/* dlaexc.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__1 = 1;
static integer c__4 = 4;
static logical c_false = FALSE_;
static integer c_n1 = -1;
static integer c__2 = 2;
static integer c__3 = 3;
/* Subroutine */ int dlaexc_(logical *wantq, integer *n, doublereal *t,
integer *ldt, doublereal *q, integer *ldq, integer *j1, integer *n1,
integer *n2, doublereal *work, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, t_dim1, t_offset, i__1;
doublereal d__1, d__2, d__3;
/* Local variables */
doublereal d__[16] /* was [4][4] */;
integer k;
doublereal u[3], x[4] /* was [2][2] */;
integer j2, j3, j4;
doublereal u1[3], u2[3];
integer nd;
doublereal cs, t11, t22, t33, sn, wi1, wi2, wr1, wr2, eps, tau, tau1,
tau2;
integer ierr;
doublereal temp;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
doublereal scale, dnorm, xnorm;
extern /* Subroutine */ int dlanv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *), dlasy2_(
logical *, logical *, integer *, integer *, integer *, doublereal
*, integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *), dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), dlarfx_(char *, integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *);
doublereal thresh, smlnum;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in */
/* an upper quasi-triangular matrix T by an orthogonal similarity */
/* transformation. */
/* T must be in Schur canonical form, that is, block upper triangular */
/* with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block */
/* has its diagonal elemnts equal and its off-diagonal elements of */
/* opposite sign. */
/* Arguments */
/* ========= */
/* WANTQ (input) LOGICAL */
/* = .TRUE. : accumulate the transformation in the matrix Q; */
/* = .FALSE.: do not accumulate the transformation. */
/* N (input) INTEGER */
/* The order of the matrix T. N >= 0. */
/* T (input/output) DOUBLE PRECISION array, dimension (LDT,N) */
/* On entry, the upper quasi-triangular matrix T, in Schur */
/* canonical form. */
/* On exit, the updated matrix T, again in Schur canonical form. */
/* LDT (input) INTEGER */
/* The leading dimension of the array T. LDT >= max(1,N). */
/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */
/* On entry, if WANTQ is .TRUE., the orthogonal matrix Q. */
/* On exit, if WANTQ is .TRUE., the updated matrix Q. */
/* If WANTQ is .FALSE., Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. */
/* LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N. */
/* J1 (input) INTEGER */
/* The index of the first row of the first block T11. */
/* N1 (input) INTEGER */
/* The order of the first block T11. N1 = 0, 1 or 2. */
/* N2 (input) INTEGER */
/* The order of the second block T22. N2 = 0, 1 or 2. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* = 1: the transformed matrix T would be too far from Schur */
/* form; the blocks are not swapped and T and Q are */
/* unchanged. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0 || *n1 == 0 || *n2 == 0) {
return 0;
}
if (*j1 + *n1 > *n) {
return 0;
}
j2 = *j1 + 1;
j3 = *j1 + 2;
j4 = *j1 + 3;
if (*n1 == 1 && *n2 == 1) {
/* Swap two 1-by-1 blocks. */
t11 = t[*j1 + *j1 * t_dim1];
t22 = t[j2 + j2 * t_dim1];
/* Determine the transformation to perform the interchange. */
