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/* ../../../dependencies/lapack/src/dgghrd.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"
/* Table of constant values */
static doublereal c_b10 = 0.;
static doublereal c_b11 = 1.;
static integer c__1 = 1;
/* Subroutine */ int dgghrd_(char *compq, char *compz, integer *n, integer *
ilo, integer *ihi, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *q, integer *ldq, doublereal *z__, integer *
ldz, integer *info, ftnlen compq_len, ftnlen compz_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1,
z_offset, i__1, i__2, i__3;
/* Local variables */
static doublereal c__, s;
static logical ilq, ilz;
static integer jcol;
static doublereal temp;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
static integer jrow;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, ftnlen),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), xerbla_(char *, integer *, ftnlen);
static integer icompq, icompz;
/* -- 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 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* 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.) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode COMPQ */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
/* Function Body */
if (lsame_(compq, "N", (ftnlen)1, (ftnlen)1)) {
ilq = FALSE_;
icompq = 1;
} else if (lsame_(compq, "V", (ftnlen)1, (ftnlen)1)) {
ilq = TRUE_;
icompq = 2;
} else if (lsame_(compq, "I", (ftnlen)1, (ftnlen)1)) {
ilq = TRUE_;
icompq = 3;
} else {
icompq = 0;
}
/* Decode COMPZ */
if (lsame_(compz, "N", (ftnlen)1, (ftnlen)1)) {
ilz = FALSE_;
icompz = 1;
} else if (lsame_(compz, "V", (ftnlen)1, (ftnlen)1)) {
ilz = TRUE_;
icompz = 2;
} else if (lsame_(compz, "I", (ftnlen)1, (ftnlen)1)) {
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, (ftnlen)6);
return 0;
}
/* Initialize Q and Z if desired. */
if (icompq == 3) {
dlaset_("Full", n, n, &c_b10, &c_b11, &q[q_offset], ldq, (ftnlen)4);
}
if (icompz == 3) {
dlaset_("Full", n, n, &c_b10, &c_b11, &z__[z_offset], ldz, (ftnlen)4);
}
/* Quick return if possible */
if (*n <= 1) {
return 0;
}
/* Zero out lower triangle of B */
i__1 = *n - 1;
for (jcol = 1; jcol <= i__1; ++jcol) {
i__2 = *n;
for (jrow = jcol + 1; jrow <= i__2; ++jrow) {
b[jrow + jcol * b_dim1] = 0.;
/* L10: */
}
/* L20: */
}
/* Reduce A and B */
i__1 = *ihi - 2;
for (jcol = *ilo; jcol <= i__1; ++jcol) {
i__2 = jcol + 2;
for (jrow = *ihi; jrow >= i__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__3 = *n - jcol;
drot_(&i__3, &a[jrow - 1 + (jcol + 1) * a_dim1], lda, &a[jrow + (
jcol + 1) * a_dim1], lda, &c__, &s);
i__3 = *n + 2 - jrow;
drot_(&i__3, &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__3 = jrow - 1;
drot_(&i__3, &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);
}
/* L30: */
}
/* L40: */
}
return 0;
/* End of DGGHRD */
} /* dgghrd_ */
|
