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|
/* lapack/double/dtgex2.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__16 = 16;
static doublereal c_b3 = 0.;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__2 = 2;
static doublereal c_b38 = 1.;
static doublereal c_b44 = -1.;
/*< >*/
/* Subroutine */ int dtgex2_(logical *wantq, logical *wantz, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
q, integer *ldq, doublereal *z__, integer *ldz, integer *j1, integer *
n1, integer *n2, 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, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal f, g;
integer i__, m;
doublereal s[16] /* was [4][4] */, t[16] /* was [4][4] */, be[2], ai[2]
, ar[2], sa, sb, li[16] /* was [4][4] */, ir[16] /*
was [4][4] */, ss, ws, eps;
logical weak;
doublereal ddum;
integer idum;
doublereal taul[4], dsum;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
doublereal taur[4], scpy[16] /* was [4][4] */, tcpy[16] /*
was [4][4] */;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal scale, bqra21, brqa21;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen);
doublereal licop[16] /* was [4][4] */;
integer linfo;
doublereal ircop[16] /* was [4][4] */;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal dnorm;
integer iwork[4];
extern /* Subroutine */ int dlagv2_(doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *
, doublereal *, doublereal *, doublereal *), dgeqr2_(integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *), dgerq2_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dorg2r_(integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *), dorgr2_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dorm2r_(char *, char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, ftnlen, ftnlen), dormr2_(char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
ftnlen, ftnlen), dtgsy2_(char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *, ftnlen);
extern doublereal dlamch_(char *, ftnlen);
doublereal dscale;
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, ftnlen),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
logical dtrong;
doublereal thresh, smlnum;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< LOGICAL WANTQ, WANTZ >*/
/*< INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 >*/
/* .. */
/* .. Array Arguments .. */
/*< >*/
/* .. */
/* Purpose */
/* ======= */
/* DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) */
/* of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair */
/* (A, B) by an orthogonal equivalence transformation. */
/* (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 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDZ,N) */
/* On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N) */
/* On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N. */
/* N1 (input) INTEGER */
/* The order of the first block (A11, B11). N1 = 0, 1 or 2. */
/* N2 (input) INTEGER */
/* The order of the second block (A22, B22). N2 = 0, 1 or 2. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK). */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) */
/* INFO (output) INTEGER */
/* =0: Successful exit */
/* >0: If INFO = 1, the transformed matrix (A, B) would be */
