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

1.1       bertrand    1:       SUBROUTINE ZLAQSB( UPLO, N, KD, AB, LDAB, 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            KD, LDAB, N
                     11:       DOUBLE PRECISION   AMAX, SCOND
                     12: *     ..
                     13: *     .. Array Arguments ..
                     14:       DOUBLE PRECISION   S( * )
                     15:       COMPLEX*16         AB( LDAB, * )
                     16: *     ..
                     17: *
                     18: *  Purpose
                     19: *  =======
                     20: *
                     21: *  ZLAQSB equilibrates a symmetric band matrix A using the scaling
                     22: *  factors 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: *  KD      (input) INTEGER
                     37: *          The number of super-diagonals of the matrix A if UPLO = 'U',
                     38: *          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
                     39: *
                     40: *  AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
                     41: *          On entry, the upper or lower triangle of the symmetric band
                     42: *          matrix A, stored in the first KD+1 rows of the array.  The
                     43: *          j-th column of A is stored in the j-th column of the array AB
                     44: *          as follows:
                     45: *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                     46: *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
                     47: *
                     48: *          On exit, if INFO = 0, the triangular factor U or L from the
                     49: *          Cholesky factorization A = U'*U or A = L*L' of the band
                     50: *          matrix A, in the same storage format as A.
                     51: *
                     52: *  LDAB    (input) INTEGER
                     53: *          The leading dimension of the array AB.  LDAB >= KD+1.
                     54: *
                     55: *  S       (input) DOUBLE PRECISION array, dimension (N)
                     56: *          The scale factors for A.
                     57: *
                     58: *  SCOND   (input) DOUBLE PRECISION
                     59: *          Ratio of the smallest S(i) to the largest S(i).
                     60: *
                     61: *  AMAX    (input) DOUBLE PRECISION
                     62: *          Absolute value of largest matrix entry.
                     63: *
                     64: *  EQUED   (output) CHARACTER*1
                     65: *          Specifies whether or not equilibration was done.
                     66: *          = 'N':  No equilibration.
                     67: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
                     68: *                  diag(S) * A * diag(S).
                     69: *
                     70: *  Internal Parameters
                     71: *  ===================
                     72: *
                     73: *  THRESH is a threshold value used to decide if scaling should be done
                     74: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
                     75: *  scaling is done.
                     76: *
                     77: *  LARGE and SMALL are threshold values used to decide if scaling should
                     78: *  be done based on the absolute size of the largest matrix element.
                     79: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
                     80: *
                     81: *  =====================================================================
                     82: *
                     83: *     .. Parameters ..
                     84:       DOUBLE PRECISION   ONE, THRESH
                     85:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
                     86: *     ..
                     87: *     .. Local Scalars ..
                     88:       INTEGER            I, J
                     89:       DOUBLE PRECISION   CJ, LARGE, SMALL
                     90: *     ..
                     91: *     .. External Functions ..
                     92:       LOGICAL            LSAME
                     93:       DOUBLE PRECISION   DLAMCH
                     94:       EXTERNAL           LSAME, DLAMCH
                     95: *     ..
                     96: *     .. Intrinsic Functions ..
                     97:       INTRINSIC          MAX, MIN
                     98: *     ..
                     99: *     .. Executable Statements ..
                    100: *
                    101: *     Quick return if possible
                    102: *
                    103:       IF( N.LE.0 ) THEN
                    104:          EQUED = 'N'
                    105:          RETURN
                    106:       END IF
                    107: *
                    108: *     Initialize LARGE and SMALL.
                    109: *
                    110:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
                    111:       LARGE = ONE / SMALL
                    112: *
                    113:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
                    114: *
                    115: *        No equilibration
                    116: *
                    117:          EQUED = 'N'
                    118:       ELSE
                    119: *
                    120: *        Replace A by diag(S) * A * diag(S).
                    121: *
                    122:          IF( LSAME( UPLO, 'U' ) ) THEN
                    123: *
                    124: *           Upper triangle of A is stored in band format.
                    125: *
                    126:             DO 20 J = 1, N
                    127:                CJ = S( J )
                    128:                DO 10 I = MAX( 1, J-KD ), J
                    129:                   AB( KD+1+I-J, J ) = CJ*S( I )*AB( KD+1+I-J, J )
                    130:    10          CONTINUE
                    131:    20       CONTINUE
                    132:          ELSE
                    133: *
                    134: *           Lower triangle of A is stored.
                    135: *
                    136:             DO 40 J = 1, N
                    137:                CJ = S( J )
                    138:                DO 30 I = J, MIN( N, J+KD )
                    139:                   AB( 1+I-J, J ) = CJ*S( I )*AB( 1+I-J, J )
                    140:    30          CONTINUE
                    141:    40       CONTINUE
                    142:          END IF
                    143:          EQUED = 'Y'
                    144:       END IF
                    145: *
                    146:       RETURN
                    147: *
                    148: *     End of ZLAQSB
                    149: *
                    150:       END