Return to zpoequb.f CVS log

Up to [local] / rpl / lapack / lapack

Première mise à jour de lapack et blas.

    1: *> \brief \b ZPOEQUB
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZPOEQUB + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpoequb.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpoequb.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpoequb.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, LDA, N
   25: *       DOUBLE PRECISION   AMAX, SCOND
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       COMPLEX*16         A( LDA, * )
   29: *       DOUBLE PRECISION   S( * )
   30: *       ..
   31: *
   32: *
   33: *> \par Purpose:
   34: *  =============
   35: *>
   36: *> \verbatim
   37: *>
   38: *> ZPOEQUB computes row and column scalings intended to equilibrate a
   39: *> Hermitian positive definite matrix A and reduce its condition number
   40: *> (with respect to the two-norm).  S contains the scale factors,
   41: *> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
   42: *> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
   43: *> choice of S puts the condition number of B within a factor N of the
   44: *> smallest possible condition number over all possible diagonal
   45: *> scalings.
   46: *>
   47: *> This routine differs from ZPOEQU by restricting the scaling factors
   48: *> to a power of the radix.  Barring over- and underflow, scaling by
   49: *> these factors introduces no additional rounding errors.  However, the
   50: *> scaled diagonal entries are no longer approximately 1 but lie
   51: *> between sqrt(radix) and 1/sqrt(radix).
   52: *> \endverbatim
   53: *
   54: *  Arguments:
   55: *  ==========
   56: *
   57: *> \param[in] N
   58: *> \verbatim
   59: *>          N is INTEGER
   60: *>          The order of the matrix A.  N >= 0.
   61: *> \endverbatim
   62: *>
   63: *> \param[in] A
   64: *> \verbatim
   65: *>          A is COMPLEX*16 array, dimension (LDA,N)
   66: *>          The N-by-N Hermitian positive definite matrix whose scaling
   67: *>          factors are to be computed.  Only the diagonal elements of A
   68: *>          are referenced.
   69: *> \endverbatim
   70: *>
   71: *> \param[in] LDA
   72: *> \verbatim
   73: *>          LDA is INTEGER
   74: *>          The leading dimension of the array A.  LDA >= max(1,N).
   75: *> \endverbatim
   76: *>
   77: *> \param[out] S
   78: *> \verbatim
   79: *>          S is DOUBLE PRECISION array, dimension (N)
   80: *>          If INFO = 0, S contains the scale factors for A.
   81: *> \endverbatim
   82: *>
   83: *> \param[out] SCOND
   84: *> \verbatim
   85: *>          SCOND is DOUBLE PRECISION
   86: *>          If INFO = 0, S contains the ratio of the smallest S(i) to
   87: *>          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
   88: *>          large nor too small, it is not worth scaling by S.
   89: *> \endverbatim
   90: *>
   91: *> \param[out] AMAX
   92: *> \verbatim
   93: *>          AMAX is DOUBLE PRECISION
   94: *>          Absolute value of largest matrix element.  If AMAX is very
   95: *>          close to overflow or very close to underflow, the matrix
   96: *>          should be scaled.
   97: *> \endverbatim
   98: *>
   99: *> \param[out] INFO
  100: *> \verbatim
  101: *>          INFO is INTEGER
  102: *>          = 0:  successful exit
  103: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  104: *>          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
  105: *> \endverbatim
  106: *
  107: *  Authors:
  108: *  ========
  109: *
  110: *> \author Univ. of Tennessee
  111: *> \author Univ. of California Berkeley
  112: *> \author Univ. of Colorado Denver
  113: *> \author NAG Ltd.
  114: *
  115: *> \ingroup complex16POcomputational
  116: *
  117: *  =====================================================================
  118:       SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
  119: *
  120: *  -- LAPACK computational routine --
  121: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  122: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  123: *
  124: *     .. Scalar Arguments ..
  125:       INTEGER            INFO, LDA, N
  126:       DOUBLE PRECISION   AMAX, SCOND
  127: *     ..
  128: *     .. Array Arguments ..
  129:       COMPLEX*16         A( LDA, * )
  130:       DOUBLE PRECISION   S( * )
  131: *     ..
  132: *
  133: *  =====================================================================
  134: *
  135: *     .. Parameters ..
  136:       DOUBLE PRECISION   ZERO, ONE
  137:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
  138: *     ..
  139: *     .. Local Scalars ..
  140:       INTEGER            I
  141:       DOUBLE PRECISION   SMIN, BASE, TMP
  142: *     ..
  143: *     .. External Functions ..
  144:       DOUBLE PRECISION   DLAMCH
  145:       EXTERNAL           DLAMCH
  146: *     ..
  147: *     .. External Subroutines ..
  148:       EXTERNAL           XERBLA
  149: *     ..
  150: *     .. Intrinsic Functions ..
  151:       INTRINSIC          MAX, MIN, SQRT, LOG, INT, REAL, DIMAG
  152: *     ..
  153: *     .. Executable Statements ..
  154: *
  155: *     Test the input parameters.
  156: *
  157: *     Positive definite only performs 1 pass of equilibration.
  158: *
  159:       INFO = 0
  160:       IF( N.LT.0 ) THEN
  161:          INFO = -1
  162:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  163:          INFO = -3
  164:       END IF
  165:       IF( INFO.NE.0 ) THEN
  166:          CALL XERBLA( 'ZPOEQUB', -INFO )
  167:          RETURN
  168:       END IF
  169: *
  170: *     Quick return if possible.
  171: *
  172:       IF( N.EQ.0 ) THEN
  173:          SCOND = ONE
  174:          AMAX = ZERO
  175:          RETURN
  176:       END IF
  177: 
  178:       BASE = DLAMCH( 'B' )
  179:       TMP = -0.5D+0 / LOG ( BASE )
  180: *
  181: *     Find the minimum and maximum diagonal elements.
  182: *
  183:       S( 1 ) = DBLE( A( 1, 1 ) )
  184:       SMIN = S( 1 )
  185:       AMAX = S( 1 )
  186:       DO 10 I = 2, N
  187:          S( I ) = DBLE( A( I, I ) )
  188:          SMIN = MIN( SMIN, S( I ) )
  189:          AMAX = MAX( AMAX, S( I ) )
  190:    10 CONTINUE
  191: *
  192:       IF( SMIN.LE.ZERO ) THEN
  193: *
  194: *        Find the first non-positive diagonal element and return.
  195: *
  196:          DO 20 I = 1, N
  197:             IF( S( I ).LE.ZERO ) THEN
  198:                INFO = I
  199:                RETURN
  200:             END IF
  201:    20    CONTINUE
  202:       ELSE
  203: *
  204: *        Set the scale factors to the reciprocals
  205: *        of the diagonal elements.
  206: *
  207:          DO 30 I = 1, N
  208:             S( I ) = BASE ** INT( TMP * LOG( S( I ) ) )
  209:    30    CONTINUE
  210: *
  211: *        Compute SCOND = min(S(I)) / max(S(I)).
  212: *
  213:          SCOND = SQRT( SMIN ) / SQRT( AMAX )
  214:       END IF
  215: *
  216:       RETURN
  217: *
  218: *     End of ZPOEQUB
  219: *
  220:       END