zla_porcond_x.c

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/* zla_porcond_x.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;

doublereal zla_porcond_x__(char *uplo, integer *n, doublecomplex *a, integer *
        lda, doublecomplex *af, integer *ldaf, doublecomplex *x, integer *
        info, doublecomplex *work, doublereal *rwork, ftnlen uplo_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4;
    doublereal ret_val, d__1, d__2;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double d_imag(doublecomplex *);
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);

    /* Local variables */
    integer i__, j;
    logical up;
    doublereal tmp;
    integer kase;
    extern logical lsame_(char *, char *);
    integer isave[3];
    doublereal anorm;
    extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, 
            doublecomplex *, doublereal *, integer *, integer *), xerbla_(
            char *, integer *);
    doublereal ainvnm;
    extern /* Subroutine */ int zpotrs_(char *, integer *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *, integer *);


/*     -- LAPACK routine (version 3.2.1)                                 -- */
/*     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/*     -- Jason Riedy of Univ. of California Berkeley.                 -- */
/*     -- April 2009                                                   -- */

/*     -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/*     -- Univ. of California Berkeley and NAG Ltd.                    -- */

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

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

/*     ZLA_PORCOND_X Computes the infinity norm condition number of */
/*     op(A) * diag(X) where X is a COMPLEX*16 vector. */

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

/*     UPLO    (input) CHARACTER*1 */
/*       = 'U':  Upper triangle of A is stored; */
/*       = 'L':  Lower triangle of A is stored. */

/*     N       (input) INTEGER */
/*     The number of linear equations, i.e., the order of the */
/*     matrix A.  N >= 0. */

/*     A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*     On entry, the N-by-N matrix A. */

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

/*     AF      (input) COMPLEX*16 array, dimension (LDAF,N) */
/*     The triangular factor U or L from the Cholesky factorization */
/*     A = U**T*U or A = L*L**T, as computed by ZPOTRF. */

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

/*     X       (input) COMPLEX*16 array, dimension (N) */
/*     The vector X in the formula op(A) * diag(X). */

/*     INFO    (output) INTEGER */
/*       = 0:  Successful exit. */
/*     i > 0:  The ith argument is invalid. */

/*     WORK    (input) COMPLEX*16 array, dimension (2*N). */
/*     Workspace. */

/*     RWORK   (input) DOUBLE PRECISION array, dimension (N). */
/*     Workspace. */

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

/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function Definitions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    af_dim1 = *ldaf;
    af_offset = 1 + af_dim1;
    af -= af_offset;
    --x;
    --work;
    --rwork;

    /* Function Body */
    ret_val = 0.;

    *info = 0;
    if (*n < 0) {
        *info = -2;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZLA_PORCOND_X", &i__1);
        return ret_val;
    }
    up = FALSE_;
    if (lsame_(uplo, "U")) {
        up = TRUE_;
    }

/*     Compute norm of op(A)*op2(C). */

    anorm = 0.;
    if (up) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            tmp = 0.;
            i__2 = i__;
            for (j = 1; j <= i__2; ++j) {
                i__3 = j + i__ * a_dim1;
                i__4 = j;
                z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, 
                        z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4]
                        .r;
                z__1.r = z__2.r, z__1.i = z__2.i;
                tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), 
                        abs(d__2));
            }
            i__2 = *n;
            for (j = i__ + 1; j <= i__2; ++j) {
                i__3 = i__ + j * a_dim1;
                i__4 = j;
                z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, 
                        z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4]
                        .r;
                z__1.r = z__2.r, z__1.i = z__2.i;
                tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), 
                        abs(d__2));
            }
            rwork[i__] = tmp;
            anorm = max(anorm,tmp);
        }
    } else {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            tmp = 0.;
            i__2 = i__;
            for (j = 1; j <= i__2; ++j) {
                i__3 = i__ + j * a_dim1;
                i__4 = j;
                z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, 
                        z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4]
                        .r;
                z__1.r = z__2.r, z__1.i = z__2.i;
                tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), 
                        abs(d__2));
            }
            i__2 = *n;
            for (j = i__ + 1; j <= i__2; ++j) {
                i__3 = j + i__ * a_dim1;
                i__4 = j;
                z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, 
                        z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4]
                        .r;
                z__1.r = z__2.r, z__1.i = z__2.i;
                tmp += (d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), 
                        abs(d__2));
            }
            rwork[i__] = tmp;
            anorm = max(anorm,tmp);
        }
    }

/*     Quick return if possible. */

    if (*n == 0) {
        ret_val = 1.;
        return ret_val;
    } else if (anorm == 0.) {
        return ret_val;
    }

/*     Estimate the norm of inv(op(A)). */

    ainvnm = 0.;

    kase = 0;
L10:
    zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
    if (kase != 0) {
        if (kase == 2) {

/*           Multiply by R. */

            i__1 = *n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                i__2 = i__;
                i__3 = i__;
                i__4 = i__;
                z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] * 
                        work[i__3].i;
                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
            }

            if (up) {
                zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n, 
                        info);
            } else {
                zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n, 
                        info);
            }

/*           Multiply by inv(X). */

            i__1 = *n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                i__2 = i__;
                z_div(&z__1, &work[i__], &x[i__]);
                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
            }
        } else {

/*           Multiply by inv(X'). */

            i__1 = *n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                i__2 = i__;
                z_div(&z__1, &work[i__], &x[i__]);
                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
            }

            if (up) {
                zpotrs_("U", n, &c__1, &af[af_offset], ldaf, &work[1], n, 
                        info);
            } else {
                zpotrs_("L", n, &c__1, &af[af_offset], ldaf, &work[1], n, 
                        info);
            }

/*           Multiply by R. */

            i__1 = *n;
            for (i__ = 1; i__ <= i__1; ++i__) {
                i__2 = i__;
                i__3 = i__;
                i__4 = i__;
                z__1.r = rwork[i__4] * work[i__3].r, z__1.i = rwork[i__4] * 
                        work[i__3].i;
                work[i__2].r = z__1.r, work[i__2].i = z__1.i;
            }
        }
        goto L10;
    }

/*     Compute the estimate of the reciprocal condition number. */

    if (ainvnm != 0.) {
        ret_val = 1. / ainvnm;
    }

    return ret_val;

} /* zla_porcond_x__ */