1*> \brief \b ZHPGV 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download ZHPGV + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgv.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgv.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgv.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 22* RWORK, INFO ) 23* 24* .. Scalar Arguments .. 25* CHARACTER JOBZ, UPLO 26* INTEGER INFO, ITYPE, LDZ, N 27* .. 28* .. Array Arguments .. 29* DOUBLE PRECISION RWORK( * ), W( * ) 30* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 31* .. 32* 33* 34*> \par Purpose: 35* ============= 36*> 37*> \verbatim 38*> 39*> ZHPGV computes all the eigenvalues and, optionally, the eigenvectors 40*> of a complex generalized Hermitian-definite eigenproblem, of the form 41*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. 42*> Here A and B are assumed to be Hermitian, stored in packed format, 43*> and B is also positive definite. 44*> \endverbatim 45* 46* Arguments: 47* ========== 48* 49*> \param[in] ITYPE 50*> \verbatim 51*> ITYPE is INTEGER 52*> Specifies the problem type to be solved: 53*> = 1: A*x = (lambda)*B*x 54*> = 2: A*B*x = (lambda)*x 55*> = 3: B*A*x = (lambda)*x 56*> \endverbatim 57*> 58*> \param[in] JOBZ 59*> \verbatim 60*> JOBZ is CHARACTER*1 61*> = 'N': Compute eigenvalues only; 62*> = 'V': Compute eigenvalues and eigenvectors. 63*> \endverbatim 64*> 65*> \param[in] UPLO 66*> \verbatim 67*> UPLO is CHARACTER*1 68*> = 'U': Upper triangles of A and B are stored; 69*> = 'L': Lower triangles of A and B are stored. 70*> \endverbatim 71*> 72*> \param[in] N 73*> \verbatim 74*> N is INTEGER 75*> The order of the matrices A and B. N >= 0. 76*> \endverbatim 77*> 78*> \param[in,out] AP 79*> \verbatim 80*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 81*> On entry, the upper or lower triangle of the Hermitian matrix 82*> A, packed columnwise in a linear array. The j-th column of A 83*> is stored in the array AP as follows: 84*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 85*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 86*> 87*> On exit, the contents of AP are destroyed. 88*> \endverbatim 89*> 90*> \param[in,out] BP 91*> \verbatim 92*> BP is COMPLEX*16 array, dimension (N*(N+1)/2) 93*> On entry, the upper or lower triangle of the Hermitian matrix 94*> B, packed columnwise in a linear array. The j-th column of B 95*> is stored in the array BP as follows: 96*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; 97*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. 98*> 99*> On exit, the triangular factor U or L from the Cholesky 100*> factorization B = U**H*U or B = L*L**H, in the same storage 101*> format as B. 102*> \endverbatim 103*> 104*> \param[out] W 105*> \verbatim 106*> W is DOUBLE PRECISION array, dimension (N) 107*> If INFO = 0, the eigenvalues in ascending order. 108*> \endverbatim 109*> 110*> \param[out] Z 111*> \verbatim 112*> Z is COMPLEX*16 array, dimension (LDZ, N) 113*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 114*> eigenvectors. The eigenvectors are normalized as follows: 115*> if ITYPE = 1 or 2, Z**H*B*Z = I; 116*> if ITYPE = 3, Z**H*inv(B)*Z = I. 117*> If JOBZ = 'N', then Z is not referenced. 118*> \endverbatim 119*> 120*> \param[in] LDZ 121*> \verbatim 122*> LDZ is INTEGER 123*> The leading dimension of the array Z. LDZ >= 1, and if 124*> JOBZ = 'V', LDZ >= max(1,N). 