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/* ztgex2.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 integer c__2 = 2;
static integer c__1 = 1;
/* Subroutine */ int ztgex2_(logical *wantq, logical *wantz, integer *n,
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
doublecomplex *q, integer *ldq, doublecomplex *z__, integer *ldz,
integer *j1, 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;
doublereal d__1;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
double sqrt(doublereal), z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
doublecomplex f, g;
integer i__, m;
doublecomplex s[4] /* was [2][2] */, t[4] /* was [2][2] */;
doublereal cq, sa, sb, cz;
doublecomplex sq;
doublereal ss, ws;
doublecomplex sz;
doublereal eps, sum;
logical weak;
doublecomplex cdum, work[8];
extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *);
doublereal scale;
extern doublereal dlamch_(char *);
logical dtrong;
doublereal thresh;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlartg_(doublecomplex *, doublecomplex *, doublereal *,
doublecomplex *, doublecomplex *);
doublereal smlnum;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) */
/* in an upper triangular matrix pair (A, B) by an unitary equivalence */
/* transformation. */
/* (A, B) must be in generalized Schur canonical form, that is, A and */
/* B are both upper triangular. */
/* Optionally, the matrices Q and Z of generalized Schur vectors are */
/* updated. */
/* Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' */
/* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' */
/* Arguments */
/* ========= */
/* WANTQ (input) LOGICAL */
/* .TRUE. : update the left transformation matrix Q; */
/* .FALSE.: do not update Q. */
/* WANTZ (input) LOGICAL */
/* .TRUE. : update the right transformation matrix Z; */
/* .FALSE.: do not update Z. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* A (input/output) COMPLEX*16 arrays, dimensions (LDA,N) */
/* On entry, the matrix A in the pair (A, B). */
/* On exit, the updated matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) COMPLEX*16 arrays, dimensions (LDB,N) */
/* On entry, the matrix B in the pair (A, B). */
/* On exit, the updated matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* Q (input/output) COMPLEX*16 array, dimension (LDZ,N) */
/* If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, */
/* the updated matrix Q. */
/* Not referenced if WANTQ = .FALSE.. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= 1; */
/* If WANTQ = .TRUE., LDQ >= N. */
/* Z (input/output) COMPLEX*16 array, dimension (LDZ,N) */
/* If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, */
/* the updated matrix Z. */
/* Not referenced if WANTZ = .FALSE.. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1; */
/* If WANTZ = .TRUE., LDZ >= N. */
/* J1 (input) INTEGER */
/* The index to the first block (A11, B11). */
/* INFO (output) INTEGER */
/* =0: Successful exit. */
/* =1: The transformed matrix pair (A, B) would be too far */
/* from generalized Schur form; the problem is ill- */
/* conditioned. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* In the current code both weak and strong stability tests are */
/* performed. The user can omit the strong stability test by changing */
/* the internal logical parameter WANDS to .FALSE.. See ref. [2] for */
/* details. */
/* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/* M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */
/* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/* Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/* Estimation: Theory, Algorithms and Software, Report UMINF-94.04, */
/* Department of Computing Science, Umea University, S-901 87 Umea, */
/* Sweden, 1994. Also as LAPACK Working Note 87. To appear in */
/* Numerical Algorithms, 1996. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 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 */
*info = 0;
/* Quick return if possible */
if (*n <= 1) {
return 0;
}
m = 2;
weak = FALSE_;
dtrong = FALSE_;
/* Make a local copy of selected block in (A, B) */
zlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__2);
zlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__2);
/* Compute the threshold for testing the acceptance of swapping. */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
