LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
chpgvd.f
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00001 *> \brief \b CHPGST
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CHPGVD + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chpgvd.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chpgvd.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00022 *                          LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          JOBZ, UPLO
00026 *       INTEGER            INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       INTEGER            IWORK( * )
00030 *       REAL               RWORK( * ), W( * )
00031 *       COMPLEX            AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
00032 *       ..
00033 *  
00034 *
00035 *> \par Purpose:
00036 *  =============
00037 *>
00038 *> \verbatim
00039 *>
00040 *> CHPGVD computes all the eigenvalues and, optionally, the eigenvectors
00041 *> of a complex generalized Hermitian-definite eigenproblem, of the form
00042 *> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
00043 *> B are assumed to be Hermitian, stored in packed format, and B is also
00044 *> positive definite.
00045 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
00046 *>
00047 *> The divide and conquer algorithm makes very mild assumptions about
00048 *> floating point arithmetic. It will work on machines with a guard
00049 *> digit in add/subtract, or on those binary machines without guard
00050 *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00051 *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
00052 *> without guard digits, but we know of none.
00053 *> \endverbatim
00054 *
00055 *  Arguments:
00056 *  ==========
00057 *
00058 *> \param[in] ITYPE
00059 *> \verbatim
00060 *>          ITYPE is INTEGER
00061 *>          Specifies the problem type to be solved:
00062 *>          = 1:  A*x = (lambda)*B*x
00063 *>          = 2:  A*B*x = (lambda)*x
00064 *>          = 3:  B*A*x = (lambda)*x
00065 *> \endverbatim
00066 *>
00067 *> \param[in] JOBZ
00068 *> \verbatim
00069 *>          JOBZ is CHARACTER*1
00070 *>          = 'N':  Compute eigenvalues only;
00071 *>          = 'V':  Compute eigenvalues and eigenvectors.
00072 *> \endverbatim
00073 *>
00074 *> \param[in] UPLO
00075 *> \verbatim
00076 *>          UPLO is CHARACTER*1
00077 *>          = 'U':  Upper triangles of A and B are stored;
00078 *>          = 'L':  Lower triangles of A and B are stored.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] N
00082 *> \verbatim
00083 *>          N is INTEGER
00084 *>          The order of the matrices A and B.  N >= 0.
00085 *> \endverbatim
00086 *>
00087 *> \param[in,out] AP
00088 *> \verbatim
00089 *>          AP is COMPLEX array, dimension (N*(N+1)/2)
00090 *>          On entry, the upper or lower triangle of the Hermitian matrix
00091 *>          A, packed columnwise in a linear array.  The j-th column of A
00092 *>          is stored in the array AP as follows:
00093 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00094 *>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
00095 *>
00096 *>          On exit, the contents of AP are destroyed.
00097 *> \endverbatim
00098 *>
00099 *> \param[in,out] BP
00100 *> \verbatim
00101 *>          BP is COMPLEX array, dimension (N*(N+1)/2)
00102 *>          On entry, the upper or lower triangle of the Hermitian matrix
00103 *>          B, packed columnwise in a linear array.  The j-th column of B
00104 *>          is stored in the array BP as follows:
00105 *>          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
00106 *>          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
00107 *>
00108 *>          On exit, the triangular factor U or L from the Cholesky
00109 *>          factorization B = U**H*U or B = L*L**H, in the same storage
00110 *>          format as B.
00111 *> \endverbatim
00112 *>
00113 *> \param[out] W
00114 *> \verbatim
00115 *>          W is REAL array, dimension (N)
00116 *>          If INFO = 0, the eigenvalues in ascending order.
00117 *> \endverbatim
00118 *>
00119 *> \param[out] Z
00120 *> \verbatim
00121 *>          Z is COMPLEX array, dimension (LDZ, N)
00122 *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00123 *>          eigenvectors.  The eigenvectors are normalized as follows:
00124 *>          if ITYPE = 1 or 2, Z**H*B*Z = I;
00125 *>          if ITYPE = 3, Z**H*inv(B)*Z = I.
00126 *>          If JOBZ = 'N', then Z is not referenced.
00127 *> \endverbatim
00128 *>
00129 *> \param[in] LDZ
00130 *> \verbatim
00131 *>          LDZ is INTEGER
00132 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00133 *>          JOBZ = 'V', LDZ >= max(1,N).
