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Annotation of rpl/lapack/lapack/dlaqsy.f, revision 1.1.1.1

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