d__1 = t22 - t11;
dlartg_(&t[*j1 + j2 * t_dim1], &d__1, &cs, &sn, &temp);
/* Apply transformation to the matrix T. */
if (j3 <= *n) {
i__1 = *n - *j1 - 1;
drot_(&i__1, &t[*j1 + j3 * t_dim1], ldt, &t[j2 + j3 * t_dim1],
ldt, &cs, &sn);
}
i__1 = *j1 - 1;
drot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &c__1,
&cs, &sn);
t[*j1 + *j1 * t_dim1] = t22;
t[j2 + j2 * t_dim1] = t11;
if (*wantq) {
/* Accumulate transformation in the matrix Q. */
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &c__1,
&cs, &sn);
}
} else {
/* Swapping involves at least one 2-by-2 block. */
/* Copy the diagonal block of order N1+N2 to the local array D */
/* and compute its norm. */
nd = *n1 + *n2;
dlacpy_("Full", &nd, &nd, &t[*j1 + *j1 * t_dim1], ldt, d__, &c__4);
dnorm = dlange_("Max", &nd, &nd, d__, &c__4, &work[1]);
/* Compute machine-dependent threshold for test for accepting */
/* swap. */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
/* Computing MAX */
d__1 = eps * 10. * dnorm;
thresh = max(d__1,smlnum);
/* Solve T11*X - X*T22 = scale*T12 for X. */
dlasy2_(&c_false, &c_false, &c_n1, n1, n2, d__, &c__4, &d__[*n1 + 1 +
(*n1 + 1 << 2) - 5], &c__4, &d__[(*n1 + 1 << 2) - 4], &c__4, &
scale, x, &c__2, &xnorm, &ierr);
/* Swap the adjacent diagonal blocks. */
k = *n1 + *n1 + *n2 - 3;
switch (k) {
case 1: goto L10;
case 2: goto L20;
case 3: goto L30;
}
L10:
/* N1 = 1, N2 = 2: generate elementary reflector H so that: */
/* ( scale, X11, X12 ) H = ( 0, 0, * ) */
u[0] = scale;
u[1] = x[0];
u[2] = x[2];
dlarfg_(&c__3, &u[2], u, &c__1, &tau);
u[2] = 1.;
t11 = t[*j1 + *j1 * t_dim1];
/* Perform swap provisionally on diagonal block in D. */
dlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
dlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
/* Test whether to reject swap. */
/* Computing MAX */
d__2 = abs(d__[2]), d__3 = abs(d__[6]), d__2 = max(d__2,d__3), d__3 =
(d__1 = d__[10] - t11, abs(d__1));
if (max(d__2,d__3) > thresh) {
goto L50;
}
/* Accept swap: apply transformation to the entire matrix T. */
i__1 = *n - *j1 + 1;
dlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + *j1 * t_dim1], ldt, &
work[1]);
dlarfx_("R", &j2, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
t[j3 + *j1 * t_dim1] = 0.;
t[j3 + j2 * t_dim1] = 0.;
t[j3 + j3 * t_dim1] = t11;
if (*wantq) {
/* Accumulate transformation in the matrix Q. */
dlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
1]);
}
goto L40;
L20:
/* N1 = 2, N2 = 1: generate elementary reflector H so that: */
/* H ( -X11 ) = ( * ) */
/* ( -X21 ) = ( 0 ) */
/* ( scale ) = ( 0 ) */
u[0] = -x[0];
u[1] = -x[1];
u[2] = scale;
dlarfg_(&c__3, u, &u[1], &c__1, &tau);
u[0] = 1.;
t33 = t[j3 + j3 * t_dim1];
/* Perform swap provisionally on diagonal block in D. */
dlarfx_("L", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
dlarfx_("R", &c__3, &c__3, u, &tau, d__, &c__4, &work[1]);
/* Test whether to reject swap. */
/* Computing MAX */
d__2 = abs(d__[1]), d__3 = abs(d__[2]), d__2 = max(d__2,d__3), d__3 =
(d__1 = d__[0] - t33, abs(d__1));
if (max(d__2,d__3) > thresh) {
goto L50;
}
/* Accept swap: apply transformation to the entire matrix T. */
dlarfx_("R", &j3, &c__3, u, &tau, &t[*j1 * t_dim1 + 1], ldt, &work[1]);