00134 *> \endverbatim
00135 *>
00136 *> \param[out] WORK
00137 *> \verbatim
00138 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
00139 *>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
00140 *> \endverbatim
00141 *>
00142 *> \param[in] LWORK
00143 *> \verbatim
00144 *>          LWORK is INTEGER
00145 *>          The dimension of array WORK.
00146 *>          If N <= 1,               LWORK >= 1.
00147 *>          If JOBZ = 'N' and N > 1, LWORK >= N.
00148 *>          If JOBZ = 'V' and N > 1, LWORK >= 2*N.
00149 *>
00150 *>          If LWORK = -1, then a workspace query is assumed; the routine
00151 *>          only calculates the required sizes of the WORK, RWORK and
00152 *>          IWORK arrays, returns these values as the first entries of
00153 *>          the WORK, RWORK and IWORK arrays, and no error message
00154 *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00155 *> \endverbatim
00156 *>
00157 *> \param[out] RWORK
00158 *> \verbatim
00159 *>          RWORK is REAL array, dimension (MAX(1,LRWORK))
00160 *>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
00161 *> \endverbatim
00162 *>
00163 *> \param[in] LRWORK
00164 *> \verbatim
00165 *>          LRWORK is INTEGER
00166 *>          The dimension of array RWORK.
00167 *>          If N <= 1,               LRWORK >= 1.
00168 *>          If JOBZ = 'N' and N > 1, LRWORK >= N.
00169 *>          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
00170 *>
00171 *>          If LRWORK = -1, then a workspace query is assumed; the
00172 *>          routine only calculates the required sizes of the WORK, RWORK
00173 *>          and IWORK arrays, returns these values as the first entries
00174 *>          of the WORK, RWORK and IWORK arrays, and no error message
00175 *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00176 *> \endverbatim
00177 *>
00178 *> \param[out] IWORK
00179 *> \verbatim
00180 *>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
00181 *>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
00182 *> \endverbatim
00183 *>
00184 *> \param[in] LIWORK
00185 *> \verbatim
00186 *>          LIWORK is INTEGER
00187 *>          The dimension of array IWORK.
00188 *>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
00189 *>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
00190 *>
00191 *>          If LIWORK = -1, then a workspace query is assumed; the
00192 *>          routine only calculates the required sizes of the WORK, RWORK
00193 *>          and IWORK arrays, returns these values as the first entries
00194 *>          of the WORK, RWORK and IWORK arrays, and no error message
00195 *>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00196 *> \endverbatim
00197 *>
00198 *> \param[out] INFO
00199 *> \verbatim
00200 *>          INFO is INTEGER
00201 *>          = 0:  successful exit
00202 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00203 *>          > 0:  CPPTRF or CHPEVD returned an error code:
00204 *>             <= N:  if INFO = i, CHPEVD failed to converge;
00205 *>                    i off-diagonal elements of an intermediate
00206 *>                    tridiagonal form did not convergeto zero;
00207 *>             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
00208 *>                    minor of order i of B is not positive definite.
00209 *>                    The factorization of B could not be completed and
00210 *>                    no eigenvalues or eigenvectors were computed.
00211 *> \endverbatim
00212 *
00213 *  Authors:
00214 *  ========
00215 *
00216 *> \author Univ. of Tennessee 
00217 *> \author Univ. of California Berkeley 
00218 *> \author Univ. of Colorado Denver 
00219 *> \author NAG Ltd. 
00220 *
00221 *> \date November 2011
00222 *
00223 *> \ingroup complexOTHEReigen
00224 *
00225 *> \par Contributors:
00226 *  ==================
00227 *>
00228 *>     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
00229 *
00230 *  =====================================================================
00231       SUBROUTINE CHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00232      $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
00233 *
00234 *  -- LAPACK driver routine (version 3.4.0) --
00235 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00236 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00237 *     November 2011
00238 *
00239 *     .. Scalar Arguments ..
00240       CHARACTER          JOBZ, UPLO
00241       INTEGER            INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
00242 *     ..
00243 *     .. Array Arguments ..
00244       INTEGER            IWORK( * )
00245       REAL               RWORK( * ), W( * )
00246       COMPLEX            AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
00247 *     ..
00248 *
00249 *  =====================================================================
00250 *
00251 *     .. Local Scalars ..
00252       LOGICAL            LQUERY, UPPER, WANTZ
00253       CHARACTER          TRANS
00254       INTEGER            J, LIWMIN, LRWMIN, LWMIN, NEIG
00255 *     ..
00256 *     .. External Functions ..
