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523 lines
16 KiB
523 lines
16 KiB
/* slalsd.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__1 = 1; |
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static real c_b6 = 0.f; |
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static integer c__0 = 0; |
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static real c_b11 = 1.f; |
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|
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/* Subroutine */ int slalsd_(char *uplo, integer *smlsiz, integer *n, integer |
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*nrhs, real *d__, real *e, real *b, integer *ldb, real *rcond, |
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integer *rank, real *work, integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer b_dim1, b_offset, i__1, i__2; |
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real r__1; |
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/* Builtin functions */ |
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double log(doublereal), r_sign(real *, real *); |
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/* Local variables */ |
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integer c__, i__, j, k; |
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real r__; |
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integer s, u, z__; |
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real cs; |
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integer bx; |
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real sn; |
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integer st, vt, nm1, st1; |
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real eps; |
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integer iwk; |
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real tol; |
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integer difl, difr; |
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real rcnd; |
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integer perm, nsub, nlvl, sqre, bxst; |
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extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, |
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integer *, real *, real *), sgemm_(char *, char *, integer *, |
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integer *, integer *, real *, real *, integer *, real *, integer * |
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, real *, real *, integer *); |
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integer poles, sizei, nsize; |
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extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, |
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integer *); |
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integer nwork, icmpq1, icmpq2; |
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extern doublereal slamch_(char *); |
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extern /* Subroutine */ int slasda_(integer *, integer *, integer *, |
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integer *, real *, real *, real *, integer *, real *, integer *, |
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real *, real *, real *, real *, integer *, integer *, integer *, |
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integer *, real *, real *, real *, real *, integer *, integer *), |
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xerbla_(char *, integer *), slalsa_(integer *, integer *, |
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integer *, integer *, real *, integer *, real *, integer *, real * |
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, integer *, real *, integer *, real *, real *, real *, real *, |
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integer *, integer *, integer *, integer *, real *, real *, real * |
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, real *, integer *, integer *), slascl_(char *, integer *, |
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integer *, real *, real *, integer *, integer *, real *, integer * |
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, integer *); |
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integer givcol; |
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extern integer isamax_(integer *, real *, integer *); |
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extern /* Subroutine */ int slasdq_(char *, integer *, integer *, integer |
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*, integer *, integer *, real *, real *, real *, integer *, real * |
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, integer *, real *, integer *, real *, integer *), |
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slacpy_(char *, integer *, integer *, real *, integer *, real *, |
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integer *), slartg_(real *, real *, real *, real *, real * |
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), slaset_(char *, integer *, integer *, real *, real *, real *, |
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integer *); |
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real orgnrm; |
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integer givnum; |
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extern doublereal slanst_(char *, integer *, real *, real *); |
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extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *); |
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integer givptr, smlszp; |
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/* -- LAPACK 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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/* Purpose */ |
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/* ======= */ |
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/* SLALSD uses the singular value decomposition of A to solve the least */ |
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/* squares problem of finding X to minimize the Euclidean norm of each */ |
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/* column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */ |
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/* are N-by-NRHS. The solution X overwrites B. */ |
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/* The singular values of A smaller than RCOND times the largest */ |
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/* singular value are treated as zero in solving the least squares */ |
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/* problem; in this case a minimum norm solution is returned. */ |
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/* The actual singular values are returned in D in ascending order. */ |
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/* This code makes very mild assumptions about floating point */ |
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/* arithmetic. It will work on machines with a guard digit in */ |
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/* add/subtract, or on those binary machines without guard digits */ |
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/* which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */ |
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/* It could conceivably fail on hexadecimal or decimal machines */ |
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/* without guard digits, but we know of none. */ |
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/* Arguments */ |
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/* ========= */ |
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/* UPLO (input) CHARACTER*1 */ |
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/* = 'U': D and E define an upper bidiagonal matrix. */ |
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/* = 'L': D and E define a lower bidiagonal matrix. */ |
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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 dimension of the bidiagonal matrix. N >= 0. */ |
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/* NRHS (input) INTEGER */ |
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/* The number of columns of B. NRHS must be at least 1. */ |
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/* D (input/output) REAL array, dimension (N) */ |
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/* On entry D contains the main diagonal of the bidiagonal */ |
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/* matrix. On exit, if INFO = 0, D contains its singular values. */ |
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/* E (input/output) REAL array, dimension (N-1) */ |
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/* Contains the super-diagonal entries of the bidiagonal matrix. */ |
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/* On exit, E has been destroyed. */ |
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/* B (input/output) REAL array, dimension (LDB,NRHS) */ |
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/* On input, B contains the right hand sides of the least */ |
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/* squares problem. On output, B contains the solution X. */ |
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/* LDB (input) INTEGER */ |
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/* The leading dimension of B in the calling subprogram. */ |
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/* LDB must be at least max(1,N). */ |
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/* RCOND (input) REAL */ |
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/* The singular values of A less than or equal to RCOND times */ |
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/* the largest singular value are treated as zero in solving */ |
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/* the least squares problem. If RCOND is negative, */ |
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/* machine precision is used instead. */ |
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/* For example, if diag(S)*X=B were the least squares problem, */ |
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/* where diag(S) is a diagonal matrix of singular values, the */ |
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/* solution would be X(i) = B(i) / S(i) if S(i) is greater than */ |
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/* RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to */ |
