LAPACK 3.3.1 Linear Algebra PACKage

# zhpgvd.f

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```00001       SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
00002      \$                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
00003 *
00004 *  -- LAPACK driver routine (version 3.3.1) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *  -- April 2011                                                      --
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          JOBZ, UPLO
00011       INTEGER            INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            IWORK( * )
00015       DOUBLE PRECISION   RWORK( * ), W( * )
00016       COMPLEX*16         AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
00023 *  of a complex generalized Hermitian-definite eigenproblem, of the form
00024 *  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
00025 *  B are assumed to be Hermitian, stored in packed format, and B is also
00026 *  positive definite.
00027 *  If eigenvectors are desired, it uses a divide and conquer algorithm.
00028 *
00029 *  The divide and conquer algorithm makes very mild assumptions about
00030 *  floating point arithmetic. It will work on machines with a guard
00031 *  digit in add/subtract, or on those binary machines without guard
00032 *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00033 *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
00034 *  without guard digits, but we know of none.
00035 *
00036 *  Arguments
00037 *  =========
00038 *
00039 *  ITYPE   (input) INTEGER
00040 *          Specifies the problem type to be solved:
00041 *          = 1:  A*x = (lambda)*B*x
00042 *          = 2:  A*B*x = (lambda)*x
00043 *          = 3:  B*A*x = (lambda)*x
00044 *
00045 *  JOBZ    (input) CHARACTER*1
00046 *          = 'N':  Compute eigenvalues only;
00047 *          = 'V':  Compute eigenvalues and eigenvectors.
00048 *
00049 *  UPLO    (input) CHARACTER*1
00050 *          = 'U':  Upper triangles of A and B are stored;
00051 *          = 'L':  Lower triangles of A and B are stored.
00052 *
00053 *  N       (input) INTEGER
00054 *          The order of the matrices A and B.  N >= 0.
00055 *
00056 *  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
00057 *          On entry, the upper or lower triangle of the Hermitian matrix
00058 *          A, packed columnwise in a linear array.  The j-th column of A
00059 *          is stored in the array AP as follows:
00060 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00061 *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
00062 *
00063 *          On exit, the contents of AP are destroyed.
00064 *
00065 *  BP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
00066 *          On entry, the upper or lower triangle of the Hermitian matrix
00067 *          B, packed columnwise in a linear array.  The j-th column of B
00068 *          is stored in the array BP as follows:
00069 *          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
00070 *          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
00071 *
00072 *          On exit, the triangular factor U or L from the Cholesky
00073 *          factorization B = U**H*U or B = L*L**H, in the same storage
00074 *          format as B.
00075 *
00076 *  W       (output) DOUBLE PRECISION array, dimension (N)
00077 *          If INFO = 0, the eigenvalues in ascending order.
00078 *
00079 *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
00080 *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00081 *          eigenvectors.  The eigenvectors are normalized as follows:
00082 *          if ITYPE = 1 or 2, Z**H*B*Z = I;
00083 *          if ITYPE = 3, Z**H*inv(B)*Z = I.
00084 *          If JOBZ = 'N', then Z is not referenced.
00085 *
00086 *  LDZ     (input) INTEGER
00087 *          The leading dimension of the array Z.  LDZ >= 1, and if
00088 *          JOBZ = 'V', LDZ >= max(1,N).
00089 *
00090 *  WORK    (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
00091 *          On exit, if INFO = 0, WORK(1) returns the required LWORK.
00092 *
00093 *  LWORK   (input) INTEGER
00094 *          The dimension of the array WORK.
00095 *          If N <= 1,               LWORK >= 1.
00096 *          If JOBZ = 'N' and N > 1, LWORK >= N.
00097 *          If JOBZ = 'V' and N > 1, LWORK >= 2*N.
00098 *
00099 *          If LWORK = -1, then a workspace query is assumed; the routine
00100 *          only calculates the required sizes of the WORK, RWORK and
00101 *          IWORK arrays, returns these values as the first entries of
00102 *          the WORK, RWORK and IWORK arrays, and no error message
00103 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00104 *
00105 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
00106 *          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
00107 *
00108 *  LRWORK  (input) INTEGER
00109 *          The dimension of array RWORK.
00110 *          If N <= 1,               LRWORK >= 1.
00111 *          If JOBZ = 'N' and N > 1, LRWORK >= N.
00112 *          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
00113 *
00114 *          If LRWORK = -1, then a workspace query is assumed; the
00115 *          routine only calculates the required sizes of the WORK, RWORK
00116 *          and IWORK arrays, returns these values as the first entries
00117 *          of the WORK, RWORK and IWORK arrays, and no error message
00118 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00119 *
00120 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
00121 *          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
00122 *
00123 *  LIWORK  (input) INTEGER
00124 *          The dimension of array IWORK.
