zlqt01.c
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00001 /* zlqt01.f -- translated by f2c (version 20061008).
00002    You must link the resulting object file with libf2c:
00003         on Microsoft Windows system, link with libf2c.lib;
00004         on Linux or Unix systems, link with .../path/to/libf2c.a -lm
00005         or, if you install libf2c.a in a standard place, with -lf2c -lm
00006         -- in that order, at the end of the command line, as in
00007                 cc *.o -lf2c -lm
00008         Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
00009 
00010                 http://www.netlib.org/f2c/libf2c.zip
00011 */
00012 
00013 #include "f2c.h"
00014 #include "blaswrap.h"
00015 
00016 /* Common Block Declarations */
00017 
00018 struct {
00019     char srnamt[32];
00020 } srnamc_;
00021 
00022 #define srnamc_1 srnamc_
00023 
00024 /* Table of constant values */
00025 
00026 static doublecomplex c_b1 = {-1e10,-1e10};
00027 static doublecomplex c_b10 = {0.,0.};
00028 static doublecomplex c_b15 = {-1.,0.};
00029 static doublecomplex c_b16 = {1.,0.};
00030 static doublereal c_b24 = -1.;
00031 static doublereal c_b25 = 1.;
00032 
00033 /* Subroutine */ int zlqt01_(integer *m, integer *n, doublecomplex *a, 
00034         doublecomplex *af, doublecomplex *q, doublecomplex *l, integer *lda, 
00035         doublecomplex *tau, doublecomplex *work, integer *lwork, doublereal *
00036         rwork, doublereal *result)
00037 {
00038     /* System generated locals */
00039     integer a_dim1, a_offset, af_dim1, af_offset, l_dim1, l_offset, q_dim1, 
00040             q_offset, i__1;
00041 
00042     /* Builtin functions */
00043     /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
00044 
00045     /* Local variables */
00046     doublereal eps;
00047     integer info;
00048     doublereal resid, anorm;
00049     integer minmn;
00050     extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 
00051             integer *, doublecomplex *, doublecomplex *, integer *, 
00052             doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
00053             integer *), zherk_(char *, char *, integer *, 
00054             integer *, doublereal *, doublecomplex *, integer *, doublereal *, 
00055              doublecomplex *, integer *);
00056     extern doublereal dlamch_(char *), zlange_(char *, integer *, 
00057             integer *, doublecomplex *, integer *, doublereal *);
00058     extern /* Subroutine */ int zgelqf_(integer *, integer *, doublecomplex *, 
00059              integer *, doublecomplex *, doublecomplex *, integer *, integer *
00060 ), zlacpy_(char *, integer *, integer *, doublecomplex *, integer 
00061             *, doublecomplex *, integer *), zlaset_(char *, integer *, 
00062              integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
00063             integer *);
00064     extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, 
00065             integer *, doublereal *);
00066     extern /* Subroutine */ int zunglq_(integer *, integer *, integer *, 
00067             doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
00068             integer *, integer *);
00069 
00070 
00071 /*  -- LAPACK test routine (version 3.1) -- */
00072 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00073 /*     November 2006 */
00074 
00075 /*     .. Scalar Arguments .. */
00076 /*     .. */
00077 /*     .. Array Arguments .. */
00078 /*     .. */
00079 
00080 /*  Purpose */
00081 /*  ======= */
00082 
00083 /*  ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n */
00084 /*  matrix A, and partially tests ZUNGLQ which forms the n-by-n */
00085 /*  orthogonal matrix Q. */
00086 
00087 /*  ZLQT01 compares L with A*Q', and checks that Q is orthogonal. */
00088 
00089 /*  Arguments */
00090 /*  ========= */
00091 
00092 /*  M       (input) INTEGER */
00093 /*          The number of rows of the matrix A.  M >= 0. */
00094 
00095 /*  N       (input) INTEGER */
00096 /*          The number of columns of the matrix A.  N >= 0. */
00097 
00098 /*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
00099 /*          The m-by-n matrix A. */
00100 
00101 /*  AF      (output) COMPLEX*16 array, dimension (LDA,N) */
00102 /*          Details of the LQ factorization of A, as returned by ZGELQF. */
00103 /*          See ZGELQF for further details. */
00104 
