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SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. LOGICAL WANTQ, WANTZ INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), $ Z( LDZ, * ) * .. * * Purpose * ======= * * ZTGEXC reorders the generalized Schur decomposition of a complex * matrix pair (A,B), using an unitary equivalence transformation * (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with * row index IFST is moved to row ILST. * * (A, B) must be in generalized Schur canonical form, that is, A and * B are both upper triangular. * * Optionally, the matrices Q and Z of generalized Schur vectors are * updated. * * Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H * Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H * * 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) COMPLEX*16 array, dimension (LDA,N) * On entry, the upper triangular 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) COMPLEX*16 array, dimension (LDB,N) * On entry, the upper triangular 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) COMPLEX*16 array, dimension (LDZ,N) * On entry, if WANTQ = .TRUE., the unitary 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) COMPLEX*16 array, dimension (LDZ,N) * On entry, if WANTZ = .TRUE., the unitary 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) 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. * * 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. * * [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. * * [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software * for Solving the Generalized Sylvester Equation and Estimating the * Separation between Regular Matrix Pairs, Report UMINF - 93.23, * Department of Computing Science, Umea University, S-901 87 Umea, * Sweden, December 1993, Revised April 1994, Also as LAPACK working * Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, * 1996. * * ===================================================================== * * .. Local Scalars .. INTEGER HERE * .. * .. External Subroutines .. EXTERNAL XERBLA, ZTGEX2 * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Decode and test input arguments. INFO = 0 IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN INFO = -9 ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN INFO = -11 ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN INFO = -12 ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN INFO = -13 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTGEXC', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.1 ) $ RETURN IF( IFST.EQ.ILST ) $ RETURN * IF( IFST.LT.ILST ) THEN * HERE = IFST * 10 CONTINUE * * Swap with next one below * CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, $ HERE, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF HERE = HERE + 1 IF( HERE.LT.ILST ) $ GO TO 10 HERE = HERE - 1 ELSE HERE = IFST - 1 * 20 CONTINUE * * Swap with next one above * CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, $ HERE, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF HERE = HERE - 1 IF( HERE.GE.ILST ) $ GO TO 20 HERE = HERE + 1 END IF ILST = HERE RETURN * * End of ZTGEXC * END |