Interpolation (`cmlabs.interpolate`)

The cmlabs.interpolate module provides a collection of interpolation methods and related utilities.

Lagrange/Newton interpolation

`lagrange`	Lagrange interpolation polynomial value at \(x\).
`remainder`	Remainder in interpolation formulas.
`divided_differences`	Return the ordered divided differences list.
`newton`	Newton interpolation polynomial value at \(x\).

`finite_differences`	Return the finite differences table.
`forward_differences`	Return the forward differences list for \(f(x_0)\).
`backward_differences`	Return the backward differences list for \(f(x_n)\).
`newtonfd`	Newton's forward interpolation formula.
`newtonbd`	Newton's backward interpolation formula.
`gaussfd`	Gauss’s forward interpolation formula.
`gaussbd`	Gauss’s backward interpolation formula.
`stirling`	Stirling's interpolation formula.
`bessel`	Bessel's interpolation formula.
`interpolate`	Interpolate the value of a function at a given point.

Cubic spline data interpolator.

`test_lagrange_degree`	Calculate Lagrange interpolation polynomial of degree 1 at \(x^*\).
`test_lagrange_remainder_1`	Estimate the derivative and remainder degree 1.
`test_lagrange_degree_2`	Calculate Lagrange interpolation polynomial of degree 2 at \(x^*\).
`test_lagrange_remainder_2`	Estimate the derivative and remainder degree 2.
`test_lagrange_compare_with_newton`	Compare Lagrange and Newton interpolation.
`test_interpolate_remainder`	Estimate the remainder of interpolation.
`test_cubic_spline`	Cubic spline interpolation/differentiation.
`test_lagrange_from_docs_example`	Lagrange interpolation from docs example.
`test_remainder_from_docs_example`	Remainder from docs example.
`test_newton_from_docs_example`	Newton interpolation from docs example.
`test_finite_differences_from_docs_example`	Finite differences from docs example.
`test_forward_differences_from_docs_example`	Forward differences from docs example.
`test_backward_differences_from_docs_example`	Backward differences from docs example.
`test_newtonfd_from_docs_example`	Newton's forward interpolation formula from docs example.
`test_newtonbd_from_docs_example`	Newton's backward interpolation formula from docs example.
`test_gaussfd_from_docs_example`	Gauss’s forward interpolation formula from docs example.
`test_gaussbd_from_docs_example`	Gauss’s backward interpolation formula from docs example.
`test_cubic_spline_from_docs_example`	Cubic spline interpolation from docs example.