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# scipy.interpolate.PchipInterpolator

class `scipy.interpolate.``PchipInterpolator`(x, y, axis=0, extrapolate=None)

  PCHIP 1-d monotonic cubic interpolation.

  `x` and y are arrays of values used to approximate some function f, with `y = f(x)`. The interpolant uses monotonic cubic splines to find the value of new points. (PCHIP stands for Piecewise Cubic Hermite Interpolating Polynomial).

  Parameters:

  x : ndarray

  > A 1-D array of monotonically increasing real values. `x` cannot include duplicate values (otherwise f is overspecified)

  y : ndarray

  > A 1-D array of real values. y‘s length along the interpolation axis must be equal to the length of `x`. If N-D array, use `axis` parameter to select correct axis.

  axis : int, optional

  > Axis in the y array corresponding to the x-coordinate values.

  extrapolate : bool, optional

  > Whether to extrapolate to ouf-of-bounds points based on first and last intervals, or to return NaNs.

  See also

  `Akima1DInterpolator`

  Notes

  The interpolator preserves monotonicity in the interpolation data and does not overshoot if the data is not smooth.

  The first derivatives are guaranteed to be continuous, but the second derivatives may jump at \(x_k\).

  Determines the derivatives at the points \(x_k\), \(f'_k\), by using PCHIP algorithm [R49].

  Let \(h_k = x_{k+1} - x_k\), and \(d_k = (y_{k+1} - y_k) / h_k\) are the slopes at internal points \(x_k\). If the signs of \(d_k\) and \(d_{k-1}\) are different or either of them equals zero, then \(f'_k = 0\). Otherwise, it is given by the weighted harmonic mean

  \[\frac{w_1 + w_2}{f'_k} = \frac{w_1}{d_{k-1}} + \frac{w_2}{d_k}\]

  where \(w_1 = 2 h_k + h_{k-1}\) and \(w_2 = h_k + 2 h_{k-1}\).

  The end slopes are set using a one-sided scheme [R50].

  References

  [R49] | (1, 2) F. N. Fritsch and R. E. Carlson, Monotone Piecewise Cubic Interpolation, SIAM J. Numer. Anal., 17(2), 238 (1980). DOI:10.1137/0717021

  [R50] | (1, 2) see, e.g., C. Moler, Numerical Computing with Matlab, 2004. DOI: http://dx.doi.org/10.1137/1.9780898717952

  Methods

  `__call__`(x[, nu, extrapolate]) | Evaluate the piecewise polynomial or its derivative
  `derivative`([nu]) | Construct a new piecewise polynomial representing the derivative.
  `antiderivative`([nu]) | Construct a new piecewise polynomial representing the antiderivative.
  `roots`() | Return the roots of the interpolated function.