LAPACK 3.3.0

zhbevd.f

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00001       SUBROUTINE ZHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
00002      $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
00003 *
00004 *  -- LAPACK driver routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          JOBZ, UPLO
00011       INTEGER            INFO, KD, LDAB, LDZ, LIWORK, LRWORK, LWORK, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            IWORK( * )
00015       DOUBLE PRECISION   RWORK( * ), W( * )
00016       COMPLEX*16         AB( LDAB, * ), WORK( * ), Z( LDZ, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
00023 *  a complex Hermitian band matrix A.  If eigenvectors are desired, it
00024 *  uses a divide and conquer algorithm.
00025 *
00026 *  The divide and conquer algorithm makes very mild assumptions about
00027 *  floating point arithmetic. It will work on machines with a guard
00028 *  digit in add/subtract, or on those binary machines without guard
00029 *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
00030 *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
00031 *  without guard digits, but we know of none.
00032 *
00033 *  Arguments
00034 *  =========
00035 *
00036 *  JOBZ    (input) CHARACTER*1
00037 *          = 'N':  Compute eigenvalues only;
00038 *          = 'V':  Compute eigenvalues and eigenvectors.
00039 *
00040 *  UPLO    (input) CHARACTER*1
00041 *          = 'U':  Upper triangle of A is stored;
00042 *          = 'L':  Lower triangle of A is stored.
00043 *
00044 *  N       (input) INTEGER
00045 *          The order of the matrix A.  N >= 0.
00046 *
00047 *  KD      (input) INTEGER
00048 *          The number of superdiagonals of the matrix A if UPLO = 'U',
00049 *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
00050 *
00051 *  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)
00052 *          On entry, the upper or lower triangle of the Hermitian band
00053 *          matrix A, stored in the first KD+1 rows of the array.  The
00054 *          j-th column of A is stored in the j-th column of the array AB
00055 *          as follows:
00056 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00057 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00058 *
00059 *          On exit, AB is overwritten by values generated during the
00060 *          reduction to tridiagonal form.  If UPLO = 'U', the first
00061 *          superdiagonal and the diagonal of the tridiagonal matrix T
00062 *          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
00063 *          the diagonal and first subdiagonal of T are returned in the
00064 *          first two rows of AB.
00065 *
00066 *  LDAB    (input) INTEGER
00067 *          The leading dimension of the array AB.  LDAB >= KD + 1.
00068 *
00069 *  W       (output) DOUBLE PRECISION array, dimension (N)
00070 *          If INFO = 0, the eigenvalues in ascending order.
00071 *
00072 *  Z       (output) COMPLEX*16 array, dimension (LDZ, N)
00073 *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
00074 *          eigenvectors of the matrix A, with the i-th column of Z
00075 *          holding the eigenvector associated with W(i).
00076 *          If JOBZ = 'N', then Z is not referenced.
00077 *
00078 *  LDZ     (input) INTEGER
00079 *          The leading dimension of the array Z.  LDZ >= 1, and if
00080 *          JOBZ = 'V', LDZ >= max(1,N).
00081 *
00082 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
00083 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00084 *
00085 *  LWORK   (input) INTEGER
00086 *          The dimension of the array WORK.
00087 *          If N <= 1,               LWORK must be at least 1.
00088 *          If JOBZ = 'N' and N > 1, LWORK must be at least N.
00089 *          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
00090 *
00091 *          If LWORK = -1, then a workspace query is assumed; the routine
00092 *          only calculates the optimal sizes of the WORK, RWORK and
00093 *          IWORK arrays, returns these values as the first entries of
00094 *          the WORK, RWORK and IWORK arrays, and no error message
00095 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00096 *
00097 *  RWORK   (workspace/output) DOUBLE PRECISION array,
00098 *                                         dimension (LRWORK)
00099 *          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
00100 *
00101 *  LRWORK  (input) INTEGER
00102 *          The dimension of array RWORK.
00103 *          If N <= 1,               LRWORK must be at least 1.
00104 *          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
00105 *          If JOBZ = 'V' and N > 1, LRWORK must be at least
00106 *                        1 + 5*N + 2*N**2.
00107 *
00108 *          If LRWORK = -1, then a workspace query is assumed; the
00109 *          routine only calculates the optimal sizes of the WORK, RWORK
00110 *          and IWORK arrays, returns these values as the first entries
00111 *          of the WORK, RWORK and IWORK arrays, and no error message
00112 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00113 *
00114 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
00115 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
00116 *
00117 *  LIWORK  (input) INTEGER
00118 *          The dimension of array IWORK.
00119 *          If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
00120 *          If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .
00121 *
00122 *          If LIWORK = -1, then a workspace query is assumed; the
00123 *          routine only calculates the optimal sizes of the WORK, RWORK
00124 *          and IWORK arrays, returns these values as the first entries
00125 *          of the WORK, RWORK and IWORK arrays, and no error message
00126 *          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
00127 *
00128 *  INFO    (output) INTEGER
00129 *          = 0:  successful exit.
00130 *          < 0:  if INFO = -i, the i-th argument had an illegal value.
00131 *          > 0:  if INFO = i, the algorithm failed to converge; i
00132 *                off-diagonal elements of an intermediate tridiagonal
00133 *                form did not converge to zero.
00134 *
00135 *  =====================================================================
00136 *
00137 *     .. Parameters ..
00138       DOUBLE PRECISION   ZERO, ONE
00139       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
00140       COMPLEX*16         CZERO, CONE
00141       PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
00142      $                   CONE = ( 1.0D0, 0.0D0 ) )
00143 *     ..