/* too far from generalized Schur form; the blocks are */
/* not swapped and (A, B) and (Q, Z) are unchanged. */
/* The problem of swapping is too ill-conditioned. */
/* <0: If INFO = -16: LWORK is too small. Appropriate value */
/* for LWORK is returned in WORK(1). */
/* 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 .. */
/*< DOUBLE PRECISION ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/*< DOUBLE PRECISION TEN >*/
/*< PARAMETER ( TEN = 1.0D+01 ) >*/
/*< INTEGER LDST >*/
/*< PARAMETER ( LDST = 4 ) >*/
/*< LOGICAL WANDS >*/
/*< PARAMETER ( WANDS = .TRUE. ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL DTRONG, WEAK >*/
/*< INTEGER I, IDUM, LINFO, M >*/
/*< >*/
/* .. */
/* .. Local Arrays .. */
/*< INTEGER IWORK( LDST ) >*/
/*< >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH >*/
/*< EXTERNAL DLAMCH >*/
/* .. */
/* .. External Subroutines .. */
/*< >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX, SQRT >*/
/* .. */
/* .. Executable Statements .. */
/*< INFO = 0 >*/
/* 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;
/* Quick return if possible */
/*< >*/
if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
return 0;
}
/*< >*/
if (*n1 > *n || *j1 + *n1 > *n) {
return 0;
}
/*< M = N1 + N2 >*/
m = *n1 + *n2;
/*< IF( LWORK.LT.MAX( N*M, M*M*2 ) ) THEN >*/
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
if (*lwork < max(i__1,i__2)) {
/*< INFO = -16 >*/
*info = -16;
/*< WORK( 1 ) = MAX( N*M, M*M*2 ) >*/
/* Computing MAX */
i__1 = *n * m, i__2 = m * m << 1;
work[1] = (doublereal) max(i__1,i__2);
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< WEAK = .FALSE. >*/
weak = FALSE_;
/*< DTRONG = .FALSE. >*/
dtrong = FALSE_;
/* Make a local copy of selected block */
/*< CALL DCOPY( LDST*LDST, ZERO, 0, LI, 1 ) >*/
dcopy_(&c__16, &c_b3, &c__0, li, &c__1);
/*< CALL DCOPY( LDST*LDST, ZERO, 0, IR, 1 ) >*/
dcopy_(&c__16, &c_b3, &c__0, ir, &c__1);
/*< CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) >*/
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4, (ftnlen)4);
/*< CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) >*/
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4, (ftnlen)4);
/* Compute threshold for testing acceptance of swapping. */
/*< EPS = DLAMCH( 'P' ) >*/
eps = dlamch_("P", (ftnlen)1);
/*< SMLNUM = DLAMCH( 'S' ) / EPS >*/
smlnum = dlamch_("S", (ftnlen)1) / eps;
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< CALL DLACPY( 'Full', M, M, S, LDST, WORK, M ) >*/
dlacpy_("Full", &m, &m, s, &c__4, &work[1], &m, (ftnlen)4);
/*< CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
/*< CALL DLACPY( 'Full', M, M, T, LDST, WORK, M ) >*/
dlacpy_("Full", &m, &m, t, &c__4, &work[1], &m, (ftnlen)4);
/*< CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[1], &c__1, &dscale, &dsum);
/*< DNORM = DSCALE*SQRT( DSUM ) >*/
dnorm = dscale * sqrt(dsum);
/*< THRESH = MAX( TEN*EPS*DNORM, SMLNUM ) >*/
/* Computing MAX */
d__1 = eps * 10. * dnorm;
thresh = max(d__1,smlnum);
/*< IF( M.EQ.2 ) THEN >*/
if (m == 2) {
/* CASE 1: Swap 1-by-1 and 1-by-1 blocks. */
/* Compute orthogonal QL and RQ that swap 1-by-1 and 1-by-1 blocks */
/* using Givens rotations and perform the swap tentatively. */
