516 lines
15 KiB
C
516 lines
15 KiB
C
/* dgels.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 integer c_n1 = -1;
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static doublereal c_b33 = 0.;
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static integer c__0 = 0;
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/* Subroutine */ int dgels_(char *trans, integer *m, integer *n, integer *
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nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb,
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doublereal *work, integer *lwork, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
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/* Local variables */
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integer i__, j, nb, mn;
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doublereal anrm, bnrm;
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integer brow;
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logical tpsd;
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integer iascl, ibscl;
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extern logical lsame_(char *, char *);
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integer wsize;
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doublereal rwork[1];
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extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
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extern doublereal dlamch_(char *), dlange_(char *, integer *,
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integer *, doublereal *, integer *, doublereal *);
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extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *, integer *),
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dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
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integer *, integer *, doublereal *, integer *, integer *),
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dgeqrf_(integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *), dlaset_(char *,
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integer *, integer *, doublereal *, doublereal *, doublereal *,
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integer *), xerbla_(char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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integer scllen;
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doublereal bignum;
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extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, integer *),
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dormqr_(char *, char *, integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, integer *);
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doublereal smlnum;
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logical lquery;
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extern /* Subroutine */ int dtrtrs_(char *, char *, char *, integer *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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integer *);
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/* -- LAPACK driver 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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/* DGELS solves overdetermined or underdetermined real linear systems */
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/* involving an M-by-N matrix A, or its transpose, using a QR or LQ */
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/* factorization of A. It is assumed that A has full rank. */
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/* The following options are provided: */
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/* 1. If TRANS = 'N' and m >= n: find the least squares solution of */
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/* an overdetermined system, i.e., solve the least squares problem */
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/* minimize || B - A*X ||. */
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/* 2. If TRANS = 'N' and m < n: find the minimum norm solution of */
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/* an underdetermined system A * X = B. */
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/* 3. If TRANS = 'T' and m >= n: find the minimum norm solution of */
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/* an undetermined system A**T * X = B. */
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/* 4. If TRANS = 'T' and m < n: find the least squares solution of */
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/* an overdetermined system, i.e., solve the least squares problem */
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/* minimize || B - A**T * X ||. */
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/* Several right hand side vectors b and solution vectors x can be */
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/* handled in a single call; they are stored as the columns of the */
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/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
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/* matrix X. */
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/* Arguments */
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/* ========= */
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/* TRANS (input) CHARACTER*1 */
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/* = 'N': the linear system involves A; */
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/* = 'T': the linear system involves A**T. */
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/* M (input) INTEGER */
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/* The number of rows of the matrix A. M >= 0. */
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/* N (input) INTEGER */
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/* The number of columns of the matrix A. N >= 0. */
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/* NRHS (input) INTEGER */
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/* The number of right hand sides, i.e., the number of */
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/* columns of the matrices B and X. NRHS >=0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the M-by-N matrix A. */
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/* On exit, */
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/* if M >= N, A is overwritten by details of its QR */
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/* factorization as returned by DGEQRF; */
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/* if M < N, A is overwritten by details of its LQ */
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/* factorization as returned by DGELQF. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,M). */
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/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
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/* On entry, the matrix B of right hand side vectors, stored */
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/* columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS */
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/* if TRANS = 'T'. */
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/* On exit, if INFO = 0, B is overwritten by the solution */
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/* vectors, stored columnwise: */
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/* if TRANS = 'N' and m >= n, rows 1 to n of B contain the least */
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/* squares solution vectors; the residual sum of squares for the */
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/* solution in each column is given by the sum of squares of */
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/* elements N+1 to M in that column; */
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/* if TRANS = 'N' and m < n, rows 1 to N of B contain the */
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/* minimum norm solution vectors; */
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/* if TRANS = 'T' and m >= n, rows 1 to M of B contain the */
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/* minimum norm solution vectors; */
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/* if TRANS = 'T' and m < n, rows 1 to M of B contain the */
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/* least squares solution vectors; the residual sum of squares */
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/* for the solution in each column is given by the sum of */
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/* squares of elements M+1 to N in that column. */
