/* Subroutine */ int dtrexc_(char *compq, integer *n, doublereal *t, integer *
ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst,
doublereal *work, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, t_dim1, t_offset, i__1;
/* Local variables */
integer nbf, nbl, here;
extern logical lsame_(char *, char *);
logical wantq;
extern /* Subroutine */ int dlaexc_(logical *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *, integer
*, doublereal *, integer *), xerbla_(char *, integer *);
integer nbnext;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTREXC reorders the real Schur factorization of a real matrix */
/* A = Q*T*Q**T, so that the diagonal block of T with row index IFST is */
/* moved to row ILST. */
/* The real Schur form T is reordered by an orthogonal similarity */
/* transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors */
/* is updated by postmultiplying it with Z. */
/* T must be in Schur canonical form (as returned by DHSEQR), that is, */
/* block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each */
/* 2-by-2 diagonal block has its diagonal elements equal and its */
/* off-diagonal elements of opposite sign. */
/* Arguments */
/* ========= */
/* COMPQ (input) CHARACTER*1 */
/* = 'V': update the matrix Q of Schur vectors; */
/* = 'N': do not update Q. */
/* 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 */
/* Schur canonical form. */
/* On exit, the reordered upper quasi-triangular matrix, 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 COMPQ = 'V', the matrix Q of Schur vectors. */
/* On exit, if COMPQ = 'V', Q has been postmultiplied by the */
/* orthogonal transformation matrix Z which reorders T. */
/* If COMPQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N). */
/* IFST (input/output) INTEGER */
/* ILST (input/output) INTEGER */
/* Specify the reordering of the diagonal blocks of T. */
/* The block with row index IFST is moved to row ILST, by a */
/* sequence of transpositions 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 <= N; 1 <= ILST <= N. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* = 1: two adjacent blocks were too close to swap (the problem */
/* is very ill-conditioned); T may have been partially */
/* reordered, and ILST points to the first row of the */
/* current position of the block being moved. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Decode and test the input arguments. */
/* 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;
wantq = lsame_(compq, "V");
if (! wantq && ! lsame_(compq, "N")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldt < max(1,*n)) {
*info = -4;
} else if (*ldq < 1 || wantq && *ldq < max(1,*n)) {
*info = -6;
} else if (*ifst < 1 || *ifst > *n) {
*info = -7;
} else if (*ilst < 1 || *ilst > *n) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTREXC", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 1) {
return 0;
}
/* Determine the first row of specified block */
/* and find out it is 1 by 1 or 2 by 2. */
if (*ifst > 1) {
if (t[*ifst + (*ifst - 1) * t_dim1] != 0.) {
--(*ifst);
}
}
nbf = 1;
if (*ifst < *n) {
if (t[*ifst + 1 + *ifst * t_dim1] != 0.) {
nbf = 2;
}
}
/* Determine the first row of the final block */
/* and find out it is 1 by 1 or 2 by 2. */
if (*ilst > 1) {
if (t[*ilst + (*ilst - 1) * t_dim1] != 0.) {
--(*ilst);
}
}
nbl = 1;
if (*ilst < *n) {
if (t[*ilst + 1 + *ilst * t_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 block 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 (t[here + nbf + 1 + (here + nbf) * t_dim1] != 0.) {
nbnext = 2;
}
}
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &here, &
nbf, &nbnext, &work[1], 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 (t[here + 1 + here * t_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 (t[here + 3 + (here + 2) * t_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here + 1;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
c__1, &nbnext, &work[1], info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1 by 1 blocks, no problems possible */
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
here, &c__1, &nbnext, &work[1], info);
++here;
} else {
/* Recompute NBNEXT in case 2 by 2 split */
if (t[here + 2 + (here + 1) * t_dim1] == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2 by 2 Block did not split */
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
here, &c__1, &nbnext, &work[1], info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += 2;
} else {
/* 2 by 2 Block did split */
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
here, &c__1, &c__1, &work[1], info);
i__1 = here + 1;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
i__1, &c__1, &c__1, &work[1], info);
here += 2;
}
}
}
if (here < *ilst) {
goto L10;
}
} else {
here = *ifst;
L20:
/* Swap block with next one above */
if (nbf == 1 || nbf == 2) {
/* Current block either 1 by 1 or 2 by 2 */
nbnext = 1;
if (here >= 3) {
if (t[here - 1 + (here - 2) * t_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
nbnext, &nbf, &work[1], 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 (t[here + 1 + here * t_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 (t[here - 1 + (here - 2) * t_dim1] != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, &
nbnext, &c__1, &work[1], info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1 by 1 blocks, no problems possible */
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
here, &nbnext, &c__1, &work[1], info);
--here;
} else {
/* Recompute NBNEXT in case 2 by 2 split */
if (t[here + (here - 1) * t_dim1] == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2 by 2 Block did not split */
i__1 = here - 1;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
i__1, &c__2, &c__1, &work[1], info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += -2;
} else {
/* 2 by 2 Block did split */
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
here, &c__1, &c__1, &work[1], info);
i__1 = here - 1;
dlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &
i__1, &c__1, &c__1, &work[1], info);
here += -2;
}
}
}
if (here > *ilst) {
goto L20;
}
}
*ilst = here;
return 0;
/* End of DTREXC */
} /* dtrexc_ */
/* Subroutine */ int dtrexc_(char *compq, integer *n, doublereal *t, integer *
ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst,
doublereal *work, integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DTREXC reorders the real Schur factorization of a real matrix
A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
moved to row ILST.
The real Schur form T is reordered by an orthogonal similarity
transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
is updated by postmultiplying it with Z.
