#include "blaswrap.h" /* dqrt02.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_b4 = -1e10; static doublereal c_b9 = 0.; static doublereal c_b14 = -1.; static doublereal c_b15 = 1.; /* Subroutine */ int dqrt02_(integer *m, integer *n, integer *k, 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; 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 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 ======= DQRT02 tests DORGQR, which generates an m-by-n matrix Q with orthonornmal columns that is defined as the product of k elementary reflectors. Given the QR factorization of an m-by-n matrix A, DQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal. Arguments ========= M (input) INTEGER The number of rows of the matrix Q to be generated. M >= 0. N (input) INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0. K (input) INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The m-by-n matrix A which was factorized by DQRT01. AF (input) DOUBLE PRECISION array, dimension (LDA,N) Details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details. Q (workspace) DOUBLE PRECISION array, dimension (LDA,N) R (workspace) DOUBLE PRECISION array, dimension (LDA,N) LDA (input) INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M. TAU (input) DOUBLE PRECISION array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF. 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 */ eps = dlamch_("Epsilon"); /* Copy the first k columns of the factorization to the array Q */ dlaset_("Full", m, n, &c_b4, &c_b4, &q[q_offset], lda); i__1 = *m - 1; dlacpy_("Lower", &i__1, k, &af[af_dim1 + 2], lda, &q[q_dim1 + 2], lda); /* Generate the first n columns of the matrix Q */ s_copy(srnamc_1.srnamt, "DORGQR", (ftnlen)6, (ftnlen)6); dorgqr_(m, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info); /* Copy R(1:n,1:k) */ dlaset_("Full", n, k, &c_b9, &c_b9, &r__[r_offset], lda); dlacpy_("Upper", n, k, &af[af_offset], lda, &r__[r_offset], lda); /* Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k) */ dgemm_("Transpose", "No transpose", n, k, m, &c_b14, &q[q_offset], lda, & a[a_offset], lda, &c_b15, &r__[r_offset], lda); /* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . */ anorm = dlange_("1", m, k, &a[a_offset], lda, &rwork[1]); resid = dlange_("1", n, k, &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", n, n, &c_b9, &c_b15, &r__[r_offset], lda); dsyrk_("Upper", "Transpose", n, m, &c_b14, &q[q_offset], lda, &c_b15, & r__[r_offset], lda); /* Compute norm( I - Q'*Q ) / ( M * EPS ) . */ resid = dlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]); result[2] = resid / (doublereal) max(1,*m) / eps; return 0; /* End of DQRT02 */ } /* dqrt02_ */