slacn2.c

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/* slacn2.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;
static real c_b11 = 1.f;

/* Subroutine */ int slacn2_(integer *n, real *v, real *x, integer *isgn, 
        real *est, integer *kase, integer *isave)
{
    /* System generated locals */
    integer i__1;
    real r__1;

    /* Builtin functions */
    double r_sign(real *, real *);
    integer i_nint(real *);

    /* Local variables */
    integer i__;
    real temp;
    integer jlast;
    extern doublereal sasum_(integer *, real *, integer *);
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
            integer *);
    extern integer isamax_(integer *, real *, integer *);
    real altsgn, estold;


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  SLACN2 estimates the 1-norm of a square, real matrix A. */
/*  Reverse communication is used for evaluating matrix-vector products. */

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

/*  N      (input) INTEGER */
/*         The order of the matrix.  N >= 1. */

/*  V      (workspace) REAL array, dimension (N) */
/*         On the final return, V = A*W,  where  EST = norm(V)/norm(W) */
/*         (W is not returned). */

/*  X      (input/output) REAL array, dimension (N) */
/*         On an intermediate return, X should be overwritten by */
/*               A * X,   if KASE=1, */
/*               A' * X,  if KASE=2, */
/*         and SLACN2 must be re-called with all the other parameters */
/*         unchanged. */

/*  ISGN   (workspace) INTEGER array, dimension (N) */

/*  EST    (input/output) REAL */
/*         On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be */
/*         unchanged from the previous call to SLACN2. */
/*         On exit, EST is an estimate (a lower bound) for norm(A). */

/*  KASE   (input/output) INTEGER */
/*         On the initial call to SLACN2, KASE should be 0. */
/*         On an intermediate return, KASE will be 1 or 2, indicating */
/*         whether X should be overwritten by A * X  or A' * X. */
/*         On the final return from SLACN2, KASE will again be 0. */

/*  ISAVE  (input/output) INTEGER array, dimension (3) */
/*         ISAVE is used to save variables between calls to SLACN2 */

/*  Further Details */
/*  ======= ======= */

/*  Contributed by Nick Higham, University of Manchester. */
/*  Originally named SONEST, dated March 16, 1988. */

/*  Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of */
/*  a real or complex matrix, with applications to condition estimation", */
/*  ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. */

/*  This is a thread safe version of SLACON, which uses the array ISAVE */
/*  in place of a SAVE statement, as follows: */

/*     SLACON     SLACN2 */
/*      JUMP     ISAVE(1) */
/*      J        ISAVE(2) */
/*      ITER     ISAVE(3) */

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

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

    /* Parameter adjustments */
    --isave;
    --isgn;
    --x;
    --v;

    /* Function Body */
    if (*kase == 0) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            x[i__] = 1.f / (real) (*n);
/* L10: */
        }
        *kase = 1;
        isave[1] = 1;
        return 0;
    }

    switch (isave[1]) {
        case 1:  goto L20;
        case 2:  goto L40;
        case 3:  goto L70;
        case 4:  goto L110;
        case 5:  goto L140;
    }

/*     ................ ENTRY   (ISAVE( 1 ) = 1) */
/*     FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY A*X. */

L20:
    if (*n == 1) {
        v[1] = x[1];
        *est = dabs(v[1]);
/*        ... QUIT */
        goto L150;
    }
    *est = sasum_(n, &x[1], &c__1);

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        x[i__] = r_sign(&c_b11, &x[i__]);
        isgn[i__] = i_nint(&x[i__]);
/* L30: */
    }
    *kase = 2;
    isave[1] = 2;
    return 0;

/*     ................ ENTRY   (ISAVE( 1 ) = 2) */
/*     FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */

L40:
    isave[2] = isamax_(n, &x[1], &c__1);
    isave[3] = 2;

/*     MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */

L50:
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        x[i__] = 0.f;
/* L60: */
    }
    x[isave[2]] = 1.f;
    *kase = 1;
    isave[1] = 3;
    return 0;

/*     ................ ENTRY   (ISAVE( 1 ) = 3) */
/*     X HAS BEEN OVERWRITTEN BY A*X. */

L70:
    scopy_(n, &x[1], &c__1, &v[1], &c__1);
    estold = *est;
    *est = sasum_(n, &v[1], &c__1);
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        r__1 = r_sign(&c_b11, &x[i__]);
        if (i_nint(&r__1) != isgn[i__]) {
            goto L90;
        }
/* L80: */
    }
/*     REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */
    goto L120;

L90:
/*     TEST FOR CYCLING. */
    if (*est <= estold) {
        goto L120;
    }

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        x[i__] = r_sign(&c_b11, &x[i__]);
        isgn[i__] = i_nint(&x[i__]);
/* L100: */
    }
    *kase = 2;
    isave[1] = 4;
    return 0;

/*     ................ ENTRY   (ISAVE( 1 ) = 4) */
/*     X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */

L110:
    jlast = isave[2];
    isave[2] = isamax_(n, &x[1], &c__1);
    if (x[jlast] != (r__1 = x[isave[2]], dabs(r__1)) && isave[3] < 5) {
        ++isave[3];
        goto L50;
    }

/*     ITERATION COMPLETE.  FINAL STAGE. */

L120:
    altsgn = 1.f;
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        x[i__] = altsgn * ((real) (i__ - 1) / (real) (*n - 1) + 1.f);
        altsgn = -altsgn;
/* L130: */
    }
    *kase = 1;
    isave[1] = 5;
    return 0;

/*     ................ ENTRY   (ISAVE( 1 ) = 5) */
/*     X HAS BEEN OVERWRITTEN BY A*X. */

L140:
    temp = sasum_(n, &x[1], &c__1) / (real) (*n * 3) * 2.f;
    if (temp > *est) {
        scopy_(n, &x[1], &c__1, &v[1], &c__1);
        *est = temp;
    }

L150:
    *kase = 0;
    return 0;

/*     End of SLACN2 */

} /* slacn2_ */