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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHEGS2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHEGS2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegs2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegs2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegs2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER UPLO 00025 * INTEGER INFO, ITYPE, LDA, LDB, N 00026 * .. 00027 * .. Array Arguments .. 00028 * COMPLEX*16 A( LDA, * ), B( LDB, * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> ZHEGS2 reduces a complex Hermitian-definite generalized 00038 *> eigenproblem to standard form. 00039 *> 00040 *> If ITYPE = 1, the problem is A*x = lambda*B*x, 00041 *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) 00042 *> 00043 *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or 00044 *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L. 00045 *> 00046 *> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF. 00047 *> \endverbatim 00048 * 00049 * Arguments: 00050 * ========== 00051 * 00052 *> \param[in] ITYPE 00053 *> \verbatim 00054 *> ITYPE is INTEGER 00055 *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); 00056 *> = 2 or 3: compute U*A*U**H or L**H *A*L. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] UPLO 00060 *> \verbatim 00061 *> UPLO is CHARACTER*1 00062 *> Specifies whether the upper or lower triangular part of the 00063 *> Hermitian matrix A is stored, and how B has been factorized. 00064 *> = 'U': Upper triangular 00065 *> = 'L': Lower triangular 00066 *> \endverbatim 00067 *> 00068 *> \param[in] N 00069 *> \verbatim 00070 *> N is INTEGER 00071 *> The order of the matrices A and B. N >= 0. 00072 *> \endverbatim 00073 *> 00074 *> \param[in,out] A 00075 *> \verbatim 00076 *> A is COMPLEX*16 array, dimension (LDA,N) 00077 *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading 00078 *> n by n upper triangular part of A contains the upper 00079 *> triangular part of the matrix A, and the strictly lower 00080 *> triangular part of A is not referenced. If UPLO = 'L', the 00081 *> leading n by n lower triangular part of A contains the lower 00082 *> triangular part of the matrix A, and the strictly upper 00083 *> triangular part of A is not referenced. 00084 *> 00085 *> On exit, if INFO = 0, the transformed matrix, stored in the 00086 *> same format as A. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] LDA 00090 *> \verbatim 00091 *> LDA is INTEGER 00092 *> The leading dimension of the array A. LDA >= max(1,N). 00093 *> \endverbatim 00094 *> 00095 *> \param[in] B 00096 *> \verbatim 00097 *> B is COMPLEX*16 array, dimension (LDB,N) 00098 *> The triangular factor from the Cholesky factorization of B, 00099 *> as returned by ZPOTRF. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] LDB 00103 *> \verbatim 00104 *> LDB is INTEGER 00105 *> The leading dimension of the array B. LDB >= max(1,N). 00106 *> \endverbatim 00107 *> 00108 *> \param[out] INFO 00109 *> \verbatim 00110 *> INFO is INTEGER 00111 *> = 0: successful exit. 00112 *> < 0: if INFO = -i, the i-th argument had an illegal value. 00113 *> \endverbatim 00114 * 00115 * Authors: 00116 * ======== 00117 * 00118 *> \author Univ. of Tennessee 00119 *> \author Univ. of California Berkeley 00120 *> \author Univ. of Colorado Denver 00121 *> \author NAG Ltd. 00122 * 00123 *> \date November 2011 00124 * 00125 *> \ingroup complex16HEcomputational 00126 * 00127 * ===================================================================== 00128 SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) 00129 * 00130 * -- LAPACK computational routine (version 3.4.0) -- 00131 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00132 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00133 * November 2011 00134 * 00135 * .. Scalar Arguments .. 00136 CHARACTER UPLO 00137 INTEGER INFO, ITYPE, LDA, LDB, N 00138 * .. 00139 * .. Array Arguments .. 00140 COMPLEX*16 A( LDA, * ), B( LDB, * ) 00141 * .. 00142 * 00143 * ===================================================================== 00144 * 00145 * .. Parameters .. 00146 DOUBLE PRECISION ONE, HALF 00147 PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 ) 00148 COMPLEX*16 CONE 00149 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 00150 * .. 