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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Diagrams-CubicSpline-Internal.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">diagrams-lib-0.5: Embedded domain-specific language for declarative graphics</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Maintainer</th><td>diagrams-discuss@googlegroups.com</td></tr><tr><th>Safe Haskell</th><td>Safe-Infered</td></tr></table><p class="caption">Diagrams.CubicSpline.Internal</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Solving for spline coefficents
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A <em>cubic spline</em> 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.
</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:solveTriDiagonal">solveTriDiagonal</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a] -> [a] -> [a] -> [a]</li><li class="src short"><a href="#v:solveCyclicTriDiagonal">solveCyclicTriDiagonal</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a] -> [a] -> [a] -> a -> a -> [a]</li><li class="src short"><a href="#v:solveCubicSplineDerivatives">solveCubicSplineDerivatives</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a]</li><li class="src short"><a href="#v:solveCubicSplineDerivativesClosed">solveCubicSplineDerivativesClosed</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a]</li><li class="src short"><a href="#v:solveCubicSplineCoefficients">solveCubicSplineCoefficients</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Data-Bool.html#t:Bool">Bool</a> -> [a] -> [[a]]</li></ul></div><div id="interface"><h1 id="g:1">Solving for spline coefficents
</h1><div class="top"><p class="src"><a name="v:solveTriDiagonal" class="def">solveTriDiagonal</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a] -> [a] -> [a] -> [a]<a href="src/Diagrams-CubicSpline-Internal.html#solveTriDiagonal" class="link">Source</a></p><div class="doc"><p>Solves a system of the form 'A*X=D' for <code>x</code> where <code>A</code> is an
<code>n</code> by <code>n</code> matrix with <code>bs</code> as the main diagonal and
<code>as</code> the diagonal below and <code>cs</code> the diagonal above.
See: <a href="http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm">http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm</a>
</p></div></div><div class="top"><p class="src"><a name="v:solveCyclicTriDiagonal" class="def">solveCyclicTriDiagonal</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a] -> [a] -> [a] -> a -> a -> [a]<a href="src/Diagrams-CubicSpline-Internal.html#solveCyclicTriDiagonal" class="link">Source</a></p><div class="doc"><p>Solves a system similar to the tri-diagonal system using a special case
of the Sherman-Morrison formula <a href="http://en.wikipedia.org/wiki/Sherman-Morrison_formula">http://en.wikipedia.org/wiki/Sherman-Morrison_formula</a>.
This code is based on <em>Numerical Recpies in C</em>'s <code>cyclic</code> function in section 2.7.
</p></div></div><div class="top"><p class="src"><a name="v:solveCubicSplineDerivatives" class="def">solveCubicSplineDerivatives</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a]<a href="src/Diagrams-CubicSpline-Internal.html#solveCubicSplineDerivatives" class="link">Source</a></p><div class="doc"><p>Use the tri-diagonal solver with the appropriate parameters for an open cubic spline.
</p></div></div><div class="top"><p class="src"><a name="v:solveCubicSplineDerivativesClosed" class="def">solveCubicSplineDerivativesClosed</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => [a] -> [a]<a href="src/Diagrams-CubicSpline-Internal.html#solveCubicSplineDerivativesClosed" class="link">Source</a></p><div class="doc"><p>Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.
</p></div></div><div class="top"><p class="src"><a name="v:solveCubicSplineCoefficients" class="def">solveCubicSplineCoefficients</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.5.0.0/Data-Bool.html#t:Bool">Bool</a> -> [a] -> [[a]]<a href="src/Diagrams-CubicSpline-Internal.html#solveCubicSplineCoefficients" class="link">Source</a></p><div class="doc"><p>Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.
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