T must be in Schur canonical form (as returned by DHSEQR), that is,
block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
2-by-2 diagonal block has its diagonal elements equal and its
off-diagonal elements of opposite sign.
Arguments
=========
COMPQ (input) CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
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
Schur canonical form.
On exit, the reordered upper quasi-triangular matrix, 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 COMPQ = 'V', the matrix Q of Schur vectors.
On exit, if COMPQ = 'V', Q has been postmultiplied by the
orthogonal transformation matrix Z which reorders T.
If COMPQ = 'N', Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IFST (input/output) INTEGER
ILST (input/output) INTEGER
Specify the reordering of the diagonal blocks of T.
The block with row index IFST is moved to row ILST, by a
sequence of transpositions 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 <= N; 1 <= ILST <= N.
WORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: two adjacent blocks were too close to swap (the problem
is very ill-conditioned); T may have been partially
reordered, and ILST points to the first row of the
current position of the block being moved.
=====================================================================
Decode and test the input arguments.
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c__2 = 2;
/* System generated locals */
integer q_dim1, q_offset, t_dim1, t_offset, i__1;
/* Local variables */
static integer here;
extern logical lsame_(char *, char *);
static logical wantq;
extern /* Subroutine */ int dlaexc_(logical *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *, integer
*, doublereal *, integer *), xerbla_(char *, integer *);
static integer nbnext, nbf, nbl;
#define WORK(I) work[(I)-1]
#define T(I,J) t[(I)-1 + ((J)-1)* ( *ldt)]
#define Q(I,J) q[(I)-1 + ((J)-1)* ( *ldq)]
*info = 0;
wantq = lsame_(compq, "V");
if (! wantq && ! lsame_(compq, "N")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldt < max(1,*n)) {
*info = -4;
} else if (*ldq < 1 || wantq && *ldq < max(1,*n)) {
*info = -6;
} else if (*ifst < 1 || *ifst > *n) {
*info = -7;
} else if (*ilst < 1 || *ilst > *n) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTREXC", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 1) {
return 0;
}
/* Determine the first row of specified block
and find out it is 1 by 1 or 2 by 2. */
if (*ifst > 1) {
if (T(*ifst,*ifst-1) != 0.) {
--(*ifst);
}
}
nbf = 1;
if (*ifst < *n) {
if (T(*ifst+1,*ifst) != 0.) {
nbf = 2;
}
}
/* Determine the first row of the final block
and find out it is 1 by 1 or 2 by 2. */
if (*ilst > 1) {
if (T(*ilst,*ilst-1) != 0.) {
--(*ilst);
}
}
nbl = 1;
if (*ilst < *n) {
if (T(*ilst+1,*ilst) != 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 block 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 (T(here+nbf+1,here+nbf) != 0.) {
nbnext = 2;
}
}
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &here, &
nbf, &nbnext, &WORK(1), 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 (T(here+1,here) == 0.) {
nbf = 3;
}
}
} else {
/* Current block consists of two 1 by 1 blocks each of w
hich
must be swapped individually */
nbnext = 1;
if (here + 3 <= *n) {
if (T(here+3,here+2) != 0.) {
nbnext = 2;
}
}
i__1 = here + 1;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &i__1, &
c__1, &nbnext, &WORK(1), info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1 by 1 blocks, no problems possible
*/
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
here, &c__1, &nbnext, &WORK(1), info);
++here;
} else {
/* Recompute NBNEXT in case 2 by 2 split */
if (T(here+2,here+1) == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2 by 2 Block did not split */
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
here, &c__1, &nbnext, &WORK(1), info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += 2;
} else {
/* 2 by 2 Block did split */
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
here, &c__1, &c__1, &WORK(1), info);
i__1 = here + 1;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
i__1, &c__1, &c__1, &WORK(1), info);
here += 2;
}
}
}
if (here < *ilst) {
goto L10;
}
} else {
here = *ifst;
L20:
/* Swap block with next one above */
if (nbf == 1 || nbf == 2) {
/* Current block either 1 by 1 or 2 by 2 */
nbnext = 1;
if (here >= 3) {
if (T(here-1,here-2) != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &i__1, &
nbnext, &nbf, &WORK(1), 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 (T(here+1,here) == 0.) {
nbf = 3;
}
}
} else {
/* Current block consists of two 1 by 1 blocks each of w
hich
must be swapped individually */
nbnext = 1;
if (here >= 3) {
if (T(here-1,here-2) != 0.) {
nbnext = 2;
}
}
i__1 = here - nbnext;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &i__1, &
nbnext, &c__1, &WORK(1), info);
if (*info != 0) {
*ilst = here;
return 0;
}
if (nbnext == 1) {
/* Swap two 1 by 1 blocks, no problems possible
*/
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
here, &nbnext, &c__1, &WORK(1), info);
--here;
} else {
/* Recompute NBNEXT in case 2 by 2 split */
if (T(here,here-1) == 0.) {
nbnext = 1;
}
if (nbnext == 2) {
/* 2 by 2 Block did not split */
i__1 = here - 1;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
i__1, &c__2, &c__1, &WORK(1), info);
if (*info != 0) {
*ilst = here;
return 0;
}
here += -2;
} else {
/* 2 by 2 Block did split */
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
here, &c__1, &c__1, &WORK(1), info);
i__1 = here - 1;
dlaexc_(&wantq, n, &T(1,1), ldt, &Q(1,1), ldq, &
i__1, &c__1, &c__1, &WORK(1), info);
here += -2;
}
}
}
if (here > *ilst) {
goto L20;
}
}
*ilst = here;
return 0;
/* End of DTREXC */
} /* dtrexc_ */