00151 * .. Local Scalars .. 00152 LOGICAL UPPER 00153 INTEGER K 00154 DOUBLE PRECISION AKK, BKK 00155 COMPLEX*16 CT 00156 * .. 00157 * .. External Subroutines .. 00158 EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHER2, ZLACGV, ZTRMV, 00159 $ ZTRSV 00160 * .. 00161 * .. Intrinsic Functions .. 00162 INTRINSIC MAX 00163 * .. 00164 * .. External Functions .. 00165 LOGICAL LSAME 00166 EXTERNAL LSAME 00167 * .. 00168 * .. Executable Statements .. 00169 * 00170 * Test the input parameters. 00171 * 00172 INFO = 0 00173 UPPER = LSAME( UPLO, 'U' ) 00174 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00175 INFO = -1 00176 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00177 INFO = -2 00178 ELSE IF( N.LT.0 ) THEN 00179 INFO = -3 00180 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 00181 INFO = -5 00182 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 00183 INFO = -7 00184 END IF 00185 IF( INFO.NE.0 ) THEN 00186 CALL XERBLA( 'ZHEGS2', -INFO ) 00187 RETURN 00188 END IF 00189 * 00190 IF( ITYPE.EQ.1 ) THEN 00191 IF( UPPER ) THEN 00192 * 00193 * Compute inv(U**H)*A*inv(U) 00194 * 00195 DO 10 K = 1, N 00196 * 00197 * Update the upper triangle of A(k:n,k:n) 00198 * 00199 AKK = A( K, K ) 00200 BKK = B( K, K ) 00201 AKK = AKK / BKK**2 00202 A( K, K ) = AKK 00203 IF( K.LT.N ) THEN 00204 CALL ZDSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) 00205 CT = -HALF*AKK 00206 CALL ZLACGV( N-K, A( K, K+1 ), LDA ) 00207 CALL ZLACGV( N-K, B( K, K+1 ), LDB ) 00208 CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), 00209 $ LDA ) 00210 CALL ZHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA, 00211 $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) 00212 CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), 00213 $ LDA ) 00214 CALL ZLACGV( N-K, B( K, K+1 ), LDB ) 00215 CALL ZTRSV( UPLO, 'Conjugate transpose', 'Non-unit', 00216 $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ), 00217 $ LDA ) 00218 CALL ZLACGV( N-K, A( K, K+1 ), LDA ) 00219 END IF 00220 10 CONTINUE 00221 ELSE 00222 * 00223 * Compute inv(L)*A*inv(L**H) 00224 * 00225 DO 20 K = 1, N 00226 * 00227 * Update the lower triangle of A(k:n,k:n) 00228 * 00229 AKK = A( K, K ) 00230 BKK = B( K, K ) 00231 AKK = AKK / BKK**2 00232 A( K, K ) = AKK 00233 IF( K.LT.N ) THEN 00234 CALL ZDSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) 00235 CT = -HALF*AKK 00236 CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) 00237 CALL ZHER2( UPLO, N-K, -CONE, A( K+1, K ), 1, 00238 $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) 00239 CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) 00240 CALL ZTRSV( UPLO, 'No transpose', 'Non-unit', N-K, 00241 $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) 00242 END IF 00243 20 CONTINUE 00244 END IF 00245 ELSE 00246 IF( UPPER ) THEN 00247 * 00248 * Compute U*A*U**H 00249 * 00250 DO 30 K = 1, N 00251 * 00252 * Update the upper triangle of A(1:k,1:k) 00253 * 00254 AKK = A( K, K ) 00255 BKK = B( K, K ) 00256 CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, 00257 $ LDB, A( 1, K ), 1 ) 00258 CT = HALF*AKK 00259 CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) 00260 CALL ZHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1, 00261 $ A, LDA ) 00262 CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) 00263 CALL ZDSCAL( K-1, BKK, A( 1, K ), 1 ) 00264 A( K, K ) = AKK*BKK**2 00265 30 CONTINUE 00266 ELSE 00267 * 00268 * Compute L**H *A*L 00269 * 00270 DO 40 K = 1, N 00271 * 00272 * Update the lower triangle of A(1:k,1:k) 00273 * 00274 AKK = A( K, K ) 00275 BKK = B( K, K ) 00276 CALL ZLACGV( K-1, A( K, 1 ), LDA ) 00277 CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, 00278 $ B, LDB, A( K, 1 ), LDA ) 00279 CT = HALF*AKK 00280 CALL ZLACGV( K-1, B( K, 1 ), LDB ) 00281 CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) 00282 CALL ZHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ), 00283 $ LDB, A, LDA ) 00284 CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) 00285 CALL ZLACGV( K-1, B( K, 1 ), LDB ) 00286 CALL ZDSCAL( K-1, BKK, A( K, 1 ), LDA ) 00287 CALL ZLACGV( K-1, A( K, 1 ), LDA ) 00288 A( K, K ) = AKK*BKK**2 00289 40 CONTINUE 00290 END IF 00291 END IF 00292 RETURN 00293 * 00294 * End of ZHEGS2 00295 * 00296 END