/* sqrt01.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Common Block Declarations */
struct {
char srnamt[32];
} srnamc_;
#define srnamc_1 srnamc_
/* Table of constant values */
static real c_b6 = -1e10f;
static real c_b11 = 0.f;
static real c_b16 = -1.f;
static real c_b17 = 1.f;
/* Subroutine */ int sqrt01_(integer *m, integer *n, real *a, real *af, real *
q, real *r__, integer *lda, real *tau, real *work, integer *lwork,
real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1,
r_offset, i__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real eps;
integer info;
real resid;
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
real anorm;
integer minmn;
extern /* Subroutine */ int ssyrk_(char *, char *, integer *, integer *,
real *, real *, integer *, real *, real *, integer *);
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer
*, real *, real *, integer *, integer *), slacpy_(char *, integer
*, integer *, real *, integer *, real *, integer *),
slaset_(char *, integer *, integer *, real *, real *, real *,
integer *);
extern doublereal slansy_(char *, char *, integer *, real *, integer *,
real *);
extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real
*, integer *, real *, real *, integer *, integer *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n */
/* matrix A, and partially tests SORGQR which forms the m-by-m */
/* orthogonal matrix Q. */
/* SQRT01 compares R with Q'*A, and checks that Q is orthogonal. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* A (input) REAL array, dimension (LDA,N) */
/* The m-by-n matrix A. */
/* AF (output) REAL array, dimension (LDA,N) */
/* Details of the QR factorization of A, as returned by SGEQRF. */
/* See SGEQRF for further details. */
/* Q (output) REAL array, dimension (LDA,M) */
/* The m-by-m orthogonal matrix Q. */
/* R (workspace) REAL array, dimension (LDA,max(M,N)) */
/* LDA (input) INTEGER */
/* The leading dimension of the arrays A, AF, Q and R. */
/* LDA >= max(M,N). */
/* TAU (output) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors, as returned */
/* by SGEQRF. */
/* WORK (workspace) REAL array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* RWORK (workspace) REAL array, dimension (M) */
/* RESULT (output) REAL array, dimension (2) */
/* The test ratios: */
/* RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) */
/* RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
r_dim1 = *lda;
r_offset = 1 + r_dim1;
r__ -= r_offset;
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
af_dim1 = *lda;
af_offset = 1 + af_dim1;
af -= af_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
minmn = min(*m,*n);
eps = slamch_("Epsilon");
/* Copy the matrix A to the array AF. */
slacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
/* Factorize the matrix A in the array AF. */
s_copy(srnamc_1.srnamt, "SGEQRF", (ftnlen)32, (ftnlen)6);
sgeqrf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy details of Q */
slaset_("Full", m, m, &c_b6, &c_b6, &q[q_offset], lda);
i__1 = *m - 1;
slacpy_("Lower", &i__1, n, &af[af_dim1 + 2], lda, &q[q_dim1 + 2], lda);
/* Generate the m-by-m matrix Q */
s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)32, (ftnlen)6);
sorgqr_(m, m, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
/* Copy R */
slaset_("Full", m, n, &c_b11, &c_b11, &r__[r_offset], lda);
slacpy_("Upper", m, n, &af[af_offset], lda, &r__[r_offset], lda);
/* Compute R - Q'*A */
sgemm_("Transpose", "No transpose", m, n, m, &c_b16, &q[q_offset], lda, &
a[a_offset], lda, &c_b17, &r__[r_offset], lda);
/* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . */
anorm = slange_("1", m, n, &a[a_offset], lda, &rwork[1]);
resid = slange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
if (anorm > 0.f) {
result[1] = resid / (real) max(1,*m) / anorm / eps;
} else {
result[1] = 0.f;
}
/* Compute I - Q'*Q */
slaset_("Full", m, m, &c_b11, &c_b17, &r__[r_offset], lda);
ssyrk_("Upper", "Transpose", m, m, &c_b16, &q[q_offset], lda, &c_b17, &
r__[r_offset], lda);
/* Compute norm( I - Q'*Q ) / ( M * EPS ) . */
resid = slansy_("1", "Upper", m, &r__[r_offset], lda, &rwork[1]);
result[2] = resid / (real) max(1,*m) / eps;
return 0;
/* End of SQRT01 */
} /* sqrt01_ */