SUBROUTINE DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, $ LDZ, J1, N1, N2, WORK, LWORK, INFO ) * * -- LAPACK auxiliary routine (version 3.2) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL WANTQ, WANTZ INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), $ WORK( * ), Z( LDZ, * ) * .. * * 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 (MAX(1,LWORK)). * * LWORK (input) INTEGER * The dimension of the array WORK. * LWORK >= MAX( 1, 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. * * ===================================================================== * Replaced various illegal calls to DCOPY by calls to DLASET, or by DO * loops. Sven Hammarling, 1/5/02. * * .. 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 DOUBLE PRECISION BQRA21, BRQA21, DDUM, DNORM, DSCALE, DSUM, EPS, $ F, G, SA, SB, SCALE, SMLNUM, SS, THRESH, WS * .. * .. Local Arrays .. INTEGER IWORK( LDST ) DOUBLE PRECISION AI( 2 ), AR( 2 ), BE( 2 ), IR( LDST, LDST ), $ IRCOP( LDST, LDST ), LI( LDST, LDST ), $ LICOP( LDST, LDST ), S( LDST, LDST ), $ SCPY( LDST, LDST ), T( LDST, LDST ), $ TAUL( LDST ), TAUR( LDST ), TCPY( LDST, LDST ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DGEMM, DGEQR2, DGERQ2, DLACPY, DLAGV2, DLARTG, $ DLASET, DLASSQ, DORG2R, DORGR2, DORM2R, DORMR2, $ DROT, DSCAL, DTGSY2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * INFO = 0 * * Quick return if possible * IF( N.LE.1 .OR. N1.LE.0 .OR. N2.LE.0 ) $ RETURN IF( N1.GT.N .OR. ( J1+N1 ).GT.N ) $ RETURN M = N1 + N2 IF( LWORK.LT.MAX( 1, N*M, M*M*2 ) ) THEN INFO = -16 WORK( 1 ) = MAX( 1, N*M, M*M*2 ) RETURN END IF * WEAK = .FALSE. DTRONG = .FALSE. * * Make a local copy of selected block * CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, LI, LDST ) CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, IR, LDST ) CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) * * Compute threshold for testing acceptance of swapping. * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) / EPS DSCALE = ZERO DSUM = ONE CALL DLACPY( 'Full', M, M, S, LDST, WORK, M ) CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) CALL DLACPY( 'Full', M, M, T, LDST, WORK, M ) CALL DLASSQ( M*M, WORK, 1, DSCALE, DSUM ) DNORM = DSCALE*SQRT( DSUM ) THRESH = MAX( TEN*EPS*DNORM, SMLNUM ) * IF( M.EQ.2 ) THEN * * 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 ) G = S( 2, 2 )*T( 1, 2 ) - T( 2, 2 )*S( 1, 2 ) SB = ABS( T( 2, 2 ) ) SA = ABS( S( 2, 2 ) ) CALL DLARTG( F, G, IR( 1, 2 ), IR( 1, 1 ), DDUM ) IR( 2, 1 ) = -IR( 1, 2 ) IR( 2, 2 ) = IR( 1, 1 ) CALL DROT( 2, S( 1, 1 ), 1, S( 1, 2 ), 1, IR( 1, 1 ), $ IR( 2, 1 ) ) CALL DROT( 2, T( 1, 1 ), 1, T( 1, 2 ), 1, IR( 1, 1 ), $ IR( 2, 1 ) ) IF( SA.GE.SB ) THEN CALL DLARTG( S( 1, 1 ), S( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), $ DDUM ) ELSE CALL DLARTG( T( 1, 1 ), T( 2, 1 ), LI( 1, 1 ), LI( 2, 1 ), $ DDUM ) END IF CALL DROT( 2, S( 1, 1 ), LDST, S( 2, 1 ), LDST, LI( 1, 1 ), $ LI( 2, 1 ) ) CALL DROT( 2, T( 1, 1 ), LDST, T( 2, 1 ), LDST, LI( 1, 1 ), $ LI( 2, 1 ) ) LI( 2, 2 ) = LI( 1, 1 ) LI( 1, 2 ) = -LI( 2, 1 ) * * Weak stability test: * |S21| + |T21| <= O(EPS * F-norm((S, T))) * WS = ABS( S( 2, 1 ) ) + ABS( T( 2, 1 ) ) WEAK = WS.LE.THRESH IF( .NOT.WEAK ) $ GO TO 70 * IF( WANDS ) THEN * * Strong stability test: * F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B))) * CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), $ M ) CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, $ WORK( M*M+1 ), M ) DSCALE = ZERO DSUM = ONE CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) * CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), $ M ) CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'T', M, M, M, -ONE, WORK, M, IR, LDST, ONE, $ WORK( M*M+1 ), M ) CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) SS = DSCALE*SQRT( DSUM ) DTRONG = SS.LE.THRESH IF( .NOT.DTRONG ) $ GO TO 70 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)). * CALL DROT( J1+1, A( 1, J1 ), 1, A( 1, J1+1 ), 1, IR( 1, 1 ), $ IR( 2, 1 ) ) CALL DROT( J1+1, B( 1, J1 ), 1, B( 1, J1+1 ), 1, IR( 1, 1 ), $ IR( 2, 1 ) ) CALL DROT( N-J1+1, A( J1, J1 ), LDA, A( J1+1, J1 ), LDA, $ LI( 1, 1 ), LI( 2, 1 ) ) CALL DROT( N-J1+1, B( J1, J1 ), LDB, B( J1+1, J1 ), LDB, $ LI( 1, 1 ), LI( 2, 1 ) ) * * Set N1-by-N2 (2,1) - blocks to ZERO. * A( J1+1, J1 ) = ZERO B( J1+1, J1 ) = ZERO * * Accumulate transformations into Q and Z if requested. * IF( WANTZ ) $ CALL DROT( N, Z( 1, J1 ), 1, Z( 1, J1+1 ), 1, IR( 1, 1 ), $ IR( 2, 1 ) ) IF( WANTQ ) $ CALL DROT( N, Q( 1, J1 ), 1, Q( 1, J1+1 ), 1, LI( 1, 1 ), $ LI( 2, 1 ) ) * * Exit with INFO = 0 if swap was successfully performed. * RETURN * 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 ) CALL DLACPY( 'Full', N1, N2, S( 1, N1+1 ), LDST, $ IR( N2+1, N1+1 ), LDST ) CALL DTGSY2( 'N', 0, N1, N2, S, LDST, S( N1+1, N1+1 ), LDST, $ IR( N2+1, N1+1 ), LDST, T, LDST, T( N1+1, N1+1 ), $ LDST, LI, LDST, SCALE, DSUM, DSCALE, IWORK, IDUM, $ LINFO ) * * Compute orthogonal matrix QL: * * QL' * LI = [ TL ] * [ 0 ] * where * LI = [ -L ] * [ SCALE * identity(N2) ] * DO 10 I = 1, N2 CALL DSCAL( N1, -ONE, LI( 1, I ), 1 ) LI( N1+I, I ) = SCALE 10 CONTINUE CALL DGEQR2( M, N2, LI, LDST, TAUL, WORK, LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 CALL DORG2R( M, M, N2, LI, LDST, TAUL, WORK, LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 * * Compute orthogonal matrix RQ: * * IR * RQ' = [ 0 TR], * * where IR = [ SCALE * identity(N1), R ] * DO 20 I = 1, N1 IR( N2+I, I ) = SCALE 20 CONTINUE CALL DGERQ2( N1, M, IR( N2+1, 1 ), LDST, TAUR, WORK, LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 CALL DORGR2( M, M, N1, IR, LDST, TAUR, WORK, LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 * * Perform