dget07.c
Go to the documentation of this file.
00001 /* dget07.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 /* Table of constant values */
00017 
00018 static integer c__1 = 1;
00019 
00020 /* Subroutine */ int dget07_(char *trans, integer *n, integer *nrhs, 
00021         doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
00022         x, integer *ldx, doublereal *xact, integer *ldxact, doublereal *ferr, 
00023         logical *chkferr, doublereal *berr, doublereal *reslts)
00024 {
00025     /* System generated locals */
00026     integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, xact_dim1, 
00027             xact_offset, i__1, i__2, i__3;
00028     doublereal d__1, d__2, d__3;
00029 
00030     /* Local variables */
00031     integer i__, j, k;
00032     doublereal eps, tmp, diff, axbi;
00033     integer imax;
00034     doublereal unfl, ovfl;
00035     extern logical lsame_(char *, char *);
00036     doublereal xnorm;
00037     extern doublereal dlamch_(char *);
00038     extern integer idamax_(integer *, doublereal *, integer *);
00039     doublereal errbnd;
00040     logical notran;
00041 
00042 
00043 /*  -- LAPACK test routine (version 3.1) -- */
00044 /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
00045 /*     November 2006 */
00046 
00047 /*     .. Scalar Arguments .. */
00048 /*     .. */
00049 /*     .. Array Arguments .. */
00050 /*     .. */
00051 
00052 /*  Purpose */
00053 /*  ======= */
00054 
00055 /*  DGET07 tests the error bounds from iterative refinement for the */
00056 /*  computed solution to a system of equations op(A)*X = B, where A is a */
00057 /*  general n by n matrix and op(A) = A or A**T, depending on TRANS. */
00058 
00059 /*  RESLTS(1) = test of the error bound */
00060 /*            = norm(X - XACT) / ( norm(X) * FERR ) */
00061 
00062 /*  A large value is returned if this ratio is not less than one. */
00063 
00064 /*  RESLTS(2) = residual from the iterative refinement routine */
00065 /*            = the maximum of BERR / ( (n+1)*EPS + (*) ), where */
00066 /*              (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) */
00067 
00068 /*  Arguments */
00069 /*  ========= */
00070 
00071 /*  TRANS   (input) CHARACTER*1 */
00072 /*          Specifies the form of the system of equations. */
00073 /*          = 'N':  A * X = B     (No transpose) */
00074 /*          = 'T':  A**T * X = B  (Transpose) */
00075 /*          = 'C':  A**H * X = B  (Conjugate transpose = Transpose) */
00076 
00077 /*  N       (input) INTEGER */
00078 /*          The number of rows of the matrices X and XACT.  N >= 0. */
00079 
00080 /*  NRHS    (input) INTEGER */
00081 /*          The number of columns of the matrices X and XACT.  NRHS >= 0. */
00082 
00083 /*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
00084 /*          The original n by n matrix A. */
00085 
00086 /*  LDA     (input) INTEGER */
00087 /*          The leading dimension of the array A.  LDA >= max(1,N). */
00088 
00089 /*  B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
00090 /*          The right hand side vectors for the system of linear */
00091 /*          equations. */
00092 
00093 /*  LDB     (input) INTEGER */
00094 /*          The leading dimension of the array B.  LDB >= max(1,N). */
00095 
00096 /*  X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS) */
00097 /*          The computed solution vectors.  Each vector is stored as a */
00098 /*          column of the matrix X. */
00099 
00100 /*  LDX     (input) INTEGER */
00101 /*          The leading dimension of the array X.  LDX >= max(1,N). */
00102 
00103 /*  XACT    (input) DOUBLE PRECISION array, dimension (LDX,NRHS) */
00104 /*          The exact solution vectors.  Each vector is stored as a */
00105 /*          column of the matrix XACT. */
00106 
00107 /*  LDXACT  (input) INTEGER */
00108 /*          The leading dimension of the array XACT.  LDXACT >= max(1,N). */
00109 
00110 /*  FERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
00111 /*          The estimated forward error bounds for each solution vector */
00112 /*          X.  If XTRUE is the true solution, FERR bounds the magnitude */
00113 /*          of the largest entry in (X - XTRUE) divided by the magnitude */
00114 /*          of the largest entry in X. */
00115 
00116 /*  CHKFERR (input) LOGICAL */
00117 /*          Set to .TRUE. to check FERR, .FALSE. not to check FERR. */
00118 /*          When the test system is ill-conditioned, the "true" */
00119 /*          solution in XACT may be incorrect. */
00120 
00121 /*  BERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
00122 /*          The componentwise relative backward error of each solution */
00123 /*          vector (i.e., the smallest relative change in any entry of A */
