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    1: *> \brief \b ZLAQHE scales a Hermitian matrix.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download ZLAQHE + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqhe.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqhe.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqhe.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          EQUED, UPLO
   25: *       INTEGER            LDA, N
   26: *       DOUBLE PRECISION   AMAX, SCOND
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   S( * )
   30: *       COMPLEX*16         A( LDA, * )
   31: *       ..
   32: *
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
   40: *> in the vector S.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] UPLO
   47: *> \verbatim
   48: *>          UPLO is CHARACTER*1
   49: *>          Specifies whether the upper or lower triangular part of the
   50: *>          Hermitian matrix A is stored.
   51: *>          = 'U':  Upper triangular
   52: *>          = 'L':  Lower triangular
   53: *> \endverbatim
   54: *>
   55: *> \param[in] N
   56: *> \verbatim
   57: *>          N is INTEGER
   58: *>          The order of the matrix A.  N >= 0.
   59: *> \endverbatim
   60: *>
   61: *> \param[in,out] A
   62: *> \verbatim
   63: *>          A is COMPLEX*16 array, dimension (LDA,N)
   64: *>          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
   65: *>          n by n upper triangular part of A contains the upper
   66: *>          triangular part of the matrix A, and the strictly lower
   67: *>          triangular part of A is not referenced.  If UPLO = 'L', the
   68: *>          leading n by n lower triangular part of A contains the lower
   69: *>          triangular part of the matrix A, and the strictly upper
   70: *>          triangular part of A is not referenced.
   71: *>
   72: *>          On exit, if EQUED = 'Y', the equilibrated matrix:
   73: *>          diag(S) * A * diag(S).
   74: *> \endverbatim
   75: *>
   76: *> \param[in] LDA
   77: *> \verbatim
   78: *>          LDA is INTEGER
   79: *>          The leading dimension of the array A.  LDA >= max(N,1).
   80: *> \endverbatim
   81: *>
   82: *> \param[in] S
   83: *> \verbatim
   84: *>          S is DOUBLE PRECISION array, dimension (N)
   85: *>          The scale factors for A.
   86: *> \endverbatim
   87: *>
   88: *> \param[in] SCOND
   89: *> \verbatim
   90: *>          SCOND is DOUBLE PRECISION
   91: *>          Ratio of the smallest S(i) to the largest S(i).
   92: *> \endverbatim
   93: *>
   94: *> \param[in] AMAX
   95: *> \verbatim
   96: *>          AMAX is DOUBLE PRECISION
   97: *>          Absolute value of largest matrix entry.
   98: *> \endverbatim
   99: *>
  100: *> \param[out] EQUED
  101: *> \verbatim
  102: *>          EQUED is CHARACTER*1
  103: *>          Specifies whether or not equilibration was done.
  104: *>          = 'N':  No equilibration.
  105: *>          = 'Y':  Equilibration was done, i.e., A has been replaced by
  106: *>                  diag(S) * A * diag(S).
  107: *> \endverbatim
  108: *
  109: *> \par Internal Parameters:
  110: *  =========================
  111: *>
  112: *> \verbatim
  113: *>  THRESH is a threshold value used to decide if scaling should be done
  114: *>  based on the ratio of the scaling factors.  If SCOND < THRESH,
  115: *>  scaling is done.
  116: *>
  117: *>  LARGE and SMALL are threshold values used to decide if scaling should
  118: *>  be done based on the absolute size of the largest matrix element.
  119: *>  If AMAX > LARGE or AMAX < SMALL, scaling is done.
  120: *> \endverbatim
  121: *
  122: *  Authors:
  123: *  ========
  124: *
  125: *> \author Univ. of Tennessee
  126: *> \author Univ. of California Berkeley
  127: *> \author Univ. of Colorado Denver
  128: *> \author NAG Ltd.
  129: *
  130: *> \ingroup complex16HEauxiliary
  131: *
  132: *  =====================================================================
  133:       SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
  134: *
  135: *  -- LAPACK auxiliary routine --
  136: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  137: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  138: *
  139: *     .. Scalar Arguments ..
  140:       CHARACTER          EQUED, UPLO
  141:       INTEGER            LDA, N
  142:       DOUBLE PRECISION   AMAX, SCOND
  143: *     ..
  144: *     .. Array Arguments ..
  145:       DOUBLE PRECISION   S( * )
  146:       COMPLEX*16         A( LDA, * )
  147: *     ..
  148: *
  149: *  =====================================================================
  150: *
  151: *     .. Parameters ..
  152:       DOUBLE PRECISION   ONE, THRESH
  153:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
  154: *     ..
  155: *     .. Local Scalars ..
  156:       INTEGER            I, J
  157:       DOUBLE PRECISION   CJ, LARGE, SMALL
  158: *     ..
  159: *     .. External Functions ..
  160:       LOGICAL            LSAME
  161:       DOUBLE PRECISION   DLAMCH
  162:       EXTERNAL           LSAME, DLAMCH
  163: *     ..
  164: *     .. Intrinsic Functions ..
  165:       INTRINSIC          DBLE
  166: *     ..
  167: *     .. Executable Statements ..
  168: *
  169: *     Quick return if possible
  170: *
  171:       IF( N.LE.0 ) THEN
  172:          EQUED = 'N'
  173:          RETURN
  174:       END IF
  175: *
  176: *     Initialize LARGE and SMALL.
  177: *
  178:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  179:       LARGE = ONE / SMALL
  180: *
  181:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
  182: *
  183: *        No equilibration
  184: *
  185:          EQUED = 'N'
  186:       ELSE
  187: *
  188: *        Replace A by diag(S) * A * diag(S).
  189: *
  190:          IF( LSAME( UPLO, 'U' ) ) THEN
  191: *
  192: *           Upper triangle of A is stored.
  193: *
  194:             DO 20 J = 1, N
  195:                CJ = S( J )
  196:                DO 10 I = 1, J - 1
  197:                   A( I, J ) = CJ*S( I )*A( I, J )
  198:    10          CONTINUE
  199:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
  200:    20       CONTINUE
  201:          ELSE
  202: *
  203: *           Lower triangle of A is stored.
  204: *
  205:             DO 40 J = 1, N
  206:                CJ = S( J )
  207:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
  208:                DO 30 I = J + 1, N
  209:                   A( I, J ) = CJ*S( I )*A( I, J )
  210:    30          CONTINUE
  211:    40       CONTINUE
  212:          END IF
  213:          EQUED = 'Y'
  214:       END IF
  215: *
  216:       RETURN
  217: *
  218: *     End of ZLAQHE
  219: *
  220:       END