zpbt05.c

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/* zpbt05.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"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;

/* Subroutine */ int zpbt05_(char *uplo, integer *n, integer *kd, integer *
        nrhs, doublecomplex *ab, integer *ldab, doublecomplex *b, integer *
        ldb, doublecomplex *x, integer *ldx, doublecomplex *xact, integer *
        ldxact, doublereal *ferr, doublereal *berr, doublereal *reslts)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, xact_dim1,
             xact_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3, d__4;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double d_imag(doublecomplex *);

    /* Local variables */
    integer i__, j, k, nz;
    doublereal eps, tmp, diff, axbi;
    integer imax;
    doublereal unfl, ovfl;
    extern logical lsame_(char *, char *);
    logical upper;
    doublereal xnorm;
    extern doublereal dlamch_(char *);
    doublereal errbnd;
    extern integer izamax_(integer *, doublecomplex *, integer *);


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZPBT05 tests the error bounds from iterative refinement for the */
/*  computed solution to a system of equations A*X = B, where A is a */
/*  Hermitian band matrix. */

/*  RESLTS(1) = test of the error bound */
/*            = norm(X - XACT) / ( norm(X) * FERR ) */

/*  A large value is returned if this ratio is not less than one. */

/*  RESLTS(2) = residual from the iterative refinement routine */
/*            = the maximum of BERR / ( NZ*EPS + (*) ), where */
/*              (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */
/*              and NZ = max. number of nonzeros in any row of A, plus 1 */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          Hermitian matrix A is stored. */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The number of rows of the matrices X, B, and XACT, and the */
/*          order of the matrix A.  N >= 0. */

/*  KD      (input) INTEGER */
/*          The number of super-diagonals of the matrix A if UPLO = 'U', */
/*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0. */

/*  NRHS    (input) INTEGER */
/*          The number of columns of the matrices X, B, and XACT. */
/*          NRHS >= 0. */

/*  AB      (input) COMPLEX*16 array, dimension (LDAB,N) */
/*          The upper or lower triangle of the Hermitian band matrix A, */
/*          stored in the first KD+1 rows of the array.  The j-th column */
/*          of A is stored in the j-th column of the array AB as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KD+1. */

/*  B       (input) COMPLEX*16 array, dimension (LDB,NRHS) */
/*          The right hand side vectors for the system of linear */
/*          equations. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  LDB >= max(1,N). */

/*  X       (input) COMPLEX*16 array, dimension (LDX,NRHS) */
/*          The computed solution vectors.  Each vector is stored as a */
/*          column of the matrix X. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X.  LDX >= max(1,N). */

/*  XACT    (input) COMPLEX*16 array, dimension (LDX,NRHS) */
/*          The exact solution vectors.  Each vector is stored as a */
/*          column of the matrix XACT. */

/*  LDXACT  (input) INTEGER */
/*          The leading dimension of the array XACT.  LDXACT >= max(1,N). */

/*  FERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
/*          The estimated forward error bounds for each solution vector */
/*          X.  If XTRUE is the true solution, FERR bounds the magnitude */
/*          of the largest entry in (X - XTRUE) divided by the magnitude */
/*          of the largest entry in X. */

/*  BERR    (input) DOUBLE PRECISION array, dimension (NRHS) */
/*          The componentwise relative backward error of each solution */
/*          vector (i.e., the smallest relative change in any entry of A */
/*          or B that makes X an exact solution). */

/*  RESLTS  (output) DOUBLE PRECISION array, dimension (2) */
/*          The maximum over the NRHS solution vectors of the ratios: */
/*          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) */
/*          RESLTS(2) = BERR / ( NZ*EPS + (*) ) */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick exit if N = 0 or NRHS = 0. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    xact_dim1 = *ldxact;
    xact_offset = 1 + xact_dim1;
    xact -= xact_offset;
    --ferr;
    --berr;
    --reslts;

    /* Function Body */
    if (*n <= 0 || *nrhs <= 0) {
        reslts[1] = 0.;
        reslts[2] = 0.;
        return 0;
    }

    eps = dlamch_("Epsilon");
    unfl = dlamch_("Safe minimum");
    ovfl = 1. / unfl;
    upper = lsame_(uplo, "U");
/* Computing MAX */
    i__1 = *kd, i__2 = *n - 1;
    nz = (max(i__1,i__2) << 1) + 1;

/*     Test 1:  Compute the maximum of */
/*        norm(X - XACT) / ( norm(X) * FERR ) */
/*     over all the vectors X and XACT using the infinity-norm. */

    errbnd = 0.;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        imax = izamax_(n, &x[j * x_dim1 + 1], &c__1);
/* Computing MAX */
        i__2 = imax + j * x_dim1;
        d__3 = (d__1 = x[i__2].r, abs(d__1)) + (d__2 = d_imag(&x[imax + j * 
                x_dim1]), abs(d__2));
        xnorm = max(d__3,unfl);
        diff = 0.;
        i__2 = *n;
        for (i__ = 1; i__ <= i__2; ++i__) {
            i__3 = i__ + j * x_dim1;
            i__4 = i__ + j * xact_dim1;
            z__2.r = x[i__3].r - xact[i__4].r, z__2.i = x[i__3].i - xact[i__4]
                    .i;
            z__1.r = z__2.r, z__1.i = z__2.i;
/* Computing MAX */
            d__3 = diff, d__4 = (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&
                    z__1), abs(d__2));
            diff = max(d__3,d__4);
/* L10: */
        }

        if (xnorm > 1.) {
            goto L20;
        } else if (diff <= ovfl * xnorm) {
            goto L20;
        } else {
            errbnd = 1. / eps;
            goto L30;
        }

