#include "blaswrap.h" /* dqrt01.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" /* Common Block Declarations */ struct { char srnamt[6]; } srnamc_; #define srnamc_1 srnamc_ /* Table of constant values */ static doublereal c_b6 = -1e10; static doublereal c_b11 = 0.; static doublereal c_b16 = -1.; static doublereal c_b17 = 1.; /* Subroutine */ int dqrt01_(integer *m, integer *n, doublereal *a, doublereal *af, doublereal *q, doublereal *r__, integer *lda, doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork, doublereal *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 */ static doublereal eps; static integer info; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); static doublereal resid, anorm; static integer minmn; extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *); extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *); extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n matrix A, and partially tests DORGQR which forms the m-by-m orthogonal matrix Q. DQRT01 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) DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A. AF (output) DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details. Q (output) DOUBLE PRECISION array, dimension (LDA,M) The m-by-m orthogonal matrix Q. R (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors, as returned by DGEQRF. WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) LWORK (input) INTEGER The dimension of the array WORK. RWORK (workspace) DOUBLE PRECISION array, dimension (M) RESULT (output) DOUBLE PRECISION array, dimension (2) The test ratios: RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) ===================================================================== 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 = dlamch_("Epsilon"); /* Copy the matrix A to the array AF. */ dlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda); /* Factorize the matrix A in the array AF. */ s_copy(srnamc_1.srnamt, "DGEQRF", (ftnlen)6, (ftnlen)6); dgeqrf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info); /* Copy details of Q */ dlaset_("Full", m, m, &c_b6, &c_b6, &q[q_offset], lda); i__1 = *m - 1; dlacpy_("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, "DORGQR", (ftnlen)6, (ftnlen)6); dorgqr_(m, m, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info); /* Copy R */ dlaset_("Full", m, n, &c_b11, &c_b11, &r__[r_offset], lda); dlacpy_("Upper", m, n, &af[af_offset], lda, &r__[r_offset], lda); /* Compute R - Q'*A */ dgemm_("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 = dlange_("1", m, n, &a[a_offset], lda, &rwork[1]); resid = dlange_("1", m, n, &r__[r_offset], lda, &rwork[1]); if (anorm > 0.) { result[1] = resid / (doublereal) max(1,*m) / anorm / eps; } else { result[1] = 0.; } /* Compute I - Q'*Q */ dlaset_("Full", m, m, &c_b11, &c_b17, &r__[r_offset], lda); dsyrk_("Upper", "Transpose", m, m, &c_b16, &q[q_offset], lda, &c_b17, & r__[r_offset], lda); /* Compute norm( I - Q'*Q ) / ( M * EPS ) . */ resid = dlansy_("1", "Upper", m, &r__[r_offset], lda, &rwork[1]); result[2] = resid / (doublereal) max(1,*m) / eps; return 0; /* End of DQRT01 */ } /* dqrt01_ */