Return to zppequ.f CVS log

Up to [local] / rpl / lapack / lapack

Mise à jour de lapack.

    1: *> \brief \b ZPPEQU
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZPPEQU + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zppequ.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zppequ.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppequ.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, N
   26: *       DOUBLE PRECISION   AMAX, SCOND
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   S( * )
   30: *       COMPLEX*16         AP( * )
   31: *       ..
   32: *  
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> ZPPEQU computes row and column scalings intended to equilibrate a
   40: *> Hermitian positive definite matrix A in packed storage and reduce
   41: *> its condition number (with respect to the two-norm).  S contains the
   42: *> scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
   43: *> B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
   44: *> This choice of S puts the condition number of B within a factor N of
   45: *> the smallest possible condition number over all possible diagonal
   46: *> scalings.
   47: *> \endverbatim
   48: *
   49: *  Arguments:
   50: *  ==========
   51: *
   52: *> \param[in] UPLO
   53: *> \verbatim
   54: *>          UPLO is CHARACTER*1
   55: *>          = 'U':  Upper triangle of A is stored;
   56: *>          = 'L':  Lower triangle of A is stored.
   57: *> \endverbatim
   58: *>
   59: *> \param[in] N
   60: *> \verbatim
   61: *>          N is INTEGER
   62: *>          The order of the matrix A.  N >= 0.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] AP
   66: *> \verbatim
   67: *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   68: *>          The upper or lower triangle of the Hermitian matrix A, packed
   69: *>          columnwise in a linear array.  The j-th column of A is stored
   70: *>          in the array AP as follows:
   71: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   72: *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   73: *> \endverbatim
   74: *>
   75: *> \param[out] S
   76: *> \verbatim
   77: *>          S is DOUBLE PRECISION array, dimension (N)
   78: *>          If INFO = 0, S contains the scale factors for A.
   79: *> \endverbatim
   80: *>
   81: *> \param[out] SCOND
   82: *> \verbatim
   83: *>          SCOND is DOUBLE PRECISION
   84: *>          If INFO = 0, S contains the ratio of the smallest S(i) to
   85: *>          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
   86: *>          large nor too small, it is not worth scaling by S.
   87: *> \endverbatim
   88: *>
   89: *> \param[out] AMAX
   90: *> \verbatim
   91: *>          AMAX is DOUBLE PRECISION
   92: *>          Absolute value of largest matrix element.  If AMAX is very
   93: *>          close to overflow or very close to underflow, the matrix
   94: *>          should be scaled.
   95: *> \endverbatim
   96: *>
   97: *> \param[out] INFO
   98: *> \verbatim
   99: *>          INFO is INTEGER
  100: *>          = 0:  successful exit
  101: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  102: *>          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
  103: *> \endverbatim
  104: *
  105: *  Authors:
  106: *  ========
  107: *
  108: *> \author Univ. of Tennessee 
  109: *> \author Univ. of California Berkeley 
  110: *> \author Univ. of Colorado Denver 
  111: *> \author NAG Ltd. 
  112: *
  113: *> \date November 2011
  114: *
  115: *> \ingroup complex16OTHERcomputational
  116: *
  117: *  =====================================================================
  118:       SUBROUTINE ZPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
  119: *
  120: *  -- LAPACK computational routine (version 3.4.0) --
  121: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  122: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  123: *     November 2011
  124: *
  125: *     .. Scalar Arguments ..
  126:       CHARACTER          UPLO
  127:       INTEGER            INFO, N
  128:       DOUBLE PRECISION   AMAX, SCOND
  129: *     ..
  130: *     .. Array Arguments ..
  131:       DOUBLE PRECISION   S( * )
  132:       COMPLEX*16         AP( * )
  133: *     ..
  134: *
  135: *  =====================================================================
  136: *
  137: *     .. Parameters ..
  138:       DOUBLE PRECISION   ONE, ZERO
  139:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
  140: *     ..
  141: *     .. Local Scalars ..
  142:       LOGICAL            UPPER
  143:       INTEGER            I, JJ
  144:       DOUBLE PRECISION   SMIN
  145: *     ..
  146: *     .. External Functions ..
  147:       LOGICAL            LSAME
  148:       EXTERNAL           LSAME
  149: *     ..
  150: *     .. External Subroutines ..
  151:       EXTERNAL           XERBLA
  152: *     ..
  153: *     .. Intrinsic Functions ..
  154:       INTRINSIC          DBLE, MAX, MIN, SQRT
  155: *     ..
  156: *     .. Executable Statements ..
  157: *
  158: *     Test the input parameters.
  159: *
  160:       INFO = 0
  161:       UPPER = LSAME( UPLO, 'U' )
  162:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  163:          INFO = -1
  164:       ELSE IF( N.LT.0 ) THEN
  165:          INFO = -2
  166:       END IF
  167:       IF( INFO.NE.0 ) THEN
  168:          CALL XERBLA( 'ZPPEQU', -INFO )
  169:          RETURN
  170:       END IF
  171: *
  172: *     Quick return if possible
  173: *
  174:       IF( N.EQ.0 ) THEN
  175:          SCOND = ONE
  176:          AMAX = ZERO
  177:          RETURN
  178:       END IF
  179: *
  180: *     Initialize SMIN and AMAX.
  181: *
  182:       S( 1 ) = DBLE( AP( 1 ) )
  183:       SMIN = S( 1 )
  184:       AMAX = S( 1 )
  185: *
  186:       IF( UPPER ) THEN
  187: *
  188: *        UPLO = 'U':  Upper triangle of A is stored.
  189: *        Find the minimum and maximum diagonal elements.
  190: *
  191:          JJ = 1
  192:          DO 10 I = 2, N
  193:             JJ = JJ + I
  194:             S( I ) = DBLE( AP( JJ ) )
  195:             SMIN = MIN( SMIN, S( I ) )
  196:             AMAX = MAX( AMAX, S( I ) )
  197:    10    CONTINUE
  198: *
  199:       ELSE
  200: *
  201: *        UPLO = 'L':  Lower triangle of A is stored.
  202: *        Find the minimum and maximum diagonal elements.
  203: *
  204:          JJ = 1
  205:          DO 20 I = 2, N
  206:             JJ = JJ + N - I + 2
  207:             S( I ) = DBLE( AP( JJ ) )
  208:             SMIN = MIN( SMIN, S( I ) )
  209:             AMAX = MAX( AMAX, S( I ) )
  210:    20    CONTINUE
  211:       END IF
  212: *
  213:       IF( SMIN.LE.ZERO ) THEN
  214: *
  215: *        Find the first non-positive diagonal element and return.
  216: *
  217:          DO 30 I = 1, N
  218:             IF( S( I ).LE.ZERO ) THEN
  219:                INFO = I
  220:                RETURN
  221:             END IF
  222:    30    CONTINUE
  223:       ELSE
  224: *
  225: *        Set the scale factors to the reciprocals
  226: *        of the diagonal elements.
  227: *
  228:          DO 40 I = 1, N
  229:             S( I ) = ONE / SQRT( S( I ) )
  230:    40    CONTINUE
  231: *
  232: *        Compute SCOND = min(S(I)) / max(S(I))
  233: *
  234:          SCOND = SQRT( SMIN ) / SQRT( AMAX )
  235:       END IF
  236:       RETURN
  237: *
  238: *     End of ZPPEQU
  239: *
  240:       END