#include "blaswrap.h" /* zlqt02.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 doublecomplex c_b1 = {-1e10,-1e10}; static doublecomplex c_b8 = {0.,0.}; static doublecomplex c_b13 = {-1.,0.}; static doublecomplex c_b14 = {1.,0.}; static doublereal c_b22 = -1.; static doublereal c_b23 = 1.; /* Subroutine */ int zlqt02_(integer *m, integer *n, integer *k, doublecomplex *a, doublecomplex *af, doublecomplex *q, doublecomplex * l, integer *lda, doublecomplex *tau, doublecomplex *work, integer * lwork, doublereal *rwork, doublereal *result) { /* System generated locals */ integer a_dim1, a_offset, af_dim1, af_offset, l_dim1, l_offset, q_dim1, q_offset, i__1; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ static doublereal eps; static integer info; static doublereal resid, anorm; extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zherk_(char *, char *, integer *, integer *, doublereal *, doublecomplex *, integer *, doublereal *, doublecomplex *, integer *); extern doublereal dlamch_(char *), zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int zunglq_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *); /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with orthonornmal rows that is defined as the product of k elementary reflectors. Given the LQ factorization of an m-by-n matrix A, ZLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and checks that the rows 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. N >= M >= 0. K (input) INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0. A (input) COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A which was factorized by ZLQT01. AF (input) COMPLEX*16 array, dimension (LDA,N) Details of the LQ factorization of A, as returned by ZGELQF. See ZGELQF for further details. Q (workspace) COMPLEX*16 array, dimension (LDA,N) L (workspace) COMPLEX*16 array, dimension (LDA,M) LDA (input) INTEGER The leading dimension of the arrays A, AF, Q and L. LDA >= N. TAU (input) COMPLEX*16 array, dimension (M) The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF. WORK (workspace) COMPLEX*16 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( L - A*Q' ) / ( N * norm(A) * EPS ) RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) ===================================================================== Parameter adjustments */ l_dim1 = *lda; l_offset = 1 + l_dim1; l -= l_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 rows of the factorization to the array Q */ zlaset_("Full", m, n, &c_b1, &c_b1, &q[q_offset], lda); i__1 = *n - 1; zlacpy_("Upper", k, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 << 1) + 1], lda); /* Generate the first n columns of the matrix Q */ s_copy(srnamc_1.srnamt, "ZUNGLQ", (ftnlen)6, (ftnlen)6); zunglq_(m, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info); /* Copy L(1:k,1:m) */ zlaset_("Full", k, m, &c_b8, &c_b8, &l[l_offset], lda); zlacpy_("Lower", k, m, &af[af_offset], lda, &l[l_offset], lda); /* Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)' */ zgemm_("No transpose", "Conjugate transpose", k, m, n, &c_b13, &a[ a_offset], lda, &q[q_offset], lda, &c_b14, &l[l_offset], lda); /* Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) . */ anorm = zlange_("1", k, n, &a[a_offset], lda, &rwork[1]); resid = zlange_("1", k, m, &l[l_offset], lda, &rwork[1]); if (anorm > 0.) { result[1] = resid / (doublereal) max(1,*n) / anorm / eps; } else { result[1] = 0.; } /* Compute I - Q*Q' */ zlaset_("Full", m, m, &c_b8, &c_b14, &l[l_offset], lda); zherk_("Upper", "No transpose", m, n, &c_b22, &q[q_offset], lda, &c_b23, & l[l_offset], lda); /* Compute norm( I - Q*Q' ) / ( N * EPS ) . */ resid = zlansy_("1", "Upper", m, &l[l_offset], lda, &rwork[1]); result[2] = resid / (doublereal) max(1,*n) / eps; return 0; /* End of ZLQT02 */ } /* zlqt02_ */