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    1: *> \brief \b DLAQSP scales a symmetric/Hermitian matrix in packed storage, using scaling factors computed by sppequ.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DLAQSP + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqsp.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqsp.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqsp.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          EQUED, UPLO
   25: *       INTEGER            N
   26: *       DOUBLE PRECISION   AMAX, SCOND
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   AP( * ), S( * )
   30: *       ..
   31: *
   32: *
   33: *> \par Purpose:
   34: *  =============
   35: *>
   36: *> \verbatim
   37: *>
   38: *> DLAQSP equilibrates a symmetric matrix A using the scaling factors
   39: *> in the vector S.
   40: *> \endverbatim
   41: *
   42: *  Arguments:
   43: *  ==========
   44: *
   45: *> \param[in] UPLO
   46: *> \verbatim
   47: *>          UPLO is CHARACTER*1
   48: *>          Specifies whether the upper or lower triangular part of the
   49: *>          symmetric matrix A is stored.
   50: *>          = 'U':  Upper triangular
   51: *>          = 'L':  Lower triangular
   52: *> \endverbatim
   53: *>
   54: *> \param[in] N
   55: *> \verbatim
   56: *>          N is INTEGER
   57: *>          The order of the matrix A.  N >= 0.
   58: *> \endverbatim
   59: *>
   60: *> \param[in,out] AP
   61: *> \verbatim
   62: *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
   63: *>          On entry, the upper or lower triangle of the symmetric matrix
   64: *>          A, packed columnwise in a linear array.  The j-th column of A
   65: *>          is stored in the array AP as follows:
   66: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   67: *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   68: *>
   69: *>          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
   70: *>          the same storage format as A.
   71: *> \endverbatim
   72: *>
   73: *> \param[in] S
   74: *> \verbatim
   75: *>          S is DOUBLE PRECISION array, dimension (N)
   76: *>          The scale factors for A.
   77: *> \endverbatim
   78: *>
   79: *> \param[in] SCOND
   80: *> \verbatim
   81: *>          SCOND is DOUBLE PRECISION
   82: *>          Ratio of the smallest S(i) to the largest S(i).
   83: *> \endverbatim
   84: *>
   85: *> \param[in] AMAX
   86: *> \verbatim
   87: *>          AMAX is DOUBLE PRECISION
   88: *>          Absolute value of largest matrix entry.
   89: *> \endverbatim
   90: *>
   91: *> \param[out] EQUED
   92: *> \verbatim
   93: *>          EQUED is CHARACTER*1
   94: *>          Specifies whether or not equilibration was done.
   95: *>          = 'N':  No equilibration.
   96: *>          = 'Y':  Equilibration was done, i.e., A has been replaced by
   97: *>                  diag(S) * A * diag(S).
   98: *> \endverbatim
   99: *
  100: *> \par Internal Parameters:
  101: *  =========================
  102: *>
  103: *> \verbatim
  104: *>  THRESH is a threshold value used to decide if scaling should be done
  105: *>  based on the ratio of the scaling factors.  If SCOND < THRESH,
  106: *>  scaling is done.
  107: *>
  108: *>  LARGE and SMALL are threshold values used to decide if scaling should
  109: *>  be done based on the absolute size of the largest matrix element.
  110: *>  If AMAX > LARGE or AMAX < SMALL, scaling is done.
  111: *> \endverbatim
  112: *
  113: *  Authors:
  114: *  ========
  115: *
  116: *> \author Univ. of Tennessee
  117: *> \author Univ. of California Berkeley
  118: *> \author Univ. of Colorado Denver
  119: *> \author NAG Ltd.
  120: *
  121: *> \ingroup doubleOTHERauxiliary
  122: *
  123: *  =====================================================================
  124:       SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
  125: *
  126: *  -- LAPACK auxiliary routine --
  127: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  128: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  129: *
  130: *     .. Scalar Arguments ..
  131:       CHARACTER          EQUED, UPLO
  132:       INTEGER            N
  133:       DOUBLE PRECISION   AMAX, SCOND
  134: *     ..
  135: *     .. Array Arguments ..
  136:       DOUBLE PRECISION   AP( * ), S( * )
  137: *     ..
  138: *
  139: *  =====================================================================
  140: *
  141: *     .. Parameters ..
  142:       DOUBLE PRECISION   ONE, THRESH
  143:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
  144: *     ..
  145: *     .. Local Scalars ..
  146:       INTEGER            I, J, JC
  147:       DOUBLE PRECISION   CJ, LARGE, SMALL
  148: *     ..
  149: *     .. External Functions ..
  150:       LOGICAL            LSAME
  151:       DOUBLE PRECISION   DLAMCH
  152:       EXTERNAL           LSAME, DLAMCH
  153: *     ..
  154: *     .. Executable Statements ..
  155: *
  156: *     Quick return if possible
  157: *
  158:       IF( N.LE.0 ) THEN
  159:          EQUED = 'N'
  160:          RETURN
  161:       END IF
  162: *
  163: *     Initialize LARGE and SMALL.
  164: *
  165:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  166:       LARGE = ONE / SMALL
  167: *
  168:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
  169: *
  170: *        No equilibration
  171: *
  172:          EQUED = 'N'
  173:       ELSE
  174: *
  175: *        Replace A by diag(S) * A * diag(S).
  176: *
  177:          IF( LSAME( UPLO, 'U' ) ) THEN
  178: *
  179: *           Upper triangle of A is stored.
  180: *
  181:             JC = 1
  182:             DO 20 J = 1, N
  183:                CJ = S( J )
  184:                DO 10 I = 1, J
  185:                   AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
  186:    10          CONTINUE
  187:                JC = JC + J
  188:    20       CONTINUE
  189:          ELSE
  190: *
  191: *           Lower triangle of A is stored.
  192: *
  193:             JC = 1
  194:             DO 40 J = 1, N
  195:                CJ = S( J )
  196:                DO 30 I = J, N
  197:                   AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
  198:    30          CONTINUE
  199:                JC = JC + N - J + 1
  200:    40       CONTINUE
  201:          END IF
  202:          EQUED = 'Y'
  203:       END IF
  204: *
  205:       RETURN
  206: *
  207: *     End of DLAQSP
  208: *
  209:       END