Annotation of rpl/lapack/lapack/ztgexc.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
! 2: $ LDZ, IFST, ILST, INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: LOGICAL WANTQ, WANTZ
! 11: INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 15: $ Z( LDZ, * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZTGEXC reorders the generalized Schur decomposition of a complex
! 22: * matrix pair (A,B), using an unitary equivalence transformation
! 23: * (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with
! 24: * row index IFST is moved to row ILST.
! 25: *
! 26: * (A, B) must be in generalized Schur canonical form, that is, A and
! 27: * B are both upper triangular.
! 28: *
! 29: * Optionally, the matrices Q and Z of generalized Schur vectors are
! 30: * updated.
! 31: *
! 32: * Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
! 33: * Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
! 34: *
! 35: * Arguments
! 36: * =========
! 37: *
! 38: * WANTQ (input) LOGICAL
! 39: * .TRUE. : update the left transformation matrix Q;
! 40: * .FALSE.: do not update Q.
! 41: *
! 42: * WANTZ (input) LOGICAL
! 43: * .TRUE. : update the right transformation matrix Z;
! 44: * .FALSE.: do not update Z.
! 45: *
! 46: * N (input) INTEGER
! 47: * The order of the matrices A and B. N >= 0.
! 48: *
! 49: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 50: * On entry, the upper triangular matrix A in the pair (A, B).
! 51: * On exit, the updated matrix A.
! 52: *
! 53: * LDA (input) INTEGER
! 54: * The leading dimension of the array A. LDA >= max(1,N).
! 55: *
! 56: * B (input/output) COMPLEX*16 array, dimension (LDB,N)
! 57: * On entry, the upper triangular matrix B in the pair (A, B).
! 58: * On exit, the updated matrix B.
! 59: *
! 60: * LDB (input) INTEGER
! 61: * The leading dimension of the array B. LDB >= max(1,N).
! 62: *
! 63: * Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
! 64: * On entry, if WANTQ = .TRUE., the unitary matrix Q.
! 65: * On exit, the updated matrix Q.
! 66: * If WANTQ = .FALSE., Q is not referenced.
! 67: *
! 68: * LDQ (input) INTEGER
! 69: * The leading dimension of the array Q. LDQ >= 1;
! 70: * If WANTQ = .TRUE., LDQ >= N.
! 71: *
! 72: * Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
! 73: * On entry, if WANTZ = .TRUE., the unitary matrix Z.
! 74: * On exit, the updated matrix Z.
! 75: * If WANTZ = .FALSE., Z is not referenced.
! 76: *
! 77: * LDZ (input) INTEGER
! 78: * The leading dimension of the array Z. LDZ >= 1;
! 79: * If WANTZ = .TRUE., LDZ >= N.
! 80: *
! 81: * IFST (input) INTEGER
! 82: * ILST (input/output) INTEGER
! 83: * Specify the reordering of the diagonal blocks of (A, B).
! 84: * The block with row index IFST is moved to row ILST, by a
! 85: * sequence of swapping between adjacent blocks.
! 86: *
! 87: * INFO (output) INTEGER
! 88: * =0: Successful exit.
! 89: * <0: if INFO = -i, the i-th argument had an illegal value.
! 90: * =1: The transformed matrix pair (A, B) would be too far
! 91: * from generalized Schur form; the problem is ill-
! 92: * conditioned. (A, B) may have been partially reordered,
! 93: * and ILST points to the first row of the current
! 94: * position of the block being moved.
! 95: *
! 96: *
! 97: * Further Details
! 98: * ===============
! 99: *
! 100: * Based on contributions by
! 101: * Bo Kagstrom and Peter Poromaa, Department of Computing Science,
! 102: * Umea University, S-901 87 Umea, Sweden.
! 103: *
! 104: * [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
! 105: * Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
! 106: * M.S. Moonen et al (eds), Linear Algebra for Large Scale and
! 107: * Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
! 108: *
! 109: * [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
! 110: * Eigenvalues of a Regular Matrix Pair (A, B) and Condition
! 111: * Estimation: Theory, Algorithms and Software, Report
! 112: * UMINF - 94.04, Department of Computing Science, Umea University,
! 113: * S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
! 114: * To appear in Numerical Algorithms, 1996.
! 115: *
! 116: * [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
! 117: * for Solving the Generalized Sylvester Equation and Estimating the
! 118: * Separation between Regular Matrix Pairs, Report UMINF - 93.23,
! 119: * Department of Computing Science, Umea University, S-901 87 Umea,
! 120: * Sweden, December 1993, Revised April 1994, Also as LAPACK working
! 121: * Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
! 122: * 1996.
! 123: *
! 124: * =====================================================================
! 125: *
! 126: * .. Local Scalars ..
! 127: INTEGER HERE
! 128: * ..
! 129: * .. External Subroutines ..
! 130: EXTERNAL XERBLA, ZTGEX2
! 131: * ..
! 132: * .. Intrinsic Functions ..
! 133: INTRINSIC MAX
! 134: * ..
! 135: * .. Executable Statements ..
! 136: *
! 137: * Decode and test input arguments.
! 138: INFO = 0
! 139: IF( N.LT.0 ) THEN
! 140: INFO = -3
! 141: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 142: INFO = -5
! 143: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 144: INFO = -7
! 145: ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
! 146: INFO = -9
! 147: ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
! 148: INFO = -11
! 149: ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
! 150: INFO = -12
! 151: ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
! 152: INFO = -13
! 153: END IF
! 154: IF( INFO.NE.0 ) THEN
! 155: CALL XERBLA( 'ZTGEXC', -INFO )
! 156: RETURN
! 157: END IF
! 158: *
! 159: * Quick return if possible
! 160: *
! 161: IF( N.LE.1 )
! 162: $ RETURN
! 163: IF( IFST.EQ.ILST )
! 164: $ RETURN
! 165: *
! 166: IF( IFST.LT.ILST ) THEN
! 167: *
! 168: HERE = IFST
! 169: *
! 170: 10 CONTINUE
! 171: *
! 172: * Swap with next one below
! 173: *
! 174: CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
! 175: $ HERE, INFO )
! 176: IF( INFO.NE.0 ) THEN
! 177: ILST = HERE
! 178: RETURN
! 179: END IF
! 180: HERE = HERE + 1
! 181: IF( HERE.LT.ILST )
! 182: $ GO TO 10
! 183: HERE = HERE - 1
! 184: ELSE
! 185: HERE = IFST - 1
! 186: *
! 187: 20 CONTINUE
! 188: *
! 189: * Swap with next one above
! 190: *
! 191: CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
! 192: $ HERE, INFO )
! 193: IF( INFO.NE.0 ) THEN
! 194: ILST = HERE
! 195: RETURN
! 196: END IF
! 197: HERE = HERE - 1
! 198: IF( HERE.GE.ILST )
! 199: $ GO TO 20
! 200: HERE = HERE + 1
! 201: END IF
! 202: ILST = HERE
! 203: RETURN
! 204: *
! 205: * End of ZTGEXC
! 206: *
! 207: END
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