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/* lapack/complex16/zlacn2.f -- translated by f2c (version 20090411).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
/*< SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE ) >*/
/* Subroutine */ int zlacn2_(integer *n, doublecomplex *v, doublecomplex *x,
doublereal *est, integer *kase, integer *isave)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
double z_abs(doublecomplex *), d_imag(doublecomplex *);
/* Local variables */
integer i__;
doublereal temp, absxi;
integer jlast;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern integer izmax1_(integer *, doublecomplex *, integer *);
extern doublereal dzsum1_(integer *, doublecomplex *, integer *), dlamch_(
char *, ftnlen);
doublereal safmin, altsgn, estold;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/*< INTEGER KASE, N >*/
/*< DOUBLE PRECISION EST >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER ISAVE( 3 ) >*/
/*< COMPLEX*16 V( * ), X( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZLACN2 estimates the 1-norm of a square, complex matrix A. */
/* Reverse communication is used for evaluating matrix-vector products. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix. N >= 1. */
/* V (workspace) COMPLEX*16 array, dimension (N) */
/* On the final return, V = A*W, where EST = norm(V)/norm(W) */
/* (W is not returned). */
/* X (input/output) COMPLEX*16 array, dimension (N) */
/* On an intermediate return, X should be overwritten by */
/* A * X, if KASE=1, */
/* A' * X, if KASE=2, */
/* where A' is the conjugate transpose of A, and ZLACN2 must be */
/* re-called with all the other parameters unchanged. */
/* EST (input/output) DOUBLE PRECISION */
/* On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be */
/* unchanged from the previous call to ZLACN2. */
/* On exit, EST is an estimate (a lower bound) for norm(A). */
/* KASE (input/output) INTEGER */
/* On the initial call to ZLACN2, 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 ZLACN2, KASE will again be 0. */
/* ISAVE (input/output) INTEGER array, dimension (3) */
/* ISAVE is used to save variables between calls to ZLACN2 */
/* Further Details */
/* ======= ======= */
/* Contributed by Nick Higham, University of Manchester. */
/* Originally named CONEST, 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. */
/* Last modified: April, 1999 */
/* This is a thread safe version of ZLACON, which uses the array ISAVE */
/* in place of a SAVE statement, as follows: */
/* ZLACON ZLACN2 */
/* JUMP ISAVE(1) */
/* J ISAVE(2) */
/* ITER ISAVE(3) */
/* ===================================================================== */
/* .. Parameters .. */
/*< INTEGER ITMAX >*/
/*< PARAMETER ( ITMAX = 5 ) >*/
/*< DOUBLE PRECISION ONE, TWO >*/
/*< PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 ) >*/
/*< COMPLEX*16 CZERO, CONE >*/
/*< >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, JLAST >*/
/*< DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER IZMAX1 >*/
/*< DOUBLE PRECISION DLAMCH, DZSUM1 >*/
/*< EXTERNAL IZMAX1, DLAMCH, DZSUM1 >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL ZCOPY >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, DBLE, DCMPLX, DIMAG >*/
/* .. */
/* .. Executable Statements .. */
/*< SAFMIN = DLAMCH( 'Safe minimum' ) >*/
/* Parameter adjustments */
--isave;
--x;
--v;
/* Function Body */
safmin = dlamch_("Safe minimum", (ftnlen)12);
/*< IF( KASE.EQ.0 ) THEN >*/
if (*kase == 0) {
/*< DO 10 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< X( I ) = DCMPLX( ONE / DBLE( N ) ) >*/
i__2 = i__;
d__1 = 1. / (doublereal) (*n);
z__1.r = d__1, z__1.i = 0.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< KASE = 1 >*/
*kase = 1;
/*< ISAVE( 1 ) = 1 >*/
isave[1] = 1;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 ) >*/
switch (isave[1]) {
case 1: goto L20;
case 2: goto L40;
case 3: goto L70;
case 4: goto L90;
case 5: goto L120;
}
/* ................ ENTRY (ISAVE( 1 ) = 1) */
