Maintainer | diagrams-discuss@googlegroups.com |
---|---|

Safe Haskell | Safe-Inferred |

A *cubic spline* is a smooth, connected sequence of cubic curves
passing through a given sequence of points. This module implements
a straightforward spline generation algorithm based on solving
tridiagonal systems of linear equations.

- solveTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]
- solveCyclicTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> a -> a -> [a]
- solveCubicSplineDerivatives :: Fractional a => [a] -> [a]
- solveCubicSplineDerivativesClosed :: Fractional a => [a] -> [a]
- solveCubicSplineCoefficients :: Fractional a => Bool -> [a] -> [[a]]

# Solving for spline coefficents

solveTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]Source

Solves a system of the form 'A*X=D' for `x`

where `A`

is an
`n`

by `n`

matrix with `bs`

as the main diagonal and
`as`

the diagonal below and `cs`

the diagonal above.
See: http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

solveCyclicTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> a -> a -> [a]Source

Solves a system similar to the tri-diagonal system using a special case
of the Sherman-Morrison formula http://en.wikipedia.org/wiki/Sherman-Morrison_formula.
This code is based on *Numerical Recpies in C*'s `cyclic`

function in section 2.7.

solveCubicSplineDerivatives :: Fractional a => [a] -> [a]Source

Use the tri-diagonal solver with the appropriate parameters for an open cubic spline.

solveCubicSplineDerivativesClosed :: Fractional a => [a] -> [a]Source

Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.

solveCubicSplineCoefficients :: Fractional a => Bool -> [a] -> [[a]]Source

Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.