i__1 = *n - *j1;
dlarfx_("L", &c__3, &i__1, u, &tau, &t[*j1 + j2 * t_dim1], ldt, &work[
1]);
t[*j1 + *j1 * t_dim1] = t33;
t[j2 + *j1 * t_dim1] = 0.;
t[j3 + *j1 * t_dim1] = 0.;
if (*wantq) {
/* Accumulate transformation in the matrix Q. */
dlarfx_("R", n, &c__3, u, &tau, &q[*j1 * q_dim1 + 1], ldq, &work[
1]);
}
goto L40;
L30:
/* N1 = 2, N2 = 2: generate elementary reflectors H(1) and H(2) so */
/* that: */
/* H(2) H(1) ( -X11 -X12 ) = ( * * ) */
/* ( -X21 -X22 ) ( 0 * ) */
/* ( scale 0 ) ( 0 0 ) */
/* ( 0 scale ) ( 0 0 ) */
u1[0] = -x[0];
u1[1] = -x[1];
u1[2] = scale;
dlarfg_(&c__3, u1, &u1[1], &c__1, &tau1);
u1[0] = 1.;
temp = -tau1 * (x[2] + u1[1] * x[3]);
u2[0] = -temp * u1[1] - x[3];
u2[1] = -temp * u1[2];
u2[2] = scale;
dlarfg_(&c__3, u2, &u2[1], &c__1, &tau2);
u2[0] = 1.;
/* Perform swap provisionally on diagonal block in D. */
dlarfx_("L", &c__3, &c__4, u1, &tau1, d__, &c__4, &work[1])
;
dlarfx_("R", &c__4, &c__3, u1, &tau1, d__, &c__4, &work[1])
;
dlarfx_("L", &c__3, &c__4, u2, &tau2, &d__[1], &c__4, &work[1]);
dlarfx_("R", &c__4, &c__3, u2, &tau2, &d__[4], &c__4, &work[1]);
/* Test whether to reject swap. */
/* Computing MAX */
d__1 = abs(d__[2]), d__2 = abs(d__[6]), d__1 = max(d__1,d__2), d__2 =
abs(d__[3]), d__1 = max(d__1,d__2), d__2 = abs(d__[7]);
if (max(d__1,d__2) > thresh) {
goto L50;
}
/* Accept swap: apply transformation to the entire matrix T. */
i__1 = *n - *j1 + 1;
dlarfx_("L", &c__3, &i__1, u1, &tau1, &t[*j1 + *j1 * t_dim1], ldt, &
work[1]);
dlarfx_("R", &j4, &c__3, u1, &tau1, &t[*j1 * t_dim1 + 1], ldt, &work[
1]);
i__1 = *n - *j1 + 1;
dlarfx_("L", &c__3, &i__1, u2, &tau2, &t[j2 + *j1 * t_dim1], ldt, &
work[1]);
dlarfx_("R", &j4, &c__3, u2, &tau2, &t[j2 * t_dim1 + 1], ldt, &work[1]
);
t[j3 + *j1 * t_dim1] = 0.;
t[j3 + j2 * t_dim1] = 0.;
t[j4 + *j1 * t_dim1] = 0.;
t[j4 + j2 * t_dim1] = 0.;
if (*wantq) {
/* Accumulate transformation in the matrix Q. */
dlarfx_("R", n, &c__3, u1, &tau1, &q[*j1 * q_dim1 + 1], ldq, &
work[1]);
dlarfx_("R", n, &c__3, u2, &tau2, &q[j2 * q_dim1 + 1], ldq, &work[
1]);
}
L40:
if (*n2 == 2) {
/* Standardize new 2-by-2 block T11 */
dlanv2_(&t[*j1 + *j1 * t_dim1], &t[*j1 + j2 * t_dim1], &t[j2 + *
j1 * t_dim1], &t[j2 + j2 * t_dim1], &wr1, &wi1, &wr2, &
wi2, &cs, &sn);
i__1 = *n - *j1 - 1;
drot_(&i__1, &t[*j1 + (*j1 + 2) * t_dim1], ldt, &t[j2 + (*j1 + 2)
* t_dim1], ldt, &cs, &sn);
i__1 = *j1 - 1;
drot_(&i__1, &t[*j1 * t_dim1 + 1], &c__1, &t[j2 * t_dim1 + 1], &
c__1, &cs, &sn);
if (*wantq) {
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[j2 * q_dim1 + 1], &
c__1, &cs, &sn);
}
}
if (*n1 == 2) {
/* Standardize new 2-by-2 block T22 */
j3 = *j1 + *n2;
j4 = j3 + 1;
dlanv2_(&t[j3 + j3 * t_dim1], &t[j3 + j4 * t_dim1], &t[j4 + j3 *
t_dim1], &t[j4 + j4 * t_dim1], &wr1, &wi1, &wr2, &wi2, &
cs, &sn);
if (j3 + 2 <= *n) {
i__1 = *n - j3 - 1;
drot_(&i__1, &t[j3 + (j3 + 2) * t_dim1], ldt, &t[j4 + (j3 + 2)
* t_dim1], ldt, &cs, &sn);
}
i__1 = j3 - 1;
drot_(&i__1, &t[j3 * t_dim1 + 1], &c__1, &t[j4 * t_dim1 + 1], &
c__1, &cs, &sn);
if (*wantq) {
drot_(n, &q[j3 * q_dim1 + 1], &c__1, &q[j4 * q_dim1 + 1], &
c__1, &cs, &sn);
}
}
}
return 0;
/* Exit with INFO = 1 if swap was rejected. */
L50:
*info = 1;
return 0;
/* End of DLAEXC */
} /* dlaexc_ */
