API Documentation Generated by Endo, 2006-08-14

Function summary

• cumtrapz(y, x = None, dx = 1.0, axis = -Const(1))
• fixed_quad(func, a, b, args = (), n = 5)
• quadrature(func, a, b, args = (), tol = 1.4899999999999999e-008, maxiter = 50, vec_func = True)
• romb(y, dx = 1.0, axis = -Const(1), show = False)
• romberg(function, a, b, args = (), tol = 1.48e-008, show = False, divmax = 10, vec_func = False)
• simps(y, x = None, dx = 1, axis = -Const(1), even = 'avg')
• tupleset(t, i, value)
• vectorize1(func, args = (), vec_func = False)

Functions

• cumtrapz(y, x = None, dx = 1.0, axis = -Const(1))

  Cumulatively integrate y(x) using samples along the given axis and the composite trapezoidal rule. If x is None, spacing given by dx is assumed.

• fixed_quad(func, a, b, args = (), n = 5)

  Compute a definite integral using fixed-order Gaussian quadrature.
  
  Description:
  
    Integrate func from a to b using Gaussian quadrature of order n.
  
  Inputs:
  
    func -- a Python function or method to integrate
            (must accept vector inputs)
    a -- lower limit of integration
    b -- upper limit of integration
    args -- extra arguments to pass to function.
    n -- order of quadrature integration.
  
  Outputs: (val, None)
  
    val -- Gaussian quadrature approximation to the integral.
  
    

• quadrature(func, a, b, args = (), tol = 1.4899999999999999e-008, maxiter = 50, vec_func = True)

  Compute a definite integral using fixed-tolerance Gaussian quadrature.
  
  Description:
  
    Integrate func from a to b using Gaussian quadrature
    with absolute tolerance tol.
  
  Inputs:
  
    func -- a Python function or method to integrate.
    a -- lower limit of integration.
    b -- upper limit of integration.
    args -- extra arguments to pass to function.
    tol -- iteration stops when error between last two iterates is less than
           tolerance.
    maxiter -- maximum number of iterations.
    vec_func -- True or False if func handles arrays as arguments (is
                a "vector" function ). Default is True.
  
  Outputs: (val, err)
  
    val -- Gaussian quadrature approximation (within tolerance) to integral.
    err -- Difference between last two estimates of the integral.
  
    

• romb(y, dx = 1.0, axis = -Const(1), show = False)

  Uses Romberg integration to integrate y(x) using N samples along the given axis which are assumed equally spaced with distance dx. The number of samples must be 1 + a non-negative power of two: N=2**k + 1

• romberg(function, a, b, args = (), tol = 1.48e-008, show = False, divmax = 10, vec_func = False)

  Romberg integration of a callable function or method.
  
  Returns the integral of |function| (a function of one variable)
  over |interval| (a sequence of length two containing the lower and
  upper limit of the integration interval), calculated using
  Romberg integration up to the specified |accuracy|. If |show| is 1,
  the triangular array of the intermediate results will be printed.
  If |vec_func| is True (default is False), then |function| is
  assumed to support vector arguments.
  

• simps(y, x = None, dx = 1, axis = -Const(1), even = 'avg')

  Integrate y(x) using samples along the given axis and the composite Simpson's rule. If x is None, spacing of dx is assumed.

  If there are an even number of samples, N, then there are an odd number of intervals (N-1), but Simpson's rule requires an even number of intervals. The parameter 'even' controls how this is handled as follows:

  even='avg': Average two results: 1) use the first N-2 intervals with

  a trapezoidal rule on the last interval and 2) use the last N-2 intervals with a trapezoidal rule on the first interval

  even='first': Use Simpson's rule for the first N-2 intervals with

  a trapezoidal rule on the last interval.

  even='last': Use Simpson's rule for the last N-2 intervals with a

  trapezoidal rule on the first interval.

  For an odd number of samples that are equally spaced the result is

  exact if the function is a polynomial of order 3 or less. If the samples are not equally spaced, then the result is exact only if the function is a polynomial of order 2 or less.

• tupleset(t, i, value)
• vectorize1(func, args = (), vec_func = False)

Imported names