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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: *> \date September 2012
  122: *
  123: *> \ingroup doubleOTHERauxiliary
  124: *
  125: *  =====================================================================
  126:       SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
  127: *
  128: *  -- LAPACK auxiliary routine (version 3.4.2) --
  129: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  130: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  131: *     September 2012
  132: *
  133: *     .. Scalar Arguments ..
  134:       CHARACTER          EQUED, UPLO
  135:       INTEGER            N
  136:       DOUBLE PRECISION   AMAX, SCOND
  137: *     ..
  138: *     .. Array Arguments ..
  139:       DOUBLE PRECISION   AP( * ), S( * )
  140: *     ..
  141: *
  142: *  =====================================================================
  143: *
  144: *     .. Parameters ..
  145:       DOUBLE PRECISION   ONE, THRESH
  146:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
  147: *     ..
  148: *     .. Local Scalars ..
  149:       INTEGER            I, J, JC
  150:       DOUBLE PRECISION   CJ, LARGE, SMALL
  151: *     ..
  152: *     .. External Functions ..
  153:       LOGICAL            LSAME
  154:       DOUBLE PRECISION   DLAMCH
  155:       EXTERNAL           LSAME, DLAMCH
  156: *     ..
  157: *     .. Executable Statements ..
  158: *
  159: *     Quick return if possible
  160: *
  161:       IF( N.LE.0 ) THEN
  162:          EQUED = 'N'
  163:          RETURN
  164:       END IF
  165: *
  166: *     Initialize LARGE and SMALL.
  167: *
  168:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  169:       LARGE = ONE / SMALL
  170: *
  171:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
  172: *
  173: *        No equilibration
  174: *
  175:          EQUED = 'N'
  176:       ELSE
  177: *
  178: *        Replace A by diag(S) * A * diag(S).
  179: *
  180:          IF( LSAME( UPLO, 'U' ) ) THEN
  181: *
  182: *           Upper triangle of A is stored.
  183: *
  184:             JC = 1
  185:             DO 20 J = 1, N
  186:                CJ = S( J )
  187:                DO 10 I = 1, J
  188:                   AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
  189:    10          CONTINUE
  190:                JC = JC + J
  191:    20       CONTINUE
  192:          ELSE
  193: *
  194: *           Lower triangle of A is stored.
  195: *
  196:             JC = 1
  197:             DO 40 J = 1, N
  198:                CJ = S( J )
  199:                DO 30 I = J, N
  200:                   AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
  201:    30          CONTINUE
  202:                JC = JC + N - J + 1
  203:    40       CONTINUE
  204:          END IF
  205:          EQUED = 'Y'
  206:       END IF
  207: *
  208:       RETURN
  209: *
  210: *     End of DLAQSP
  211: *
  212:       END