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/* RCOND*max(S). */ |
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/* RANK (output) INTEGER */ |
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/* The number of singular values of A greater than RCOND times */ |
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/* the largest singular value. */ |
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/* WORK (workspace) REAL array, dimension at least */ |
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/* (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */ |
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/* where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */ |
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/* IWORK (workspace) INTEGER array, dimension at least */ |
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/* (3*N*NLVL + 11*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: The algorithm failed to compute an singular value while */ |
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/* working on the submatrix lying in rows and columns */ |
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/* INFO/(N+1) through MOD(INFO,N+1). */ |
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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 Ren-Cang Li, Computer Science Division, University of */ |
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/* California at Berkeley, USA */ |
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/* Osni Marques, LBNL/NERSC, 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 Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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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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b_dim1 = *ldb; |
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b_offset = 1 + b_dim1; |
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b -= b_offset; |
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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 (*n < 0) { |
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*info = -3; |
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} else if (*nrhs < 1) { |
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*info = -4; |
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} else if (*ldb < 1 || *ldb < *n) { |
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*info = -8; |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("SLALSD", &i__1); |
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return 0; |
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} |
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eps = slamch_("Epsilon"); |
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/* Set up the tolerance. */ |
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if (*rcond <= 0.f || *rcond >= 1.f) { |
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rcnd = eps; |
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} else { |
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rcnd = *rcond; |
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} |
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*rank = 0; |
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/* Quick return if possible. */ |
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if (*n == 0) { |
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return 0; |
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} else if (*n == 1) { |
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if (d__[1] == 0.f) { |
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slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb); |
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} else { |
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*rank = 1; |
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slascl_("G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[ |
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b_offset], ldb, info); |
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d__[1] = dabs(d__[1]); |
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} |
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return 0; |
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} |
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/* Rotate the matrix if it is lower bidiagonal. */ |
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if (*(unsigned char *)uplo == 'L') { |
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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 (*nrhs == 1) { |
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srot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], & |
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c__1, &cs, &sn); |
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} else { |
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work[(i__ << 1) - 1] = cs; |
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work[i__ * 2] = sn; |
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} |
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/* L10: */ |
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} |
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if (*nrhs > 1) { |
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i__1 = *nrhs; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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i__2 = *n - 1; |
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for (j = 1; j <= i__2; ++j) { |
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cs = work[(j << 1) - 1]; |
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sn = work[j * 2]; |
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srot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * |
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b_dim1], &c__1, &cs, &sn); |
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/* L20: */ |
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} |
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/* L30: */ |
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} |
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} |
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} |
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/* Scale. */ |
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nm1 = *n - 1; |
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orgnrm = slanst_("M", n, &d__[1], &e[1]); |
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if (orgnrm == 0.f) { |
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slaset_("A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb); |
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return 0; |
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} |
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slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info); |
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slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, |
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info); |
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/* If N is smaller than the minimum divide size SMLSIZ, then solve */ |
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/* the problem with another solver. */ |
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if (*n <= *smlsiz) { |
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nwork = *n * *n + 1; |
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slaset_("A", n, n, &c_b6, &c_b11, &work[1], n); |
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slasdq_("U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, & |
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work[1], n, &b[b_offset], ldb, &work[nwork], info); |
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if (*info != 0) { |
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return 0; |
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} |
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tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], dabs(r__1)); |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if (d__[i__] <= tol) { |
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slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb); |
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} else { |
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slascl_("G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[ |
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i__ + b_dim1], ldb, info); |
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++(*rank); |
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} |
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/* L40: */ |
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} |
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sgemm_("T", "N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, & |
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c_b6, &work[nwork], n); |
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slacpy_("A", n, nrhs, &work[nwork], n, &b[b_offset], ldb); |
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/* Unscale. */ |
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slascl_("G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, |
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info); |
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slasrt_("D", n, &d__[1], info); |
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slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], |
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ldb, info); |
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return 0; |
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} |
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/* Book-keeping and setting up some constants. */ |
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nlvl = (integer) (log((real) (*n) / (real) (*smlsiz + 1)) / log(2.f)) + 1; |
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smlszp = *smlsiz + 1; |
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u = 1; |
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vt = *smlsiz * *n + 1; |
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difl = vt + smlszp * *n; |
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difr = difl + nlvl * *n; |
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z__ = difr + (nlvl * *n << 1); |
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c__ = z__ + nlvl * *n; |
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s = c__ + *n; |
