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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHPGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHPGV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgv.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgv.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgv.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 00022 * RWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER JOBZ, UPLO 00026 * INTEGER INFO, ITYPE, LDZ, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION RWORK( * ), W( * ) 00030 * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> ZHPGV computes all the eigenvalues and, optionally, the eigenvectors 00040 *> of a complex generalized Hermitian-definite eigenproblem, of the form 00041 *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 00042 *> Here A and B are assumed to be Hermitian, stored in packed format, 00043 *> and B is also positive definite. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] ITYPE 00050 *> \verbatim 00051 *> ITYPE is INTEGER 00052 *> Specifies the problem type to be solved: 00053 *> = 1: A*x = (lambda)*B*x 00054 *> = 2: A*B*x = (lambda)*x 00055 *> = 3: B*A*x = (lambda)*x 00056 *> \endverbatim 00057 *> 00058 *> \param[in] JOBZ 00059 *> \verbatim 00060 *> JOBZ is CHARACTER*1 00061 *> = 'N': Compute eigenvalues only; 00062 *> = 'V': Compute eigenvalues and eigenvectors. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] UPLO 00066 *> \verbatim 00067 *> UPLO is CHARACTER*1 00068 *> = 'U': Upper triangles of A and B are stored; 00069 *> = 'L': Lower triangles of A and B are stored. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] N 00073 *> \verbatim 00074 *> N is INTEGER 00075 *> The order of the matrices A and B. N >= 0. 00076 *> \endverbatim 00077 *> 00078 *> \param[in,out] AP 00079 *> \verbatim 00080 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00081 *> On entry, the upper or lower triangle of the Hermitian matrix 00082 *> A, packed columnwise in a linear array. The j-th column of A 00083 *> is stored in the array AP as follows: 00084 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00085 *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 00086 *> 00087 *> On exit, the contents of AP are destroyed. 00088 *> \endverbatim 00089 *> 00090 *> \param[in,out] BP 00091 *> \verbatim 00092 *> BP is COMPLEX*16 array, dimension (N*(N+1)/2) 00093 *> On entry, the upper or lower triangle of the Hermitian matrix 00094 *> B, packed columnwise in a linear array. The j-th column of B 00095 *> is stored in the array BP as follows: 00096 *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 00097 *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 00098 *> 00099 *> On exit, the triangular factor U or L from the Cholesky 00100 *> factorization B = U**H*U or B = L*L**H, in the same storage 00101 *> format as B. 00102 *> \endverbatim 00103 *> 00104 *> \param[out] W 00105 *> \verbatim 00106 *> W is DOUBLE PRECISION array, dimension (N) 00107 *> If INFO = 0, the eigenvalues in ascending order. 00108 *> \endverbatim 00109 *> 00110 *> \param[out] Z 00111 *> \verbatim 00112 *> Z is COMPLEX*16 array, dimension (LDZ, N) 00113 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00114 *> eigenvectors. The eigenvectors are normalized as follows: 00115 *> if ITYPE = 1 or 2, Z**H*B*Z = I; 00116 *> if ITYPE = 3, Z**H*inv(B)*Z = I. 00117 *> If JOBZ = 'N', then Z is not referenced. 00118 *> \endverbatim 00119 *> 00120 *> \param[in] LDZ 00121 *> \verbatim 00122 *> LDZ is INTEGER 00123 *> The leading dimension of the array Z. LDZ >= 1, and if 00124 *> JOBZ = 'V', LDZ >= max(1,N). 