LAPACK 3.3.0

chbgvd.f

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00001       SUBROUTINE CHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
00002      $                   Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
00003      $                   LIWORK, INFO )
00004 *
00005 *  -- LAPACK driver routine (version 3.2) --
00006 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00007 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00008 *     November 2006
00009 *
00010 *     .. Scalar Arguments ..
00011       CHARACTER          JOBZ, UPLO
00012       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
00013      $                   LWORK, N
00014 *     ..
00015 *     .. Array Arguments ..
00016       INTEGER            IWORK( * )
00017       REAL               RWORK( * ), W( * )
00018       COMPLEX            AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
00019      $                   Z( LDZ, * )
00020 *     ..
00021 *
00022 *  Purpose
00023 *  =======
00024 *
00025 *  CHBGVD computes all the eigenvalues, and optionally, the eigenvectors
00026 *  of a complex generalized Hermitian-definite banded eigenproblem, of
00027 *  the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
00028 *  and banded, and B is also positive definite.  If eigenvectors are
00029 *  desired, it uses a divide and conquer algorithm.
00030 *
00031 *  The divide and conquer algorithm makes very mild assumptions about
00032 *  floating point arithmetic. It will work on machines with a guard
00033 *  digit in add/subtract, or on those binary machines without guard
00034 *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00035 *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
00036 *  without guard digits, but we know of none.
00037 *
00038 *  Arguments
00039 *  =========
00040 *
00041 *  JOBZ    (input) CHARACTER*1
00042 *          = 'N':  Compute eigenvalues only;
00043 *          = 'V':  Compute eigenvalues and eigenvectors.
00044 *
00045 *  UPLO    (input) CHARACTER*1
00046 *          = 'U':  Upper triangles of A and B are stored;
00047 *          = 'L':  Lower triangles of A and B are stored.
00048 *
00049 *  N       (input) INTEGER
00050 *          The order of the matrices A and B.  N >= 0.
00051 *
00052 *  KA      (input) INTEGER
00053 *          The number of superdiagonals of the matrix A if UPLO = 'U',
00054 *          or the number of subdiagonals if UPLO = 'L'. KA >= 0.
00055 *
00056 *  KB      (input) INTEGER
00057 *          The number of superdiagonals of the matrix B if UPLO = 'U',
00058 *          or the number of subdiagonals if UPLO = 'L'. KB >= 0.
00059 *
00060 *  AB      (input/output) COMPLEX array, dimension (LDAB, N)
00061 *          On entry, the upper or lower triangle of the Hermitian band
00062 *          matrix A, stored in the first ka+1 rows of the array.  The
00063 *          j-th column of A is stored in the j-th column of the array AB
00064 *          as follows:
00065 *          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
00066 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
00067 *
00068 *          On exit, the contents of AB are destroyed.
00069 *
00070 *  LDAB    (input) INTEGER
00071 *          The leading dimension of the array AB.  LDAB >= KA+1.
00072 *
00073 *  BB      (input/output) COMPLEX array, dimension (LDBB, N)
00074 *          On entry, the upper or lower triangle of the Hermitian band
00075 *          matrix B, stored in the first kb+1 rows of the array.  The
00076 *          j-th column of B is stored in the j-th column of the array BB
00077 *          as follows:
00078 *          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
00079 *          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
00080 *
00081 *          On exit, the factor S from the split Cholesky factorization
00082 *          B = S**H*S, as returned by CPBSTF.
00083 *
00084 *  LDBB    (input) INTEGER
00085 *          The leading dimension of the array BB.  LDBB >= KB+1.
00086 *
00087 *  W       (output) REAL array, dimension (N)
00088 *          If INFO = 0, the eigenvalues in ascending order.
00089 *
00090 *  Z       (output) COMPLEX array, dimension (LDZ, N)
00091 *          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00092 *          eigenvectors, with the i-th column of Z holding the
00093 *          eigenvector associated with W(i). The eigenvectors are
00094 *          normalized so that Z**H*B*Z = I.
