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Annotation of rpl/lapack/lapack/zlaqhe.f, revision 1.6

1.1       bertrand    1:       SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
                      2: *
                      3: *  -- LAPACK auxiliary routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       CHARACTER          EQUED, UPLO
                     10:       INTEGER            LDA, N
                     11:       DOUBLE PRECISION   AMAX, SCOND
                     12: *     ..
                     13: *     .. Array Arguments ..
                     14:       DOUBLE PRECISION   S( * )
                     15:       COMPLEX*16         A( LDA, * )
                     16: *     ..
                     17: *
                     18: *  Purpose
                     19: *  =======
                     20: *
                     21: *  ZLAQHE equilibrates a Hermitian matrix A using the scaling factors
                     22: *  in the vector S.
                     23: *
                     24: *  Arguments
                     25: *  =========
                     26: *
                     27: *  UPLO    (input) CHARACTER*1
                     28: *          Specifies whether the upper or lower triangular part of the
                     29: *          Hermitian matrix A is stored.
                     30: *          = 'U':  Upper triangular
                     31: *          = 'L':  Lower triangular
                     32: *
                     33: *  N       (input) INTEGER
                     34: *          The order of the matrix A.  N >= 0.
                     35: *
                     36: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                     37: *          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
                     38: *          n by n upper triangular part of A contains the upper
                     39: *          triangular part of the matrix A, and the strictly lower
                     40: *          triangular part of A is not referenced.  If UPLO = 'L', the
                     41: *          leading n by n lower triangular part of A contains the lower
                     42: *          triangular part of the matrix A, and the strictly upper
                     43: *          triangular part of A is not referenced.
                     44: *
                     45: *          On exit, if EQUED = 'Y', the equilibrated matrix:
                     46: *          diag(S) * A * diag(S).
                     47: *
                     48: *  LDA     (input) INTEGER
                     49: *          The leading dimension of the array A.  LDA >= max(N,1).
                     50: *
                     51: *  S       (input) DOUBLE PRECISION array, dimension (N)
                     52: *          The scale factors for A.
                     53: *
                     54: *  SCOND   (input) DOUBLE PRECISION
                     55: *          Ratio of the smallest S(i) to the largest S(i).
                     56: *
                     57: *  AMAX    (input) DOUBLE PRECISION
                     58: *          Absolute value of largest matrix entry.
                     59: *
                     60: *  EQUED   (output) CHARACTER*1
                     61: *          Specifies whether or not equilibration was done.
                     62: *          = 'N':  No equilibration.
                     63: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
                     64: *                  diag(S) * A * diag(S).
                     65: *
                     66: *  Internal Parameters
                     67: *  ===================
                     68: *
                     69: *  THRESH is a threshold value used to decide if scaling should be done
                     70: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
                     71: *  scaling is done.
                     72: *
                     73: *  LARGE and SMALL are threshold values used to decide if scaling should
                     74: *  be done based on the absolute size of the largest matrix element.
                     75: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
                     76: *
                     77: *  =====================================================================
                     78: *
                     79: *     .. Parameters ..
                     80:       DOUBLE PRECISION   ONE, THRESH
                     81:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
                     82: *     ..
                     83: *     .. Local Scalars ..
                     84:       INTEGER            I, J
                     85:       DOUBLE PRECISION   CJ, LARGE, SMALL
                     86: *     ..
                     87: *     .. External Functions ..
                     88:       LOGICAL            LSAME
                     89:       DOUBLE PRECISION   DLAMCH
                     90:       EXTERNAL           LSAME, DLAMCH
                     91: *     ..
                     92: *     .. Intrinsic Functions ..
                     93:       INTRINSIC          DBLE
                     94: *     ..
                     95: *     .. Executable Statements ..
                     96: *
                     97: *     Quick return if possible
                     98: *
                     99:       IF( N.LE.0 ) THEN
                    100:          EQUED = 'N'
                    101:          RETURN
                    102:       END IF
                    103: *
                    104: *     Initialize LARGE and SMALL.
                    105: *
                    106:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
                    107:       LARGE = ONE / SMALL
                    108: *
                    109:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
                    110: *
                    111: *        No equilibration
                    112: *
                    113:          EQUED = 'N'
                    114:       ELSE
                    115: *
                    116: *        Replace A by diag(S) * A * diag(S).
                    117: *
                    118:          IF( LSAME( UPLO, 'U' ) ) THEN
                    119: *
                    120: *           Upper triangle of A is stored.
                    121: *
                    122:             DO 20 J = 1, N
                    123:                CJ = S( J )
                    124:                DO 10 I = 1, J - 1
                    125:                   A( I, J ) = CJ*S( I )*A( I, J )
                    126:    10          CONTINUE
                    127:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
                    128:    20       CONTINUE
                    129:          ELSE
                    130: *
                    131: *           Lower triangle of A is stored.
                    132: *
                    133:             DO 40 J = 1, N
                    134:                CJ = S( J )
                    135:                A( J, J ) = CJ*CJ*DBLE( A( J, J ) )
                    136:                DO 30 I = J + 1, N
                    137:                   A( I, J ) = CJ*S( I )*A( I, J )
                    138:    30          CONTINUE
                    139:    40       CONTINUE
                    140:          END IF
                    141:          EQUED = 'Y'
                    142:       END IF
                    143: *
                    144:       RETURN
                    145: *
                    146: *     End of ZLAQHE
                    147: *
                    148:       END