dtrt01.c

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/* dtrt01.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 dtrt01_(char *uplo, char *diag, integer *n, doublereal *
        a, integer *lda, doublereal *ainv, integer *ldainv, doublereal *rcond, 
         doublereal *work, doublereal *resid)
{
    /* System generated locals */
    integer a_dim1, a_offset, ainv_dim1, ainv_offset, i__1, i__2;

    /* Local variables */
    integer j;
    doublereal eps;
    extern logical lsame_(char *, char *);
    doublereal anorm;
    extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, 
            doublereal *, integer *, doublereal *, integer *);
    extern doublereal dlamch_(char *), dlantr_(char *, char *, char *, 
             integer *, integer *, doublereal *, integer *, doublereal *);
    doublereal ainvnm;


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

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

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

/*  DTRT01 computes the residual for a triangular matrix A times its */
/*  inverse: */
/*     RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ), */
/*  where EPS is the machine epsilon. */

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

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

/*  DIAG    (input) CHARACTER*1 */
/*          Specifies whether or not the matrix A is unit triangular. */
/*          = 'N':  Non-unit triangular */
/*          = 'U':  Unit triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
/*          The triangular matrix A.  If UPLO = 'U', the leading n by n */
/*          upper triangular part of the array A contains the upper */
/*          triangular matrix, and the strictly lower triangular part of */
/*          A is not referenced.  If UPLO = 'L', the leading n by n lower */
/*          triangular part of the array A contains the lower triangular */
/*          matrix, and the strictly upper triangular part of A is not */
/*          referenced.  If DIAG = 'U', the diagonal elements of A are */
/*          also not referenced and are assumed to be 1. */

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

/*  AINV    (input/output) DOUBLE PRECISION array, dimension (LDAINV,N) */
/*          On entry, the (triangular) inverse of the matrix A, in the */
/*          same storage format as A. */
/*          On exit, the contents of AINV are destroyed. */

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

/*  RCOND   (output) DOUBLE PRECISION */
/*          The reciprocal condition number of A, computed as */
/*          1/(norm(A) * norm(AINV)). */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (N) */

/*  RESID   (output) DOUBLE PRECISION */
/*          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick exit if N = 0 */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    ainv_dim1 = *ldainv;
    ainv_offset = 1 + ainv_dim1;
    ainv -= ainv_offset;
    --work;

    /* Function Body */
    if (*n <= 0) {
        *rcond = 1.;
        *resid = 0.;
        return 0;
    }

/*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. */

    eps = dlamch_("Epsilon");
    anorm = dlantr_("1", uplo, diag, n, n, &a[a_offset], lda, &work[1]);
    ainvnm = dlantr_("1", uplo, diag, n, n, &ainv[ainv_offset], ldainv, &work[
            1]);
    if (anorm <= 0. || ainvnm <= 0.) {
        *rcond = 0.;
        *resid = 1. / eps;
        return 0;
    }
    *rcond = 1. / anorm / ainvnm;

/*     Set the diagonal of AINV to 1 if AINV has unit diagonal. */

    if (lsame_(diag, "U")) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            ainv[j + j * ainv_dim1] = 1.;
/* L10: */
        }
    }

/*     Compute A * AINV, overwriting AINV. */

    if (lsame_(uplo, "U")) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            dtrmv_("Upper", "No transpose", diag, &j, &a[a_offset], lda, &
                    ainv[j * ainv_dim1 + 1], &c__1);
/* L20: */
        }
    } else {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            i__2 = *n - j + 1;
            dtrmv_("Lower", "No transpose", diag, &i__2, &a[j + j * a_dim1], 
                    lda, &ainv[j + j * ainv_dim1], &c__1);
/* L30: */
        }
    }

/*     Subtract 1 from each diagonal element to form A*AINV - I. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        ainv[j + j * ainv_dim1] += -1.;
/* L40: */
    }

/*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) */

    *resid = dlantr_("1", uplo, "Non-unit", n, n, &ainv[ainv_offset], ldainv, 
            &work[1]);

    *resid = *resid * *rcond / (doublereal) (*n) / eps;

    return 0;

/*     End of DTRT01 */

} /* dtrt01_ */