/*< F = S( 2, 2 )*T( 1, 1 ) - T( 2, 2 )*S( 1, 1 ) >*/
f = s[5] * t[0] - t[5] * s[0];
/*< G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 ) >*/
g = s[5] * t[4] - t[5] * s[4];
/*< SB = ABS( T( 2, 2 ) ) >*/
sb = abs(t[5]);
/*< SA = ABS( S( 2, 2 ) ) >*/
sa = abs(s[5]);
/*< CALL DLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM ) >*/
dlartg_(&f, &g, &ir[4], ir, &ddum);
/*< IR( 2, 1 ) = -IR( 1, 2 ) >*/
ir[1] = -ir[4];
/*< IR( 2, 2 ) = IR( 1, 1 ) >*/
ir[5] = ir[0];
/*< >*/
drot_(&c__2, s, &c__1, &s[4], &c__1, ir, &ir[1]);
/*< >*/
drot_(&c__2, t, &c__1, &t[4], &c__1, ir, &ir[1]);
/*< IF( SA.GE.SB ) THEN >*/
if (sa >= sb) {
/*< >*/
dlartg_(s, &s[1], li, &li[1], &ddum);
/*< ELSE >*/
} else {
/*< >*/
dlartg_(t, &t[1], li, &li[1], &ddum);
/*< END IF >*/
}
/*< >*/
drot_(&c__2, s, &c__4, &s[1], &c__4, li, &li[1]);
/*< >*/
drot_(&c__2, t, &c__4, &t[1], &c__4, li, &li[1]);
/*< LI( 2, 2 ) = LI( 1, 1 ) >*/
li[5] = li[0];
/*< LI( 1, 2 ) = -LI( 2, 1 ) >*/
li[4] = -li[1];
/* Weak stability test: */
/* |S21| + |T21| <= O(EPS * F-norm((S, T))) */
/*< WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) ) >*/
ws = abs(s[1]) + abs(t[1]);
/*< WEAK = WS.LE.THRESH >*/
weak = ws <= thresh;
/*< >*/
if (! weak) {
goto L70;
}
/*< IF( WANDS ) THEN >*/
if (TRUE_) {
/* Strong stability test: */
/* F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) */
/*< >*/
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
+ 1], &m, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "T", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m, (ftnlen)1, (ftnlen)1);
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
/*< >*/
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
+ 1], &m, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "T", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
/*< SS = DSCALE*SQRT( DSUM ) >*/
ss = dscale * sqrt(dsum);
/*< DTRONG = SS.LE.THRESH >*/
dtrong = ss <= thresh;
/*< >*/
if (! dtrong) {
goto L70;
}
/*< END IF >*/
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
/*< >*/
i__1 = *j1 + 1;
drot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1],
&c__1, ir, &ir[1]);
/*< >*/
i__1 = *j1 + 1;
drot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1],
&c__1, ir, &ir[1]);
/*< >*/
i__1 = *n - *j1 + 1;
drot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1],
lda, li, &li[1]);
/*< >*/
i__1 = *n - *j1 + 1;
drot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1],
ldb, li, &li[1]);
/* Set N1-by-N2 (2,1) - blocks to ZERO. */
/*< A( J1+1, J1 ) = ZERO >*/
a[*j1 + 1 + *j1 * a_dim1] = 0.;
/*< B( J1+1, J1 ) = ZERO >*/
b[*j1 + 1 + *j1 * b_dim1] = 0.;
/* Accumulate transformations into Q and Z if requested. */
/*< >*/
if (*wantz) {
drot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 +
1], &c__1, ir, &ir[1]);
}
/*< >*/
if (*wantq) {
drot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1],
&c__1, li, &li[1]);
}
/* Exit with INFO = 0 if swap was successfully performed. */
/*< RETURN >*/
return 0;
/*< ELSE >*/
} else {
/* CASE 2: Swap 1-by-1 and 2-by-2 blocks, or 2-by-2 */
/* and 2-by-2 blocks. */
/* Solve the generalized Sylvester equation */
/* S11 * R - L * S22 = SCALE * S12 */
/* T11 * R - L * T22 = SCALE * T12 */
/* for R and L. Solutions in LI and IR. */
