tf_quant_finance.math.integration.simpson

Last updated: 2023-03-16.

tf_quant_finance.math.integration.simpson#

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Evaluates definite integral using composite Simpson’s 1/3 rule.

tf_quant_finance.math.integration.simpson(
    func, lower, upper, num_points=1001, dtype=None, name=None
)

Integrates func using composite Simpson’s 1/3 rule [1].

Evaluates function at points of evenly spaced grid of num_points points, then uses obtained values to interpolate func with quadratic polynomials and integrates these polynomials.

References#

[1] Weisstein, Eric W. “Simpson’s Rule.” From MathWorld - A Wolfram Web Resource. http://mathworld.wolfram.com/SimpsonsRule.html

Example#

  f = lambda x: x*x
  a = tf.constant(0.0)
  b = tf.constant(3.0)
  simpson(f, a, b, num_points=1001) # 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 function func will be evaluated. Must be odd and at least 3. Default value: 1001.

  • 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 ‘integrate_simpson_composite’.

Returns:#

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

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