LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhegs2.f
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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 *
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00009 *> Download ZHEGS2 + dependencies 
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00013 *> [ZIP]</a> 
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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
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