/*< CALL DLACPY( 'Full', N1, N2, T( 1, N1+1 ), LDST, LI, LDST ) >*/
dlacpy_("Full", n1, n2, &t[((*n1 + 1) << 2) - 4], &c__4, li, &c__4, (
ftnlen)4);
/*< >*/
dlacpy_("Full", n1, n2, &s[((*n1 + 1) << 2) - 4], &c__4, &ir[*n2 + 1 + (
(*n1 + 1) << 2) - 5], &c__4, (ftnlen)4);
/*< >*/
dtgsy2_("N", &c__0, n1, n2, s, &c__4, &s[(*n1 + 1) + ((*n1 + 1) << 2) - 5]
, &c__4, &ir[*n2 + 1 + ((*n1 + 1) << 2) - 5], &c__4, t, &c__4, &
t[(*n1 + 1) + ((*n1 + 1) << 2) - 5], &c__4, li, &c__4, &scale, &
dsum, &dscale, iwork, &idum, &linfo, (ftnlen)1);
/* Compute orthogonal matrix QL: */
/* QL' * LI = [ TL ] */
/* [ 0 ] */
/* where */
/* LI = [ -L ] */
/* [ SCALE * identity(N2) ] */
/*< DO 10 I = 1, N2 >*/
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< CALL DSCAL( N1, -ONE, LI( 1, I ), 1 ) >*/
dscal_(n1, &c_b44, &li[(i__ << 2) - 4], &c__1);
/*< LI( N1+I, I ) = SCALE >*/
li[*n1 + i__ + (i__ << 2) - 5] = scale;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< CALL DGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO ) >*/
dgeqr2_(&m, n2, li, &c__4, taul, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/*< CALL DORG2R( M, M, N2, LI, LDST, TAUL, WORK, LINFO ) >*/
dorg2r_(&m, &m, n2, li, &c__4, taul, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/* Compute orthogonal matrix RQ: */
/* IR * RQ' = [ 0 TR], */
/* where IR = [ SCALE * identity(N1), R ] */
/*< DO 20 I = 1, N1 >*/
i__1 = *n1;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IR( N2+I, I ) = SCALE >*/
ir[*n2 + i__ + (i__ << 2) - 5] = scale;
/*< 20 CONTINUE >*/
/* L20: */
}
/*< CALL DGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO ) >*/
dgerq2_(n1, &m, &ir[*n2], &c__4, taur, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/*< CALL DORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO ) >*/
dorgr2_(&m, &m, n1, ir, &c__4, taur, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/* Perform the swapping tentatively: */
/*< >*/
dgemm_("T", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "T", &m, &m, &m, &c_b38, &work[1], &m, ir, &c__4, &c_b3,
s, &c__4, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("T", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "T", &m, &m, &m, &c_b38, &work[1], &m, ir, &c__4, &c_b3,
t, &c__4, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, S, LDST, SCPY, LDST ) >*/
dlacpy_("F", &m, &m, s, &c__4, scpy, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, T, LDST, TCPY, LDST ) >*/
dlacpy_("F", &m, &m, t, &c__4, tcpy, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, IR, LDST, IRCOP, LDST ) >*/
dlacpy_("F", &m, &m, ir, &c__4, ircop, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, LI, LDST, LICOP, LDST ) >*/
dlacpy_("F", &m, &m, li, &c__4, licop, &c__4, (ftnlen)1);
/* Triangularize the B-part by an RQ factorization. */
/* Apply transformation (from left) to A-part, giving S. */
/*< CALL DGERQ2( M, M, T, LDST, TAUR, WORK, LINFO ) >*/
dgerq2_(&m, &m, t, &c__4, taur, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/*< >*/
dormr2_("R", "T", &m, &m, &m, t, &c__4, taur, s, &c__4, &work[1], &
linfo, (ftnlen)1, (ftnlen)1);
/*< >*/
if (linfo != 0) {
goto L70;
}
/*< >*/
dormr2_("L", "N", &m, &m, &m, t, &c__4, taur, ir, &c__4, &work[1], &
linfo, (ftnlen)1, (ftnlen)1);
/*< >*/