L20:
        if (diff / xnorm <= ferr[j]) {
/* Computing MAX */
            d__1 = errbnd, d__2 = diff / xnorm / ferr[j];
            errbnd = max(d__1,d__2);
        } else {
            errbnd = 1. / eps;
        }
L30:
        ;
    }
    reslts[1] = errbnd;

/*     Test 2:  Compute the maximum of BERR / ( NZ*EPS + (*) ), where */
/*     (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) */

    i__1 = *nrhs;
    for (k = 1; k <= i__1; ++k) {
        i__2 = *n;
        for (i__ = 1; i__ <= i__2; ++i__) {
            i__3 = i__ + k * b_dim1;
            tmp = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[i__ + k * 
                    b_dim1]), abs(d__2));
            if (upper) {
/* Computing MAX */
                i__3 = i__ - *kd;
                i__4 = i__ - 1;
                for (j = max(i__3,1); j <= i__4; ++j) {
                    i__3 = *kd + 1 - i__ + j + i__ * ab_dim1;
                    i__5 = j + k * x_dim1;
                    tmp += ((d__1 = ab[i__3].r, abs(d__1)) + (d__2 = d_imag(&
                            ab[*kd + 1 - i__ + j + i__ * ab_dim1]), abs(d__2))
                            ) * ((d__3 = x[i__5].r, abs(d__3)) + (d__4 = 
                            d_imag(&x[j + k * x_dim1]), abs(d__4)));
/* L40: */
                }
                i__4 = *kd + 1 + i__ * ab_dim1;
                i__3 = i__ + k * x_dim1;
                tmp += (d__1 = ab[i__4].r, abs(d__1)) * ((d__2 = x[i__3].r, 
                        abs(d__2)) + (d__3 = d_imag(&x[i__ + k * x_dim1]), 
                        abs(d__3)));
/* Computing MIN */
                i__3 = i__ + *kd;
                i__4 = min(i__3,*n);
                for (j = i__ + 1; j <= i__4; ++j) {
                    i__3 = *kd + 1 + i__ - j + j * ab_dim1;
                    i__5 = j + k * x_dim1;
                    tmp += ((d__1 = ab[i__3].r, abs(d__1)) + (d__2 = d_imag(&
                            ab[*kd + 1 + i__ - j + j * ab_dim1]), abs(d__2))) 
                            * ((d__3 = x[i__5].r, abs(d__3)) + (d__4 = d_imag(
                            &x[j + k * x_dim1]), abs(d__4)));
/* L50: */
                }
            } else {
/* Computing MAX */
                i__4 = i__ - *kd;
                i__3 = i__ - 1;
                for (j = max(i__4,1); j <= i__3; ++j) {
                    i__4 = i__ + 1 - j + j * ab_dim1;
                    i__5 = j + k * x_dim1;
                    tmp += ((d__1 = ab[i__4].r, abs(d__1)) + (d__2 = d_imag(&
                            ab[i__ + 1 - j + j * ab_dim1]), abs(d__2))) * ((
                            d__3 = x[i__5].r, abs(d__3)) + (d__4 = d_imag(&x[
                            j + k * x_dim1]), abs(d__4)));
/* L60: */
                }
                i__3 = i__ * ab_dim1 + 1;
                i__4 = i__ + k * x_dim1;
                tmp += (d__1 = ab[i__3].r, abs(d__1)) * ((d__2 = x[i__4].r, 
                        abs(d__2)) + (d__3 = d_imag(&x[i__ + k * x_dim1]), 
                        abs(d__3)));
/* Computing MIN */
                i__4 = i__ + *kd;
                i__3 = min(i__4,*n);
                for (j = i__ + 1; j <= i__3; ++j) {
                    i__4 = j + 1 - i__ + i__ * ab_dim1;
                    i__5 = j + k * x_dim1;
                    tmp += ((d__1 = ab[i__4].r, abs(d__1)) + (d__2 = d_imag(&
                            ab[j + 1 - i__ + i__ * ab_dim1]), abs(d__2))) * ((
                            d__3 = x[i__5].r, abs(d__3)) + (d__4 = d_imag(&x[
                            j + k * x_dim1]), abs(d__4)));
/* L70: */
                }
            }
            if (i__ == 1) {
                axbi = tmp;
            } else {
                axbi = min(axbi,tmp);
            }
/* L80: */
        }
/* Computing MAX */
        d__1 = axbi, d__2 = nz * unfl;
        tmp = berr[k] / (nz * eps + nz * unfl / max(d__1,d__2));
        if (k == 1) {
            reslts[2] = tmp;
        } else {
            reslts[2] = max(reslts[2],tmp);
        }
/* L90: */
    }

    return 0;

/*     End of ZPBT05 */

} /* zpbt05_ */