dgghrd.c

InsightToolkit-1.4.0(有大量的优化算法程序)

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

/* Table of constant values */

static doublereal c_b10 = 0.;
static doublereal c_b11 = 1.;
static integer c__1 = 1;

/* Subroutine */ void dgghrd_(compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
const char *compq, *compz;
const integer *n;
integer *ilo, *ihi;
doublereal *a;
const integer *lda;
doublereal *b;
const integer *ldb;
doublereal *q;
const integer *ldq;
doublereal *z;
const integer *ldz;
integer *info;
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, z_offset, i__1;

    /* Local variables */
    static integer jcol;
    static doublereal temp;
    static integer jrow;
    static doublereal c, s;
    static integer icompq, icompz;
    static logical ilq, ilz;


/*  -- LAPACK routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     September 30, 1994 */

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

/*  DGGHRD reduces a pair of real matrices (A,B) to generalized upper */
/*  Hessenberg form using orthogonal transformations, where A is a */
/*  general matrix and B is upper triangular:  Q' * A * Z = H and */
/*  Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular, */
/*  and Q and Z are orthogonal, and ' means transpose. */

/*  The orthogonal matrices Q and Z are determined as products of Givens */
/*  rotations.  They may either be formed explicitly, or they may be */
/*  postmultiplied into input matrices Q1 and Z1, so that */

/*       Q1 * A * Z1' = (Q1*Q) * H * (Z1*Z)' */
/*       Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)' */

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

/*  COMPQ   (input) CHARACTER*1 */
/*          = 'N': do not compute Q; */
/*          = 'I': Q is initialized to the unit matrix, and the */
/*                 orthogonal matrix Q is returned; */
/*          = 'V': Q must contain an orthogonal matrix Q1 on entry, */
/*                 and the product Q1*Q is returned. */

/*  COMPZ   (input) CHARACTER*1 */
/*          = 'N': do not compute Z; */
/*          = 'I': Z is initialized to the unit matrix, and the */
/*                 orthogonal matrix Z is returned; */
/*          = 'V': Z must contain an orthogonal matrix Z1 on entry, */
/*                 and the product Z1*Z is returned. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B.  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 DGGBAL; otherwise they should be set */
/*          to 1 and N respectively. */
/*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */

/*  A       (input/output) DOUBLE PRECISION 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 */
/*          rest is set to zero. */

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

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N) */
/*          On entry, the N-by-N upper triangular matrix B. */
/*          On exit, the upper triangular matrix T = Q' B Z.  The */
/*          elements below the diagonal are set to zero. */

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

/*  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */
/*          If COMPQ='N':  Q is not referenced. */
/*          If COMPQ='I':  on entry, Q need not be set, and on exit it */
/*                         contains the orthogonal matrix Q, where Q' */
/*                         is the product of the Givens transformations */
/*                         which are applied to A and B on the left. */
/*          If COMPQ='V':  on entry, Q must contain an orthogonal matrix */
/*                         Q1, and on exit this is overwritten by Q1*Q. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q. */
/*          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. */

/*  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N) */
/*          If COMPZ='N':  Z is not referenced. */
/*          If COMPZ='I':  on entry, Z need not be set, and on exit it */
/*                         contains the orthogonal matrix Z, which is */
/*                         the product of the Givens transformations */
/*                         which are applied to A and B on the right. */
/*          If COMPZ='V':  on entry, Z must contain an orthogonal matrix */
/*                         Z1, and on exit this is overwritten by Z1*Z. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z. */
/*          LDZ >= N if COMPZ='V' or 'I'; LDZ >= 1 otherwise. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

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

/*  This routine reduces A to Hessenberg and B to triangular form by */
/*  an unblocked reduction, as described in _Matrix_Computations_, */
/*  by Golub and Van Loan (Johns Hopkins Press.) */

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

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z -= z_offset;