scale = 0.;
sum = 1.;
zlacpy_("Full", &m, &m, s, &c__2, work, &m);
zlacpy_("Full", &m, &m, t, &c__2, &work[m * m], &m);
i__1 = (m << 1) * m;
zlassq_(&i__1, work, &c__1, &scale, &sum);
sa = scale * sqrt(sum);
/* Computing MAX */
d__1 = eps * 10. * sa;
thresh = max(d__1,smlnum);
/* Compute unitary QL and RQ that swap 1-by-1 and 1-by-1 blocks */
/* using Givens rotations and perform the swap tentatively. */
z__2.r = s[3].r * t[0].r - s[3].i * t[0].i, z__2.i = s[3].r * t[0].i + s[
3].i * t[0].r;
z__3.r = t[3].r * s[0].r - t[3].i * s[0].i, z__3.i = t[3].r * s[0].i + t[
3].i * s[0].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
f.r = z__1.r, f.i = z__1.i;
z__2.r = s[3].r * t[2].r - s[3].i * t[2].i, z__2.i = s[3].r * t[2].i + s[
3].i * t[2].r;
z__3.r = t[3].r * s[2].r - t[3].i * s[2].i, z__3.i = t[3].r * s[2].i + t[
3].i * s[2].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
g.r = z__1.r, g.i = z__1.i;
sa = z_abs(&s[3]);
sb = z_abs(&t[3]);
zlartg_(&g, &f, &cz, &sz, &cdum);
z__1.r = -sz.r, z__1.i = -sz.i;
sz.r = z__1.r, sz.i = z__1.i;
d_cnjg(&z__1, &sz);
zrot_(&c__2, s, &c__1, &s[2], &c__1, &cz, &z__1);
d_cnjg(&z__1, &sz);
zrot_(&c__2, t, &c__1, &t[2], &c__1, &cz, &z__1);
if (sa >= sb) {
zlartg_(s, &s[1], &cq, &sq, &cdum);
} else {
zlartg_(t, &t[1], &cq, &sq, &cdum);
}
zrot_(&c__2, s, &c__2, &s[1], &c__2, &cq, &sq);
zrot_(&c__2, t, &c__2, &t[1], &c__2, &cq, &sq);
/* Weak stability test: |S21| + |T21| <= O(EPS F-norm((S, T))) */
ws = z_abs(&s[1]) + z_abs(&t[1]);
weak = ws <= thresh;
if (! weak) {
goto L20;
}
if (TRUE_) {
/* Strong stability test: */
/* F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A, B))) */
zlacpy_("Full", &m, &m, s, &c__2, work, &m);
zlacpy_("Full", &m, &m, t, &c__2, &work[m * m], &m);
d_cnjg(&z__2, &sz);
z__1.r = -z__2.r, z__1.i = -z__2.i;
zrot_(&c__2, work, &c__1, &work[2], &c__1, &cz, &z__1);
d_cnjg(&z__2, &sz);
z__1.r = -z__2.r, z__1.i = -z__2.i;
zrot_(&c__2, &work[4], &c__1, &work[6], &c__1, &cz, &z__1);
z__1.r = -sq.r, z__1.i = -sq.i;
zrot_(&c__2, work, &c__2, &work[1], &c__2, &cq, &z__1);
z__1.r = -sq.r, z__1.i = -sq.i;
zrot_(&c__2, &work[4], &c__2, &work[5], &c__2, &cq, &z__1);
for (i__ = 1; i__ <= 2; ++i__) {
i__1 = i__ - 1;
i__2 = i__ - 1;
i__3 = *j1 + i__ - 1 + *j1 * a_dim1;
z__1.r = work[i__2].r - a[i__3].r, z__1.i = work[i__2].i - a[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = i__ + 1;
i__2 = i__ + 1;
i__3 = *j1 + i__ - 1 + (*j1 + 1) * a_dim1;
z__1.r = work[i__2].r - a[i__3].r, z__1.i = work[i__2].i - a[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = i__ + 3;
i__2 = i__ + 3;
i__3 = *j1 + i__ - 1 + *j1 * b_dim1;
z__1.r = work[i__2].r - b[i__3].r, z__1.i = work[i__2].i - b[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = i__ + 5;
i__2 = i__ + 5;
i__3 = *j1 + i__ - 1 + (*j1 + 1) * b_dim1;
z__1.r = work[i__2].r - b[i__3].r, z__1.i = work[i__2].i - b[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
/* L10: */
}
scale = 0.;
sum = 1.;
i__1 = (m << 1) * m;
zlassq_(&i__1, work, &c__1, &scale, &sum);
ss = scale * sqrt(sum);
dtrong = ss <= thresh;
if (! dtrong) {
goto L20;
}
}
/* If the swap is accepted ("weakly" and "strongly"), apply the */
/* equivalence transformations to the original matrix pair (A,B) */
i__1 = *j1 + 1;
d_cnjg(&z__1, &sz);
zrot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1], &
c__1, &cz, &z__1);
i__1 = *j1 + 1;
d_cnjg(&z__1, &sz);
zrot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1], &
c__1, &cz, &z__1);
i__1 = *n - *j1 + 1;
zrot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1], lda,
&cq, &sq);
i__1 = *n - *j1 + 1;
zrot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1], ldb,
&cq, &sq);
/* Set N1 by N2 (2,1) blocks to 0 */
i__1 = *j1 + 1 + *j1 * a_dim1;
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = *j1 + 1 + *j1 * b_dim1;
b[i__1].r = 0., b[i__1].i = 0.;
/* Accumulate transformations into Q and Z if requested. */
if (*wantz) {
d_cnjg(&z__1, &sz);
zrot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 + 1],
&c__1, &cz, &z__1);
}
if (*wantq) {
d_cnjg(&z__1, &sq);
zrot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1], &
c__1, &cq, &z__1);
}
/* Exit with INFO = 0 if swap was successfully performed. */
return 0;
/* Exit with INFO = 1 if swap was rejected. */
L20:
*info = 1;
return 0;
/* End of ZTGEX2 */
} /* ztgex2_ */
|