125*> \endverbatim 126*> 127*> \param[out] WORK 128*> \verbatim 129*> WORK is COMPLEX*16 array, dimension (max(1, 2*N-1)) 130*> \endverbatim 131*> 132*> \param[out] RWORK 133*> \verbatim 134*> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) 135*> \endverbatim 136*> 137*> \param[out] INFO 138*> \verbatim 139*> INFO is INTEGER 140*> = 0: successful exit 141*> < 0: if INFO = -i, the i-th argument had an illegal value 142*> > 0: ZPPTRF or ZHPEV returned an error code: 143*> <= N: if INFO = i, ZHPEV failed to converge; 144*> i off-diagonal elements of an intermediate 145*> tridiagonal form did not convergeto zero; 146*> > N: if INFO = N + i, for 1 <= i <= n, then the leading 147*> minor of order i of B is not positive definite. 148*> The factorization of B could not be completed and 149*> no eigenvalues or eigenvectors were computed. 150*> \endverbatim 151* 152* Authors: 153* ======== 154* 155*> \author Univ. of Tennessee 156*> \author Univ. of California Berkeley 157*> \author Univ. of Colorado Denver 158*> \author NAG Ltd. 159* 160*> \ingroup complex16OTHEReigen 161* 162* ===================================================================== 163 SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, 164 $ RWORK, INFO ) 165* 166* -- LAPACK driver routine -- 167* -- LAPACK is a software package provided by Univ. of Tennessee, -- 168* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 169* 170* .. Scalar Arguments .. 171 CHARACTER JOBZ, UPLO 172 INTEGER INFO, ITYPE, LDZ, N 173* .. 174* .. Array Arguments .. 175 DOUBLE PRECISION RWORK( * ), W( * ) 176 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) 177* .. 178* 179* ===================================================================== 180* 181* .. Local Scalars .. 182 LOGICAL UPPER, WANTZ 183 CHARACTER TRANS 184 INTEGER J, NEIG 185* .. 186* .. External Functions .. 187 LOGICAL LSAME 188 EXTERNAL LSAME 189* .. 190* .. External Subroutines .. 191 EXTERNAL XERBLA, ZHPEV, ZHPGST, ZPPTRF, ZTPMV, ZTPSV 192* .. 193* .. Executable Statements .. 194* 195* Test the input parameters. 196* 197 WANTZ = LSAME( JOBZ, 'V' ) 198 UPPER = LSAME( UPLO, 'U' ) 199* 200 INFO = 0 201 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN 202 INFO = -1 203 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 204 INFO = -2 205 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 206 INFO = -3 207 ELSE IF( N.LT.0 ) THEN 208 INFO = -4 209 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 210 INFO = -9 211 END IF 212 IF( INFO.NE.0 ) THEN 213 CALL XERBLA( 'ZHPGV ', -INFO ) 214 RETURN 215 END IF 216* 217* Quick return if possible 218* 219 IF( N.EQ.0 ) 220 $ RETURN 221* 222* Form a Cholesky factorization of B. 223* 224 CALL ZPPTRF( UPLO, N, BP, INFO ) 225 IF( INFO.NE.0 ) THEN 226 INFO = N + INFO 227 RETURN 228 END IF 229* 230* Transform problem to standard eigenvalue problem and solve. 231* 232 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) 233 CALL ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO ) 234* 235 IF( WANTZ ) THEN 236* 237* Backtransform eigenvectors to the original problem. 238* 239 NEIG = N 240 IF( INFO.GT.0 ) 241 $ NEIG = INFO - 1 242 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN 243* 244* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; 245* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y 246* 247 IF( UPPER ) THEN 248 TRANS = 'N' 249 ELSE 250 TRANS = 'C' 251 END IF 252* 253 DO 10 J = 1, NEIG 254 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 255 $ 1 ) 256 10 CONTINUE 257* 258 ELSE IF( ITYPE.EQ.3 ) THEN 259* 260* For B*A*x=(lambda)*x; 261* backtransform eigenvectors: x = L*y or U**H *y 262* 263 IF( UPPER ) THEN 264 TRANS = 'C' 265 ELSE 266 TRANS = 'N' 267 END IF 268* 269 DO 20 J = 1, NEIG 270 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), 271 $ 1 ) 272 20 CONTINUE 273 END IF 274 END IF 275 RETURN 276* 277* End of ZHPGV 278* 279 END 280