00095 *          If JOBZ = 'N', then Z is not referenced.
00096 *
00097 *  LDZ     (input) INTEGER
00098 *          The leading dimension of the array Z.  LDZ >= 1, and if
00099 *          JOBZ = 'V', LDZ >= N.
00100 *
00101 *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
00102 *          On exit, if INFO=0, WORK(1) returns the optimal LWORK.
00103 *
00104 *  LWORK   (input) INTEGER
00105 *          The dimension of the array WORK.
00106 *          If N <= 1,               LWORK >= 1.
00107 *          If JOBZ = 'N' and N > 1, LWORK >= N.
00108 *          If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
00109 *
00110 *          If LWORK = -1, then a workspace query is assumed; the routine
00111 *          only calculates the optimal sizes of the WORK, RWORK and
00112 *          IWORK arrays, returns these values as the first entries of
00113 *          the WORK, RWORK and IWORK arrays, and no error message
00114 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00115 *
00116 *  RWORK   (workspace/output) REAL array, dimension (MAX(1,LRWORK))
00117 *          On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
00118 *
00119 *  LRWORK  (input) INTEGER
00120 *          The dimension of array RWORK.
00121 *          If N <= 1,               LRWORK >= 1.
00122 *          If JOBZ = 'N' and N > 1, LRWORK >= N.
00123 *          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
00124 *
00125 *          If LRWORK = -1, then a workspace query is assumed; the
00126 *          routine only calculates the optimal sizes of the WORK, RWORK
00127 *          and IWORK arrays, returns these values as the first entries
00128 *          of the WORK, RWORK and IWORK arrays, and no error message
00129 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00130 *
00131 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
00132 *          On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
00133 *
00134 *  LIWORK  (input) INTEGER
00135 *          The dimension of array IWORK.
00136 *          If JOBZ = 'N' or N <= 1, LIWORK >= 1.
00137 *          If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
00138 *
00139 *          If LIWORK = -1, then a workspace query is assumed; the
00140 *          routine only calculates the optimal sizes of the WORK, RWORK
00141 *          and IWORK arrays, returns these values as the first entries
00142 *          of the WORK, RWORK and IWORK arrays, and no error message
00143 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00144 *
00145 *  INFO    (output) INTEGER
00146 *          = 0:  successful exit
00147 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00148 *          > 0:  if INFO = i, and i is:
00149 *             <= N:  the algorithm failed to converge:
00150 *                    i off-diagonal elements of an intermediate
00151 *                    tridiagonal form did not converge to zero;
00152 *             > N:   if INFO = N + i, for 1 <= i <= N, then CPBSTF
00153 *                    returned INFO = i: B is not positive definite.
00154 *                    The factorization of B could not be completed and
00155 *                    no eigenvalues or eigenvectors were computed.
00156 *
00157 *  Further Details
00158 *  ===============
00159 *
00160 *  Based on contributions by
00161 *     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
00162 *
00163 *  =====================================================================
00164 *
00165 *     .. Parameters ..
00166       COMPLEX            CONE, CZERO
00167       PARAMETER          ( CONE = ( 1.0E+0, 0.0E+0 ),
00168      $                   CZERO = ( 0.0E+0, 0.0E+0 ) )
00169 *     ..
00170 *     .. Local Scalars ..
00171       LOGICAL            LQUERY, UPPER, WANTZ
00172       CHARACTER          VECT
00173       INTEGER            IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
00174      $                   LLWK2, LRWMIN, LWMIN
00175 *     ..
00176 *     .. External Functions ..
00177       LOGICAL            LSAME
00178       EXTERNAL           LSAME
00179 *     ..
00180 *     .. External Subroutines ..
