dpot05.c
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00001 /* dpot05.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 dpot05_(char *uplo, 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         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     logical upper;
00037     doublereal xnorm;
00038     extern doublereal dlamch_(char *);
00039     extern integer idamax_(integer *, doublereal *, integer *);
00040     doublereal errbnd;
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 /*  DPOT05 tests the error bounds from iterative refinement for the */
00056 /*  computed solution to a system of equations A*X = B, where A is a */
00057 /*  symmetric n by n matrix. */
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(A)*abs(X) +abs(b))_i ) */
00067 
00068 /*  Arguments */
00069 /*  ========= */
00070 
00071 /*  UPLO    (input) CHARACTER*1 */
00072 /*          Specifies whether the upper or lower triangular part of the */
00073 /*          symmetric matrix A is stored. */
00074 /*          = 'U':  Upper triangular */
00075 /*          = 'L':  Lower triangular */
00076 
00077 /*  N       (input) INTEGER */
00078 /*          The number of rows of the matrices X, B, and XACT, and the */
00079 /*          order of the matrix A.  N >= 0. */
00080 
00081 /*  NRHS    (input) INTEGER */
00082 /*          The number of columns of the matrices X, B, and XACT. */
00083 /*          NRHS >= 0. */
00084 
00085 /*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
00086 /*          The symmetric matrix A.  If UPLO = 'U', the leading n by n */
00087 /*          upper triangular part of A contains the upper triangular part */
00088 /*          of the matrix A, and the strictly lower triangular part of A */
00089 /*          is not referenced.  If UPLO = 'L', the leading n by n lower */
00090 /*          triangular part of A contains the lower triangular part of */
00091 /*          the matrix A, and the strictly upper triangular part of A is */
00092 /*          not referenced. */
00093 
00094 /*  LDA     (input) INTEGER */
00095 /*          The leading dimension of the array A.  LDA >= max(1,N). */
00096 
00097 /*  B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS) */
00098 /*          The right hand side vectors for the system of linear */
00099 /*          equations. */
00100 
00101 /*  LDB     (input) INTEGER */
00102 /*          The leading dimension of the array B.  LDB >= max(1,N). */
00103 
00104 /*  X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS) */
00105 /*          The computed solution vectors.  Each vector is stored as a */
00106 /*          column of the matrix X. */
00107 
00108 /*  LDX     (input) INTEGER */
00109 /*          The leading dimension of the array X.  LDX >= max(1,N). */
00110 
00111 /*  XACT    (input) DOUBLE PRECISION array, dimension (LDX,NRHS) */
00112 /*          The exact solution vectors.  Each vector is stored as a */
00113 /*          column of the matrix XACT. */
00114 
00115 /*  LDXACT  (input) INTEGER */
00116 /*          The leading dimension of the array XACT.  LDXACT >= max(1,N). */
00117 
00118 /*  FERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
00119 /*          The estimated forward error bounds for each solution vector */
00120 /*          X.  If XTRUE is the true solution, FERR bounds the magnitude */
00121 /*          of the largest entry in (X - XTRUE) divided by the magnitude */
00122 /*          of the largest entry in X. */
00123 
00124 /*  BERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
00125 /*          The componentwise relative backward error of each solution */
00126 /*          vector (i.e., the smallest relative change in any entry of A */
00127 /*          or B that makes X an exact solution). */
00128 
00129 /*  RESLTS  (output) DOUBLE PRECISION array, dimension (2) */
00130 /*          The maximum over the NRHS solution vectors of the ratios: */
00131 /*          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) */
00132 /*          RESLTS(2) = BERR / ( (n+1)*EPS + (*) ) */
00133 
00134 /*  ===================================================================== */
00135 
00136 /*     .. Parameters .. */
00137 /*     .. */
00138 /*     .. Local Scalars .. */
00139 /*     .. */
00140 /*     .. External Functions .. */
00141 /*     .. */
00142 /*     .. Intrinsic Functions .. */
00143 /*     .. */
00144 /*     .. Executable Statements .. */
00145 
00146 /*     Quick exit if N = 0 or NRHS = 0. */
