Interpolate (compmech.interpolate)

This module includes some interpolation utilities that will be used in other modules.

compmech.interpolate.inv_weighted(data, mesh, num_sub, col, ncp=5, power_parameter=2)[source]

Interpolates the values taken at one group of points into another using an inverse-weighted algorithm

In the inverse-weighted algorithm a number of n_{CP} measured points of the input parameter data that are closest to a given node in the input parameter mesh are found and the imperfection value of this node (represented by the normal displacement {w_0}_{node}) is calculated as follows:

{w_0}_{node} = \frac{\sum_{i}^{n_{CP}}{{w_0}_i\frac{1}{w_i}}}
                    {\sum_{i}^{n_{CP}}{\frac{1}{w_i}}}

where w_i is the imperfection at each measured point, calculated as:

w_i = \left[(x_{node}-x_i)^2+(y_{node}-y_i)^2+(z_{node}-y_i)^2
      \right]^p

with p being a power parameter that when increased will increase the relative influence of a closest point.

Parameters:

data : numpy.ndarray, shape (N, ndim+1)

The data or an array containing the imperfection file. The values to be interpolated must be in the last column.

mesh : numpy.ndarray, shape (M, ndim)

The new coordinates where the values will be interpolated to.

num_sub : int

The number of sub-sets used during the interpolation. The points are divided in sub-sets to increase the algorithm’s efficiency.

col : int

The index of the column to be used in order to divide the data in sub-sets. Note that the first column index is 0.

ncp : int, optional

Number of closest points used in the inverse-weighted interpolation.

power_parameter : float, optional

Power of inverse weighted interpolation function.

Returns:

ans : numpy.ndarray

A 1-D array with the interpolated values. The size of this array is mesh.shape[0].

compmech.interpolate.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.

Note

This function has been incorporated in NumPy >= 1.10.0 and will be soon removed from here.

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 : float, optional

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

Interpolation with periodic x-coordinates:

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