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BRQA21. (T21 is 0.) */
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< DO 30 I = 1, N2 >*/
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< CALL DLASSQ( N1, S( N2+1, I ), 1, DSCALE, DSUM ) >*/
dlassq_(n1, &s[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &dsum);
/*< 30 CONTINUE >*/
/* L30: */
}
/*< BRQA21 = DSCALE*SQRT( DSUM ) >*/
brqa21 = dscale * sqrt(dsum);
/* Triangularize the B-part by a QR factorization. */
/* Apply transformation (from right) to A-part, giving S. */
/*< CALL DGEQR2( M, M, TCPY, LDST, TAUL, WORK, LINFO ) >*/
dgeqr2_(&m, &m, tcpy, &c__4, taul, &work[1], &linfo);
/*< >*/
if (linfo != 0) {
goto L70;
}
/*< >*/
dorm2r_("L", "T", &m, &m, &m, tcpy, &c__4, taul, scpy, &c__4, &work[1]
, info, (ftnlen)1, (ftnlen)1);
/*< >*/
dorm2r_("R", "N", &m, &m, &m, tcpy, &c__4, taul, licop, &c__4, &work[
1], info, (ftnlen)1, (ftnlen)1);
/*< >*/
if (linfo != 0) {
goto L70;
}
/* Compute F-norm(S21) in BQRA21. (T21 is 0.) */
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< DO 40 I = 1, N2 >*/
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< CALL DLASSQ( N1, SCPY( N2+1, I ), 1, DSCALE, DSUM ) >*/
dlassq_(n1, &scpy[*n2 + 1 + (i__ << 2) - 5], &c__1, &dscale, &
dsum);
/*< 40 CONTINUE >*/
/* L40: */
}
/*< BQRA21 = DSCALE*SQRT( DSUM ) >*/
bqra21 = dscale * sqrt(dsum);
/* Decide which method to use. */
/* Weak stability test: */
/* F-norm(S21) <= O(EPS * F-norm((S, T))) */
/*< IF( BQRA21.LE.BRQA21 .AND. BQRA21.LE.THRESH ) THEN >*/
if (bqra21 <= brqa21 && bqra21 <= thresh) {
/*< CALL DLACPY( 'F', M, M, SCPY, LDST, S, LDST ) >*/
dlacpy_("F", &m, &m, scpy, &c__4, s, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, TCPY, LDST, T, LDST ) >*/
dlacpy_("F", &m, &m, tcpy, &c__4, t, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, IRCOP, LDST, IR, LDST ) >*/
dlacpy_("F", &m, &m, ircop, &c__4, ir, &c__4, (ftnlen)1);
/*< CALL DLACPY( 'F', M, M, LICOP, LDST, LI, LDST ) >*/
dlacpy_("F", &m, &m, licop, &c__4, li, &c__4, (ftnlen)1);
/*< ELSE IF( BRQA21.GE.THRESH ) THEN >*/
} else if (brqa21 >= thresh) {
/*< GO TO 70 >*/
goto L70;
/*< END IF >*/
}
/* Set lower triangle of B-part to zero */
/*< DO 50 I = 2, M >*/
i__1 = m;
for (i__ = 2; i__ <= i__1; ++i__) {
/*< CALL DCOPY( M-I+1, ZERO, 0, T( I, I-1 ), 1 ) >*/
i__2 = m - i__ + 1;
dcopy_(&i__2, &c_b3, &c__0, &t[i__ + ((i__ - 1) << 2) - 5], &c__1);
/*< 50 CONTINUE >*/
/* L50: */
}
/*< IF( WANDS ) THEN >*/
if (TRUE_) {
/* Strong stability test: */
/* F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) */
/*< >*/
dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, &work[m * m
+ 1], &m, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, s, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m, (ftnlen)1, (ftnlen)1);
/*< DSCALE = ZERO >*/
dscale = 0.;
/*< DSUM = ONE >*/
dsum = 1.;
/*< CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
/*< >*/
dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, &work[m * m
+ 1], &m, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, t, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b44, &work[1], &m, ir, &c__4, &
c_b38, &work[m * m + 1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) >*/
i__1 = m * m;