the swapping tentatively: * CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, S, $ LDST ) CALL DGEMM( 'T', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'T', M, M, M, ONE, WORK, M, IR, LDST, ZERO, T, $ LDST ) CALL DLACPY( 'F', M, M, S, LDST, SCPY, LDST ) CALL DLACPY( 'F', M, M, T, LDST, TCPY, LDST ) CALL DLACPY( 'F', M, M, IR, LDST, IRCOP, LDST ) CALL DLACPY( 'F', M, M, LI, LDST, LICOP, LDST ) * * 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 ) IF( LINFO.NE.0 ) $ GO TO 70 CALL DORMR2( 'R', 'T', M, M, M, T, LDST, TAUR, S, LDST, WORK, $ LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 CALL DORMR2( 'L', 'N', M, M, M, T, LDST, TAUR, IR, LDST, WORK, $ LINFO ) IF( LINFO.NE.0 ) $ GO TO 70 * * Compute F-norm(S21) in BRQA21. (T21 is 0.) * DSCALE = ZERO DSUM = ONE DO 30 I = 1, N2 CALL DLASSQ( N1, S( N2+1, I ), 1, DSCALE, DSUM ) 30 CONTINUE 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 ) IF( LINFO.NE.0 ) $ GO TO 70 CALL DORM2R( 'L', 'T', M, M, M, TCPY, LDST, TAUL, SCPY, LDST, $ WORK, INFO ) CALL DORM2R( 'R', 'N', M, M, M, TCPY, LDST, TAUL, LICOP, LDST, $ WORK, INFO ) IF( LINFO.NE.0 ) $ GO TO 70 * * Compute F-norm(S21) in BQRA21. (T21 is 0.) * DSCALE = ZERO DSUM = ONE DO 40 I = 1, N2 CALL DLASSQ( N1, SCPY( N2+1, I ), 1, DSCALE, DSUM ) 40 CONTINUE 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 CALL DLACPY( 'F', M, M, SCPY, LDST, S, LDST ) CALL DLACPY( 'F', M, M, TCPY, LDST, T, LDST ) CALL DLACPY( 'F', M, M, IRCOP, LDST, IR, LDST ) CALL DLACPY( 'F', M, M, LICOP, LDST, LI, LDST ) ELSE IF( BRQA21.GE.THRESH ) THEN GO TO 70 END IF * * Set lower triangle of B-part to zero * CALL DLASET( 'Lower', M-1, M-1, ZERO, ZERO, T(2,1), LDST ) * IF( WANDS ) THEN * * Strong stability test: * F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B))) * CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ), $ M ) CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, S, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, $ WORK( M*M+1 ), M ) DSCALE = ZERO DSUM = ONE CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) * CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, WORK( M*M+1 ), $ M ) CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, T, LDST, ZERO, $ WORK, M ) CALL DGEMM( 'N', 'N', M, M, M, -ONE, WORK, M, IR, LDST, ONE, $ WORK( M*M+1 ), M ) CALL DLASSQ( M*M, WORK( M*M+1 ), 1, DSCALE, DSUM ) SS = DSCALE*SQRT( DSUM ) DTRONG = ( SS.LE.THRESH ) IF( .NOT.DTRONG ) $ GO TO 70 * END IF * * If the swap is accepted ("weakly" and "strongly"), apply the * transformations and set N1-by-N2 (2,1)-block to zero. * CALL DLASET( 'Full', N1, N2, ZERO, ZERO, S(N2+1,1), LDST ) * * 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 ) CALL DLACPY( 'F', M, M, T, LDST, B( J1, J1 ), LDB ) CALL DLASET( 'Full', LDST, LDST, ZERO, ZERO, T, LDST ) * * Standardize existing 2-by-2 blocks. * DO 50 I = 1, M*M