SciPy 0.6.0 API Documentation Generated by Endo, 2007-10-17

Function summary

• composite(f, x = None, dx = 1, axis = -Const(1), n = 5)
• cumtrapz(y, x = None, dx = 1.0, axis = -Const(1))
• fixed_quad(func, a, b, args = (), n = 5)
• newton_cotes(rn, equal = 0)
• quadrature(func, a, b, args = (), tol = 1.4899999999999999e-08, maxiter = 50, vec_func = True)
• romb(y, dx = 1.0, axis = -Const(1), show = False)
• romberg(function, a, b, args = (), tol = 1.48e-08, 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

• composite(f, x = None, dx = 1, axis = -Const(1), n = 5)
• 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.

  See also:

  quad - adaptive quadrature using QUADPACK romberg - adaptive Romberg quadrature quadrature - adaptive Gaussian quadrature fixed_quad - fixed-order Gaussian quadrature dblquad, tplquad - double and triple integrals romb, trapz - integrators for sampled data cumtrapz - cumulative integration for sampled data ode, odeint - ODE integrators

• 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.
  
  See also:
    
    quad - adaptive quadrature using QUADPACK
    dblquad, tplquad - double and triple integrals
    romberg - adaptive Romberg quadrature
    quadrature - adaptive Gaussian quadrature
    romb, simps, trapz - integrators for sampled data
    cumtrapz - cumulative integration for sampled data
    ode, odeint - ODE integrators
    

• newton_cotes(rn, equal = 0)

  Return weights and error coefficient for Netwon-Cotes integration.
  
   Suppose we have (N+1) samples of f at the positions
     x_0, x_1, ..., x_N.  Then an N-point Newton-Cotes formula for the
     integral between x_0 and x_N is:
  
   $\int_{x_0}^{x_N} f(x)dx = \Delta x \sum_{i=0}^{N} a_i f(x_i)
                              + B_N (\Delta x)^{N+2} f^{N+1} (\xi)$
  
     where $\xi \in [x_0,x_N]$ and $\Delta x = \frac{x_N-x_0}{N}$ is the
     averages samples spacing. 
  
   If the samples are equally-spaced and N is even, then the error
   term is $B_N (\Delta x)^{N+3} f^{N+2}(\xi)$.
  
   Normally, the Newton-Cotes rules are used on smaller integration
   regions and a composite rule is used to return the total integral.
  
  Inputs:
      rn    -- the integer order for equally-spaced data
               or the relative positions of the samples with
               the first sample at 0 and the last at N, where
               N+1 is the length of rn.  N is the order of the Newt
      equal -- Set to 1 to enforce equally spaced data
  
  Outputs:
      an    -- 1-d array of weights to apply to the function at
               the provided sample positions.
      B     -- error coefficient
  

• quadrature(func, a, b, args = (), tol = 1.4899999999999999e-08, 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.
  
  See also:
    
    romberg - adaptive Romberg quadrature
    fixed_quad - fixed-order Gaussian quadrature
    quad - adaptive quadrature using QUADPACK
    dblquad, tplquad - double and triple integrals
    romb, simps, trapz - integrators for sampled data
    cumtrapz - cumulative integration for sampled data
    ode, odeint - ODE integrators
    

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

  Romberg integration using samples of a function
  
  Inputs:
  
     y    -  a vector of 2**k + 1 equally-spaced samples of a fucntion
     dx   -  the sample spacing.
     axis -  the axis along which to integrate
     show -  When y is a single 1-d array, then if this argument is True
             print the table showing Richardson extrapolation from the
             samples.
  
  Output: ret
  
     ret  - The integrated result for each axis. 
  
  See also:
  
    quad - adaptive quadrature using QUADPACK
    romberg - adaptive Romberg quadrature
    quadrature - adaptive Gaussian quadrature
    fixed_quad - fixed-order Gaussian quadrature
    dblquad, tplquad - double and triple integrals
    simps, trapz - integrators for sampled data
    cumtrapz - cumulative integration for sampled data
    ode, odeint - ODE integrators
  

• romberg(function, a, b, args = (), tol = 1.48e-08, 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.
  
  See also:
  
    quad - adaptive quadrature using QUADPACK
    quadrature - adaptive Gaussian quadrature
    fixed_quad - fixed-order Gaussian quadrature
    dblquad, tplquad - double and triple integrals
    romb, simps, trapz - integrators for sampled data
    cumtrapz - cumulative integration for sampled data
    ode, odeint - ODE integrators
  

• 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.

  See also:

  quad - adaptive quadrature using QUADPACK romberg - adaptive Romberg quadrature quadrature - adaptive Gaussian quadrature fixed_quad - fixed-order Gaussian quadrature dblquad, tplquad - double and triple integrals romb, trapz - integrators for sampled data cumtrapz - cumulative integration for sampled data ode, odeint - ODE integrators

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

Imported Names