00124 /*          or B that makes X an exact solution). */
00125 
00126 /*  RESLTS  (output) DOUBLE PRECISION array, dimension (2) */
00127 /*          The maximum over the NRHS solution vectors of the ratios: */
00128 /*          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) */
00129 /*          RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) */
00130 
00131 /*  ===================================================================== */
00132 
00133 /*     .. Parameters .. */
00134 /*     .. */
00135 /*     .. Local Scalars .. */
00136 /*     .. */
00137 /*     .. External Functions .. */
00138 /*     .. */
00139 /*     .. Intrinsic Functions .. */
00140 /*     .. */
00141 /*     .. Executable Statements .. */
00142 
00143 /*     Quick exit if N = 0 or NRHS = 0. */
00144 
00145     /* Parameter adjustments */
00146     a_dim1 = *lda;
00147     a_offset = 1 + a_dim1;
00148     a -= a_offset;
00149     b_dim1 = *ldb;
00150     b_offset = 1 + b_dim1;
00151     b -= b_offset;
00152     x_dim1 = *ldx;
00153     x_offset = 1 + x_dim1;
00154     x -= x_offset;
00155     xact_dim1 = *ldxact;
00156     xact_offset = 1 + xact_dim1;
00157     xact -= xact_offset;
00158     --ferr;
00159     --berr;
00160     --reslts;
00161 
00162     /* Function Body */
00163     if (*n <= 0 || *nrhs <= 0) {
00164         reslts[1] = 0.;
00165         reslts[2] = 0.;
00166         return 0;
00167     }
00168 
00169     eps = dlamch_("Epsilon");
00170     unfl = dlamch_("Safe minimum");
00171     ovfl = 1. / unfl;
00172     notran = lsame_(trans, "N");
00173 
00174 /*     Test 1:  Compute the maximum of */
00175 /*        norm(X - XACT) / ( norm(X) * FERR ) */
00176 /*     over all the vectors X and XACT using the infinity-norm. */
00177 
00178     errbnd = 0.;
00179     if (*chkferr) {
00180         i__1 = *nrhs;
00181         for (j = 1; j <= i__1; ++j) {
00182             imax = idamax_(n, &x[j * x_dim1 + 1], &c__1);
00183 /* Computing MAX */
00184             d__2 = (d__1 = x[imax + j * x_dim1], abs(d__1));
00185             xnorm = max(d__2,unfl);
00186             diff = 0.;
00187             i__2 = *n;
00188             for (i__ = 1; i__ <= i__2; ++i__) {
00189 /* Computing MAX */
00190                 d__2 = diff, d__3 = (d__1 = x[i__ + j * x_dim1] - xact[i__ + 
00191                         j * xact_dim1], abs(d__1));
00192                 diff = max(d__2,d__3);
00193 /* L10: */
00194             }
00195 
00196             if (xnorm > 1.) {
00197                 goto L20;
00198             } else if (diff <= ovfl * xnorm) {
00199                 goto L20;
00200             } else {
00201                 errbnd = 1. / eps;
00202                 goto L30;
00203             }
00204 
00205 L20:
00206             if (diff / xnorm <= ferr[j]) {
00207 /* Computing MAX */
00208                 d__1 = errbnd, d__2 = diff / xnorm / ferr[j];
00209                 errbnd = max(d__1,d__2);
00210             } else {
00211                 errbnd = 1. / eps;
00212             }
00213 L30:
00214             ;
00215         }
00216     }
00217     reslts[1] = errbnd;
00218 
00219 /*     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where */
00220 /*     (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i ) */
00221 
00222     i__1 = *nrhs;
00223     for (k = 1; k <= i__1; ++k) {
00224         i__2 = *n;
00225         for (i__ = 1; i__ <= i__2; ++i__) {
00226             tmp = (d__1 = b[i__ + k * b_dim1], abs(d__1));
00227             if (notran) {
00228                 i__3 = *n;
00229                 for (j = 1; j <= i__3; ++j) {
00230                     tmp += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * (d__2 = 
00231                             x[j + k * x_dim1], abs(d__2));
00232 /* L40: */
00233                 }
00234             } else {
00235                 i__3 = *n;
00236                 for (j = 1; j <= i__3; ++j) {
00237                     tmp += (d__1 = a[j + i__ * a_dim1], abs(d__1)) * (d__2 = 
00238                             x[j + k * x_dim1], abs(d__2));
00239 /* L50: */
00240                 }
00241             }
00242             if (i__ == 1) {
00243                 axbi = tmp;
00244             } else {
00245                 axbi = min(axbi,tmp);
00246             }
00247 /* L60: */
00248         }
00249 /* Computing MAX */
00250         d__1 = axbi, d__2 = (*n + 1) * unfl;
00251         tmp = berr[k] / ((*n + 1) * eps + (*n + 1) * unfl / max(d__1,d__2));
00252         if (k == 1) {
00253             reslts[2] = tmp;
00254         } else {
00255             reslts[2] = max(reslts[2],tmp);
00256         }
00257 /* L70: */
00258     }
00259 
00260     return 0;
00261 
00262 /*     End of DGET07 */
00263 
00264 } /* dget07_ */


swiftnav
Author(s):
autogenerated on Sat Jun 8 2019 18:55:44