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-/* 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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-
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- http://www.netlib.org/f2c/libf2c.zip
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-*/
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-
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-#include "f2c.h"
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-#include "blaswrap.h"
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-
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-/* Table of constant values */
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-
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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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-
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-/* Subroutine */ int _starpu_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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-
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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 _starpu_lsame_(char *, char *);
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- integer wsize;
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- doublereal rwork[1];
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- extern /* Subroutine */ int _starpu_dlabad_(doublereal *, doublereal *);
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- extern doublereal _starpu_dlamch_(char *), _starpu_dlange_(char *, integer *,
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- integer *, doublereal *, integer *, doublereal *);
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- extern /* Subroutine */ int _starpu_dgelqf_(integer *, integer *, doublereal *,
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- integer *, doublereal *, doublereal *, integer *, integer *),
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- _starpu_dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
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- integer *, integer *, doublereal *, integer *, integer *),
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- _starpu_dgeqrf_(integer *, integer *, doublereal *, integer *,
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- doublereal *, doublereal *, integer *, integer *), _starpu_dlaset_(char *,
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- integer *, integer *, doublereal *, doublereal *, doublereal *,
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- integer *), _starpu_xerbla_(char *, integer *);
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- extern integer _starpu_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 _starpu_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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- _starpu_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 _starpu_dtrtrs_(char *, char *, char *, integer *,
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- integer *, doublereal *, integer *, doublereal *, integer *,
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- integer *);
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-
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-
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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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-
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-/* .. Scalar Arguments .. */
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-/* .. */
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-/* .. Array Arguments .. */
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-/* .. */
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-
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-/* Purpose */
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-/* ======= */
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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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-
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-/* The following options are provided: */
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-
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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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-
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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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-
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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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-
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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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-
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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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-
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-/* Arguments */
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-/* ========= */
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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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-/* ===================================================================== */
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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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-
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-/* Test the input arguments. */
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-
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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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-
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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 (! (_starpu_lsame_(trans, "N") || _starpu_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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-
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-/* Figure out optimal block size */
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-
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- if (*info == 0 || *info == -10) {
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-
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- tpsd = TRUE_;
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- if (_starpu_lsame_(trans, "N")) {
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- tpsd = FALSE_;
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- }
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-
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- if (*m >= *n) {
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- nb = _starpu_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 = _starpu_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 = _starpu_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 = _starpu_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 = _starpu_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 = _starpu_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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-
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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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- }
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-
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- if (*info != 0) {
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- i__1 = -(*info);
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- _starpu_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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-
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-/* Quick return if possible */
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-
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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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- _starpu_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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-