00125 *          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
00126 *          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
00127 *
00128 *          If LIWORK = -1, then a workspace query is assumed; the
00129 *          routine only calculates the required sizes of the WORK, RWORK
00130 *          and IWORK arrays, returns these values as the first entries
00131 *          of the WORK, RWORK and IWORK arrays, and no error message
00132 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00133 *
00134 *  INFO    (output) INTEGER
00135 *          = 0:  successful exit
00136 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00137 *          > 0:  ZPPTRF or ZHPEVD returned an error code:
00138 *             <= N:  if INFO = i, ZHPEVD failed to converge;
00139 *                    i off-diagonal elements of an intermediate
00140 *                    tridiagonal form did not convergeto zero;
00141 *             > N:   if INFO = N + i, for 1 <= i <= n, then the leading
00142 *                    minor of order i of B is not positive definite.
00143 *                    The factorization of B could not be completed and
00144 *                    no eigenvalues or eigenvectors were computed.
00145 *
00146 *  Further Details
00147 *  ===============
00148 *
00149 *  Based on contributions by
00150 *     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
00151 *
00152 *  =====================================================================
00153 *
00154 *     .. Local Scalars ..
00155       LOGICAL            LQUERY, UPPER, WANTZ
00156       CHARACTER          TRANS
00157       INTEGER            J, LIWMIN, LRWMIN, LWMIN, NEIG
00158 *     ..
00159 *     .. External Functions ..
00160       LOGICAL            LSAME
00161       EXTERNAL           LSAME
00162 *     ..
00163 *     .. External Subroutines ..
00164       EXTERNAL           XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
00165 *     ..
00166 *     .. Intrinsic Functions ..
00167       INTRINSIC          DBLE, MAX
00168 *     ..
00169 *     .. Executable Statements ..
00170 *
00171 *     Test the input parameters.
00172 *
00173       WANTZ = LSAME( JOBZ, 'V' )
00174       UPPER = LSAME( UPLO, 'U' )
00175       LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00176 *
00177       INFO = 0
00178       IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
00179          INFO = -1
00180       ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00181          INFO = -2
00182       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00183          INFO = -3
00184       ELSE IF( N.LT.0 ) THEN
00185          INFO = -4
00186       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00187          INFO = -9
00188       END IF
00189 *
00190       IF( INFO.EQ.0 ) THEN
00191          IF( N.LE.1 ) THEN
00192             LWMIN = 1
00193             LIWMIN = 1
00194             LRWMIN = 1
00195          ELSE
00196             IF( WANTZ ) THEN
00197                LWMIN = 2*N
00198                LRWMIN = 1 + 5*N + 2*N**2
00199                LIWMIN = 3 + 5*N
00200             ELSE
00201                LWMIN = N
00202                LRWMIN = N
00203                LIWMIN = 1
00204             END IF
00205          END IF
00206 *
00207          WORK( 1 ) = LWMIN
00208          RWORK( 1 ) = LRWMIN
00209          IWORK( 1 ) = LIWMIN
00210          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00211             INFO = -11
00212          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
00213             INFO = -13
00214          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00215             INFO = -15
00216          END IF
00217       END IF
00218 *
00219       IF( INFO.NE.0 ) THEN
00220          CALL XERBLA( 'ZHPGVD', -INFO )
00221          RETURN
00222       ELSE IF( LQUERY ) THEN
00223          RETURN
00224       END IF
00225 *
00226 *     Quick return if possible
00227 *
00228       IF( N.EQ.0 )
00229      \$   RETURN
00230 *
00231 *     Form a Cholesky factorization of B.
00232 *
00233       CALL ZPPTRF( UPLO, N, BP, INFO )
00234       IF( INFO.NE.0 ) THEN
00235          INFO = N + INFO
00236          RETURN
00237       END IF
00238 *
00239 *     Transform problem to standard eigenvalue problem and solve.
00240 *
00241       CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
00242       CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
00243      \$             LRWORK, IWORK, LIWORK, INFO )
00244       LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
00245       LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) )
00246       LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
00247 *
00248       IF( WANTZ ) THEN
00249 *
00250 *        Backtransform eigenvectors to the original problem.
00251 *
00252          NEIG = N
00253          IF( INFO.GT.0 )
00254      \$      NEIG = INFO - 1
00255          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
00256 *
00257 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
00258 *           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
00259 *
00260             IF( UPPER ) THEN
00261                TRANS = 'N'
00262             ELSE
00263                TRANS = 'C'
00264             END IF
00265 *
00266             DO 10 J = 1, NEIG
00267                CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00268      \$                     1 )
00269    10       CONTINUE
00270 *
00271          ELSE IF( ITYPE.EQ.3 ) THEN
00272 *
00273 *           For B*A*x=(lambda)*x;
00274 *           backtransform eigenvectors: x = L*y or U**H *y
00275 *
00276             IF( UPPER ) THEN
00277                TRANS = 'C'
00278             ELSE
00279                TRANS = 'N'
00280             END IF
00281 *
00282             DO 20 J = 1, NEIG
00283                CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
00284      \$                     1 )
00285    20       CONTINUE
00286          END IF
00287       END IF
00288 *
00289       WORK( 1 ) = LWMIN
00290       RWORK( 1 ) = LRWMIN
00291       IWORK( 1 ) = LIWMIN
00292       RETURN
00293 *
00294 *     End of ZHPGVD
00295 *
00296       END
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