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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html><head><meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1">
<title>polylib.c File Reference</title>
<link href="doxygen.css" rel="stylesheet" type="text/css">
</head><body>
<!-- Generated by Doxygen 1.3 -->
<center>
<a class="qindex" href="index.html">Main Page</a> <a class="qindex" href="files.html">File List</a> <a class="qindex" href="globals.html">File Members</a> </center>
<hr><h1>polylib.c File Reference</h1><code>#include <stdlib.h></code><br>
<code>#include <sys/types.h></code><br>
<code>#include <stdio.h></code><br>
<code>#include <float.h></code><br>
<code>#include <math.h></code><br>
<code>#include "<a class="el" href="polylib_8h-source.html">polylib.h</a>"</code><br>
<p>
<a href="polylib_8c-source.html">Go to the source code of this file.</a><table border=0 cellpadding=0 cellspacing=0>
<tr><td></td></tr>
<tr><td colspan=2><br><h2>Defines</h2></td></tr>
<tr><td nowrap align=right valign=top>#define </td><td valign=bottom><a class="el" href="polylib_8c.html#a0">STOP</a> 30</td></tr>
<tr><td nowrap align=right valign=top>#define </td><td valign=bottom><a class="el" href="polylib_8c.html#a1">EPS</a> 100*DBL_EPSILON</td></tr>
<tr><td nowrap align=right valign=top>#define </td><td valign=bottom><a class="el" href="polylib_8c.html#a2">sign</a>(a, b) ((b)<0 ? -fabs(a) : fabs(a))</td></tr>
<tr><td nowrap align=right valign=top>#define </td><td valign=bottom><a class="el" href="polylib_8c.html#a3">jacobz</a>(n, z, alpha, beta) JacZeros(n,z,alpha,beta)</td></tr>
<tr><td> </td><td><em class="mdesc">zero determination using eigenvalues of tridiagaonl matrix</em> <a href="#a3"></a><em></em><br><br></td></tr>
<tr><td colspan=2><br><h2>Functions</h2></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a4">Jacobz</a> (int n, double *z, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Calculate the <em>n</em> zeros, <em>z</em>, of the Jacobi polynomial, i.e. <img align="top" src="form_23.png"> .</em> <a href="#a4"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a5">JacZeros</a> (int n, double *a, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Zero determination through the eigenvalues of a tridiagonal matrix from teh three term recursion relationship.</em> <a href="#a5"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a6">TriQL</a> (int n, double *d, double *e)</td></tr>
<tr><td> </td><td><em class="mdesc">QL algorithm for symmetric tridiagonal matrix.</em> <a href="#a6"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>double </td><td valign=bottom><a class="el" href="polylib_8c.html#a7">gammaF</a> (double)</td></tr>
<tr><td> </td><td><em class="mdesc">Calculate the Gamma function , <img align="top" src="form_19.png"> , for integer values and halves.</em> <a href="#a7"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a8">zwgj</a> (double *z, double *w, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Gauss-Jacobi zeros and weights.</em> <a href="#a8"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a9">zwgrjm</a> (double *z, double *w, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Gauss-Radau-Jacobi zeros and weights with end point at <em>z=-1</em>.</em> <a href="#a9"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a10">zwgrjp</a> (double *z, double *w, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Gauss-Radau-Jacobi zeros and weights with end point at <em>z=1</em>.</em> <a href="#a10"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a11">zwglj</a> (double *z, double *w, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Gauss-Lobatto-Jacobi zeros and weights with end point at <em>z=-1</em>,<em>1</em>.</em> <a href="#a11"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a12">Dgj</a> (double *D, double *Dt, double *z, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.</em> <a href="#a12"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a13">Dgrjm</a> (double *D, double *Dt, double *z, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at <em>z=-1</em>.</em> <a href="#a13"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a14">Dgrjp</a> (double *D, double *Dt, double *z, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at <em>z=1</em>.</em> <a href="#a14"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a15">Dglj</a> (double *D, double *Dt, double *z, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the Derivative Matrix and its transpose associated with the Gauss-Lobatto-Jacobi zeros.</em> <a href="#a15"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>double </td><td valign=bottom><a class="el" href="polylib_8c.html#a16">hgj</a> (int i, double z, double *zgj, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Jacobi points <em>zgj</em> at the arbitrary location <em>z</em>.</em> <a href="#a16"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>double </td><td valign=bottom><a class="el" href="polylib_8c.html#a17">hgrjm</a> (int i, double z, double *zgrj, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Radau-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>. This routine assumes <em>zgrj</em> includes the point <em>-1</em>.</em> <a href="#a17"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>double </td><td valign=bottom><a class="el" href="polylib_8c.html#a18">hgrjp</a> (int i, double z, double *zgrj, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Radau-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>. This routine assumes <em>zgrj</em> includes the point <em>+1</em>.</em> <a href="#a18"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>double </td><td valign=bottom><a class="el" href="polylib_8c.html#a19">hglj</a> (int i, double z, double *zglj, int np, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Lobatto-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>.