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/* LDB (input) INTEGER */
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/* The leading dimension of the array B. LDB >= MAX(1,M,N). */
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* LWORK (input) INTEGER */
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/* The dimension of the array WORK. */
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/* LWORK >= max( 1, MN + max( MN, NRHS ) ). */
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/* For optimal performance, */
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/* LWORK >= max( 1, MN + max( MN, NRHS )*NB ). */
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/* where MN = min(M,N) and NB is the optimum block size. */
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/* If LWORK = -1, then a workspace query is assumed; the routine */
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/* only calculates the optimal size of the WORK array, returns */
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/* this value as the first entry of the WORK array, and no error */
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/* message related to LWORK is issued by XERBLA. */
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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 = i, the i-th diagonal element of the */
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/* triangular factor of A is zero, so that A does not have */
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/* full rank; the least squares solution could not be */
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/* computed. */
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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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/* .. Local Arrays .. */
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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 arguments. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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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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/* Function Body */
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*info = 0;
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mn = min(*m,*n);
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lquery = *lwork == -1;
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if (! (lsame_(trans, "N") || lsame_(trans, "T"))) {
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*info = -1;
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} else if (*m < 0) {
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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 (*nrhs < 0) {
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*info = -4;
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} else if (*lda < max(1,*m)) {
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*info = -6;
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} else /* if(complicated condition) */ {
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/* Computing MAX */
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i__1 = max(1,*m);
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if (*ldb < max(i__1,*n)) {
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*info = -8;
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} else /* if(complicated condition) */ {
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/* Computing MAX */
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i__1 = 1, i__2 = mn + max(mn,*nrhs);
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if (*lwork < max(i__1,i__2) && ! lquery) {
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*info = -10;
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}
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}
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}
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/* Figure out optimal block size */
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if (*info == 0 || *info == -10) {
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tpsd = TRUE_;
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if (lsame_(trans, "N")) {
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tpsd = FALSE_;
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}
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if (*m >= *n) {
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nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1);
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if (tpsd) {
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LN", m, nrhs, n, &
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c_n1);
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nb = max(i__1,i__2);
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} else {
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__1, "DORMQR", "LT", m, nrhs, n, &
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c_n1);
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nb = max(i__1,i__2);
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}
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} else {
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nb = ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1, &c_n1);
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if (tpsd) {
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LT", n, nrhs, m, &
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c_n1);
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nb = max(i__1,i__2);
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} else {
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/* Computing MAX */
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i__1 = nb, i__2 = ilaenv_(&c__1, "DORMLQ", "LN", n, nrhs, m, &
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c_n1);
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nb = max(i__1,i__2);
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}
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}
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/* Computing MAX */
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i__1 = 1, i__2 = mn + max(mn,*nrhs) * nb;
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wsize = max(i__1,i__2);
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work[1] = (doublereal) wsize;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGELS ", &i__1);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Quick return if possible */
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/* Computing MIN */
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i__1 = min(*m,*n);
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if (min(i__1,*nrhs) == 0) {
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i__1 = max(*m,*n);
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dlaset_("Full", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
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return 0;
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}
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/* Get machine parameters */
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smlnum = dlamch_("S") / dlamch_("P");
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bignum = 1. / smlnum;
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dlabad_(&smlnum, &bignum);
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/* Scale A, B if max element outside range [SMLNUM,BIGNUM] */
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anrm = dlange_("M", m, n, &a[a_offset], lda, rwork);
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iascl = 0;
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if (anrm > 0. && anrm < smlnum) {
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/* Scale matrix norm up to SMLNUM */
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dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
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info);
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iascl = 1;
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} else if (anrm > bignum) {
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/* Scale matrix norm down to BIGNUM */
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dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
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info);
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iascl = 2;
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} else if (anrm == 0.) {
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/* Matrix all zero. Return zero solution. */
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i__1 = max(*m,*n);
