuplo == 1 && sqre1 == 1) {
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
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d__[i__] = r__;
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e[i__] = sn * d__[i__ + 1];
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d__[i__ + 1] = cs * d__[i__ + 1];
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if (rotate) {
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work[i__] = cs;
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work[*n + i__] = sn;
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}
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/* L10: */
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}
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dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
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d__[*n] = r__;
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e[*n] = 0.;
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if (rotate) {
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work[*n] = cs;
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work[*n + *n] = sn;
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}
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iuplo = 2;
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sqre1 = 0;
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/* Update singular vectors if desired. */
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if (*ncvt > 0) {
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dlasr_("L", "V", "F", &np1, ncvt, &work[1], &work[np1], &vt[
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vt_offset], ldvt);
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}
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}
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/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
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/* by applying Givens rotations on the left. */
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if (iuplo == 2) {
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
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d__[i__] = r__;
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e[i__] = sn * d__[i__ + 1];
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d__[i__ + 1] = cs * d__[i__ + 1];
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if (rotate) {
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work[i__] = cs;
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work[*n + i__] = sn;
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}
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/* L20: */
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}
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/* If matrix (N+1)-by-N lower bidiagonal, one additional */
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/* rotation is needed. */
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if (sqre1 == 1) {
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dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__);
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d__[*n] = r__;
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if (rotate) {
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work[*n] = cs;
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work[*n + *n] = sn;
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}
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}
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/* Update singular vectors if desired. */
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if (*nru > 0) {
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if (sqre1 == 0) {
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dlasr_("R", "V", "F", nru, n, &work[1], &work[np1], &u[
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u_offset], ldu);
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} else {
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dlasr_("R", "V", "F", nru, &np1, &work[1], &work[np1], &u[
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u_offset], ldu);
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}
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}
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if (*ncc > 0) {
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if (sqre1 == 0) {
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dlasr_("L", "V", "F", n, ncc, &work[1], &work[np1], &c__[
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c_offset], ldc);
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} else {
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dlasr_("L", "V", "F", &np1, ncc, &work[1], &work[np1], &c__[
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c_offset], ldc);
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}
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}
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}
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/* Call DBDSQR to compute the SVD of the reduced real */
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/* N-by-N upper bidiagonal matrix. */
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dbdsqr_("U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[
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u_offset], ldu, &c__[c_offset], ldc, &work[1], info);
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/* Sort the singular values into ascending order (insertion sort on */
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/* singular values, but only one transposition per singular vector) */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Scan for smallest D(I). */
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isub = i__;
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smin = d__[i__];
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i__2 = *n;
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for (j = i__ + 1; j <= i__2; ++j) {
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if (d__[j] < smin) {
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isub = j;
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smin = d__[j];
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}
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/* L30: */
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}
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if (isub != i__) {
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/* Swap singular values and vectors. */
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d__[isub] = d__[i__];
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d__[i__] = smin;
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if (*ncvt > 0) {
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dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1],
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ldvt);
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}
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if (*nru > 0) {
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dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1]
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, &c__1);
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}
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if (*ncc > 0) {
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dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc)
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;
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}
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}
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/* L40: */
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}
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return 0;
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/* End of DLASDQ */
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} /* dlasdq_ */
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