</em> <a href="#a19"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a20">Imgj</a> (double *im, double *zgj, double *zm, int nz, int mz, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Interpolation Operator from Gauss-Jacobi points to an arbitrary distrubtion at points <em>zm</em>.</em> <a href="#a20"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a21">Imgrjm</a> (double *im, double *zgrj, double *zm, int nz, int mz, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Interpolation Operator from Gauss-Radau-Jacobi points (including <em>z=-1</em>) to an arbitrary distrubtion at points <em>zm</em>.</em> <a href="#a21"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a22">Imgrjp</a> (double *im, double *zgrj, double *zm, int nz, int mz, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Interpolation Operator from Gauss-Radau-Jacobi points (including <em>z=1</em>) to an arbitrary distrubtion at points <em>zm</em>.</em> <a href="#a22"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a23">Imglj</a> (double *im, double *zglj, double *zm, int nz, int mz, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points <em>zm</em>.</em> <a href="#a23"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a24">jacobfd</a> (int np, double *z, double *poly_in, double *polyd, int n, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Routine to calculate Jacobi polynomials, <img align="top" src="form_11.png"> , and their first derivative, <img align="top" src="form_12.png"> .</em> <a href="#a24"></a><em></em><br><br></td></tr>
<tr><td nowrap align=right valign=top>void </td><td valign=bottom><a class="el" href="polylib_8c.html#a25">jacobd</a> (int np, double *z, double *polyd, int n, double alpha, double beta)</td></tr>
<tr><td> </td><td><em class="mdesc">Calculate the derivative of Jacobi polynomials.</em> <a href="#a25"></a><em></em><br><br></td></tr>
</table>
<hr><h2>Define Documentation</h2>
<a name="a1" doxytag="polylib.c::EPS"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
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<td class="md" nowrap valign="top"> #define EPS 100*DBL_EPSILON
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
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<td>
</td>
<td>
<p>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00009">9</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00532">hgj()</a>, <a class="el" href="polylib_8c-source.html#l00651">hglj()</a>, <a class="el" href="polylib_8c-source.html#l00569">hgrjm()</a>, <a class="el" href="polylib_8c-source.html#l00610">hgrjp()</a>, and <a class="el" href="polylib_8c-source.html#l00984">Jacobz()</a>. </td>
</tr>
</table>
<a name="a3" doxytag="polylib.c::jacobz"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
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<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
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<td class="md" nowrap valign="top"> #define jacobz</td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">n, <tr>
<td></td>
<td></td>
<td class="md" nowrap>z, <tr>
<td></td>
<td></td>
<td class="md" nowrap>alpha, <tr>
<td></td>
<td></td>
<td class="md" nowrap>beta </td>
<td class="mdname1" valign="top" nowrap> </td>
<td class="md" valign="top"> ) </td>
<td class="md" nowrap> JacZeros(n,z,alpha,beta)
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<table cellspacing=5 cellpadding=0 border=0>
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<td>
</td>
<td>
<p>
zero determination using eigenvalues of tridiagaonl matrix
<p>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00164">164</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00186">zwgj()</a>, <a class="el" href="polylib_8c-source.html#l00282">zwglj()</a>, <a class="el" href="polylib_8c-source.html#l00212">zwgrjm()</a>, and <a class="el" href="polylib_8c-source.html#l00248">zwgrjp()</a>. </td>
</tr>
</table>
<a name="a2" doxytag="polylib.c::sign"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> #define sign</td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">a, <tr>
<td></td>
<td></td>
<td class="md" nowrap>b </td>
<td class="mdname1" valign="top" nowrap> </td>
<td class="md" valign="top"> ) </td>
<td class="md" nowrap> ((b)<0 ? -fabs(a) : fabs(a))
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00010">10</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l01096">TriQL()</a>. </td>
</tr>
</table>
<a name="a0" doxytag="polylib.c::STOP"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> #define STOP 30
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00008">8</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00984">Jacobz()</a>, and <a class="el" href="polylib_8c-source.html#l01096">TriQL()</a>. </td>
</tr>
</table>
<hr><h2>Function Documentation</h2>
<a name="a12" doxytag="polylib.c::Dgj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Dgj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>D</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>Dt</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.
<p>
<ul>
<li>Compute the derivative matrix, <em>d</em>, and its transpose, <em>dt</em>, associated with the n_th order Lagrangian interpolants through the <em>np</em> Gauss-Jacobi points <em>z</em> such that <br>
<img align="top" src="form_4.png"> </li>
</ul>
<ul>
<li>d and dt are both square matrices. </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00321">321</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>. </td>
</tr>
</table>
<a name="a15" doxytag="polylib.c::Dglj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Dglj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>D</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>Dt</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the Derivative Matrix and its transpose associated with the Gauss-Lobatto-Jacobi zeros.
