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

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                     58: *          = 'Y':  Equilibration was done, i.e., A has been replaced by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