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/* zgghrd.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 doublecomplex c_b1 = {1.,0.};
static doublecomplex c_b2 = {0.,0.};
static integer c__1 = 1;
/* Subroutine */ int zgghrd_(char *compq, char *compz, integer *n, integer *
ilo, integer *ihi, doublecomplex *a, integer *lda, doublecomplex *b,
integer *ldb, doublecomplex *q, integer *ldq, doublecomplex *z__,
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, i__2, i__3;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
doublereal c__;
doublecomplex s;
logical ilq, ilz;
integer jcol, jrow;
extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *);
extern logical lsame_(char *, char *);
doublecomplex ctemp;
extern /* Subroutine */ int xerbla_(char *, integer *);
integer icompq, icompz;
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlartg_(doublecomplex *, doublecomplex *, doublereal *,
doublecomplex *, doublecomplex *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper */
/* Hessenberg form using unitary transformations, where A is a */
/* general matrix and B is upper triangular. The form of the */
/* generalized eigenvalue problem is */
/* A*x = lambda*B*x, */
/* and B is typically made upper triangular by computing its QR */
/* factorization and moving the unitary matrix Q to the left side */
/* of the equation. */
/* This subroutine simultaneously reduces A to a Hessenberg matrix H: */
/* Q**H*A*Z = H */
/* and transforms B to another upper triangular matrix T: */
/* Q**H*B*Z = T */
/* in order to reduce the problem to its standard form */
/* H*y = lambda*T*y */
/* where y = Z**H*x. */
/* The unitary 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**H = (Q1*Q) * H * (Z1*Z)**H */
/* Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H */
/* If Q1 is the unitary matrix from the QR factorization of B in the */
/* original equation A*x = lambda*B*x, then ZGGHRD reduces the original */
/* problem to generalized Hessenberg form. */
/* Arguments */
/* ========= */
/* COMPQ (input) CHARACTER*1 */
/* = 'N': do not compute Q; */
/* = 'I': Q is initialized to the unit matrix, and the */
/* unitary matrix Q is returned; */
/* = 'V': Q must contain a unitary matrix Q1 on entry, */
/* and the product Q1*Q is returned. */
/* COMPZ (input) CHARACTER*1 */
/* = 'N': do not compute Q; */
/* = 'I': Q is initialized to the unit matrix, and the */
/* unitary matrix Q is returned; */
/* = 'V': Q must contain a unitary matrix Q1 on entry, */
/* and the product Q1*Q is returned. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* ILO and IHI mark the rows and columns of A which are to be */
/* reduced. 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 ZGGBAL; 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) 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 */
/* rest is set to zero. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) COMPLEX*16 array, dimension (LDB, N) */
/* On entry, the N-by-N upper triangular matrix B. */
/* On exit, the upper triangular matrix T = Q**H 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) COMPLEX*16 array, dimension (LDQ, N) */
/* On entry, if COMPQ = 'V', the unitary matrix Q1, typically */
/* from the QR factorization of B. */
/* On exit, if COMPQ='I', the unitary matrix Q, and if */
/* COMPQ = 'V', the product Q1*Q. */
/* Not referenced if COMPQ='N'. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. */
/* LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise. */
/* Z (input/output) COMPLEX*16 array, dimension (LDZ, N) */
/* On entry, if COMPZ = 'V', the unitary matrix Z1. */
/* On exit, if COMPZ='I', the unitary matrix Z, and if */
/* COMPZ = 'V', the product Z1*Z. */
/* Not referenced if COMPZ='N'. */
/* 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")) {
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_("ZGGHRD", &i__1);
return 0;
}
/* Initialize Q and Z if desired. */
if (icompq == 3) {
zlaset_("Full", n, n, &c_b2, &c_b1, &q[q_offset], ldq);
}
if (icompz == 3) {
zlaset_("Full", n, n, &c_b2, &c_b1, &z__[z_offset], ldz);
}
/* 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) {
i__3 = jrow + jcol * b_dim1;
b[i__3].r = 0., b[i__3].i = 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) */
i__3 = jrow - 1 + jcol * a_dim1;
ctemp.r = a[i__3].r, ctemp.i = a[i__3].i;
zlartg_(&ctemp, &a[jrow + jcol * a_dim1], &c__, &s, &a[jrow - 1 +
jcol * a_dim1]);
i__3 = jrow + jcol * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = *n - jcol;
zrot_(&i__3, &a[jrow - 1 + (jcol + 1) * a_dim1], lda, &a[jrow + (
jcol + 1) * a_dim1], lda, &c__, &s);
i__3 = *n + 2 - jrow;
zrot_(&i__3, &b[jrow - 1 + (jrow - 1) * b_dim1], ldb, &b[jrow + (
jrow - 1) * b_dim1], ldb, &c__, &s);
if (ilq) {
d_cnjg(&z__1, &s);
zrot_(n, &q[(jrow - 1) * q_dim1 + 1], &c__1, &q[jrow * q_dim1
+ 1], &c__1, &c__, &z__1);
}
/* Step 2: rotate columns JROW, JROW-1 to kill B(JROW,JROW-1) */
i__3 = jrow + jrow * b_dim1;
ctemp.r = b[i__3].r, ctemp.i = b[i__3].i;
zlartg_(&ctemp, &b[jrow + (jrow - 1) * b_dim1], &c__, &s, &b[jrow
+ jrow * b_dim1]);
i__3 = jrow + (jrow - 1) * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
zrot_(ihi, &a[jrow * a_dim1 + 1], &c__1, &a[(jrow - 1) * a_dim1 +
1], &c__1, &c__, &s);
i__3 = jrow - 1;
zrot_(&i__3, &b[jrow * b_dim1 + 1], &c__1, &b[(jrow - 1) * b_dim1
+ 1], &c__1, &c__, &s);
if (ilz) {
zrot_(n, &z__[jrow * z_dim1 + 1], &c__1, &z__[(jrow - 1) *
z_dim1 + 1], &c__1, &c__, &s);
}
/* L30: */
}
/* L40: */
}
return 0;
/* End of ZGGHRD */
} /* zgghrd_ */
|