00144 *     .. Local Scalars ..
00145       LOGICAL            LOWER, LQUERY, WANTZ
00146       INTEGER            IINFO, IMAX, INDE, INDWK2, INDWRK, ISCALE,
00147      $                   LIWMIN, LLRWK, LLWK2, LRWMIN, LWMIN
00148       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
00149      $                   SMLNUM
00150 *     ..
00151 *     .. External Functions ..
00152       LOGICAL            LSAME
00153       DOUBLE PRECISION   DLAMCH, ZLANHB
00154       EXTERNAL           LSAME, DLAMCH, ZLANHB
00155 *     ..
00156 *     .. External Subroutines ..
00157       EXTERNAL           DSCAL, DSTERF, XERBLA, ZGEMM, ZHBTRD, ZLACPY,
00158      $                   ZLASCL, ZSTEDC
00159 *     ..
00160 *     .. Intrinsic Functions ..
00161       INTRINSIC          SQRT
00162 *     ..
00163 *     .. Executable Statements ..
00164 *
00165 *     Test the input parameters.
00166 *
00167       WANTZ = LSAME( JOBZ, 'V' )
00168       LOWER = LSAME( UPLO, 'L' )
00169       LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 .OR. LRWORK.EQ.-1 )
00170 *
00171       INFO = 0
00172       IF( N.LE.1 ) THEN
00173          LWMIN = 1
00174          LRWMIN = 1
00175          LIWMIN = 1
00176       ELSE
00177          IF( WANTZ ) THEN
00178             LWMIN = 2*N**2
00179             LRWMIN = 1 + 5*N + 2*N**2
00180             LIWMIN = 3 + 5*N
00181          ELSE
00182             LWMIN = N
00183             LRWMIN = N
00184             LIWMIN = 1
00185          END IF
00186       END IF
00187       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00188          INFO = -1
00189       ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
00190          INFO = -2
00191       ELSE IF( N.LT.0 ) THEN
00192          INFO = -3
00193       ELSE IF( KD.LT.0 ) THEN
00194          INFO = -4
00195       ELSE IF( LDAB.LT.KD+1 ) THEN
00196          INFO = -6
00197       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00198          INFO = -9
00199       END IF
00200 *
00201       IF( INFO.EQ.0 ) THEN
00202          WORK( 1 ) = LWMIN
00203          RWORK( 1 ) = LRWMIN
00204          IWORK( 1 ) = LIWMIN
00205 *
00206          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
00207             INFO = -11
00208          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
00209             INFO = -13
00210          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
00211             INFO = -15
00212          END IF
00213       END IF
00214 *
00215       IF( INFO.NE.0 ) THEN
00216          CALL XERBLA( 'ZHBEVD', -INFO )
00217          RETURN
00218       ELSE IF( LQUERY ) THEN
00219          RETURN
00220       END IF
00221 *
00222 *     Quick return if possible
00223 *
00224       IF( N.EQ.0 )
00225      $   RETURN
00226 *
00227       IF( N.EQ.1 ) THEN
00228          W( 1 ) = AB( 1, 1 )
00229          IF( WANTZ )
00230      $      Z( 1, 1 ) = CONE
00231          RETURN
00232       END IF
00233 *
00234 *     Get machine constants.
00235 *
00236       SAFMIN = DLAMCH( 'Safe minimum' )
00237       EPS = DLAMCH( 'Precision' )
00238       SMLNUM = SAFMIN / EPS
00239       BIGNUM = ONE / SMLNUM
00240       RMIN = SQRT( SMLNUM )
00241       RMAX = SQRT( BIGNUM )
00242 *
00243 *     Scale matrix to allowable range, if necessary.
00244 *
00245       ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
00246       ISCALE = 0
00247       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
00248          ISCALE = 1
00249          SIGMA = RMIN / ANRM
00250       ELSE IF( ANRM.GT.RMAX ) THEN
00251          ISCALE = 1
00252          SIGMA = RMAX / ANRM
00253       END IF
00254       IF( ISCALE.EQ.1 ) THEN
00255          IF( LOWER ) THEN
00256             CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
00257          ELSE
00258             CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
00259          END IF
00260       END IF
00261 *
00262 *     Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
00263 *
00264       INDE = 1
00265       INDWRK = INDE + N
00266       INDWK2 = 1 + N*N
00267       LLWK2 = LWORK - INDWK2 + 1
00268       LLRWK = LRWORK - INDWRK + 1
00269       CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
00270      $             LDZ, WORK, IINFO )
00271 *
00272 *     For eigenvalues only, call DSTERF.  For eigenvectors, call ZSTEDC.
00273 *
00274       IF( .NOT.WANTZ ) THEN
00275          CALL DSTERF( N, W, RWORK( INDE ), INFO )
00276       ELSE
00277          CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
00278      $                LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
00279      $                INFO )
00280          CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
00281      $               WORK( INDWK2 ), N )
00282          CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
00283       END IF
00284 *
00285 *     If matrix was scaled, then rescale eigenvalues appropriately.
00286 *
00287       IF( ISCALE.EQ.1 ) THEN
00288          IF( INFO.EQ.0 ) THEN
00289             IMAX = N
00290          ELSE
00291             IMAX = INFO - 1
00292          END IF
00293          CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
00294       END IF
00295 *
00296       WORK( 1 ) = LWMIN
00297       RWORK( 1 ) = LRWMIN
00298       IWORK( 1 ) = LIWMIN
00299       RETURN
00300 *
00301 *     End of ZHBEVD
00302 *
00303       END
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