00001 SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER COMPQ 00010 INTEGER IFST, ILST, INFO, LDQ, LDT, N 00011 * .. 00012 * .. Array Arguments .. 00013 COMPLEX Q( LDQ, * ), T( LDT, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * CTREXC reorders the Schur factorization of a complex matrix 00020 * A = Q*T*Q**H, so that the diagonal element of T with row index IFST 00021 * is moved to row ILST. 00022 * 00023 * The Schur form T is reordered by a unitary similarity transformation 00024 * Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by 00025 * postmultplying it with Z. 00026 * 00027 * Arguments 00028 * ========= 00029 * 00030 * COMPQ (input) CHARACTER*1 00031 * = 'V': update the matrix Q of Schur vectors; 00032 * = 'N': do not update Q. 00033 * 00034 * N (input) INTEGER 00035 * The order of the matrix T. N >= 0. 00036 * 00037 * T (input/output) COMPLEX array, dimension (LDT,N) 00038 * On entry, the upper triangular matrix T. 00039 * On exit, the reordered upper triangular matrix. 00040 * 00041 * LDT (input) INTEGER 00042 * The leading dimension of the array T. LDT >= max(1,N). 00043 * 00044 * Q (input/output) COMPLEX array, dimension (LDQ,N) 00045 * On entry, if COMPQ = 'V', the matrix Q of Schur vectors. 00046 * On exit, if COMPQ = 'V', Q has been postmultiplied by the 00047 * unitary transformation matrix Z which reorders T. 00048 * If COMPQ = 'N', Q is not referenced. 00049 * 00050 * LDQ (input) INTEGER 00051 * The leading dimension of the array Q. LDQ >= max(1,N). 00052 * 00053 * IFST (input) INTEGER 00054 * ILST (input) INTEGER 00055 * Specify the reordering of the diagonal elements of T: 00056 * The element with row index IFST is moved to row ILST by a 00057 * sequence of transpositions between adjacent elements. 00058 * 1 <= IFST <= N; 1 <= ILST <= N. 00059 * 00060 * INFO (output) INTEGER 00061 * = 0: successful exit 00062 * < 0: if INFO = -i, the i-th argument had an illegal value 00063 * 00064 * ===================================================================== 00065 * 00066 * .. Local Scalars .. 00067 LOGICAL WANTQ 00068 INTEGER K, M1, M2, M3 00069 REAL CS 00070 COMPLEX SN, T11, T22, TEMP 00071 * .. 00072 * .. External Functions .. 00073 LOGICAL LSAME 00074 EXTERNAL LSAME 00075 * .. 00076 * .. External Subroutines .. 00077 EXTERNAL CLARTG, CROT, XERBLA 00078 * .. 00079 * .. Intrinsic Functions .. 00080 INTRINSIC CONJG, MAX 00081 * .. 00082 * .. Executable Statements .. 00083 * 00084 * Decode and test the input parameters. 00085 * 00086 INFO = 0 00087 WANTQ = LSAME( COMPQ, 'V' ) 00088 IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN 00089 INFO = -1 00090 ELSE IF( N.LT.0 ) THEN 00091 INFO = -2 00092 ELSE IF( LDT.LT.MAX( 1, N ) ) THEN 00093 INFO = -4 00094 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN 00095 INFO = -6 00096 ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN 00097 INFO = -7 00098 ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN 00099 INFO = -8 00100 END IF 00101 IF( INFO.NE.0 ) THEN 00102 CALL XERBLA( 'CTREXC', -INFO ) 00103 RETURN 00104 END IF 00105 * 00106 * Quick return if possible 00107 * 00108 IF( N.EQ.1 .OR. IFST.EQ.ILST ) 00109 $ RETURN 00110 * 00111 IF( IFST.LT.ILST ) THEN 00112 * 00113 * Move the IFST-th diagonal element forward down the diagonal. 00114 * 00115 M1 = 0 00116 M2 = -1 00117 M3 = 1 00118 ELSE 00119 * 00120 * Move the IFST-th diagonal element backward up the diagonal. 00121 * 00122 M1 = -1 00123 M2 = 0 00124 M3 = -1 00125 END IF 00126 * 00127 DO 10 K = IFST + M1, ILST + M2, M3 00128 * 00129 * Interchange the k-th and (k+1)-th diagonal elements. 00130 * 00131 T11 = T( K, K ) 00132 T22 = T( K+1, K+1 ) 00133 * 00134 * Determine the transformation to perform the interchange. 00135 * 00136 CALL CLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP ) 00137 * 00138 * Apply transformation to the matrix T. 00139 * 00140 IF( K+2.LE.N ) 00141 $ CALL CROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS, 00142 $ SN ) 00143 CALL CROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS, CONJG( SN ) ) 00144 * 00145 T( K, K ) = T22 00146 T( K+1, K+1 ) = T11 00147 * 00148 IF( WANTQ ) THEN 00149 * 00150 * Accumulate transformation in the matrix Q. 00151 * 00152 CALL CROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS, 00153 $ CONJG( SN ) ) 00154 END IF 00155 * 00156 10 CONTINUE 00157 * 00158 RETURN 00159 * 00160 * End of CTREXC 00161 * 00162 END
1.7.2