# 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)

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

  In the inverse-weighted algorithm a number of 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 ) is calculated as follows:

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

  with 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)

  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])