WORK(I) = ZERO 50 CONTINUE WORK( 1 ) = ONE T( 1, 1 ) = ONE IDUM = LWORK - M*M - 2 IF( N2.GT.1 ) THEN CALL DLAGV2( A( J1, J1 ), LDA, B( J1, J1 ), LDB, AR, AI, BE, $ WORK( 1 ), WORK( 2 ), T( 1, 1 ), T( 2, 1 ) ) WORK( M+1 ) = -WORK( 2 ) WORK( M+2 ) = WORK( 1 ) T( N2, N2 ) = T( 1, 1 ) T( 1, 2 ) = -T( 2, 1 ) END IF WORK( M*M ) = ONE T( M, M ) = ONE * IF( N1.GT.1 ) THEN CALL DLAGV2( A( J1+N2, J1+N2 ), LDA, B( J1+N2, J1+N2 ), LDB, $ TAUR, TAUL, WORK( M*M+1 ), WORK( N2*M+N2+1 ), $ WORK( N2*M+N2+2 ), T( N2+1, N2+1 ), $ T( M, M-1 ) ) WORK( M*M ) = WORK( N2*M+N2+1 ) WORK( M*M-1 ) = -WORK( N2*M+N2+2 ) T( M, M ) = T( N2+1, N2+1 ) T( M-1, M ) = -T( M, M-1 ) END IF CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, A( J1, J1+N2 ), $ LDA, ZERO, WORK( M*M+1 ), N2 ) CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, A( J1, J1+N2 ), $ LDA ) CALL DGEMM( 'T', 'N', N2, N1, N2, ONE, WORK, M, B( J1, J1+N2 ), $ LDB, ZERO, WORK( M*M+1 ), N2 ) CALL DLACPY( 'Full', N2, N1, WORK( M*M+1 ), N2, B( J1, J1+N2 ), $ LDB ) CALL DGEMM( 'N', 'N', M, M, M, ONE, LI, LDST, WORK, M, ZERO, $ WORK( M*M+1 ), M ) CALL DLACPY( 'Full', M, M, WORK( M*M+1 ), M, LI, LDST ) CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, A( J1, J1+N2 ), LDA, $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) CALL DLACPY( 'Full', N2, N1, WORK, N2, A( J1, J1+N2 ), LDA ) CALL DGEMM( 'N', 'N', N2, N1, N1, ONE, B( J1, J1+N2 ), LDB, $ T( N2+1, N2+1 ), LDST, ZERO, WORK, N2 ) CALL DLACPY( 'Full', N2, N1, WORK, N2, B( J1, J1+N2 ), LDB ) CALL DGEMM( 'T', 'N', M, M, M, ONE, IR, LDST, T, LDST, ZERO, $ WORK, M ) CALL DLACPY( 'Full', M, M, WORK, M, IR, LDST ) * * Accumulate transformations into Q and Z if requested. * IF( WANTQ ) THEN CALL DGEMM( 'N', 'N', N, M, M, ONE, Q( 1, J1 ), LDQ, LI, $ LDST, ZERO, WORK, N ) CALL DLACPY( 'Full', N, M, WORK, N, Q( 1, J1 ), LDQ ) * END IF * IF( WANTZ ) THEN CALL DGEMM( 'N', 'N', N, M, M, ONE, Z( 1, J1 ), LDZ, IR, $ LDST, ZERO, WORK, N ) CALL DLACPY( 'Full', N, M, WORK, N, Z( 1, J1 ), LDZ ) * 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 IF( I.LE.N ) THEN CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, $ A( J1, I ), LDA, ZERO, WORK, M ) CALL DLACPY( 'Full', M, N-I+1, WORK, M, A( J1, I ), LDA ) CALL DGEMM( 'T', 'N', M, N-I+1, M, ONE, LI, LDST, $ B( J1, I ), LDA, ZERO, WORK, M ) CALL DLACPY( 'Full', M, N-I+1, WORK, M, B( J1, I ), LDB ) END IF I = J1 - 1 IF( I.GT.0 ) THEN CALL DGEMM( 'N', 'N', I, M, M, ONE, A( 1, J1 ), LDA, IR, $ LDST, ZERO, WORK, I ) CALL DLACPY( 'Full', I, M, WORK, I, A( 1, J1 ), LDA ) CALL DGEMM( 'N', 'N', I, M, M, ONE, B( 1, J1 ), LDB, IR, $ LDST, ZERO, WORK, I ) CALL DLACPY( 'Full', I, M, WORK, I, B( 1, J1 ), LDB ) END IF * * Exit with INFO = 0 if swap was successfully performed. * RETURN * END IF * * Exit with INFO = 1 if swap was rejected. * 70 CONTINUE * INFO = 1 RETURN * * End of DTGEX2 * END