/*     Decode COMPQ */

    if (lsame_(compq, "N")) {
        ilq = FALSE_;
        icompq = 1;
    } else if (lsame_(compq, "V")) {
        ilq = TRUE_;
        icompq = 2;
    } else if (lsame_(compq, "I")) {
        ilq = TRUE_;
        icompq = 3;
    } else {
        icompq = 0;
    }

/*     Decode COMPZ */

    if (lsame_(compz, "N")) {
        ilz = FALSE_;
        icompz = 1;
    } else if (lsame_(compz, "V")) {
        ilz = TRUE_;
        icompz = 2;
    } else if (lsame_(compz, "I")) {
        ilz = TRUE_;
        icompz = 3;
    } else {
        icompz = 0;
    }

/*     Test the input parameters. */

    *info = 0;
    if (icompq <= 0) {
        *info = -1;
    } else if (icompz <= 0) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*ilo < 1) {
        *info = -4;
    } else if (*ihi > *n || *ihi < *ilo - 1) {
        *info = -5;
    } else if (*lda < max(1,*n)) {
        *info = -7;
    } else if (*ldb < max(1,*n)) {
        *info = -9;
    } else if ( (ilq && *ldq < *n ) || *ldq < 1) {
        *info = -11;
    } else if ( (ilz && *ldz < *n ) || *ldz < 1) {
        *info = -13;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGGHRD", &i__1);
        return;
    }

/*     Initialize Q and Z if desired. */

    if (icompq == 3) {
        dlaset_("Full", n, n, &c_b10, &c_b11, &q[q_offset], ldq);
    }
    if (icompz == 3) {
        dlaset_("Full", n, n, &c_b10, &c_b11, &z[z_offset], ldz);
    }

/*     Quick return if possible */

    if (*n <= 1) {
        return;
    }

/*     Zero out lower triangle of B */

    for (jcol = 1; jcol <= *n - 1; ++jcol) {
        for (jrow = jcol + 1; jrow <= *n; ++jrow) {
            b[jrow + jcol * b_dim1] = 0.;
        }
    }

/*     Reduce A and B */

    for (jcol = *ilo; jcol <= *ihi - 2; ++jcol) {

        for (jrow = *ihi; jrow >= jcol + 2; --jrow) {

/*           Step 1: rotate rows JROW-1, JROW to kill A(JROW,JCOL) */

            temp = a[jrow - 1 + jcol * a_dim1];
            dlartg_(&temp, &a[jrow + jcol * a_dim1], &c, &s, &a[jrow - 1 + jcol * a_dim1]);
            a[jrow + jcol * a_dim1] = 0.;
            i__1 = *n - jcol;
            drot_(&i__1, &a[jrow - 1 + (jcol + 1) * a_dim1], lda, &a[jrow + (jcol + 1) * a_dim1], lda, &c, &s);
            i__1 = *n + 2 - jrow;
            drot_(&i__1, &b[jrow - 1 + (jrow - 1) * b_dim1], ldb, &b[jrow + (jrow - 1) * b_dim1], ldb, &c, &s);
            if (ilq) {
                drot_(n, &q[(jrow - 1) * q_dim1 + 1], &c__1, &q[jrow * q_dim1 + 1], &c__1, &c, &s);
            }

/*           Step 2: rotate columns JROW, JROW-1 to kill B(JROW,JROW-1) */

            temp = b[jrow + jrow * b_dim1];
            dlartg_(&temp, &b[jrow + (jrow - 1) * b_dim1], &c, &s, &b[jrow + jrow * b_dim1]);
            b[jrow + (jrow - 1) * b_dim1] = 0.;
            drot_(ihi, &a[jrow * a_dim1 + 1], &c__1, &a[(jrow - 1) * a_dim1 + 1], &c__1, &c, &s);
            i__1 = jrow - 1;
            drot_(&i__1, &b[jrow * b_dim1 + 1], &c__1, &b[(jrow - 1) * b_dim1 + 1], &c__1, &c, &s);
            if (ilz) {
                drot_(n, &z[jrow * z_dim1 + 1], &c__1, &z[(jrow - 1) * z_dim1 + 1], &c__1, &c, &s);
            }
        }
    }
} /* dgghrd_ */