e3181f26b1
Changed MPI routines to hypre_MPI routines. Added hypre_printf, etc. routines. Added AUTOTEST tests to look for 'int' and 'MPI_' calls. Added a new approach for the Fortran interface (not implemented everywhere yet).
477 lines
14 KiB
C
477 lines
14 KiB
C
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#include "../blas/hypre_blas.h"
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#include "hypre_lapack.h"
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#include "f2c.h"
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/* Subroutine */ HYPRE_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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/* -- LAPACK driver routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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June 30, 1999
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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
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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, B is overwritten by the solution vectors, stored
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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 (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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=====================================================================
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Test the input arguments.
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Parameter adjustments */
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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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static doublereal c_b61 = 1.;
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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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static doublereal anrm, bnrm;
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static integer brow;
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static logical tpsd;
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static integer i__, j, iascl, ibscl;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ HYPRE_Int dtrsm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *);
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static integer wsize;
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static doublereal rwork[1];
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extern /* Subroutine */ HYPRE_Int dlabad_(doublereal *, doublereal *);
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static integer nb;
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extern doublereal dlamch_(char *), dlange_(char *, integer *,
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integer *, doublereal *, integer *, doublereal *);
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static integer mn;
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extern /* Subroutine */ HYPRE_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 *, ftnlen, ftnlen);
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static integer scllen;
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static doublereal bignum;
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extern /* Subroutine */ HYPRE_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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static doublereal smlnum;
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static logical lquery;
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#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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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, (ftnlen)6,
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(ftnlen)1);
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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, (ftnlen)6, (ftnlen)2);
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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, (ftnlen)6, (ftnlen)2);
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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, (ftnlen)6,
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(ftnlen)1);
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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, (ftnlen)6, (ftnlen)2);
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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, (ftnlen)6, (ftnlen)2);
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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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dtrsm_("Left", "Upper", "No transpose", "Non-unit", n, nrhs, &
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c_b61, &a[a_offset], lda, &b[b_offset], ldb);
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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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dtrsm_("Left", "Upper", "Transpose", "Non-unit", n, nrhs, &c_b61,
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&a[a_offset], lda, &b[b_offset], ldb);
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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_ref(i__, j) = 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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dtrsm_("Left", "Lower", "No transpose", "Non-unit", m, nrhs, &
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c_b61, &a[a_offset], lda, &b[b_offset], ldb);
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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_ref(i__, j) = 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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dtrsm_("Left", "Lower", "Transpose", "Non-unit", m, nrhs, &c_b61,
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&a[a_offset], lda, &b[b_offset], ldb);
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scllen = *m;
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}
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}
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/* Undo scaling */
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if (iascl == 1) {
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dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
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, ldb, info);
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} else if (iascl == 2) {
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dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
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, ldb, info);
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}
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if (ibscl == 1) {
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dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
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, ldb, info);
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} else if (ibscl == 2) {
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dlascl_("G", &c__0, &c__0, &bignum, &bnrm, &scllen, nrhs, &b[b_offset]
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, ldb, info);
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}
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L50:
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work[1] = (doublereal) wsize;
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return 0;
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/* End of DGELS */
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} /* dgels_ */
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#undef b_ref
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