sqrt16.c

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/* sqrt16.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 real c_b8 = -1.f;
static real c_b9 = 1.f;
static integer c__1 = 1;

/* Subroutine */ int sqrt16_(char *trans, integer *m, integer *n, integer *
        nrhs, real *a, integer *lda, real *x, integer *ldx, real *b, integer *
        ldb, real *rwork, real *resid)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
    real r__1, r__2;

    /* Local variables */
    integer j, n1, n2;
    real eps;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
            integer *, real *, real *, integer *, real *, integer *, real *, 
            real *, integer *);
    real anorm, bnorm;
    extern doublereal sasum_(integer *, real *, integer *);
    real xnorm;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
            integer *, real *, integer *, real *);


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

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

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

/*  SQRT16 computes the residual for a solution of a system of linear */
/*  equations  A*x = b  or  A'*x = b: */
/*     RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), */
/*  where EPS is the machine epsilon. */

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

/*  TRANS   (input) CHARACTER*1 */
/*          Specifies the form of the system of equations: */
/*          = 'N':  A *x = b */
/*          = 'T':  A'*x = b, where A' is the transpose of A */
/*          = 'C':  A'*x = b, where A' is the transpose of A */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A.  M >= 0. */

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

/*  NRHS    (input) INTEGER */
/*          The number of columns of B, the matrix of right hand sides. */
/*          NRHS >= 0. */

/*  A       (input) REAL array, dimension (LDA,N) */
/*          The original M x N matrix A. */

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

/*  X       (input) REAL array, dimension (LDX,NRHS) */
/*          The computed solution vectors for the system of linear */
/*          equations. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X.  If TRANS = 'N', */
/*          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). */

/*  B       (input/output) REAL array, dimension (LDB,NRHS) */
/*          On entry, the right hand side vectors for the system of */
/*          linear equations. */
/*          On exit, B is overwritten with the difference B - A*X. */

/*  LDB     (input) INTEGER */
/*          The leading dimension of the array B.  IF TRANS = 'N', */
/*          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). */

/*  RWORK   (workspace) REAL array, dimension (M) */

/*  RESID   (output) REAL */
/*          The maximum over the number of right hand sides of */
/*          norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ). */

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

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

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

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --rwork;

    /* Function Body */
    if (*m <= 0 || *n <= 0 || *nrhs == 0) {
        *resid = 0.f;
        return 0;
    }

    if (lsame_(trans, "T") || lsame_(trans, "C")) {
        anorm = slange_("I", m, n, &a[a_offset], lda, &rwork[1]);
        n1 = *n;
        n2 = *m;
    } else {
        anorm = slange_("1", m, n, &a[a_offset], lda, &rwork[1]);
        n1 = *m;
        n2 = *n;
    }

    eps = slamch_("Epsilon");

/*     Compute  B - A*X  (or  B - A'*X ) and store in B. */

    sgemm_(trans, "No transpose", &n1, nrhs, &n2, &c_b8, &a[a_offset], lda, &
            x[x_offset], ldx, &c_b9, &b[b_offset], ldb)
            ;

/*     Compute the maximum over the number of right hand sides of */
/*        norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) . */

    *resid = 0.f;
    i__1 = *nrhs;
    for (j = 1; j <= i__1; ++j) {
        bnorm = sasum_(&n1, &b[j * b_dim1 + 1], &c__1);
        xnorm = sasum_(&n2, &x[j * x_dim1 + 1], &c__1);
        if (anorm == 0.f && bnorm == 0.f) {
            *resid = 0.f;
        } else if (anorm <= 0.f || xnorm <= 0.f) {
            *resid = 1.f / eps;
        } else {
/* Computing MAX */
            r__1 = *resid, r__2 = bnorm / anorm / xnorm / (max(*m,*n) * eps);
            *resid = dmax(r__1,r__2);
        }
/* L10: */
    }

    return 0;

/*     End of SQRT16 */

} /* sqrt16_ */