drqt01.c
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00001 /* drqt01.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 doublereal c_b6 = -1e10;
00027 static doublereal c_b13 = 0.;
00028 static doublereal c_b20 = -1.;
00029 static doublereal c_b21 = 1.;
00030 
00031 /* Subroutine */ int drqt01_(integer *m, integer *n, doublereal *a, 
00032         doublereal *af, doublereal *q, doublereal *r__, integer *lda, 
00033         doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork, 
00034         doublereal *result)
00035 {
00036     /* System generated locals */
00037     integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1, 
00038             r_offset, i__1, i__2;
00039 
00040     /* Builtin functions */
00041     /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
00042 
00043     /* Local variables */
00044     doublereal eps;
00045     integer info;
00046     extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
00047             integer *, doublereal *, doublereal *, integer *, doublereal *, 
00048             integer *, doublereal *, doublereal *, integer *);
00049     doublereal resid, anorm;
00050     integer minmn;
00051     extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, 
00052             doublereal *, doublereal *, integer *, doublereal *, doublereal *, 
00053              integer *);
00054     extern doublereal dlamch_(char *), dlange_(char *, integer *, 
00055             integer *, doublereal *, integer *, doublereal *);
00056     extern /* Subroutine */ int dgerqf_(integer *, integer *, doublereal *, 
00057             integer *, doublereal *, doublereal *, integer *, integer *), 
00058             dlacpy_(char *, integer *, integer *, doublereal *, integer *, 
00059             doublereal *, integer *), dlaset_(char *, integer *, 
00060             integer *, doublereal *, doublereal *, doublereal *, integer *);
00061     extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
00062             integer *, doublereal *);
00063     extern /* Subroutine */ int dorgrq_(integer *, integer *, integer *, 
00064             doublereal *, integer *, doublereal *, doublereal *, integer *, 
00065             integer *);
00066 
00067 
00068 /*  -- LAPACK test routine (version 3.1) -- */
00069 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00070 /*     November 2006 */
00071 
00072 /*     .. Scalar Arguments .. */
00073 /*     .. */
00074 /*     .. Array Arguments .. */
00075 /*     .. */
00076 
00077 /*  Purpose */
00078 /*  ======= */
00079 
00080 /*  DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n */
00081 /*  matrix A, and partially tests DORGRQ which forms the n-by-n */
00082 /*  orthogonal matrix Q. */
00083 
00084 /*  DRQT01 compares R with A*Q', and checks that Q is orthogonal. */
00085 
00086 /*  Arguments */
00087 /*  ========= */
00088 
00089 /*  M       (input) INTEGER */
00090 /*          The number of rows of the matrix A.  M >= 0. */
00091 
00092 /*  N       (input) INTEGER */
00093 /*          The number of columns of the matrix A.  N >= 0. */
00094 
00095 /*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
00096 /*          The m-by-n matrix A. */
00097 
00098 /*  AF      (output) DOUBLE PRECISION array, dimension (LDA,N) */
00099 /*          Details of the RQ factorization of A, as returned by DGERQF. */
00100 /*          See DGERQF for further details. */
00101 
00102 /*  Q       (output) DOUBLE PRECISION array, dimension (LDA,N) */
00103 /*          The n-by-n orthogonal matrix Q. */
00104 
00105 /*  R       (workspace) DOUBLE PRECISION array, dimension (LDA,max(M,N)) */
00106 
00107 /*  LDA     (input) INTEGER */
00108 /*          The leading dimension of the arrays A, AF, Q and L. */
00109 /*          LDA >= max(M,N). */
00110 
00111 /*  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N)) */
00112 /*          The scalar factors of the elementary reflectors, as returned */
00113 /*          by DGERQF. */
00114 
00115 /*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK) */
00116 
00117 /*  LWORK   (input) INTEGER */
00118 /*          The dimension of the array WORK. */
00119 
00120 /*  RWORK   (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */
00121 
00122 /*  RESULT  (output) DOUBLE PRECISION array, dimension (2) */
00123 /*          The test ratios: */
00124 /*          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) */
00125 /*          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) */
00126 