dlassq_(&i__1, &work[m * m + 1], &c__1, &dscale, &dsum);
/*< SS = DSCALE*SQRT( DSUM ) >*/
ss = dscale * sqrt(dsum);
/*< DTRONG = ( SS.LE.THRESH ) >*/
dtrong = ss <= thresh;
/*< >*/
if (! dtrong) {
goto L70;
}
/*< END IF >*/
}
/* If the swap is accepted ("weakly" and "strongly"), apply the */
/* transformations and set N1-by-N2 (2,1)-block to zero. */
/*< DO 60 I = 1, N2 >*/
i__1 = *n2;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< CALL DCOPY( N1, ZERO, 0, S( N2+1, I ), 1 ) >*/
dcopy_(n1, &c_b3, &c__0, &s[*n2 + 1 + (i__ << 2) - 5], &c__1);
/*< 60 CONTINUE >*/
/* L60: */
}
/* copy back M-by-M diagonal block starting at index J1 of (A, B) */
/*< CALL DLACPY( 'F', M, M, S, LDST, A( J1, J1 ), LDA ) >*/
dlacpy_("F", &m, &m, s, &c__4, &a[*j1 + *j1 * a_dim1], lda, (ftnlen)1)
;
/*< CALL DLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB ) >*/
dlacpy_("F", &m, &m, t, &c__4, &b[*j1 + *j1 * b_dim1], ldb, (ftnlen)1)
;
/*< CALL DCOPY( LDST*LDST, ZERO, 0, T, 1 ) >*/
dcopy_(&c__16, &c_b3, &c__0, t, &c__1);
/* Standardize existing 2-by-2 blocks. */
/*< CALL DCOPY( M*M, ZERO, 0, WORK, 1 ) >*/
i__1 = m * m;
dcopy_(&i__1, &c_b3, &c__0, &work[1], &c__1);
/*< WORK( 1 ) = ONE >*/
work[1] = 1.;
/*< T( 1, 1 ) = ONE >*/
t[0] = 1.;
/*< IDUM = LWORK - M*M - 2 >*/
idum = *lwork - m * m - 2;
/*< IF( N2.GT.1 ) THEN >*/
if (*n2 > 1) {
/*< >*/
dlagv2_(&a[*j1 + *j1 * a_dim1], lda, &b[*j1 + *j1 * b_dim1], ldb,
ar, ai, be, &work[1], &work[2], t, &t[1]);
/*< WORK( M+1 ) = -WORK( 2 ) >*/
work[m + 1] = -work[2];
/*< WORK( M+2 ) = WORK( 1 ) >*/
work[m + 2] = work[1];
/*< T( N2, N2 ) = T( 1, 1 ) >*/
t[*n2 + (*n2 << 2) - 5] = t[0];
/*< T( 1, 2 ) = -T( 2, 1 ) >*/
t[4] = -t[1];
/*< END IF >*/
}
/*< WORK( M*M ) = ONE >*/
work[m * m] = 1.;
/*< T( M, M ) = ONE >*/
t[m + (m << 2) - 5] = 1.;
/*< IF( N1.GT.1 ) THEN >*/
if (*n1 > 1) {
/*< >*/
dlagv2_(&a[*j1 + *n2 + (*j1 + *n2) * a_dim1], lda, &b[*j1 + *n2 +
(*j1 + *n2) * b_dim1], ldb, taur, taul, &work[m * m + 1],
&work[*n2 * m + *n2 + 1], &work[*n2 * m + *n2 + 2], &t[*
n2 + 1 + ((*n2 + 1) << 2) - 5], &t[m + ((m - 1) << 2) - 5]);
/*< WORK( M*M ) = WORK( N2*M+N2+1 ) >*/
work[m * m] = work[*n2 * m + *n2 + 1];
/*< WORK( M*M-1 ) = -WORK( N2*M+N2+2 ) >*/
work[m * m - 1] = -work[*n2 * m + *n2 + 2];
/*< T( M, M ) = T( N2+1, N2+1 ) >*/
t[m + (m << 2) - 5] = t[*n2 + 1 + ((*n2 + 1) << 2) - 5];
/*< T( M-1, M ) = -T( M, M-1 ) >*/
t[m - 1 + (m << 2) - 5] = -t[m + ((m - 1) << 2) - 5];
/*< END IF >*/
}
/*< >*/
dgemm_("T", "N", n2, n1, n2, &c_b38, &work[1], &m, &a[*j1 + (*j1 + *
n2) * a_dim1], lda, &c_b3, &work[m * m + 1], n2, (ftnlen)1, (
ftnlen)1);
/*< >*/
dlacpy_("Full", n2, n1, &work[m * m + 1], n2, &a[*j1 + (*j1 + *n2) *
a_dim1], lda, (ftnlen)4);
/*< >*/
dgemm_("T", "N", n2, n1, n2, &c_b38, &work[1], &m, &b[*j1 + (*j1 + *
n2) * b_dim1], ldb, &c_b3, &work[m * m + 1], n2, (ftnlen)1, (
ftnlen)1);
/*< >*/
dlacpy_("Full", n2, n1, &work[m * m + 1], n2, &b[*j1 + (*j1 + *n2) *
b_dim1], ldb, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &m, &m, &m, &c_b38, li, &c__4, &work[1], &m, &c_b3, &
work[m * m + 1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST ) >*/
dlacpy_("Full", &m, &m, &work[m * m + 1], &m, li, &c__4, (ftnlen)4);
/*< >*/
