zgehd2.c

来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 146 行

#include "f2c.h"
#include "netlib.h"

/* Modified by Peter Vanroose, June 2001: manual optimisation and clean-up */

/* Table of constant values */
static integer c__1 = 1;

/* Subroutine */ void zgehd2_(n, ilo, ihi, a, lda, tau, work, info)
const integer *n, *ilo, *ihi;
doublecomplex *a;
const integer *lda;
doublecomplex *tau, *work;
integer *info;
{
    /* System generated locals */
    integer i__1, i__2, i__3;
    doublecomplex z__1;

    /* Local variables */
    static integer i;
    static doublecomplex alpha;

/*  -- LAPACK routine (version 2.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     September 30, 1994 */

/*  ===================================================================== */
/*                                                                        */
/*  Purpose                                                               */
/*  =======                                                               */
/*                                                                        */
/*  ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H  */
/*  by a unitary similarity transformation:  Q' * A * Q = H .             */
/*                                                                        */
/*  Arguments                                                             */
/*  =========                                                             */
/*                                                                        */
/*  N       (input) INTEGER                                               */
/*          The order of the matrix A.  N >= 0.                           */
/*                                                                        */
/*  ILO     (input) INTEGER                                               */
/*  IHI     (input) INTEGER                                               */
/*          It is assumed that A is already upper triangular in rows      */
/*          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally     */
/*          set by a previous call to ZGEBAL; otherwise they should be    */
/*          set to 1 and N respectively. See Further Details.             */
/*          1 <= ILO <= IHI <= max(1,N).                                  */
/*                                                                        */
/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N)            */
/*          On entry, the n by n general matrix to be reduced.            */
/*          On exit, the upper triangle and the first subdiagonal of A    */
/*          are overwritten with the upper Hessenberg matrix H, and the   */
/*          elements below the first subdiagonal, with the array TAU,     */
/*          represent the unitary matrix Q as a product of elementary     */
/*          reflectors. See Further Details.                              */
/*                                                                        */
/*  LDA     (input) INTEGER                                               */
/*          The leading dimension of the array A.  LDA >= max(1,N).       */
/*                                                                        */
/*  TAU     (output) COMPLEX*16 array, dimension (N-1)                    */
/*          The scalar factors of the elementary reflectors (see Further  */
/*          Details).                                                     */
/*                                                                        */
/*  WORK    (workspace) COMPLEX*16 array, dimension (N)                   */
/*                                                                        */
/*  INFO    (output) INTEGER                                              */
/*          = 0:  successful exit                                         */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value.   */
/*                                                                        */
/*  Further Details                                                       */
/*  ===============                                                       */
/*                                                                        */
/*  The matrix Q is represented as a product of (ihi-ilo) elementary      */
/*  reflectors                                                            */
/*                                                                        */
/*     Q = H(ilo) H(ilo+1) . . . H(ihi-1).                                */
/*                                                                        */
/*  Each H(i) has the form                                                */
/*                                                                        */
/*     H(i) = I - tau * v * v'                                            */
/*                                                                        */
/*  where tau is a complex scalar, and v is a complex vector with         */
/*  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on    */
/*  exit in A(i+2:ihi,i), and tau in TAU(i).                              */
/*                                                                        */
/*  The contents of A are illustrated by the following example, with      */
/*  n = 7, ilo = 2 and ihi = 6:                                           */
/*                                                                        */
/*  on entry,                        on exit,                             */
/*                                                                        */
/*  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )       */
/*  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )       */
/*  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )       */
/*  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )       */
/*  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )       */
/*  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )       */
/*  (                         a )    (                          a )       */
/*                                                                        */
/*  where a denotes an element of the original matrix A, h denotes a      */
/*  modified element of the upper Hessenberg matrix H, and vi denotes an  */
/*  element of the vector defining H(i).                                  */
/*                                                                        */
/*  ===================================================================== */

    *info = 0;
    if (*n < 0) {
        *info = -1;
    } else if (*ilo < 1 || *ilo > max(1,*n)) {
        *info = -2;
    } else if (*ihi < min(*ilo,*n) || *ihi > *n) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGEHD2", &i__1);
        return;
    }

    for (i = *ilo - 1; i < *ihi - 1; ++i) {

/*        Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) */

        i__1 = 1+i*(*lda+1);
        alpha.r = a[i__1].r, alpha.i = a[i__1].i;
        i__2 = *ihi - i - 1;
        zlarfg_(&i__2, &alpha, &a[min(1,*n-i-2)+i__1], &c__1, &tau[i]);
        a[i__1].r = 1., a[i__1].i = 0.;

/*        Apply H(i) to A(1:ihi,i+1:ihi) from the right */

        zlarf_("Right", ihi, &i__2, &a[i__1], &c__1, &tau[i], &a[(i+1)*(*lda)], lda, work);

/*        Apply H(i)' to A(i+1:ihi,i+1:n) from the left */

        d_cnjg(&z__1, &tau[i]);
        i__3 = *n - i - 1;
        zlarf_("Left", &i__2, &i__3, &a[i__1], &c__1, &z__1, &a[(i+1)*(*lda+1)], lda, work);

        a[i__1].r = alpha.r, a[i__1].i = alpha.i;
    }
} /* zgehd2_ */