relentless.math.Interpolator

class relentless.math.Interpolator(x, y)

Interpolating function.

Interpolates through a function \(y(x)\) on the domain \(a \le x \le b\). Outside this domain, y is extrapolated as a constant, i.e., \(y(x < a) = y(a)\) and \(y(x > b) = y(b)\).

Parameters:

• x (array_like) – 1D array of x coordinates that must be continually increasing.

• y (array_like) – 1D array of y coordinates.

Raises:

• ValueError – If x is a scalar.

• ValueError – If x is not 1-dimensional.

• ValueError – If y is not the same shape as x.

• ValueError – If x is not strictly increasing.

Examples

Interpolating the line \(y=2x\):

f = Interpolator(x=(-1,0,1), y=(-2,0,2))

Evaluating the function:

>>> f(0.5)
1.0
>>> f([-0.5,0.5])
(-1.0, 1.0)

Evaluate the \(n\)th derivative of the function:

>>> f.derivative(x=0.5, n=1)
2.0
>>> f.derivative(x=[-2.5,-0.5,0.5,2.5], n=1)
(0.0, 2.0, 2.0, 0.0)

Extrapolation:

>>> f(100)
2.0

Methods

derivative(x, n)

Evaluate the \(n\)th derivative of the interpolating function.

Attributes

domain	The valid domain for interpolation.
table	The interpolated data.

derivative(x, n)

Evaluate the \(n\)th derivative of the interpolating function.

Parameters:

• x (float or array_like) – 1-d array of \(x\) coordinates to evaluate.

• n (int) – The order of the derivative to take.

Returns:

result – Interpolated derivative values having the same form as x.

Return type:

float or numpy.ndarray

property domain

The valid domain for interpolation.

Type:

tuple

property table

The interpolated data.

Type:

numpy.ndarray