00105 /*  Q       (output) COMPLEX*16 array, dimension (LDA,N) */
00106 /*          The n-by-n orthogonal matrix Q. */
00107 
00108 /*  L       (workspace) COMPLEX*16 array, dimension (LDA,max(M,N)) */
00109 
00110 /*  LDA     (input) INTEGER */
00111 /*          The leading dimension of the arrays A, AF, Q and L. */
00112 /*          LDA >= max(M,N). */
00113 
00114 /*  TAU     (output) COMPLEX*16 array, dimension (min(M,N)) */
00115 /*          The scalar factors of the elementary reflectors, as returned */
00116 /*          by ZGELQF. */
00117 
00118 /*  WORK    (workspace) COMPLEX*16 array, dimension (LWORK) */
00119 
00120 /*  LWORK   (input) INTEGER */
00121 /*          The dimension of the array WORK. */
00122 
00123 /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */
00124 
00125 /*  RESULT  (output) DOUBLE PRECISION array, dimension (2) */
00126 /*          The test ratios: */
00127 /*          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) */
00128 /*          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
00129 
00130 /*  ===================================================================== */
00131 
00132 /*     .. Parameters .. */
00133 /*     .. */
00134 /*     .. Local Scalars .. */
00135 /*     .. */
00136 /*     .. External Functions .. */
00137 /*     .. */
00138 /*     .. External Subroutines .. */
00139 /*     .. */
00140 /*     .. Intrinsic Functions .. */
00141 /*     .. */
00142 /*     .. Scalars in Common .. */
00143 /*     .. */
00144 /*     .. Common blocks .. */
00145 /*     .. */
00146 /*     .. Executable Statements .. */
00147 
00148     /* Parameter adjustments */
00149     l_dim1 = *lda;
00150     l_offset = 1 + l_dim1;
00151     l -= l_offset;
00152     q_dim1 = *lda;
00153     q_offset = 1 + q_dim1;
00154     q -= q_offset;
00155     af_dim1 = *lda;
00156     af_offset = 1 + af_dim1;
00157     af -= af_offset;
00158     a_dim1 = *lda;
00159     a_offset = 1 + a_dim1;
00160     a -= a_offset;
00161     --tau;
00162     --work;
00163     --rwork;
00164     --result;
00165 
00166     /* Function Body */
00167     minmn = min(*m,*n);
00168     eps = dlamch_("Epsilon");
00169 
00170 /*     Copy the matrix A to the array AF. */
00171 
00172     zlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
00173 
00174 /*     Factorize the matrix A in the array AF. */
00175 
00176     s_copy(srnamc_1.srnamt, "ZGELQF", (ftnlen)32, (ftnlen)6);
00177     zgelqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
00178 
00179 /*     Copy details of Q */
00180 
00181     zlaset_("Full", n, n, &c_b1, &c_b1, &q[q_offset], lda);
00182     if (*n > 1) {
00183         i__1 = *n - 1;
00184         zlacpy_("Upper", m, &i__1, &af[(af_dim1 << 1) + 1], lda, &q[(q_dim1 <<
00185                  1) + 1], lda);
00186     }
00187 
00188 /*     Generate the n-by-n matrix Q */
00189 
00190     s_copy(srnamc_1.srnamt, "ZUNGLQ", (ftnlen)32, (ftnlen)6);
00191     zunglq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
00192 
00193 /*     Copy L */
00194 
00195     zlaset_("Full", m, n, &c_b10, &c_b10, &l[l_offset], lda);
00196     zlacpy_("Lower", m, n, &af[af_offset], lda, &l[l_offset], lda);
00197 
00198 /*     Compute L - A*Q' */
00199 
00200     zgemm_("No transpose", "Conjugate transpose", m, n, n, &c_b15, &a[
00201             a_offset], lda, &q[q_offset], lda, &c_b16, &l[l_offset], lda);
00202 
00203 /*     Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) . */
00204 
00205     anorm = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
00206     resid = zlange_("1", m, n, &l[l_offset], lda, &rwork[1]);
00207     if (anorm > 0.) {
00208         result[1] = resid / (doublereal) max(1,*n) / anorm / eps;
00209     } else {
00210         result[1] = 0.;
00211     }
00212 
00213 /*     Compute I - Q*Q' */
00214 
00215     zlaset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
00216     zherk_("Upper", "No transpose", n, n, &c_b24, &q[q_offset], lda, &c_b25, &
00217             l[l_offset], lda);
00218 
00219 /*     Compute norm( I - Q*Q' ) / ( N * EPS ) . */
00220 
00221     resid = zlansy_("1", "Upper", n, &l[l_offset], lda, &rwork[1]);
00222 
00223     result[2] = resid / (doublereal) max(1,*n) / eps;
00224 
00225     return 0;
00226 
00227 /*     End of ZLQT01 */
00228 
00229 } /* zlqt01_ */


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autogenerated on Sat Jun 8 2019 18:56:42