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-/* Get machine parameters */
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-
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- smlnum = _starpu_dlamch_("S") / _starpu_dlamch_("P");
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- bignum = 1. / smlnum;
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- _starpu_dlabad_(&smlnum, &bignum);
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-
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-/* Scale A, B if max element outside range [SMLNUM,BIGNUM] */
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-
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- anrm = _starpu_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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-
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-/* Scale matrix norm up to SMLNUM */
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-
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- _starpu_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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-
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-/* Scale matrix norm down to BIGNUM */
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-
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- _starpu_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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-
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-/* Matrix all zero. Return zero solution. */
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-
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- i__1 = max(*m,*n);
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- _starpu_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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-
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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 = _starpu_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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-
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-/* Scale matrix norm up to SMLNUM */
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-
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- _starpu_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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-
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-/* Scale matrix norm down to BIGNUM */
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-
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- _starpu_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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-
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- if (*m >= *n) {
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-
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-/* compute QR factorization of A */
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-
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- i__1 = *lwork - mn;
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- _starpu_dgeqrf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
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- ;
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-
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-/* workspace at least N, optimally N*NB */
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-
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- if (! tpsd) {
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-
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-/* Least-Squares Problem min || A * X - B || */
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-
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-/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
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-
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- i__1 = *lwork - mn;
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- _starpu_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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-
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-/* workspace at least NRHS, optimally NRHS*NB */
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-
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-/* B(1:N,1:NRHS) := inv(R) * B(1:N,1:NRHS) */
|
|
|
-
|
|
|
- _starpu_dtrtrs_("Upper", "No transpose", "Non-unit", n, nrhs, &a[a_offset]
|
|
|
-, lda, &b[b_offset], ldb, info);
|
|
|
-
|
|
|
- if (*info > 0) {
|
|
|
- return 0;
|
|
|
- }
|
|
|
-
|
|
|
- scllen = *n;
|
|
|
-
|
|
|
- } else {
|
|
|
-
|
|
|
-/* Overdetermined system of equations A' * X = B */
|
|
|
-
|
|
|
-/* B(1:N,1:NRHS) := inv(R') * B(1:N,1:NRHS) */
|
|
|
-
|
|
|
- _starpu_dtrtrs_("Upper", "Transpose", "Non-unit", n, nrhs, &a[a_offset],
|
|
|
- lda, &b[b_offset], ldb, info);
|
|
|
-
|
|
|
- if (*info > 0) {
|
|
|
- return 0;
|
|
|
- }
|
|
|
-
|
|
|
-/* B(N+1:M,1:NRHS) = ZERO */
|
|
|
-
|
|
|
- i__1 = *nrhs;
|
|
|
- for (j = 1; j <= i__1; ++j) {
|
|
|
- i__2 = *m;
|
|
|
- for (i__ = *n + 1; i__ <= i__2; ++i__) {
|
|
|
- b[i__ + j * b_dim1] = 0.;
|
|
|
-/* L10: */
|
|
|
- }
|
|
|
-/* L20: */
|
|
|
- }
|
|
|
-
|
|
|
-/* B(1:M,1:NRHS) := Q(1:N,:) * B(1:N,1:NRHS) */
|
|
|
-
|
|
|
- i__1 = *lwork - mn;
|
|
|
- _starpu_dormqr_("Left", "No transpose", m, nrhs, n, &a[a_offset], lda, &
|
|
|
- work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
|
|
|
-
|
|
|
-/* workspace at least NRHS, optimally NRHS*NB */
|
|
|
-
|
|
|
- scllen = *m;
|
|
|
-
|
|
|
- }
|
|
|
-
|
|
|
- } else {
|
|
|
-
|
|
|
-/* Compute LQ factorization of A */
|
|
|
-
|
|
|
- i__1 = *lwork - mn;
|
|
|
- _starpu_dgelqf_(m, n, &a[a_offset], lda, &work[1], &work[mn + 1], &i__1, info)
|
|
|
- ;
|
|
|
-
|
|
|
-/* workspace at least M, optimally M*NB. */
|
|
|
-
|
|
|
- if (! tpsd) {
|
|
|
-
|
|
|
-/* underdetermined system of equations A * X = B */
|
|
|
-
|
|
|
-/* B(1:M,1:NRHS) := inv(L) * B(1:M,1:NRHS) */
|
|
|
-
|
|
|
- _starpu_dtrtrs_("Lower", "No transpose", "Non-unit", m, nrhs, &a[a_offset]
|
|
|
-, lda, &b[b_offset], ldb, info);
|
|
|
-
|
|
|
- if (*info > 0) {
|
|
|
- return 0;
|
|
|
- }
|
|
|
-
|
|
|
-/* B(M+1:N,1:NRHS) = 0 */
|
|
|
-
|
|
|
- i__1 = *nrhs;
|
|
|
- for (j = 1; j <= i__1; ++j) {
|
|
|
- i__2 = *n;
|
|
|
- for (i__ = *m + 1; i__ <= i__2; ++i__) {
|
|
|
- b[i__ + j * b_dim1] = 0.;
|
|
|
-/* L30: */
|
|
|
- }
|
|
|
-/* L40: */
|
|
|
- }
|
|
|
-
|
|
|
-/* B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS) */
|
|
|
-
|
|
|
- i__1 = *lwork - mn;
|
|
|
- _starpu_dormlq_("Left", "Transpose", n, nrhs, m, &a[a_offset], lda, &work[
|
|
|
- 1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
|
|
|
-
|
|
|
-/* workspace at least NRHS, optimally NRHS*NB */
|
|
|
-
|
|
|
- scllen = *n;
|
|
|
-
|
|
|
- } else {
|
|
|
-
|
|
|
-/* overdetermined system min || A' * X - B || */
|
|
|
-
|
|
|
-/* B(1:N,1:NRHS) := Q * B(1:N,1:NRHS) */
|
|
|
-
|
|
|
- i__1 = *lwork - mn;
|
|
|
- _starpu_dormlq_("Left", "No transpose", n, nrhs, m, &a[a_offset], lda, &
|
|
|
- work[1], &b[b_offset], ldb, &work[mn + 1], &i__1, info);
|
|
|
-
|
|
|
-/* workspace at least NRHS, optimally NRHS*NB */
|
|
|
-
|
|
|
-/* B(1:M,1:NRHS) := inv(L') * B(1:M,1:NRHS) */
|
|
|
-
|
|
|
- _starpu_dtrtrs_("Lower", "Transpose", "Non-unit", m, nrhs, &a[a_offset],
|
|
|
- lda, &b[b_offset], ldb, info);
|
|
|
-
|
|
|
- if (*info > 0) {
|
|
|
- return 0;
|
|
|
- }
|
|
|
-
|
|
|
- scllen = *m;
|
|
|
-
|
|
|
- }
|
|
|
-
|
|
|
- }
|
|
|
-
|
|
|
-/* Undo scaling */
|
|
|
-
|
|
|
- if (iascl == 1) {
|
|
|
- _starpu_dlascl_("G", &c__0, &c__0, &anrm, &smlnum, &scllen, nrhs, &b[b_offset]
|
|
|
-, ldb, info);
|
|
|
- } else if (iascl == 2) {
|
|
|
- _starpu_dlascl_("G", &c__0, &c__0, &anrm, &bignum, &scllen, nrhs, &b[b_offset]
|
|
|
-, ldb, info);
|
|
|
- }
|
|
|
- if (ibscl == 1) {
|
|
|
- _starpu_dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, &scllen, nrhs, &b[b_offset]
|
|
|
-, ldb, info);
|
|
|
- } else if (ibscl == 2) {
|
|
|
- _starpu_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 */
|
|
|
-
|
|
|
-} /* _starpu_dgels_ */
|