00147 
00148     /* Parameter adjustments */
00149     a_dim1 = *lda;
00150     a_offset = 1 + a_dim1;
00151     a -= a_offset;
00152     b_dim1 = *ldb;
00153     b_offset = 1 + b_dim1;
00154     b -= b_offset;
00155     x_dim1 = *ldx;
00156     x_offset = 1 + x_dim1;
00157     x -= x_offset;
00158     xact_dim1 = *ldxact;
00159     xact_offset = 1 + xact_dim1;
00160     xact -= xact_offset;
00161     --ferr;
00162     --berr;
00163     --reslts;
00164 
00165     /* Function Body */
00166     if (*n <= 0 || *nrhs <= 0) {
00167         reslts[1] = 0.;
00168         reslts[2] = 0.;
00169         return 0;
00170     }
00171 
00172     eps = dlamch_("Epsilon");
00173     unfl = dlamch_("Safe minimum");
00174     ovfl = 1. / unfl;
00175     upper = lsame_(uplo, "U");
00176 
00177 /*     Test 1:  Compute the maximum of */
00178 /*        norm(X - XACT) / ( norm(X) * FERR ) */
00179 /*     over all the vectors X and XACT using the infinity-norm. */
00180 
00181     errbnd = 0.;
00182     i__1 = *nrhs;
00183     for (j = 1; j <= i__1; ++j) {
00184         imax = idamax_(n, &x[j * x_dim1 + 1], &c__1);
00185 /* Computing MAX */
00186         d__2 = (d__1 = x[imax + j * x_dim1], abs(d__1));
00187         xnorm = max(d__2,unfl);
00188         diff = 0.;
00189         i__2 = *n;
00190         for (i__ = 1; i__ <= i__2; ++i__) {
00191 /* Computing MAX */
00192             d__2 = diff, d__3 = (d__1 = x[i__ + j * x_dim1] - xact[i__ + j * 
00193                     xact_dim1], abs(d__1));
00194             diff = max(d__2,d__3);
00195 /* L10: */
00196         }
00197 
00198         if (xnorm > 1.) {
00199             goto L20;
00200         } else if (diff <= ovfl * xnorm) {
00201             goto L20;
00202         } else {
00203             errbnd = 1. / eps;
00204             goto L30;
00205         }
00206 
00207 L20:
00208         if (diff / xnorm <= ferr[j]) {
00209 /* Computing MAX */
00210             d__1 = errbnd, d__2 = diff / xnorm / ferr[j];
00211             errbnd = max(d__1,d__2);
00212         } else {
00213             errbnd = 1. / eps;
00214         }
00215 L30:
00216         ;
00217     }
00218     reslts[1] = errbnd;
00219 
00220 /*     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where */
00221 /*     (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
00222 
00223     i__1 = *nrhs;
00224     for (k = 1; k <= i__1; ++k) {
00225         i__2 = *n;
00226         for (i__ = 1; i__ <= i__2; ++i__) {
00227             tmp = (d__1 = b[i__ + k * b_dim1], abs(d__1));
00228             if (upper) {
00229                 i__3 = i__;
00230                 for (j = 1; j <= i__3; ++j) {
00231                     tmp += (d__1 = a[j + i__ * a_dim1], abs(d__1)) * (d__2 = 
00232                             x[j + k * x_dim1], abs(d__2));
00233 /* L40: */
00234                 }
00235                 i__3 = *n;
00236                 for (j = i__ + 1; j <= i__3; ++j) {
00237                     tmp += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * (d__2 = 
00238                             x[j + k * x_dim1], abs(d__2));
00239 /* L50: */
00240                 }
00241             } else {
00242                 i__3 = i__ - 1;
00243                 for (j = 1; j <= i__3; ++j) {
00244                     tmp += (d__1 = a[i__ + j * a_dim1], abs(d__1)) * (d__2 = 
00245                             x[j + k * x_dim1], abs(d__2));
00246 /* L60: */
00247                 }
00248                 i__3 = *n;
00249                 for (j = i__; j <= i__3; ++j) {
00250                     tmp += (d__1 = a[j + i__ * a_dim1], abs(d__1)) * (d__2 = 
00251                             x[j + k * x_dim1], abs(d__2));
00252 /* L70: */
00253                 }
00254             }
00255             if (i__ == 1) {
00256                 axbi = tmp;
00257             } else {
00258                 axbi = min(axbi,tmp);
00259             }
00260 /* L80: */
00261         }
00262 /* Computing MAX */
00263         d__1 = axbi, d__2 = (*n + 1) * unfl;
00264         tmp = berr[k] / ((*n + 1) * eps + (*n + 1) * unfl / max(d__1,d__2));
00265         if (k == 1) {
00266             reslts[2] = tmp;
00267         } else {
00268             reslts[2] = max(reslts[2],tmp);
00269         }
00270 /* L90: */
00271     }
00272 
00273     return 0;
00274 
00275 /*     End of DPOT05 */
00276 
00277 } /* dpot05_ */


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autogenerated on Sat Jun 8 2019 18:55:48