Return to dlaqsp.f CVS log

Up to [local] / rpl / lapack / lapack

Annotation of rpl/lapack/lapack/dlaqsp.f, revision 1.4

1.1       bertrand    1:       SUBROUTINE DLAQSP( UPLO, N, AP, 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            N
                     11:       DOUBLE PRECISION   AMAX, SCOND
                     12: *     ..
                     13: *     .. Array Arguments ..
                     14:       DOUBLE PRECISION   AP( * ), S( * )
                     15: *     ..
                     16: *
                     17: *  Purpose
                     18: *  =======
                     19: *
                     20: *  DLAQSP 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: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
                     36: *          On entry, the upper or lower triangle of the symmetric matrix
                     37: *          A, packed columnwise in a linear array.  The j-th column of A
                     38: *          is stored in the array AP as follows:
                     39: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
                     40: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
                     41: *
                     42: *          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
                     43: *          the same storage format as A.
                     44: *
                     45: *  S       (input) DOUBLE PRECISION array, dimension (N)
                     46: *          The scale factors for A.
                     47: *
                     48: *  SCOND   (input) DOUBLE PRECISION
                     49: *          Ratio of the smallest S(i) to the largest S(i).
                     50: *
                     51: *  AMAX    (input) DOUBLE PRECISION
                     52: *          Absolute value of largest matrix entry.
                     53: *
                     54: *  EQUED   (output) CHARACTER*1
                     55: *          Specifies whether or not equilibration was done.
                     56: *          = 'N':  No equilibration.
                     57: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
                     58: *                  diag(S) * A * diag(S).
                     59: *
                     60: *  Internal Parameters
                     61: *  ===================
                     62: *
                     63: *  THRESH is a threshold value used to decide if scaling should be done
                     64: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
                     65: *  scaling is done.
                     66: *
                     67: *  LARGE and SMALL are threshold values used to decide if scaling should
                     68: *  be done based on the absolute size of the largest matrix element.
                     69: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
                     70: *
                     71: *  =====================================================================
                     72: *
                     73: *     .. Parameters ..
                     74:       DOUBLE PRECISION   ONE, THRESH
                     75:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
                     76: *     ..
                     77: *     .. Local Scalars ..
                     78:       INTEGER            I, J, JC
                     79:       DOUBLE PRECISION   CJ, LARGE, SMALL
                     80: *     ..
                     81: *     .. External Functions ..
                     82:       LOGICAL            LSAME
                     83:       DOUBLE PRECISION   DLAMCH
                     84:       EXTERNAL           LSAME, DLAMCH
                     85: *     ..
                     86: *     .. Executable Statements ..
                     87: *
                     88: *     Quick return if possible
                     89: *
                     90:       IF( N.LE.0 ) THEN
                     91:          EQUED = 'N'
                     92:          RETURN
                     93:       END IF
                     94: *
                     95: *     Initialize LARGE and SMALL.
                     96: *
                     97:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
                     98:       LARGE = ONE / SMALL
                     99: *
                    100:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
                    101: *
                    102: *        No equilibration
                    103: *
                    104:          EQUED = 'N'
                    105:       ELSE
                    106: *
                    107: *        Replace A by diag(S) * A * diag(S).
                    108: *
                    109:          IF( LSAME( UPLO, 'U' ) ) THEN
                    110: *
                    111: *           Upper triangle of A is stored.
                    112: *
                    113:             JC = 1
                    114:             DO 20 J = 1, N
                    115:                CJ = S( J )
                    116:                DO 10 I = 1, J
                    117:                   AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
                    118:    10          CONTINUE
                    119:                JC = JC + J
                    120:    20       CONTINUE
                    121:          ELSE
                    122: *
                    123: *           Lower triangle of A is stored.
                    124: *
                    125:             JC = 1
                    126:             DO 40 J = 1, N
                    127:                CJ = S( J )
                    128:                DO 30 I = J, N
                    129:                   AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
                    130:    30          CONTINUE
                    131:                JC = JC + N - J + 1
                    132:    40       CONTINUE
                    133:          END IF
                    134:          EQUED = 'Y'
                    135:       END IF
                    136: *
                    137:       RETURN
                    138: *
                    139: *     End of DLAQSP
                    140: *
                    141:       END