/* dtgexc.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__2 = 2;
/* Subroutine */ int dtgexc_(logical *wantq, logical *wantz, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
q, integer *ldq, doublereal *z__, integer *ldz, integer *ifst,
integer *ilst, doublereal *work, integer *lwork, 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 */
integer nbf, nbl, here, lwmin;
extern /* Subroutine */ int dtgex2_(logical *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *, integer
*, doublereal *, integer *, integer *), xerbla_(char *, integer *);
integer nbnext;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTGEXC reorders the generalized real Schur decomposition of a real */
/* matrix pair (A,B) using an orthogonal equivalence transformation */
/* (A, B) = Q * (A, B) * Z', */
/* so that the diagonal block of (A, B) with row index IFST is moved */
/* to row ILST. */
/* (A, B) must be in generalized real Schur canonical form (as returned */
/* by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
/* diagonal blocks. B is 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) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the matrix A in generalized real Schur canonical */
/* form. */
/* On exit, the updated matrix A, again in generalized */
/* real Schur canonical form. */
/* 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 matrix B in generalized real Schur canonical */
/* form (A,B). */
/* On exit, the updated matrix B, again in generalized */
/* real Schur canonical form (A,B). */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* Q (input/output) DOUBLE PRECISION array, dimension (LDZ,N) */
/* On entry, if WANTQ = .TRUE., the orthogonal matrix Q. */
/* On exit, the updated matrix Q. */
/* If WANTQ = .FALSE., Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= 1. */
/* If WANTQ = .TRUE., LDQ >= N. */
/* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N) */
/* On entry, if WANTZ = .TRUE., the orthogonal matrix Z. */
/* On exit, the updated matrix Z. */
/* If WANTZ = .FALSE., Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1. */
/* If WANTZ = .TRUE., LDZ >= N. */
/* IFST (input/output) INTEGER */
/* ILST (input/output) INTEGER */
/* Specify the reordering of the diagonal blocks of (A, B). */
/* The block with row index IFST is moved to row ILST, by a */
/* sequence of swapping between adjacent blocks. */
/* On exit, if IFST pointed on entry to the second row of */
/* a 2-by-2 block, it is changed to point to the first row; */
/* ILST always points to the first row of the block in its */
/* final position (which may differ from its input value by */
/* +1 or -1). 1 <= IFST, ILST <= N. */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* =0: successful exit. */
/* <0: if INFO = -i, the i-th argument had an illegal value. */
/* =1: The transformed matrix pair (A, B) would be too far */
/* from generalized Schur form; the problem is ill- */
/* conditioned. (A, B) may have been partially reordered, */
/* and ILST points to the first row of the current */
/* position of the block being moved. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* Umea University, S-901 87 Umea, Sweden. */
/* [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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test input arguments. */
/* 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;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldq < 1 || *wantq && *ldq < max(1,*n)) {
*info = -9;
} else if (*ldz < 1 || *wantz && *ldz < max(1,*n)) {
*info = -11;
} else if (*ifst < 1 || *ifst > *n) {
*info = -12;
} else if (*ilst < 1 || *ilst > *n) {
*info = -13;
}
if (*info == 0) {
if (*n <= 1) {
lwmin = 1;
} else {
lwmin = (*n << 2) + 16;
}
work[1] = (doublereal) lwmin;
if (*lwork < lwmin && ! lquery) {
*info = -15;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTGEXC", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 1) {
return 0;
}
/* Determine the first row of the specified block and find out */
/* if it is 1-by-1 or 2-by-2. */
if (*ifst > 1) {
if (a[*ifst + (*ifst - 1) * a_dim1] != 0.) {
--(*ifst);
}
}
nbf = 1;
if (*ifst < *n) {
if (a[*ifst + 1 + *ifst * a_dim1] != 0.) {
nbf = 2;
}
}
/* Determine the first row of the final block */
/* and find out if it is 1-by-1 or 2-by-2. */
if (*ilst > 1) {
if (a[*ilst + (*ilst - 1) * a_dim1] != 0.) {
--(*ilst);
}
}
nbl = 1;
if (*ilst < *n) {
if (a[*ilst + 1 + *ilst * a_dim1] != 0.) {
nbl = 2;
}
}
if (*ifst == *ilst) {
return 0;
}
if (*ifst < *ilst) {
/* Update ILST. */
if (nbf == 2 && nbl == 1) {
--(*ilst);
}
if (nbf == 1 && nbl == 2) {
++(*ilst);
}
here = *ifst;
L10:
/* Swap with next one below. */
if (nbf == 1 || nbf == 2) {
/* Current block either 1-by-1 or 2-by-2. */
nbnext = 1;
if (here + nbf + 1 <= *n) {
if (a[here + nbf + 1 + (here + nbf) * a_dim1] != 0.) {
nbnext = 2;
}
}
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
q_offset], ldq, &z__[z_offset], ldz, &here, &nbf, &nbnext,
&work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += nbnext;
/* Test if 2-by-2 block breaks into two 1-by-1 blocks. */
if (nbf == 2) {
if (a[here + 1 + here * a_dim1] == 0.) {
nbf = 3;
}
}
} else {
/* Current block consists of two 1-by-1 blocks, each of which */
/* must be swapped individually. */
nbnext = 1;
if (here + 3 <= *n) {
if (a[here + 3 + (here + 2) * a_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here + 1;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
q_offset], ldq, &z__[z_offset], ldz, &i__1, &c__1, &
nbnext, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1-by-1 blocks. */
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb,
&q[q_offset], ldq, &z__[z_offset], ldz, &here, &c__1,
&c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
++here;
} else {
/* Recompute NBNEXT in case of 2-by-2 split. */
if (a[here + 2 + (here + 1) * a_dim1] == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2-by-2 block did not split. */
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
here, &c__1, &nbnext, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += 2;
} else {
/* 2-by-2 block did split. */
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
here, &c__1, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
++here;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
here, &c__1, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
++here;
}
}
}
if (here < *ilst) {
goto L10;
}
} else {
here = *ifst;
L20:
/* Swap with next one below. */
if (nbf == 1 || nbf == 2) {
/* Current block either 1-by-1 or 2-by-2. */
nbnext = 1;
if (here >= 3) {
if (a[here - 1 + (here - 2) * a_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, &nbf,
&work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
here -= nbnext;
/* Test if 2-by-2 block breaks into two 1-by-1 blocks. */
if (nbf == 2) {
if (a[here + 1 + here * a_dim1] == 0.) {
nbf = 3;
}
}
} else {
/* Current block consists of two 1-by-1 blocks, each of which */
/* must be swapped individually. */
nbnext = 1;
if (here >= 3) {
if (a[here - 1 + (here - 2) * a_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb, &q[
q_offset], ldq, &z__[z_offset], ldz, &i__1, &nbnext, &
c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1-by-1 blocks. */
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], ldb,
&q[q_offset], ldq, &z__[z_offset], ldz, &here, &
nbnext, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
--here;
} else {
/* Recompute NBNEXT in case of 2-by-2 split. */
if (a[here + (here - 1) * a_dim1] == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2-by-2 block did not split. */
i__1 = here - 1;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
i__1, &c__2, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += -2;
} else {
/* 2-by-2 block did split. */
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
here, &c__1, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
--here;
dtgex2_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset],
ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &
here, &c__1, &c__1, &work[1], lwork, info);
if (*info != 0) {
*ilst = here;
return 0;
}
--here;
}
}
}
if (here > *ilst) {
goto L20;
}
}
*ilst = here;
work[1] = (doublereal) lwmin;
return 0;
/* End of DTGEXC */
} /* dtgexc_ */