DOUBLE_DEFINITE_INTEGRAL

Compute the double integral of a symbolic input function. Example of proper syntax for the function input: 2*x*y Example of improper syntax for the function input: 2xy Params: function : str The function that we are integrating. upper_bound_x : float The upper bound for x. lower_bound_x : float The lower bound for x. upper_bound_y : float The upper bound for y. lower_bound_y : float The lower bound for y. Returns: out : Scalar The result of the double definite integral.

Python Code

from flojoy import flojoy, Scalar
from scipy import integrate
from sympy import parse_expr, lambdify


@flojoy(deps={"sympy": "1.12"})
def DOUBLE_DEFINITE_INTEGRAL(
    function: str = "",
    upper_bound_x: float = 0.0,
    lower_bound_x: float = 0.0,
    upper_bound_y: float = 0.0,
    lower_bound_y: float = 0.0,
) -> Scalar:
    """Compute the double integral of a symbolic input function.

    Example of proper syntax for the function input:
    2*x*y

    Example of improper syntax for the function input:
    2xy

    Parameters
    ----------
    function : str
        The function that we are integrating.
    upper_bound_x : float
        The upper bound for x.
    lower_bound_x : float
        The lower bound for x.
    upper_bound_y : float
        The upper bound for y.
    lower_bound_y : float
        The lower bound for y.

    Returns
    -------
    Scalar
        The result of the double definite integral.
    """

    func = parse_expr(function)
    symbols = tuple(func.free_symbols)

    f = lambdify(symbols, func)

    result = integrate.nquad(
        f, [(lower_bound_x, upper_bound_x), (lower_bound_y, upper_bound_y)]
    )[0]

    return Scalar(c=result)

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Example

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In this example, DOUBLE_DEFINITE_INTEGRAL node generates a Scalar type value with the following parameters.

Function: x*y

Upper_bound_x: 2

Lower_bound_x: 0

Upper_bound_y: 1

Lower_bound_y: 0

The DOUBLE_DEFINITE_INTEGRAL result is equal to 1. So 1 is added to the SINE node moving up every value of the sine function by 1. This difference is visible when you compare the two SCATTER nodes.