File:  [local] / rpl / lapack / lapack / dspevd.f
Revision 1.2: download - view: text, annotated - select for diffs - revision graph
Wed Apr 21 13:45:24 2010 UTC (14 years ago) by bertrand
Branches: MAIN
CVS tags: rpl-4_0_17, rpl-4_0_16, rpl-4_0_15, HEAD
En route pour la 4.0.15 !

    1:       SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
    2:      $                   IWORK, LIWORK, INFO )
    3: *
    4: *  -- LAPACK driver routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          JOBZ, UPLO
   11:       INTEGER            INFO, LDZ, LIWORK, LWORK, N
   12: *     ..
   13: *     .. Array Arguments ..
   14:       INTEGER            IWORK( * )
   15:       DOUBLE PRECISION   AP( * ), W( * ), WORK( * ), Z( LDZ, * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  DSPEVD computes all the eigenvalues and, optionally, eigenvectors
   22: *  of a real symmetric matrix A in packed storage. If eigenvectors are
   23: *  desired, it uses a divide and conquer algorithm.
   24: *
   25: *  The divide and conquer algorithm makes very mild assumptions about
   26: *  floating point arithmetic. It will work on machines with a guard
   27: *  digit in add/subtract, or on those binary machines without guard
   28: *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
   29: *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
   30: *  without guard digits, but we know of none.
   31: *
   32: *  Arguments
   33: *  =========
   34: *
   35: *  JOBZ    (input) CHARACTER*1
   36: *          = 'N':  Compute eigenvalues only;
   37: *          = 'V':  Compute eigenvalues and eigenvectors.
   38: *
   39: *  UPLO    (input) CHARACTER*1
   40: *          = 'U':  Upper triangle of A is stored;
   41: *          = 'L':  Lower triangle of A is stored.
   42: *
   43: *  N       (input) INTEGER
   44: *          The order of the matrix A.  N >= 0.
   45: *
   46: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   47: *          On entry, the upper or lower triangle of the symmetric matrix
   48: *          A, packed columnwise in a linear array.  The j-th column of A
   49: *          is stored in the array AP as follows:
   50: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   51: *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
   52: *
   53: *          On exit, AP is overwritten by values generated during the
   54: *          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
   55: *          and first superdiagonal of the tridiagonal matrix T overwrite
   56: *          the corresponding elements of A, and if UPLO = 'L', the
   57: *          diagonal and first subdiagonal of T overwrite the
   58: *          corresponding elements of A.
   59: *
   60: *  W       (output) DOUBLE PRECISION array, dimension (N)
   61: *          If INFO = 0, the eigenvalues in ascending order.
   62: *
   63: *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
   64: *          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
   65: *          eigenvectors of the matrix A, with the i-th column of Z
   66: *          holding the eigenvector associated with W(i).
   67: *          If JOBZ = 'N', then Z is not referenced.
   68: *
   69: *  LDZ     (input) INTEGER
   70: *          The leading dimension of the array Z.  LDZ >= 1, and if
   71: *          JOBZ = 'V', LDZ >= max(1,N).
   72: *
   73: *  WORK    (workspace/output) DOUBLE PRECISION array,
   74: *                                         dimension (LWORK)
   75: *          On exit, if INFO = 0, WORK(1) returns the required LWORK.
   76: *
   77: *  LWORK   (input) INTEGER
   78: *          The dimension of the array WORK.
   79: *          If N <= 1,               LWORK must be at least 1.
   80: *          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
   81: *          If JOBZ = 'V' and N > 1, LWORK must be at least
   82: *                                                 1 + 6*N + N**2.
   83: *
   84: *          If LWORK = -1, then a workspace query is assumed; the routine
   85: *          only calculates the required sizes of the WORK and IWORK
   86: *          arrays, returns these values as the first entries of the WORK
   87: *          and IWORK arrays, and no error message related to LWORK or
   88: *          LIWORK is issued by XERBLA.
   89: *
   90: *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
   91: *          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
   92: *
   93: *  LIWORK  (input) INTEGER
   94: *          The dimension of the array IWORK.
   95: *          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
   96: *          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
   97: *
   98: *          If LIWORK = -1, then a workspace query is assumed; the
   99: *          routine only calculates the required sizes of the WORK and
  100: *          IWORK arrays, returns these values as the first entries of
  101: *          the WORK and IWORK arrays, and no error message related to
  102: *          LWORK or LIWORK is issued by XERBLA.
  103: *
  104: *  INFO    (output) INTEGER
  105: *          = 0:  successful exit
  106: *          < 0:  if INFO = -i, the i-th argument had an illegal value.
  107: *          > 0:  if INFO = i, the algorithm failed to converge; i
  108: *                off-diagonal elements of an intermediate tridiagonal
  109: *                form did not converge to zero.
  110: *
  111: *  =====================================================================
  112: *
  113: *     .. Parameters ..