00127 /*  ===================================================================== */
00128 
00129 /*     .. Parameters .. */
00130 /*     .. */
00131 /*     .. Local Scalars .. */
00132 /*     .. */
00133 /*     .. External Functions .. */
00134 /*     .. */
00135 /*     .. External Subroutines .. */
00136 /*     .. */
00137 /*     .. Intrinsic Functions .. */
00138 /*     .. */
00139 /*     .. Scalars in Common .. */
00140 /*     .. */
00141 /*     .. Common blocks .. */
00142 /*     .. */
00143 /*     .. Executable Statements .. */
00144 
00145     /* Parameter adjustments */
00146     r_dim1 = *lda;
00147     r_offset = 1 + r_dim1;
00148     r__ -= r_offset;
00149     q_dim1 = *lda;
00150     q_offset = 1 + q_dim1;
00151     q -= q_offset;
00152     af_dim1 = *lda;
00153     af_offset = 1 + af_dim1;
00154     af -= af_offset;
00155     a_dim1 = *lda;
00156     a_offset = 1 + a_dim1;
00157     a -= a_offset;
00158     --tau;
00159     --work;
00160     --rwork;
00161     --result;
00162 
00163     /* Function Body */
00164     minmn = min(*m,*n);
00165     eps = dlamch_("Epsilon");
00166 
00167 /*     Copy the matrix A to the array AF. */
00168 
00169     dlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
00170 
00171 /*     Factorize the matrix A in the array AF. */
00172 
00173     s_copy(srnamc_1.srnamt, "DGERQF", (ftnlen)32, (ftnlen)6);
00174     dgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);
00175 
00176 /*     Copy details of Q */
00177 
00178     dlaset_("Full", n, n, &c_b6, &c_b6, &q[q_offset], lda);
00179     if (*m <= *n) {
00180         if (*m > 0 && *m < *n) {
00181             i__1 = *n - *m;
00182             dlacpy_("Full", m, &i__1, &af[af_offset], lda, &q[*n - *m + 1 + 
00183                     q_dim1], lda);
00184         }
00185         if (*m > 1) {
00186             i__1 = *m - 1;
00187             i__2 = *m - 1;
00188             dlacpy_("Lower", &i__1, &i__2, &af[(*n - *m + 1) * af_dim1 + 2], 
00189                     lda, &q[*n - *m + 2 + (*n - *m + 1) * q_dim1], lda);
00190         }
00191     } else {
00192         if (*n > 1) {
00193             i__1 = *n - 1;
00194             i__2 = *n - 1;
00195             dlacpy_("Lower", &i__1, &i__2, &af[*m - *n + 2 + af_dim1], lda, &
00196                     q[q_dim1 + 2], lda);
00197         }
00198     }
00199 
00200 /*     Generate the n-by-n matrix Q */
00201 
00202     s_copy(srnamc_1.srnamt, "DORGRQ", (ftnlen)32, (ftnlen)6);
00203     dorgrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);
00204 
00205 /*     Copy R */
00206 
00207     dlaset_("Full", m, n, &c_b13, &c_b13, &r__[r_offset], lda);
00208     if (*m <= *n) {
00209         if (*m > 0) {
00210             dlacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &
00211                     r__[(*n - *m + 1) * r_dim1 + 1], lda);
00212         }
00213     } else {
00214         if (*m > *n && *n > 0) {
00215             i__1 = *m - *n;
00216             dlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], 
00217                     lda);
00218         }
00219         if (*n > 0) {
00220             dlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m - 
00221                     *n + 1 + r_dim1], lda);
00222         }
00223     }
00224 
00225 /*     Compute R - A*Q' */
00226 
00227     dgemm_("No transpose", "Transpose", m, n, n, &c_b20, &a[a_offset], lda, &
00228             q[q_offset], lda, &c_b21, &r__[r_offset], lda);
00229 
00230 /*     Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . */
00231 
00232     anorm = dlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
00233     resid = dlange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
00234     if (anorm > 0.) {
00235         result[1] = resid / (doublereal) max(1,*n) / anorm / eps;
00236     } else {
00237         result[1] = 0.;
00238     }
00239 
00240 /*     Compute I - Q*Q' */
00241 
00242     dlaset_("Full", n, n, &c_b13, &c_b21, &r__[r_offset], lda);
00243     dsyrk_("Upper", "No transpose", n, n, &c_b20, &q[q_offset], lda, &c_b21, &
00244             r__[r_offset], lda);
00245 
00246 /*     Compute norm( I - Q*Q' ) / ( N * EPS ) . */
00247 
00248     resid = dlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
00249 
00250     result[2] = resid / (doublereal) max(1,*n) / eps;
00251 
00252     return 0;
00253 
00254 /*     End of DRQT01 */
00255 
00256 } /* drqt01_ */


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autogenerated on Sat Jun 8 2019 18:55:48