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366 lines
11 KiB
366 lines
11 KiB
#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 slasdq_(char *uplo, integer *sqre, integer *n, integer * |
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ncvt, integer *nru, integer *ncc, real *d__, real *e, real *vt, |
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integer *ldvt, real *u, integer *ldu, real *c__, integer *ldc, real * |
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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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real r__, cs, sn; |
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integer np1, isub; |
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real smin; |
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integer sqre1; |
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extern logical lsame_(char *, char *); |
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extern /* Subroutine */ int slasr_(char *, char *, char *, integer *, |
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integer *, real *, real *, real *, integer *); |
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integer iuplo; |
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extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, |
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integer *), xerbla_(char *, integer *), slartg_(real *, |
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real *, real *, real *, real *); |
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logical rotate; |
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extern /* Subroutine */ int sbdsqr_(char *, integer *, integer *, integer |
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*, integer *, real *, real *, real *, integer *, real *, integer * |
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, real *, integer *, real *, integer *); |
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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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/* SLASDQ 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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_("SLASDQ", &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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slartg_(&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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slartg_(&d__[*n], &e[*n], &cs, &sn, &r__); |
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d__[*n] = r__; |
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e[*n] = 0.f; |
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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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slasr_("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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slartg_(&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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slartg_(&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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slasr_("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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slasr_("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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slasr_("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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slasr_("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 SBDSQR to compute the SVD of the reduced real */ |
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/* N-by-N upper bidiagonal matrix. */ |
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sbdsqr_("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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sswap_(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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sswap_(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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sswap_(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 SLASDQ */ |
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} /* slasdq_ */
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