00125 *> \endverbatim 00126 *> 00127 *> \param[out] WORK 00128 *> \verbatim 00129 *> WORK is COMPLEX*16 array, dimension (max(1, 2*N-1)) 00130 *> \endverbatim 00131 *> 00132 *> \param[out] RWORK 00133 *> \verbatim 00134 *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) 00135 *> \endverbatim 00136 *> 00137 *> \param[out] INFO 00138 *> \verbatim 00139 *> INFO is INTEGER 00140 *> = 0: successful exit 00141 *> < 0: if INFO = -i, the i-th argument had an illegal value 00142 *> > 0: ZPPTRF or ZHPEV returned an error code: 00143 *> <= N: if INFO = i, ZHPEV failed to converge; 00144 *> i off-diagonal elements of an intermediate 00145 *> tridiagonal form did not convergeto zero; 00146 *> > N: if INFO = N + i, for 1 <= i <= n, then the leading 00147 *> minor of order i of B is not positive definite. 00148 *> The factorization of B could not be completed and 00149 *> no eigenvalues or eigenvectors were computed. 00150 *> \endverbatim 00151 * 00152 * Authors: 00153 * ======== 00154 * 00155 *> \author Univ. of Tennessee 00156 *> \author Univ. of California Berkeley 00157 *> \author Univ. of Colorado Denver 00158 *> \author NAG Ltd. 00159 * 00160 *> \date November 2011 00161 * 00162 *> \ingroup complex16OTHEReigen 00163 * 00164 * ===================================================================== 00165 SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 00166 $ RWORK, INFO ) 00167 * 00168 * -- LAPACK driver routine (version 3.4.0) -- 00169 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00170 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00171 * November 2011 00172 * 00173 * .. Scalar Arguments .. 00174 CHARACTER JOBZ, UPLO 00175 INTEGER INFO, ITYPE, LDZ, N 00176 * .. 00177 * .. Array Arguments .. 00178 DOUBLE PRECISION RWORK( * ), W( * ) 00179 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 00180 * .. 00181 * 00182 * ===================================================================== 00183 * 00184 * .. Local Scalars .. 00185 LOGICAL UPPER, WANTZ 00186 CHARACTER TRANS 00187 INTEGER J, NEIG 00188 * .. 00189 * .. External Functions .. 00190 LOGICAL LSAME 00191 EXTERNAL LSAME 00192 * .. 00193 * .. External Subroutines .. 00194 EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV 00195 * .. 00196 * .. Executable Statements .. 00197 * 00198 * Test the input parameters. 00199 * 00200 WANTZ = LSAME( JOBZ, 'V' ) 00201 UPPER = LSAME( UPLO, 'U' ) 00202 * 00203 INFO = 0 00204 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 00205 INFO = -1 00206 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00207 INFO = -2 00208 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00209 INFO = -3 00210 ELSE IF( N.LT.0 ) THEN 00211 INFO = -4 00212 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00213 INFO = -9 00214 END IF 00215 IF( INFO.NE.0 ) THEN 00216 CALL XERBLA( 'ZHPGV ', -INFO ) 00217 RETURN 00218 END IF 00219 * 00220 * Quick return if possible 00221 * 00222 IF( N.EQ.0 ) 00223 $ RETURN 00224 * 00225 * Form a Cholesky factorization of B. 00226 * 00227 CALL ZPPTRF( UPLO, N, BP, INFO ) 00228 IF( INFO.NE.0 ) THEN 00229 INFO = N + INFO 00230 RETURN 00231 END IF 00232 * 00233 * Transform problem to standard eigenvalue problem and solve. 00234 * 00235 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) 00236 CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO ) 00237 * 00238 IF( WANTZ ) THEN 00239 * 00240 * Backtransform eigenvectors to the original problem. 00241 * 00242 NEIG = N 00243 IF( INFO.GT.0 ) 00244 $ NEIG = INFO - 1 00245 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 00246 * 00247 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 00248 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y 00249 * 00250 IF( UPPER ) THEN 00251 TRANS = 'N' 00252 ELSE 00253 TRANS = 'C' 00254 END IF 00255 * 00256 DO 10 J = 1, NEIG 00257 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 00258 $ 1 ) 00259 10 CONTINUE 00260 * 00261 ELSE IF( ITYPE.EQ.3 ) THEN 00262 * 00263 * For B*A*x=(lambda)*x; 00264 * backtransform eigenvectors: x = L*y or U**H *y 00265 * 00266 IF( UPPER ) THEN 00267 TRANS = 'C' 00268 ELSE 00269 TRANS = 'N' 00270 END IF 00271 * 00272 DO 20 J = 1, NEIG 00273 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 00274 $ 1 ) 00275 20 CONTINUE 00276 END IF 00277 END IF 00278 RETURN 00279 * 00280 * End of ZHPGV 00281 * 00282 END