SciPy

numpy.interp

numpy.interp(x, xp, fp, left=None, right=None, period=None)[source]

One-dimensional linear interpolation.

Returns the one-dimensional piecewise linear interpolant to a function with given values at discrete data-points.

Parameters:

x : array_like

The x-coordinates of the interpolated values.

xp : 1-D sequence of floats

The x-coordinates of the data points, must be increasing if argument period is not specified. Otherwise, xp is internally sorted after normalizing the periodic boundaries with xp = xp % period.

fp : 1-D sequence of floats

The y-coordinates of the data points, same length as xp.

left : float, optional

Value to return for x < xp[0], default is fp[0].

right : float, optional

Value to return for x > xp[-1], default is fp[-1].

period : None or float, optional

New in version 1.10.0.

A period for the x-coordinates. This parameter allows the proper interpolation of angular x-coordinates. Parameters left and right are ignored if period is specified.

Returns:

y : {float, ndarray}

The interpolated values, same shape as x.

Raises:

ValueError

If xp and fp have different length If xp or fp are not 1-D sequences If period == 0

Notes

Does not check that the x-coordinate sequence xp is increasing. If xp is not increasing, the results are nonsense. A simple check for increasing is:

np.all(np.diff(xp) > 0)

Examples

>>> xp = [1, 2, 3]
>>> fp = [3, 2, 0]
>>> np.interp(2.5, xp, fp)
1.0
>>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)
array([ 3. ,  3. ,  2.5 ,  0.56,  0. ])
>>> UNDEF = -99.0
>>> np.interp(3.14, xp, fp, right=UNDEF)
-99.0

Plot an interpolant to the sine function:

>>> x = np.linspace(0, 2*np.pi, 10)
>>> y = np.sin(x)
>>> xvals = np.linspace(0, 2*np.pi, 50)
>>> yinterp = np.interp(xvals, x, y)
>>> import matplotlib.pyplot as plt
>>> plt.plot(x, y, 'o')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.plot(xvals, yinterp, '-x')
[<matplotlib.lines.Line2D object at 0x...>]
>>> plt.show()

(Source code, png, pdf)

../../_images/numpy-interp-1_00_00.png

Interpolation with periodic x-coordinates:

>>> x = [-180, -170, -185, 185, -10, -5, 0, 365]
>>> xp = [190, -190, 350, -350]
>>> fp = [5, 10, 3, 4]
>>> np.interp(x, xp, fp, period=360)
array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75])

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