Return to zpoequ.f CVS log

Up to [local] / rpl / lapack / lapack

Annotation of rpl/lapack/lapack/zpoequ.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
        !             2: *
        !             3: *  -- LAPACK 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:       INTEGER            INFO, LDA, N
        !            10:       DOUBLE PRECISION   AMAX, SCOND
        !            11: *     ..
        !            12: *     .. Array Arguments ..
        !            13:       DOUBLE PRECISION   S( * )
        !            14:       COMPLEX*16         A( LDA, * )
        !            15: *     ..
        !            16: *
        !            17: *  Purpose
        !            18: *  =======
        !            19: *
        !            20: *  ZPOEQU computes row and column scalings intended to equilibrate a
        !            21: *  Hermitian positive definite matrix A and reduce its condition number
        !            22: *  (with respect to the two-norm).  S contains the scale factors,
        !            23: *  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
        !            24: *  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
        !            25: *  choice of S puts the condition number of B within a factor N of the
        !            26: *  smallest possible condition number over all possible diagonal
        !            27: *  scalings.
        !            28: *
        !            29: *  Arguments
        !            30: *  =========
        !            31: *
        !            32: *  N       (input) INTEGER
        !            33: *          The order of the matrix A.  N >= 0.
        !            34: *
        !            35: *  A       (input) COMPLEX*16 array, dimension (LDA,N)
        !            36: *          The N-by-N Hermitian positive definite matrix whose scaling
        !            37: *          factors are to be computed.  Only the diagonal elements of A
        !            38: *          are referenced.
        !            39: *
        !            40: *  LDA     (input) INTEGER
        !            41: *          The leading dimension of the array A.  LDA >= max(1,N).
        !            42: *
        !            43: *  S       (output) DOUBLE PRECISION array, dimension (N)
        !            44: *          If INFO = 0, S contains the scale factors for A.
        !            45: *
        !            46: *  SCOND   (output) DOUBLE PRECISION
        !            47: *          If INFO = 0, S contains the ratio of the smallest S(i) to
        !            48: *          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
        !            49: *          large nor too small, it is not worth scaling by S.
        !            50: *
        !            51: *  AMAX    (output) DOUBLE PRECISION
        !            52: *          Absolute value of largest matrix element.  If AMAX is very
        !            53: *          close to overflow or very close to underflow, the matrix
        !            54: *          should be scaled.
        !            55: *
        !            56: *  INFO    (output) INTEGER
        !            57: *          = 0:  successful exit
        !            58: *          < 0:  if INFO = -i, the i-th argument had an illegal value
        !            59: *          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
        !            60: *
        !            61: *  =====================================================================
        !            62: *
        !            63: *     .. Parameters ..
        !            64:       DOUBLE PRECISION   ZERO, ONE
        !            65:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
        !            66: *     ..
        !            67: *     .. Local Scalars ..
        !            68:       INTEGER            I
        !            69:       DOUBLE PRECISION   SMIN
        !            70: *     ..
        !            71: *     .. External Subroutines ..
        !            72:       EXTERNAL           XERBLA
        !            73: *     ..
        !            74: *     .. Intrinsic Functions ..
        !            75:       INTRINSIC          DBLE, MAX, MIN, SQRT
        !            76: *     ..
        !            77: *     .. Executable Statements ..
        !            78: *
        !            79: *     Test the input parameters.
        !            80: *
        !            81:       INFO = 0
        !            82:       IF( N.LT.0 ) THEN
        !            83:          INFO = -1
        !            84:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
        !            85:          INFO = -3
        !            86:       END IF
        !            87:       IF( INFO.NE.0 ) THEN
        !            88:          CALL XERBLA( 'ZPOEQU', -INFO )
        !            89:          RETURN
        !            90:       END IF
        !            91: *
        !            92: *     Quick return if possible
        !            93: *
        !            94:       IF( N.EQ.0 ) THEN
        !            95:          SCOND = ONE
        !            96:          AMAX = ZERO
        !            97:          RETURN
        !            98:       END IF
        !            99: *
        !           100: *     Find the minimum and maximum diagonal elements.
        !           101: *
        !           102:       S( 1 ) = DBLE( A( 1, 1 ) )
        !           103:       SMIN = S( 1 )
        !           104:       AMAX = S( 1 )
        !           105:       DO 10 I = 2, N
        !           106:          S( I ) = DBLE( A( I, I ) )
        !           107:          SMIN = MIN( SMIN, S( I ) )
        !           108:          AMAX = MAX( AMAX, S( I ) )
        !           109:    10 CONTINUE
        !           110: *
        !           111:       IF( SMIN.LE.ZERO ) THEN
        !           112: *
        !           113: *        Find the first non-positive diagonal element and return.
        !           114: *
        !           115:          DO 20 I = 1, N
        !           116:             IF( S( I ).LE.ZERO ) THEN
        !           117:                INFO = I
        !           118:                RETURN
        !           119:             END IF
        !           120:    20    CONTINUE
        !           121:       ELSE
        !           122: *
        !           123: *        Set the scale factors to the reciprocals
        !           124: *        of the diagonal elements.
        !           125: *
        !           126:          DO 30 I = 1, N
        !           127:             S( I ) = ONE / SQRT( S( I ) )
        !           128:    30    CONTINUE
        !           129: *
        !           130: *        Compute SCOND = min(S(I)) / max(S(I))
        !           131: *
        !           132:          SCOND = SQRT( SMIN ) / SQRT( AMAX )
        !           133:       END IF
        !           134:       RETURN
        !           135: *
        !           136: *     End of ZPOEQU
        !           137: *
        !           138:       END