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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CTREXC 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CTREXC + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctrexc.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctrexc.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctrexc.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER COMPQ 00025 * INTEGER IFST, ILST, INFO, LDQ, LDT, N 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX Q( LDQ, * ), T( LDT, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> CTREXC reorders the Schur factorization of a complex matrix 00038 *> A = Q*T*Q**H, so that the diagonal element of T with row index IFST 00039 *> is moved to row ILST. 00040 *> 00041 *> The Schur form T is reordered by a unitary similarity transformation 00042 *> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by 00043 *> postmultplying it with Z. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] COMPQ 00050 *> \verbatim 00051 *> COMPQ is CHARACTER*1 00052 *> = 'V': update the matrix Q of Schur vectors; 00053 *> = 'N': do not update Q. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] N 00057 *> \verbatim 00058 *> N is INTEGER 00059 *> The order of the matrix T. N >= 0. 00060 *> \endverbatim 00061 *> 00062 *> \param[in,out] T 00063 *> \verbatim 00064 *> T is COMPLEX array, dimension (LDT,N) 00065 *> On entry, the upper triangular matrix T. 00066 *> On exit, the reordered upper triangular matrix. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] LDT 00070 *> \verbatim 00071 *> LDT is INTEGER 00072 *> The leading dimension of the array T. LDT >= max(1,N). 00073 *> \endverbatim 00074 *> 00075 *> \param[in,out] Q 00076 *> \verbatim 00077 *> Q is COMPLEX array, dimension (LDQ,N) 00078 *> On entry, if COMPQ = 'V', the matrix Q of Schur vectors. 00079 *> On exit, if COMPQ = 'V', Q has been postmultiplied by the 00080 *> unitary transformation matrix Z which reorders T. 00081 *> If COMPQ = 'N', Q is not referenced. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] LDQ 00085 *> \verbatim 00086 *> LDQ is INTEGER 00087 *> The leading dimension of the array Q. LDQ >= max(1,N). 00088 *> \endverbatim 00089 *> 00090 *> \param[in] IFST 00091 *> \verbatim 00092 *> IFST is INTEGER 00093 *> \endverbatim 00094 *> 00095 *> \param[in] ILST 00096 *> \verbatim 00097 *> ILST is INTEGER 00098 *> 00099 *> Specify the reordering of the diagonal elements of T: 00100 *> The element with row index IFST is moved to row ILST by a 00101 *> sequence of transpositions between adjacent elements. 00102 *> 1 <= IFST <= N; 1 <= ILST <= N. 00103 *> \endverbatim 00104 *> 00105 *> \param[out] INFO 00106 *> \verbatim 00107 *> INFO is INTEGER 00108 *> = 0: successful exit 00109 *> < 0: if INFO = -i, the i-th argument had an illegal value 00110 *> \endverbatim 00111 * 00112 * Authors: 00113 * ======== 00114 * 00115 *> \author Univ. of Tennessee 00116 *> \author Univ. of California Berkeley 00117 *> \author Univ. of Colorado Denver 00118 *> \author NAG Ltd. 00119 * 00120 *> \date November 2011 00121 * 00122 *> \ingroup complexOTHERcomputational 00123 * 00124 * ===================================================================== 00125 SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO ) 00126 * 00127 * -- LAPACK computational routine (version 3.4.0) -- 00128 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00130 * November 2011 00131 * 00132 * .. Scalar Arguments .. 00133 CHARACTER COMPQ 00134 INTEGER IFST, ILST, INFO, LDQ, LDT, N 00135 * .. 00136 * .. Array Arguments .. 00137 COMPLEX Q( LDQ, * ), T( LDT, * ) 00138 * .. 00139 * 00140 * ===================================================================== 00141 * 00142 * .. Local Scalars .. 00143 LOGICAL WANTQ 00144 INTEGER K, M1, M2, M3 00145 REAL CS 00146 COMPLEX SN, T11, T22, TEMP 00147 * .. 00148 * .. External Functions .. 00149 LOGICAL LSAME 00150 EXTERNAL LSAME 00151 * .. 00152 * .. External Subroutines .. 00153 EXTERNAL CLARTG, CROT, XERBLA 00154 * .. 00155 * .. Intrinsic Functions .. 00156 INTRINSIC CONJG, MAX 00157 * .. 00158 * .. Executable Statements .. 00159 * 00160 * Decode and test the input parameters. 00161 * 00162 INFO = 0 00163 WANTQ = LSAME( COMPQ, 'V' ) 00164 IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN 00165 INFO = -1 00166 ELSE IF( N.LT.0 ) THEN 00167 INFO = -2 00168 ELSE IF( LDT.LT.MAX( 1, N ) ) THEN 00169 INFO = -4 00170 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN 00171 INFO = -6 00172 ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN 00173 INFO = -7 00174 ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN 00175 INFO = -8 00176 END IF 00177 IF( INFO.NE.0 ) THEN 00178 CALL XERBLA( 'CTREXC', -INFO ) 00179 RETURN 00180 END IF 00181 * 00182 * Quick return if possible 00183 * 00184 IF( N.EQ.1 .OR. IFST.EQ.ILST ) 00185 $ RETURN 00186 * 00187 IF( IFST.LT.ILST ) THEN 00188 * 00189 * Move the IFST-th diagonal element forward down the diagonal. 00190 * 00191 M1 = 0 00192 M2 = -1 00193 M3 = 1 00194 ELSE 00195 * 00196 * Move the IFST-th diagonal element backward up the diagonal. 00197 * 00198 M1 = -1 00199 M2 = 0 00200 M3 = -1 00201 END IF 00202 * 00203 DO 10 K = IFST + M1, ILST + M2, M3 00204 * 00205 * Interchange the k-th and (k+1)-th diagonal elements. 00206 * 00207 T11 = T( K, K ) 00208 T22 = T( K+1, K+1 ) 00209 * 00210 * Determine the transformation to perform the interchange. 00211 * 00212 CALL CLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP ) 00213 * 00214 * Apply transformation to the matrix T. 00215 * 00216 IF( K+2.LE.N ) 00217 $ CALL CROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS, 00218 $ SN ) 00219 CALL CROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS, CONJG( SN ) ) 00220 * 00221 T( K, K ) = T22 00222 T( K+1, K+1 ) = T11 00223 * 00224 IF( WANTQ ) THEN 00225 * 00226 * Accumulate transformation in the matrix Q. 00227 * 00228 CALL CROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS, 00229 $ CONJG( SN ) ) 00230 END IF 00231 * 00232 10 CONTINUE 00233 * 00234 RETURN 00235 * 00236 * End of CTREXC 00237 * 00238 END