tf_quant_finance.math.integration.gauss_legendre

Last updated: 2023-03-16.

tf_quant_finance.math.integration.gauss_legendre#

View source

Evaluates definite integral using Gauss-Legendre quadrature.

tf_quant_finance.math.integration.gauss_legendre(
    func, lower, upper, num_points=32, dtype=None, name=None
)

Integrates func using Gauss-Legendre quadrature [1].

Applies change of variables to the function to obtain the [-1,1] integration interval. Takes the sum of values obtained from evaluating the new function at points given by the roots of the Legendre polynomial of degree num_points, multiplied with corresponding precalculated coefficients.

References#

[1] https://en.wikipedia.org/wiki/Gauss–Legendre_quadrature

Example#

  f = lambda x: x*x
  a = tf.constant(0.0)
  b = tf.constant(3.0)
  gauss_legendre(f, a, b, num_points=15) # 9.0

Args:#

  • func: Represents a function to be integrated. It must be a callable of a single Tensor parameter and return a Tensor of the same shape and dtype as its input. It will be called with a Tensor of shape lower.shape + [n] (where n is integer number of points) and of the same dtype as lower.

  • lower: Represents the lower limits of integration. func will be integrated between each pair of points defined by lower and upper.

  • upper: Same shape and dtype as lower representing the upper limits of intergation.

  • num_points: Number of points at which the function func will be evaluated. Implemented for 2-15,20,32. Default value: 32.

  • dtype: If supplied, the dtype for the lower and upper. Result will have the same dtype. Default value: None which maps to dtype of lower.

  • name: The name to give to the ops created by this function. Default value: None which maps to ‘gauss_legendre’.

Returns:#

Tensor of shape func_batch_shape + limits_batch_shape, containing value of the definite integral.

Contents