SplineInterpolation1D

	SplineInterpolation1D
Physical quantities and units	MonkhorstPackGrid

Name

SplineInterpolation1D — Class for performing spline interpolations between data points from a one-dimensional data set.

Synopsis

Namespace: NanoLanguage

SplineInterpolation1D(
x_values,
y_values
)

Description

Constructor for the SplineInterpolation1D object.

SplineInterpolation1D Arguments

x_values

A list of x values of data points.

Type: list(float,...)

y_values

A list of y values of data points.

Type: list(float,...)

SplineInterpolation1D Methods

A SplineInterpolation1D object provides the following methods:

__call__(x): Calculate and return the spline interpolation at x, i.e. f(x) where f is a SplineInterpolation1D object.

x

The x value to interpolate for.

Type: float
derivatives(x): Calculate and return a tuple containing the derivatives (f, df/dx, d2f/dx2) of the spline interpolation evaluated at x.

x

The x value.

Type: float

Usage Examples

Define a spline interpolation of the sin function

x = numpy.linspace(-4,9,20)
y = numpy.sin(x)
f = SplineInterpolation1D(x,y)

Using the function we obtain

 >>> print f(3)
0.141203196688

>>> print f.derivatives(3)
(0.14120319668785397, -0.98998913849695858, -0.14589372176098986) 

>>> print numpy.array(f.derivatives(3)) - \
          numpy.array((numpy.sin(3), numpy.cos(3), -numpy.sin(3)))
[  8.31886280e-05   3.35810349e-06  -4.77371370e-03]

Notes

The data points does not need to have an increasing value of x.
The data points does not need to have an equidistant separation.
Function values outside the interpolation range will be extrapolated using the outermost spline function.


Physical quantities and units		MonkhorstPackGrid