00257       LOGICAL            LSAME
00258       EXTERNAL           LSAME
00259 *     ..
00260 *     .. External Subroutines ..
00261       EXTERNAL           CHPEVD, CHPGST, CPPTRF, CTPMV, CTPSV, XERBLA
00262 *     ..
00263 *     .. Intrinsic Functions ..
00264       INTRINSIC          MAX, REAL
00265 *     ..
00266 *     .. Executable Statements ..
00267 *
00268 *     Test the input parameters.
00269 *
00270       WANTZ = LSAME( JOBZ, 'V' )
00271       UPPER = LSAME( UPLO, 'U' )
00272       LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00273 *
00274       INFO = 0
00275       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00276          INFO = -1
00277       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00278          INFO = -2
00279       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00280          INFO = -3
00281       ELSE IF( N.LT.0 ) THEN
00282          INFO = -4
00283       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00284          INFO = -9
00285       END IF
00286 *
00287       IF( INFO.EQ.0 ) THEN
00288          IF( N.LE.1 ) THEN
00289             LWMIN = 1
00290             LIWMIN = 1
00291             LRWMIN = 1
00292          ELSE
00293             IF( WANTZ ) THEN
00294                LWMIN = 2*N
00295                LRWMIN = 1 + 5*N + 2*N**2
00296                LIWMIN = 3 + 5*N
00297             ELSE
00298                LWMIN = N
00299                LRWMIN = N
00300                LIWMIN = 1
00301             END IF
00302          END IF
00303 *
00304          WORK( 1 ) = LWMIN
00305          RWORK( 1 ) = LRWMIN
00306          IWORK( 1 ) = LIWMIN
00307          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00308             INFO = -11
00309          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
00310             INFO = -13
00311          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00312             INFO = -15
00313          END IF
00314       END IF
00315 *
00316       IF( INFO.NE.0 ) THEN
00317          CALL XERBLA( 'CHPGVD', -INFO )
00318          RETURN
00319       ELSE IF( LQUERY ) THEN
00320          RETURN
00321       END IF
00322 *
00323 *     Quick return if possible
00324 *
00325       IF( N.EQ.0 )
00326      $   RETURN
00327 *
00328 *     Form a Cholesky factorization of B.
00329 *
00330       CALL CPPTRF( UPLO, N, BP, INFO )
00331       IF( INFO.NE.0 ) THEN
00332          INFO = N + INFO
00333          RETURN
00334       END IF
00335 *
00336 *     Transform problem to standard eigenvalue problem and solve.
00337 *
00338       CALL CHPGST( ITYPE, UPLO, N, AP, BP, INFO )
00339       CALL CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
00340      $             LRWORK, IWORK, LIWORK, INFO )
00341       LWMIN = MAX( REAL( LWMIN ), REAL( WORK( 1 ) ) )
00342       LRWMIN = MAX( REAL( LRWMIN ), REAL( RWORK( 1 ) ) )
00343       LIWMIN = MAX( REAL( LIWMIN ), REAL( IWORK( 1 ) ) )
00344 *
00345       IF( WANTZ ) THEN
00346 *
00347 *        Backtransform eigenvectors to the original problem.
00348 *
00349          NEIG = N
00350          IF( INFO.GT.0 )
00351      $      NEIG = INFO - 1
00352          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00353 *
00354 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00355 *           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
00356 *
00357             IF( UPPER ) THEN
00358                TRANS = 'N'
00359             ELSE
00360                TRANS = 'C'
00361             END IF
00362 *
00363             DO 10 J = 1, NEIG
00364                CALL CTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00365      $                     1 )
00366    10       CONTINUE
00367 *
00368          ELSE IF( ITYPE.EQ.3 ) THEN
00369 *
00370 *           For B*A*x=(lambda)*x;
00371 *           backtransform eigenvectors: x = L*y or U**H *y
00372 *
00373             IF( UPPER ) THEN
00374                TRANS = 'C'
00375             ELSE
00376                TRANS = 'N'
00377             END IF
00378 *
00379             DO 20 J = 1, NEIG
00380                CALL CTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00381      $                     1 )
00382    20       CONTINUE
00383          END IF
00384       END IF
00385 *
00386       WORK( 1 ) = LWMIN
00387       RWORK( 1 ) = LRWMIN
00388       IWORK( 1 ) = LIWMIN
00389       RETURN
00390 *
00391 *     End of CHPGVD
00392 *
00393       END
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