コード例 #1
0
ファイル: common.py プロジェクト: BackupTheBerlios/pulsar-svn
def central_diff_weights(Np,ndiv=1):
    """Return weights for an Np-point central derivative of order ndiv
       assuming equally-spaced function points.

       If weights are in the vector w, then 
       derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)
       
       Can be inaccurate for large number of points.
    """
    assert (Np >= ndiv+1), "Number of points must be at least the derivative order + 1."
    assert (Np % 2 == 1), "Odd-number of points only."
    ho = Np >> 1
    x = arange(-ho,ho+1.0)
    x = x[:,NewAxis]
    X = x**0.0
    for k in range(1,Np):
        X = hstack([X,x**k])
    w = product(arange(1,ndiv+1))*linalg.inv(X)[ndiv]
    return w
コード例 #2
0
ファイル: common.py プロジェクト: BackupTheBerlios/pulsar-svn
def derivative(func,x0,dx=1.0,n=1,args=(),order=3):
    """Given a function, use a central difference formula with spacing dx to
       compute the nth derivative at x0.
       
       order is the number of points to use and must be odd.

       Warning: Decreasing the step size too small can result in
       round-off error.
    """
    assert (order >= n+1), "Number of points must be at least the derivative order + 1."
    assert (order % 2 == 1), "Odd number of points only."
    # pre-computed for n=1 and 2 and low-order for speed.
    if n==1:
        if order == 3:
            weights = array([-1,0,1])/2.0
        elif order == 5:
            weights = array([1,-8,0,8,-1])/12.0
        elif order == 7:
            weights = array([-1,9,-45,0,45,-9,1])/60.0
        elif order == 9:
            weights = array([3,-32,168,-672,0,672,-168,32,-3])/840.0
        else:
            weights = central_diff_weights(order,1)
    elif n==2:
        if order == 3:
            weights = array([1,-2.0,1])
        elif order == 5:
            weights = array([-1,16,-30,16,-1])/12.0
        elif order == 7:
            weights = array([2,-27,270,-490,270,-27,2])/180.0
        elif order == 9:
            weights = array([-9,128,-1008,8064,-14350,8064,-1008,128,-9])/5040.0
        else:
            weights = central_diff_weights(order,2)
    else:
        weights = central_diff_weights(order, n)
    val = 0.0
    ho = order >> 1
    for k in range(order):
        val += weights[k]*func(x0+(k-ho)*dx,*args)
    return val / product((dx,)*n)