sdeint/wiener.py
def Ikpw(dW, h, n=5):
    """matrix I approximating repeated Ito integrals for each of N time
    intervals, based on the method of Kloeden, Platen and Wright (1992).

    Args:
      dW (array of shape (N, m)): giving m independent Weiner increments for
        each time step N. (You can make this array using sdeint.deltaW())
      h (float): the time step size
      n (int, optional): how many terms to take in the series expansion

    Returns:
      (A, I) where
        A: array of shape (N, m, m) giving the Levy areas that were used.
        I: array of shape (N, m, m) giving an m x m matrix of repeated Ito 
        integral values for each of the N time intervals.
    """
    N = dW.shape[0]
    m = dW.shape[1]
    if dW.ndim < 3:
        dW = dW.reshape((N, -1, 1)) # change to array of shape (N, m, 1)
    if dW.shape[2] != 1 or dW.ndim > 3:
        raise(ValueError)
    A = _Aterm(N, h, m, 1, dW)
    for k in range(2, n+1):
        A += _Aterm(N, h, m, k, dW)
    A = (h/(2.0*np.pi))*A
    I = 0.5*(_dot(dW, _t(dW)) - np.diag(h*np.ones(m))) + A
    dW = dW.reshape((N, -1)) # change back to shape (N, m)
    return (A, I)
matrix I approximating repeated Ito integrals for each of N time
    intervals, based on the method of Kloeden, Platen and Wright (1992).

    Args:
      dW (array of shape (N, m)): giving m independent Weiner increments for
        each time step N. (You can make this array using sdeint.deltaW())
      h (float): the time step size
      n (int, optional): how many terms to take in the series expansion

    Returns:
      (A, I) where
        A: array of shape (N, m, m) giving the Levy areas that were used.
        I: array of shape (N, m, m) giving an m x m matrix of repeated Ito 
        integral values for each of the N time intervals.
    
matrix I approximating repeated Ito integrals for each of N time
intervals, based on the method of Kloeden, Platen and Wright (1992).
matrix I approximating repeated Ito integrals for each of N time intervals based on the method of Kloeden Platen and Wright ( 1992 ) .
def Ikpw(dW, h, n=5):
    N = dW.shape[0]
    m = dW.shape[1]
    if dW.ndim < 3:
        dW = dW.reshape((N, -1, 1)) 
    if dW.shape[2] != 1 or dW.ndim > 3:
        raise(ValueError)
    A = _Aterm(N, h, m, 1, dW)
    for k in range(2, n+1):
        A += _Aterm(N, h, m, k, dW)
    A = (h/(2.0*np.pi))*A
    I = 0.5*(_dot(dW, _t(dW)) - np.diag(h*np.ones(m))) + A
    dW = dW.reshape((N, -1)) 
    return (A, I)
def Ikpw ( dW , h , n = 5 ) : N = dW . shape [ 0 ] m = dW . shape [ 1 ] if dW . ndim < 3 : dW = dW . reshape ( ( N , - 1 , 1 ) ) if dW . shape [ 2 ] != 1 or dW . ndim > 3 : raise ( ValueError ) A = _Aterm ( N , h , m , 1 , dW ) for k in range ( 2 , n + 1 ) : A += _Aterm ( N , h , m , k , dW ) A = ( h / ( 2.0 * np . pi ) ) * A I = 0.5 * ( _dot ( dW , _t ( dW ) ) - np . diag ( h * np . ones ( m ) ) ) + A dW = dW . reshape ( ( N , - 1 ) ) return ( A , I )
matrix I approximating repeated Ito integrals for each of N time
intervals, based on the method of Kloeden, Platen and Wright (1992).
matrix I approximating repeated Ito integrals for each of N time intervals based on the method of Kloeden Platen and Wright ( 1992 ) .
"""matrix I approximating repeated Ito integrals for each of N time
    intervals, based on the method of Kloeden, Platen and Wright (1992).

    Args:
      dW (array of shape (N, m)): giving m independent Weiner increments for
        each time step N. (You can make this array using sdeint.deltaW())
      h (float): the time step size
      n (int, optional): how many terms to take in the series expansion

    Returns:
      (A, I) where
        A: array of shape (N, m, m) giving the Levy areas that were used.
        I: array of shape (N, m, m) giving an m x m matrix of repeated Ito 
        integral values for each of the N time intervals.
    """ # change to array of shape (N, m, 1) # change back to shape (N, m)
(A, I) where
A: array of shape (N, m, m) giving the Levy areas that were used.
I: array of shape (N, m, m) giving an m x m matrix of repeated Ito
integral values for each of the N time intervals.
( A I ) where A : array of shape ( N m m ) giving the Levy areas that were used . I : array of shape ( N m m ) giving an m x m matrix of repeated Ito integral values for each of the N time intervals .
dW
giving m independent Weiner increments for
each time step N. (You can make this array using sdeint.deltaW())
giving m independent Weiner increments for each time step N . ( You can make this array using sdeint . deltaW () )
h
the time step size
the time step size
n
None