#### Previous topic

Interpolation (`scipy.interpolate`)

# scipy.interpolate.interp1d

class `scipy.interpolate.``interp1d`(x, y, kind='linear', axis=-1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)

  Interpolate a 1-D function.

  x and y are arrays of values used to approximate some function f: `y = f(x)`. This class returns a function whose call method uses interpolation to find the value of new points.

  Note that calling `interp1d` with NaNs present in input values results in undefined behaviour.

  Parameters:

  x : (N,) array_like

  > A 1-D array of real values.

  y : (…,N,…) array_like

  > A N-D array of real values. The length of y along the interpolation axis must be equal to the length of x.

  kind : str or int, optional

  > Specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’ where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order) or as an integer specifying the order of the spline interpolator to use. Default is ‘linear’.

  axis : int, optional

  > Specifies the axis of y along which to interpolate. Interpolation defaults to the last axis of y.

  copy : bool, optional

  > If True, the class makes internal copies of x and y. If False, references to x and y are used. The default is to copy.

  bounds_error : bool, optional

  > If True, a ValueError is raised any time interpolation is attempted on a value outside of the range of x (where extrapolation is necessary). If False, out of bounds values are assigned `fill_value`. By default, an error is raised unless fill_value=”extrapolate”.

  fill_value : array-like or (array-like, array_like) or “extrapolate”, optional

  > - if a ndarray (or float), this value will be used to fill in for requested points outside of the data range. If not provided, then the default is NaN. The array-like must broadcast properly to the dimensions of the non-interpolation axes.

  > - If a two-element tuple, then the first element is used as a fill value for `x_new < x[0]` and the second element is used for `x_new > x[-1]`. Anything that is not a 2-element tuple (e.g., list or ndarray, regardless of shape) is taken to be a single array-like argument meant to be used for both bounds as `below, above = fill_value, fill_value`.

  >   New in version 0.17.0.

  > - If “extrapolate”, then points outside the data range will be extrapolated.

  >   New in version 0.17.0.

  assume_sorted : bool, optional

  > If False, values of x can be in any order and they are sorted first. If True, x has to be an array of monotonically increasing values.

  See also

  `splrep`, `splev`

  `UnivariateSpline`
    An object-oriented wrapper of the FITPACK routines.
  `interp2d`
    2-D interpolation

  Examples

      >>> import matplotlib.pyplot as plt
      >>> from scipy import interpolate
      >>> x = np.arange(0, 10)
      >>> y = np.exp(-x/3.0)
      >>> f = interpolate.interp1d(x, y)

      >>> xnew = np.arange(0, 9, 0.1)
      >>> ynew = f(xnew)   # use interpolation function returned by `interp1d`
      >>> plt.plot(x, y, 'o', xnew, ynew, '-')
      >>> plt.show()

  (Source code)

  Attributes

  `fill_value` |

  Methods

  `__call__`(x) | Evaluate the interpolant