d7/d96/ztgexc_8f_source.html

00001       SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
00002      $                   LDZ, IFST, ILST, INFO )
00003 *
00004 *  -- LAPACK routine (version 3.3.1) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *  -- April 2011                                                      --
00008 *
00009 *     .. Scalar Arguments ..
00010       LOGICAL            WANTQ, WANTZ
00011       INTEGER            IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       COMPLEX*16         A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
00015      $                   Z( LDZ, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZTGEXC reorders the generalized Schur decomposition of a complex
00022 *  matrix pair (A,B), using an unitary equivalence transformation
00023 *  (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
00024 *  row index IFST is moved to row ILST.
00025 *
00026 *  (A, B) must be in generalized Schur canonical form, that is, A and
00027 *  B are both upper triangular.
00028 *
00029 *  Optionally, the matrices Q and Z of generalized Schur vectors are
00030 *  updated.
00031 *
00032 *         Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
00033 *         Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
00034 *
00035 *  Arguments
00036 *  =========
00037 *
00038 *  WANTQ   (input) LOGICAL
00039 *          .TRUE. : update the left transformation matrix Q;
00040 *          .FALSE.: do not update Q.
00041 *
00042 *  WANTZ   (input) LOGICAL
00043 *          .TRUE. : update the right transformation matrix Z;
00044 *          .FALSE.: do not update Z.
00045 *
00046 *  N       (input) INTEGER
00047 *          The order of the matrices A and B. N >= 0.
00048 *
00049 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
00050 *          On entry, the upper triangular matrix A in the pair (A, B).
00051 *          On exit, the updated matrix A.
00052 *
00053 *  LDA     (input)  INTEGER
00054 *          The leading dimension of the array A. LDA >= max(1,N).
00055 *
00056 *  B       (input/output) COMPLEX*16 array, dimension (LDB,N)
00057 *          On entry, the upper triangular matrix B in the pair (A, B).
00058 *          On exit, the updated matrix B.
00059 *
00060 *  LDB     (input)  INTEGER
00061 *          The leading dimension of the array B. LDB >= max(1,N).
00062 *
00063 *  Q       (input/output) COMPLEX*16 array, dimension (LDZ,N)
00064 *          On entry, if WANTQ = .TRUE., the unitary matrix Q.
00065 *          On exit, the updated matrix Q.
00066 *          If WANTQ = .FALSE., Q is not referenced.
00067 *
00068 *  LDQ     (input) INTEGER
00069 *          The leading dimension of the array Q. LDQ >= 1;
00070 *          If WANTQ = .TRUE., LDQ >= N.
00071 *
00072 *  Z       (input/output) COMPLEX*16 array, dimension (LDZ,N)
00073 *          On entry, if WANTZ = .TRUE., the unitary matrix Z.
00074 *          On exit, the updated matrix Z.
00075 *          If WANTZ = .FALSE., Z is not referenced.
00076 *
00077 *  LDZ     (input) INTEGER
00078 *          The leading dimension of the array Z. LDZ >= 1;
00079 *          If WANTZ = .TRUE., LDZ >= N.
00080 *
00081 *  IFST    (input) INTEGER
00082 *  ILST    (input/output) INTEGER
00083 *          Specify the reordering of the diagonal blocks of (A, B).
00084 *          The block with row index IFST is moved to row ILST, by a
00085 *          sequence of swapping between adjacent blocks.
00086 *
00087 *  INFO    (output) INTEGER
00088 *           =0:  Successful exit.
00089 *           <0:  if INFO = -i, the i-th argument had an illegal value.
00090 *           =1:  The transformed matrix pair (A, B) would be too far
00091 *                from generalized Schur form; the problem is ill-
00092 *                conditioned. (A, B) may have been partially reordered,
00093 *                and ILST points to the first row of the current
00094 *                position of the block being moved.
00095 *
00096 *
00097 *  Further Details
00098 *  ===============
00099 *
00100 *  Based on contributions by
00101 *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
00102 *     Umea University, S-901 87 Umea, Sweden.
00103 *
00104 *  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
00105 *      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
00106 *      M.S. Moonen et al (eds), Linear Algebra for Large Scale and
00107 *      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
00108 *
00109 *  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
00110 *      Eigenvalues of a Regular Matrix Pair (A, B) and Condition
00111 *      Estimation: Theory, Algorithms and Software, Report
00112 *      UMINF - 94.04, Department of Computing Science, Umea University,
00113 *      S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
00114 *      To appear in Numerical Algorithms, 1996.
00115 *
00116 *  [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
00117 *      for Solving the Generalized Sylvester Equation and Estimating the
00118 *      Separation between Regular Matrix Pairs, Report UMINF - 93.23,
00119 *      Department of Computing Science, Umea University, S-901 87 Umea,
00120 *      Sweden, December 1993, Revised April 1994, Also as LAPACK working
00121 *      Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
00122 *      1996.
00123 *
00124 *  =====================================================================
00125 *
00126 *     .. Local Scalars ..
00127       INTEGER            HERE
00128 *     ..
00129 *     .. External Subroutines ..
00130       EXTERNAL           XERBLA, ZTGEX2
00131 *     ..
00132 *     .. Intrinsic Functions ..
00133       INTRINSIC          MAX
00134 *     ..
00135 *     .. Executable Statements ..
00136 *
00137 *     Decode and test input arguments.
00138       INFO = 0
00139       IF( N.LT.0 ) THEN
00140          INFO = -3
00141       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00142          INFO = -5
00143       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00144          INFO = -7
00145       ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
00146          INFO = -9
00147       ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
00148          INFO = -11
00149       ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
00150          INFO = -12
00151       ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
00152          INFO = -13
00153       END IF
00154       IF( INFO.NE.0 ) THEN
00155          CALL XERBLA( 'ZTGEXC', -INFO )
00156          RETURN
00157       END IF
00158 *
00159 *     Quick return if possible
00160 *
00161       IF( N.LE.1 )
00162      $   RETURN
00163       IF( IFST.EQ.ILST )
00164      $   RETURN
00165 *
00166       IF( IFST.LT.ILST ) THEN
00167 *
00168          HERE = IFST
00169 *
00170    10    CONTINUE
00171 *
00172 *        Swap with next one below
00173 *
00174          CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
00175      $                HERE, INFO )
00176          IF( INFO.NE.0 ) THEN
00177             ILST = HERE
00178             RETURN
00179          END IF
00180          HERE = HERE + 1
00181          IF( HERE.LT.ILST )
00182      $      GO TO 10
00183          HERE = HERE - 1
00184       ELSE
00185          HERE = IFST - 1
00186 *
00187    20    CONTINUE
00188 *
00189 *        Swap with next one above
00190 *
00191          CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
00192      $                HERE, INFO )
00193          IF( INFO.NE.0 ) THEN
00194             ILST = HERE
00195             RETURN
00196          END IF
00197          HERE = HERE - 1
00198          IF( HERE.GE.ILST )
00199      $      GO TO 20
00200          HERE = HERE + 1
00201       END IF
00202       ILST = HERE
00203       RETURN
00204 *
00205 *     End of ZTGEXC
00206 *
00207       END