quadrature_2d

quadrature_2d(
    f,
    min_x,
    max_x,
    min_y,
    max_y,
    absolute_tolerance=None,
    relative_tolerance=None,
    min_depth=None,
    max_depth=None,
)

Integrate a user-written function of two variables over a rectangle.

Computes the definite integral of f(x, y) over the rectangle [min_x, max_x] x [min_y, max_y] with the ported Numerics adaptive Simpson’s rule in two dimensions (P2 “math extras”): the tensor-product 3x3-point Simpson estimate over the whole domain is compared against the sum of the four quadrant sub-estimates, and the domain is subdivided into quadrants until the two agree to the requested tolerance.

Parameters

Name	Type	Description	Default
f	callable	A function taking two numbers (x, y) and returning one number.	required
min_x	float	The bounds of the rectangle. max_x must be above min_x, and max_y above min_y.	required
max_x	float	The bounds of the rectangle. max_x must be above min_x, and max_y above min_y.	required
min_y	float	The bounds of the rectangle. max_x must be above min_x, and max_y above min_y.	required
max_y	float	The bounds of the rectangle. max_x must be above min_x, and max_y above min_y.	required
absolute_tolerance	float	The convergence tolerances on the difference between the whole-domain and quadrant-subdivided estimates. Each must lie between 1e-15 and 1. Left unset, the ported integrator’s own defaults (1e-8) apply.	None
relative_tolerance	float	The convergence tolerances on the difference between the whole-domain and quadrant-subdivided estimates. Each must lie between 1e-15 and 1. Left unset, the ported integrator’s own defaults (1e-8) apply.	None
min_depth	int	The recursion-depth bounds. Left unset, the ported class’s own defaults (0 and 100) apply.	None
max_depth	int	The recursion-depth bounds. Left unset, the ported class’s own defaults (0 and 100) apply.	None

Returns

Name	Type	Description
	QuadratureResult	The integral, a float carrying the same three fields :func:quadrature returns: status, function_evaluations, and standard_error.

Examples

>>> import corehydropy as ch
>>> round(ch.quadrature_2d(lambda x, y: x + y, 0, 1, 0, 1), 3)
1.0