  114:       DOUBLE PRECISION   ZERO, ONE
  115:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
  116: *     ..
  117: *     .. Local Scalars ..
  118:       LOGICAL            LQUERY, WANTZ
  119:       INTEGER            IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
  120:      $                   LLWORK, LWMIN
  121:       DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
  122:      $                   SMLNUM
  123: *     ..
  124: *     .. External Functions ..
  125:       LOGICAL            LSAME
  126:       DOUBLE PRECISION   DLAMCH, DLANSP
  127:       EXTERNAL           LSAME, DLAMCH, DLANSP
  128: *     ..
  129: *     .. External Subroutines ..
  130:       EXTERNAL           DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA
  131: *     ..
  132: *     .. Intrinsic Functions ..
  133:       INTRINSIC          SQRT
  134: *     ..
  135: *     .. Executable Statements ..
  136: *
  137: *     Test the input parameters.
  138: *
  139:       WANTZ = LSAME( JOBZ, 'V' )
  140:       LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
  141: *
  142:       INFO = 0
  143:       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
  144:          INFO = -1
  145:       ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
  146:      $          THEN
  147:          INFO = -2
  148:       ELSE IF( N.LT.0 ) THEN
  149:          INFO = -3
  150:       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
  151:          INFO = -7
  152:       END IF
  153: *
  154:       IF( INFO.EQ.0 ) THEN
  155:          IF( N.LE.1 ) THEN
  156:             LIWMIN = 1
  157:             LWMIN = 1
  158:          ELSE
  159:             IF( WANTZ ) THEN
  160:                LIWMIN = 3 + 5*N
  161:                LWMIN = 1 + 6*N + N**2
  162:             ELSE
  163:                LIWMIN = 1
  164:                LWMIN = 2*N
  165:             END IF
  166:          END IF
  167:          IWORK( 1 ) = LIWMIN
  168:          WORK( 1 ) = LWMIN
  169: *
  170:          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
  171:             INFO = -9
  172:          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
  173:             INFO = -11
  174:          END IF
  175:       END IF
  176: *
  177:       IF( INFO.NE.0 ) THEN
  178:          CALL XERBLA( 'DSPEVD', -INFO )
  179:          RETURN
  180:       ELSE IF( LQUERY ) THEN
  181:          RETURN
  182:       END IF
  183: *
  184: *     Quick return if possible
  185: *
  186:       IF( N.EQ.0 )
  187:      $   RETURN
  188: *
  189:       IF( N.EQ.1 ) THEN
  190:          W( 1 ) = AP( 1 )
  191:          IF( WANTZ )
  192:      $      Z( 1, 1 ) = ONE
  193:          RETURN
  194:       END IF
  195: *
  196: *     Get machine constants.
  197: *
  198:       SAFMIN = DLAMCH( 'Safe minimum' )
  199:       EPS = DLAMCH( 'Precision' )
  200:       SMLNUM = SAFMIN / EPS
  201:       BIGNUM = ONE / SMLNUM
  202:       RMIN = SQRT( SMLNUM )
  203:       RMAX = SQRT( BIGNUM )
  204: *
  205: *     Scale matrix to allowable range, if necessary.
  206: *
  207:       ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
  208:       ISCALE = 0
  209:       IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
  210:          ISCALE = 1
  211:          SIGMA = RMIN / ANRM
  212:       ELSE IF( ANRM.GT.RMAX ) THEN
  213:          ISCALE = 1
  214:          SIGMA = RMAX / ANRM
  215:       END IF
  216:       IF( ISCALE.EQ.1 ) THEN
  217:          CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
  218:       END IF
  219: *
  220: *     Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
  221: *
  222:       INDE = 1
  223:       INDTAU = INDE + N
  224:       CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
  225: *
  226: *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
  227: *     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
  228: *     tridiagonal matrix, then call DOPMTR to multiply it by the
  229: *     Householder transformations represented in AP.
  230: *
  231:       IF( .NOT.WANTZ ) THEN
  232:          CALL DSTERF( N, W, WORK( INDE ), INFO )
  233:       ELSE
  234:          INDWRK = INDTAU + N
  235:          LLWORK = LWORK - INDWRK + 1
  236:          CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
  237:      $                LLWORK, IWORK, LIWORK, INFO )
  238:          CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
  239:      $                WORK( INDWRK ), IINFO )
  240:       END IF
  241: *
  242: *     If matrix was scaled, then rescale eigenvalues appropriately.
  243: *
  244:       IF( ISCALE.EQ.1 )
  245:      $   CALL DSCAL( N, ONE / SIGMA, W, 1 )
  246: *
  247:       WORK( 1 ) = LWMIN
  248:       IWORK( 1 ) = LIWMIN
  249:       RETURN
  250: *
  251: *     End of DSPEVD
  252: *
  253:       END

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