00181       EXTERNAL           CGEMM, CHBGST, CHBTRD, CLACPY, CPBSTF, CSTEDC,
00182      $                   SSTERF, XERBLA
00183 *     ..
00184 *     .. Executable Statements ..
00185 *
00186 *     Test the input parameters.
00187 *
00188       WANTZ = LSAME( JOBZ, 'V' )
00189       UPPER = LSAME( UPLO, 'U' )
00190       LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
00191 *
00192       INFO = 0
00193       IF( N.LE.1 ) THEN
00194          LWMIN = 1
00195          LRWMIN = 1
00196          LIWMIN = 1
00197       ELSE IF( WANTZ ) THEN
00198          LWMIN = 2*N**2
00199          LRWMIN = 1 + 5*N + 2*N**2
00200          LIWMIN = 3 + 5*N
00201       ELSE
00202          LWMIN = N
00203          LRWMIN = N
00204          LIWMIN = 1
00205       END IF
00206       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00207          INFO = -1
00208       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00209          INFO = -2
00210       ELSE IF( N.LT.0 ) THEN
00211          INFO = -3
00212       ELSE IF( KA.LT.0 ) THEN
00213          INFO = -4
00214       ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
00215          INFO = -5
00216       ELSE IF( LDAB.LT.KA+1 ) THEN
00217          INFO = -7
00218       ELSE IF( LDBB.LT.KB+1 ) THEN
00219          INFO = -9
00220       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00221          INFO = -12
00222       END IF
00223 *
00224       IF( INFO.EQ.0 ) THEN
00225          WORK( 1 ) = LWMIN
00226          RWORK( 1 ) = LRWMIN
00227          IWORK( 1 ) = LIWMIN
00228 *
00229          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00230             INFO = -14
00231          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
00232             INFO = -16
00233          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00234             INFO = -18
00235          END IF
00236       END IF
00237 *
00238       IF( INFO.NE.0 ) THEN
00239          CALL XERBLA( 'CHBGVD', -INFO )
00240          RETURN
00241       ELSE IF( LQUERY ) THEN
00242          RETURN
00243       END IF
00244 *
00245 *     Quick return if possible
00246 *
00247       IF( N.EQ.0 )
00248      $   RETURN
00249 *
00250 *     Form a split Cholesky factorization of B.
00251 *
00252       CALL CPBSTF( UPLO, N, KB, BB, LDBB, INFO )
00253       IF( INFO.NE.0 ) THEN
00254          INFO = N + INFO
00255          RETURN
00256       END IF
00257 *
00258 *     Transform problem to standard eigenvalue problem.
00259 *
00260       INDE = 1
00261       INDWRK = INDE + N
00262       INDWK2 = 1 + N*N
00263       LLWK2 = LWORK - INDWK2 + 2
00264       LLRWK = LRWORK - INDWRK + 2
00265       CALL CHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
00266      $             WORK, RWORK( INDWRK ), IINFO )
00267 *
00268 *     Reduce Hermitian band matrix to tridiagonal form.
00269 *
00270       IF( WANTZ ) THEN
00271          VECT = 'U'
00272       ELSE
00273          VECT = 'N'
00274       END IF
00275       CALL CHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
00276      $             LDZ, WORK, IINFO )
00277 *
00278 *     For eigenvalues only, call SSTERF.  For eigenvectors, call CSTEDC.
00279 *
00280       IF( .NOT.WANTZ ) THEN
00281          CALL SSTERF( N, W, RWORK( INDE ), INFO )
00282       ELSE
00283          CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
00284      $                LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
00285      $                INFO )
00286          CALL CGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
00287      $               WORK( INDWK2 ), N )
00288          CALL CLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
00289       END IF
00290 *
00291       WORK( 1 ) = LWMIN
00292       RWORK( 1 ) = LRWMIN
00293       IWORK( 1 ) = LIWMIN
00294       RETURN
00295 *
00296 *     End of CHBGVD
00297 *
00298       END
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