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dlaset_("F", &i__1, nrhs, &c_b33, &c_b33, &b[b_offset], ldb);
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goto L50;
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}
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brow = *m;
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if (tpsd) {
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brow = *n;
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}
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bnrm = dlange_("M", &brow, nrhs, &b[b_offset], ldb, rwork);
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ibscl = 0;
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if (bnrm > 0. && bnrm < smlnum) {
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/* Scale matrix norm up to SMLNUM */
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dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, &brow, nrhs, &b[b_offset],
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ldb, info);
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ibscl = 1;
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} else if (bnrm > bignum) {
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/* Scale matrix norm down to BIGNUM */
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dlascl_("G", &c__0, &c__0, &bnrm, &bignum, &brow, nrhs, &b[b_offset],
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ldb, info);
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ibscl = 2;
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}
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if (*m >= *n) {
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/* compute QR factorization of A */
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i__1 = *lwork - mn;
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dgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
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;
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/* workspace at least N, optimally N*NB */
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if (! tpsd) {
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/* Least-Squares Problem min || A * X - B || */
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/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
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i__1 = *lwork - mn;
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dormqr_("Left", "Transpose", m, nrhs, n, &a[a_offset], lda, &work[
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1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
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/* workspace at least NRHS, optimally NRHS*NB */
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/* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
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dtrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
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, lda, &b[b_offset], ldb, info);
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if (*info > 0) {
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return 0;
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}
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scllen = *n;
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} else {
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/* Overdetermined system of equations A' * X = B */
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/* B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */
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dtrtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset],
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lda, &b[b_offset], ldb, info);
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if (*info > 0) {
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return 0;
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}
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/* B(N+1:M,1:NRHS) = ZERO */
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = *n + 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = 0.;
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/* L10: */
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}
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/* L20: */
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}
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/* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
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i__1 = *lwork - mn;
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dormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
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work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
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/* workspace at least NRHS, optimally NRHS*NB */
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scllen = *m;
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}
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} else {
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/* Compute LQ factorization of A */
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i__1 = *lwork - mn;
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dgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
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;
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/* workspace at least M, optimally M*NB. */
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if (! tpsd) {
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/* underdetermined system of equations A * X = B */
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/* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
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dtrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
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, lda, &b[b_offset], ldb, info);
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if (*info > 0) {
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return 0;
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}
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/* B(M+1:N,1:NRHS) = 0 */
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i__ = *m + 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = 0.;
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/* L30: */
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}
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/* L40: */
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}
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/* B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */
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i__1 = *lwork - mn;
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dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[
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1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
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/* workspace at least NRHS, optimally NRHS*NB */
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scllen = *n;
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} else {
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/* overdetermined system min || A' * X - B || */
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/* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
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i__1 = *lwork - mn;
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dormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
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work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
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/* workspace at least NRHS, optimally NRHS*NB */
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/* B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */
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dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset],
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lda, &b[b_offset], ldb, info);
|
|
|
|
if (*info > 0) {
|
|
return 0;
|
|
}
|
|
|
|
scllen = *m;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* Undo scaling */
|
|
|
|
if (iascl == 1) {
|
|
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
|
|
, ldb, info);
|
|
} else if (iascl == 2) {
|
|
dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
|
|
, ldb, info);
|
|
}
|
|
if (ibscl == 1) {
|
|
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
|
|
, ldb, info);
|
|
} else if (ibscl == 2) {
|
|
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
|
|
, ldb, info);
|
|
}
|
|
|
|
L50:
|
|
work[1] = (doublereal) wsize;
|
|
|
|
return 0;
|
|
|
|
/* End of DGELS */
|
|
|
|
} /* dgels_ */
|