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poles = s + *n; |
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givnum = poles + (nlvl << 1) * *n; |
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bx = givnum + (nlvl << 1) * *n; |
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nwork = bx + *n * *nrhs; |
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sizei = *n + 1; |
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k = sizei + *n; |
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givptr = k + *n; |
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perm = givptr + *n; |
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givcol = perm + nlvl * *n; |
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iwk = givcol + (nlvl * *n << 1); |
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st = 1; |
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sqre = 0; |
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icmpq1 = 1; |
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icmpq2 = 0; |
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nsub = 0; |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if ((r__1 = d__[i__], dabs(r__1)) < eps) { |
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d__[i__] = r_sign(&eps, &d__[i__]); |
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} |
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/* L50: */ |
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} |
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i__1 = nm1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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if ((r__1 = e[i__], dabs(r__1)) < eps || i__ == nm1) { |
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++nsub; |
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iwork[nsub] = st; |
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/* Subproblem found. First determine its size and then */ |
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/* apply divide and conquer on it. */ |
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if (i__ < nm1) { |
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/* A subproblem with E(I) small for I < NM1. */ |
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nsize = i__ - st + 1; |
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iwork[sizei + nsub - 1] = nsize; |
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} else if ((r__1 = e[i__], dabs(r__1)) >= eps) { |
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/* A subproblem with E(NM1) not too small but I = NM1. */ |
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nsize = *n - st + 1; |
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iwork[sizei + nsub - 1] = nsize; |
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} else { |
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/* A subproblem with E(NM1) small. This implies an */ |
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/* 1-by-1 subproblem at D(N), which is not solved */ |
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/* explicitly. */ |
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nsize = i__ - st + 1; |
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iwork[sizei + nsub - 1] = nsize; |
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++nsub; |
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iwork[nsub] = *n; |
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iwork[sizei + nsub - 1] = 1; |
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scopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n); |
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} |
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st1 = st - 1; |
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if (nsize == 1) { |
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/* This is a 1-by-1 subproblem and is not solved */ |
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/* explicitly. */ |
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scopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); |
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} else if (nsize <= *smlsiz) { |
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/* This is a small subproblem and is solved by SLASDQ. */ |
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slaset_("A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], |
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n); |
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slasdq_("U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[ |
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st], &work[vt + st1], n, &work[nwork], n, &b[st + |
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b_dim1], ldb, &work[nwork], info); |
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if (*info != 0) { |
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return 0; |
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} |
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slacpy_("A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + |
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st1], n); |
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} else { |
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/* A large problem. Solve it using divide and conquer. */ |
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slasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], & |
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work[u + st1], n, &work[vt + st1], &iwork[k + st1], & |
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work[difl + st1], &work[difr + st1], &work[z__ + st1], |
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&work[poles + st1], &iwork[givptr + st1], &iwork[ |
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givcol + st1], n, &iwork[perm + st1], &work[givnum + |
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st1], &work[c__ + st1], &work[s + st1], &work[nwork], |
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&iwork[iwk], info); |
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if (*info != 0) { |
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return 0; |
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} |
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bxst = bx + st1; |
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slalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, & |
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work[bxst], n, &work[u + st1], n, &work[vt + st1], & |
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iwork[k + st1], &work[difl + st1], &work[difr + st1], |
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&work[z__ + st1], &work[poles + st1], &iwork[givptr + |
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st1], &iwork[givcol + st1], n, &iwork[perm + st1], & |
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work[givnum + st1], &work[c__ + st1], &work[s + st1], |
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&work[nwork], &iwork[iwk], info); |
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if (*info != 0) { |
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return 0; |
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} |
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} |
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st = i__ + 1; |
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} |
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/* L60: */ |
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} |
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/* Apply the singular values and treat the tiny ones as zero. */ |
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tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], dabs(r__1)); |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Some of the elements in D can be negative because 1-by-1 */ |
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/* subproblems were not solved explicitly. */ |
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if ((r__1 = d__[i__], dabs(r__1)) <= tol) { |
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slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n); |
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} else { |
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++(*rank); |
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slascl_("G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[ |
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bx + i__ - 1], n, info); |
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} |
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d__[i__] = (r__1 = d__[i__], dabs(r__1)); |
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/* L70: */ |
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} |
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/* Now apply back the right singular vectors. */ |
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icmpq2 = 1; |
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i__1 = nsub; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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st = iwork[i__]; |
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st1 = st - 1; |
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nsize = iwork[sizei + i__ - 1]; |
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bxst = bx + st1; |
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if (nsize == 1) { |
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scopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); |
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} else if (nsize <= *smlsiz) { |
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sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, |
|
&work[bxst], n, &c_b6, &b[st + b_dim1], ldb); |
|
} else { |
|
slalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + |
|
b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[ |
|
k + st1], &work[difl + st1], &work[difr + st1], &work[z__ |
|
+ st1], &work[poles + st1], &iwork[givptr + st1], &iwork[ |
|
givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], |
|
&work[c__ + st1], &work[s + st1], &work[nwork], &iwork[ |
|
iwk], info); |
|
if (*info != 0) { |
|
return 0; |
|
} |
|
} |
|
/* L80: */ |
|
} |
|
|
|
/* Unscale and sort the singular values. */ |
|
|
|
slascl_("G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info); |
|
slasrt_("D", n, &d__[1], info); |
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, |
|
info); |
|
|
|
return 0; |
|
|
|
/* End of SLALSD */ |
|
|
|
} /* slalsd_ */
|
|
|