#include "blaswrap.h" /* zqrt02.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 zqrt02_(integer *m, integer *n, integer *k, doublecomplex *a, doublecomplex *af, doublecomplex *q, doublecomplex * r__, integer *lda, doublecomplex *tau, doublecomplex *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; 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 zungqr_(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 ======= ZQRT02 tests ZUNGQR, 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, ZQRT02 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) COMPLEX*16 array, dimension (LDA,N) The m-by-n matrix A which was factorized by ZQRT01. AF (input) COMPLEX*16 array, dimension (LDA,N) Details of the QR factorization of A, as returned by ZGEQRF. See ZGEQRF for further details. Q (workspace) COMPLEX*16 array, dimension (LDA,N) R (workspace) COMPLEX*16 array, dimension (LDA,N) LDA (input) INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M. TAU (input) COMPLEX*16 array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR 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( 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 */ zlaset_("Full", m, n, &c_b1, &c_b1, &q[q_offset], lda); i__1 = *m - 1; zlacpy_("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, "ZUNGQR", (ftnlen)6, (ftnlen)6); zungqr_(m, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info); /* Copy R(1:n,1:k) */ zlaset_("Full", n, k, &c_b8, &c_b8, &r__[r_offset], lda); zlacpy_("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) */ zgemm_("Conjugate transpose", "No transpose", n, k, m, &c_b13, &q[ q_offset], lda, &a[a_offset], lda, &c_b14, &r__[r_offset], lda); /* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . */ anorm = zlange_("1", m, k, &a[a_offset], lda, &rwork[1]); resid = zlange_("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 */ zlaset_("Full", n, n, &c_b8, &c_b14, &r__[r_offset], lda); zherk_("Upper", "Conjugate transpose", n, m, &c_b22, &q[q_offset], lda, & c_b23, &r__[r_offset], lda); /* Compute norm( I - Q'*Q ) / ( M * EPS ) . */ resid = zlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]); result[2] = resid / (doublereal) max(1,*m) / eps; return 0; /* End of ZQRT02 */ } /* zqrt02_ */