dgemm_("N", "N", n2, n1, n1, &c_b38, &a[*j1 + (*j1 + *n2) * a_dim1],
lda, &t[*n2 + 1 + ((*n2 + 1) << 2) - 5], &c__4, &c_b3, &work[1],
n2, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA ) >*/
dlacpy_("Full", n2, n1, &work[1], n2, &a[*j1 + (*j1 + *n2) * a_dim1],
lda, (ftnlen)4);
/*< >*/
dgemm_("N", "N", n2, n1, n1, &c_b38, &b[*j1 + (*j1 + *n2) * b_dim1],
lda, &t[*n2 + 1 + ((*n2 + 1) << 2) - 5], &c__4, &c_b3, &work[1],
n2, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB ) >*/
dlacpy_("Full", n2, n1, &work[1], n2, &b[*j1 + (*j1 + *n2) * b_dim1],
ldb, (ftnlen)4);
/*< >*/
dgemm_("T", "N", &m, &m, &m, &c_b38, ir, &c__4, t, &c__4, &c_b3, &
work[1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', M, M, WORK, M, IR, LDST ) >*/
dlacpy_("Full", &m, &m, &work[1], &m, ir, &c__4, (ftnlen)4);
/* Accumulate transformations into Q and Z if requested. */
/*< IF( WANTQ ) THEN >*/
if (*wantq) {
/*< >*/
dgemm_("N", "N", n, &m, &m, &c_b38, &q[*j1 * q_dim1 + 1], ldq, li,
&c__4, &c_b3, &work[1], n, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ ) >*/
dlacpy_("Full", n, &m, &work[1], n, &q[*j1 * q_dim1 + 1], ldq, (
ftnlen)4);
/*< END IF >*/
}
/*< IF( WANTZ ) THEN >*/
if (*wantz) {
/*< >*/
dgemm_("N", "N", n, &m, &m, &c_b38, &z__[*j1 * z_dim1 + 1], ldz,
ir, &c__4, &c_b3, &work[1], n, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', N, M, WORK, N, Z( 1, J1 ), LDZ ) >*/
dlacpy_("Full", n, &m, &work[1], n, &z__[*j1 * z_dim1 + 1], ldz, (
ftnlen)4);
/*< END IF >*/
}
/* Update (A(J1:J1+M-1, M+J1:N), B(J1:J1+M-1, M+J1:N)) and */
/* (A(1:J1-1, J1:J1+M), B(1:J1-1, J1:J1+M)). */
/*< I = J1 + M >*/
i__ = *j1 + m;
/*< IF( I.LE.N ) THEN >*/
if (i__ <= *n) {
/*< >*/
i__1 = *n - i__ + 1;
dgemm_("T", "N", &m, &i__1, &m, &c_b38, li, &c__4, &a[*j1 + i__ *
a_dim1], lda, &c_b3, &work[1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA ) >*/
i__1 = *n - i__ + 1;
dlacpy_("Full", &m, &i__1, &work[1], &m, &a[*j1 + i__ * a_dim1],
lda, (ftnlen)4);
/*< >*/
i__1 = *n - i__ + 1;
dgemm_("T", "N", &m, &i__1, &m, &c_b38, li, &c__4, &b[*j1 + i__ *
b_dim1], lda, &c_b3, &work[1], &m, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDA ) >*/
i__1 = *n - i__ + 1;
dlacpy_("Full", &m, &i__1, &work[1], &m, &b[*j1 + i__ * b_dim1],
lda, (ftnlen)4);
/*< END IF >*/
}
/*< I = J1 - 1 >*/
i__ = *j1 - 1;
/*< IF( I.GT.0 ) THEN >*/
if (i__ > 0) {
/*< >*/
dgemm_("N", "N", &i__, &m, &m, &c_b38, &a[*j1 * a_dim1 + 1], lda,
ir, &c__4, &c_b3, &work[1], &i__, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA ) >*/
dlacpy_("Full", &i__, &m, &work[1], &i__, &a[*j1 * a_dim1 + 1],
lda, (ftnlen)4);
/*< >*/
dgemm_("N", "N", &i__, &m, &m, &c_b38, &b[*j1 * b_dim1 + 1], ldb,
ir, &c__4, &c_b3, &work[1], &i__, (ftnlen)1, (ftnlen)1);
/*< CALL DLACPY( 'Full', I, M, WORK, I, B( 1, J1 ), LDB ) >*/
dlacpy_("Full", &i__, &m, &work[1], &i__, &b[*j1 * b_dim1 + 1],
ldb, (ftnlen)4);
/*< END IF >*/
}
/* Exit with INFO = 0 if swap was successfully performed. */
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Exit with INFO = 1 if swap was rejected. */
/*< 70 CONTINUE >*/
L70:
/*< INFO = 1 >*/
*info = 1;
/*< RETURN >*/
return 0;
/* End of DTGEX2 */
/*< END >*/
} /* dtgex2_ */
#ifdef __cplusplus
}
#endif
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