/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */
/*< 20 CONTINUE >*/
L20:
/*< IF( N.EQ.1 ) THEN >*/
if (*n == 1) {
/*< V( 1 ) = X( 1 ) >*/
v[1].r = x[1].r, v[1].i = x[1].i;
/*< EST = ABS( V( 1 ) ) >*/
*est = z_abs(&v[1]);
/* ... QUIT */
/*< GO TO 130 >*/
goto L130;
/*< END IF >*/
}
/*< EST = DZSUM1( N, X, 1 ) >*/
*est = dzsum1_(n, &x[1], &c__1);
/*< DO 30 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< ABSXI = ABS( X( I ) ) >*/
absxi = z_abs(&x[i__]);
/*< IF( ABSXI.GT.SAFMIN ) THEN >*/
if (absxi > safmin) {
/*< >*/
i__2 = i__;
i__3 = i__;
d__1 = x[i__3].r / absxi;
d__2 = d_imag(&x[i__]) / absxi;
z__1.r = d__1, z__1.i = d__2;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/*< ELSE >*/
} else {
/*< X( I ) = CONE >*/
i__2 = i__;
x[i__2].r = 1., x[i__2].i = 0.;
/*< END IF >*/
}
/*< 30 CONTINUE >*/
/* L30: */
}
/*< KASE = 2 >*/
*kase = 2;
/*< ISAVE( 1 ) = 2 >*/
isave[1] = 2;
/*< RETURN >*/
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 2) */
/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. */
/*< 40 CONTINUE >*/
L40:
/*< ISAVE( 2 ) = IZMAX1( N, X, 1 ) >*/
isave[2] = izmax1_(n, &x[1], &c__1);
/*< ISAVE( 3 ) = 2 >*/
isave[3] = 2;
/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */
/*< 50 CONTINUE >*/
L50:
/*< DO 60 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< X( I ) = CZERO >*/
i__2 = i__;
x[i__2].r = 0., x[i__2].i = 0.;
/*< 60 CONTINUE >*/
/* L60: */
}
/*< X( ISAVE( 2 ) ) = CONE >*/
i__1 = isave[2];
x[i__1].r = 1., x[i__1].i = 0.;
/*< KASE = 1 >*/
*kase = 1;
/*< ISAVE( 1 ) = 3 >*/
isave[1] = 3;
/*< RETURN >*/
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 3) */
/* X HAS BEEN OVERWRITTEN BY A*X. */
/*< 70 CONTINUE >*/
L70:
/*< CALL ZCOPY( N, X, 1, V, 1 ) >*/
zcopy_(n, &x[1], &c__1, &v[1], &c__1);
/*< ESTOLD = EST >*/
estold = *est;
/*< EST = DZSUM1( N, V, 1 ) >*/
*est = dzsum1_(n, &v[1], &c__1);
/* TEST FOR CYCLING. */
/*< >*/
if (*est <= estold) {
goto L100;
}
/*< DO 80 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< ABSXI = ABS( X( I ) ) >*/
absxi = z_abs(&x[i__]);
/*< IF( ABSXI.GT.SAFMIN ) THEN >*/
if (absxi > safmin) {
/*< >*/
i__2 = i__;
i__3 = i__;
d__1 = x[i__3].r / absxi;
d__2 = d_imag(&x[i__]) / absxi;
z__1.r = d__1, z__1.i = d__2;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/*< ELSE >*/
} else {
/*< X( I ) = CONE >*/
i__2 = i__;
x[i__2].r = 1., x[i__2].i = 0.;
/*< END IF >*/
}
/*< 80 CONTINUE >*/
/* L80: */
}
/*< KASE = 2 >*/
*kase = 2;
/*< ISAVE( 1 ) = 4 >*/
isave[1] = 4;
/*< RETURN >*/
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 4) */
/* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X. */
/*< 90 CONTINUE >*/
L90:
/*< JLAST = ISAVE( 2 ) >*/
jlast = isave[2];
/*< ISAVE( 2 ) = IZMAX1( N, X, 1 ) >*/
isave[2] = izmax1_(n, &x[1], &c__1);
/*< >*/
if (z_abs(&x[jlast]) != z_abs(&x[isave[2]]) && isave[3] < 5) {
/*< ISAVE( 3 ) = ISAVE( 3 ) + 1 >*/
++isave[3];
/*< GO TO 50 >*/
goto L50;
/*< END IF >*/
}
/* ITERATION COMPLETE. FINAL STAGE. */
/*< 100 CONTINUE >*/
L100:
/*< ALTSGN = ONE >*/
altsgn = 1.;
/*< DO 110 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) ) >*/
i__2 = i__;
d__1 = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + 1.);
z__1.r = d__1, z__1.i = 0.;
x[i__2].r = z__1.r, x[i__2].i = z__1.i;
/*< ALTSGN = -ALTSGN >*/
altsgn = -altsgn;
/*< 110 CONTINUE >*/
/* L110: */
}
/*< KASE = 1 >*/
*kase = 1;
/*< ISAVE( 1 ) = 5 >*/
isave[1] = 5;
/*< RETURN >*/
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 5) */
/* X HAS BEEN OVERWRITTEN BY A*X. */
/*< 120 CONTINUE >*/
L120:
/*< TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) ) >*/
temp = dzsum1_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.;
/*< IF( TEMP.GT.EST ) THEN >*/
if (temp > *est) {
/*< CALL ZCOPY( N, X, 1, V, 1 ) >*/
zcopy_(n, &x[1], &c__1, &v[1], &c__1);
/*< EST = TEMP >*/
*est = temp;
/*< END IF >*/
}
/*< 130 CONTINUE >*/
L130:
/*< KASE = 0 >*/
*kase = 0;
/*< RETURN >*/
return 0;
/* End of ZLACN2 */
/*< END >*/
} /* zlacn2_ */
#ifdef __cplusplus
}
#endif
|
