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# scipy.interpolate.make_interp_spline

`scipy.interpolate.``make_interp_spline`(x, y, k=3, t=None, bc_type=None, axis=0, check_finite=True)

  Compute the (coefficients of) interpolating B-spline.

  Parameters: | x : array_like, shape (n,) Abscissas. y : array_like, shape (n, ...) Ordinates. k : int, optional B-spline degree. Default is cubic, k=3. t : array_like, shape (nt + k + 1,), optional. Knots. The number of knots needs to agree with the number of datapoints and the number of derivatives at the edges. Specifically, `nt - n` must equal `len(deriv_l) + len(deriv_r)`. bc_type : 2-tuple or None Boundary conditions. Default is None, which means choosing the boundary conditions automatically. Otherwise, it must be a length-two tuple where the first element sets the boundary conditions at `x[0]` and the second element sets the boundary conditions at `x[-1]`. Each of these must be an iterable of pairs `(order, value)` which gives the values of derivatives of specified orders at the given edge of the interpolation interval. axis : int, optional Interpolation axis. Default is 0. check_finite : bool, optional Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. Default is True.
  Returns: | b : a BSpline object of the degree `k` and with knots `t`.

  See also

  `BSpline`
    base class representing the B-spline objects
  `CubicSpline`
    a cubic spline in the polynomial basis
  `make_lsq_spline`
    a similar factory function for spline fitting
  `UnivariateSpline`
    a wrapper over FITPACK spline fitting routines
  `splrep`
    a wrapper over FITPACK spline fitting routines

  Examples

  Use cubic interpolation on Chebyshev nodes:

      >>> def cheb_nodes(N):
      ...     jj = 2.*np.arange(N) + 1
      ...     x = np.cos(np.pi * jj / 2 / N)[::-1]
      ...     return x

      >>> x = cheb_nodes(20)
      >>> y = np.sqrt(1 - x**2)

      >>> from scipy.interpolate import BSpline, make_interp_spline
      >>> b = make_interp_spline(x, y)
      >>> np.allclose(b(x), y)
      True

  Note that the default is a cubic spline with a not-a-knot boundary condition

      >>> b.k
      3

  Here we use a ‘natural’ spline, with zero 2nd derivatives at edges:

      >>> l, r = [(2, 0)], [(2, 0)]
      >>> b_n = make_interp_spline(x, y, bc_type=(l, r))
      >>> np.allclose(b_n(x), y)
      True
      >>> x0, x1 = x[0], x[-1]
      >>> np.allclose([b_n(x0, 2), b_n(x1, 2)], [0, 0])
      True

  Interpolation of parametric curves is also supported. As an example, we compute a discretization of a snail curve in polar coordinates

      >>> phi = np.linspace(0, 2.*np.pi, 40)
      >>> r = 0.3 + np.cos(phi)
      >>> x, y = r*np.cos(phi), r*np.sin(phi)  # convert to Cartesian coordinates

  Build an interpolating curve, parameterizing it by the angle

      >>> from scipy.interpolate import make_interp_spline
      >>> spl = make_interp_spline(phi, np.c_[x, y])

  Evaluate the interpolant on a finer grid (note that we transpose the result to unpack it into a pair of x- and y-arrays)

      >>> phi_new = np.linspace(0, 2.*np.pi, 100)
      >>> x_new, y_new = spl(phi_new).T

  Plot the result

      >>> import matplotlib.pyplot as plt
      >>> plt.plot(x, y, 'o')
      >>> plt.plot(x_new, y_new, '-')
      >>> plt.show()

  (Source code)