<p>
<ul>
<li>Compute the derivative matrix, <em>d</em>, and its transpose, <em>dt</em>, associated with the n_th order Lagrangian interpolants through the <em>np</em> Gauss-Lobatto-Jacobi points <em>z</em> such that <br>
<img align="top" src="form_4.png"> </li>
</ul>
<ul>
<li>d and dt are both square matrices. </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00469">469</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00947">gammaF()</a>, and <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>. </td>
</tr>
</table>
<a name="a13" doxytag="polylib.c::Dgrjm"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Dgrjm </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>D</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>Dt</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at <em>z=-1</em>.
<p>
<ul>
<li>Compute the derivative matrix, <em>d</em>, and its transpose, <em>dt</em>, associated with the n_th order Lagrangian interpolants through the <em>np</em> Gauss-Radau-Jacobi points <em>z</em> such that <br>
<img align="top" src="form_4.png"> </li>
</ul>
<ul>
<li>d and dt are both square matrices. </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00365">365</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00947">gammaF()</a>, and <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>. </td>
</tr>
</table>
<a name="a14" doxytag="polylib.c::Dgrjp"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Dgrjp </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>D</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>Dt</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at <em>z=1</em>.
<p>
<ul>
<li>Compute the derivative matrix, <em>d</em>, and its transpose, <em>dt</em>, associated with the n_th order Lagrangian interpolants through the <em>np</em> Gauss-Radau-Jacobi points <em>z</em> such that <br>
<img align="top" src="form_4.png"> </li>
</ul>
<ul>
<li>d and dt are both square matrices. </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00417">417</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00947">gammaF()</a>, and <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>. </td>
</tr>
</table>
<a name="a7" doxytag="polylib.c::gammaF"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> double gammaF </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double </td>
<td class="mdname1" valign="top" nowrap> <em>x</em> </td>
<td class="md" valign="top"> ) </td>
<td class="md" nowrap><code> [static]</code></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Calculate the Gamma function , <img align="top" src="form_19.png"> , for integer values and halves.
<p>
Determine the value of <img align="top" src="form_20.png"> using:<p>
<img align="top" src="form_21.png"> <p>
where <img align="top" src="form_22.png">
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00947">947</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00469">Dglj()</a>, <a class="el" href="polylib_8c-source.html#l00365">Dgrjm()</a>, <a class="el" href="polylib_8c-source.html#l00417">Dgrjp()</a>, <a class="el" href="polylib_8c-source.html#l01038">JacZeros()</a>, <a class="el" href="polylib_8c-source.html#l00186">zwgj()</a>, <a class="el" href="polylib_8c-source.html#l00282">zwglj()</a>, <a class="el" href="polylib_8c-source.html#l00212">zwgrjm()</a>, and <a class="el" href="polylib_8c-source.html#l00248">zwgrjp()</a>. </td>
</tr>
</table>
<a name="a16" doxytag="polylib.c::hgj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> double hgj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">int </td>
<td class="mdname" nowrap> <em>i</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zgj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Jacobi points <em>zgj</em> at the arbitrary location <em>z</em>.
<p>
<ul>
<li><img align="top" src="form_5.png"> </li>
</ul>
<ul>
<li>Uses the defintion of the Lagrangian interpolant:<br>
<img align="top" src="form_6.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00532">532</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00009">EPS</a>, <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>, and <a class="el" href="polylib_8c-source.html#l00821">jacobfd()</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00684">Imgj()</a>. </td>
</tr>
</table>
<a name="a19" doxytag="polylib.c::hglj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> double hglj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">int </td>
<td class="mdname" nowrap> <em>i</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zglj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Lobatto-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>.
<p>
<ul>
<li><img align="top" src="form_5.png"> </li>
</ul>
<ul>
<li>Uses the defintion of the Lagrangian interpolant:<br>
<img align="top" src="form_9.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00651">651</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00009">EPS</a>, <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>, and <a class="el" href="polylib_8c-source.html#l00821">jacobfd()</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00766">Imglj()</a>. </td>
</tr>
</table>
<a name="a17" doxytag="polylib.c::hgrjm"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> double hgrjm </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">int </td>
<td class="mdname" nowrap> <em>i</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zgrj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Radau-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>. This routine assumes <em>zgrj</em> includes the point <em>-1</em>.
<p>
<ul>
<li><img align="top" src="form_5.png"> </li>
</ul>
<ul>
<li>Uses the defintion of the Lagrangian interpolant:<br>
<img align="top" src="form_7.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00569">569</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00009">EPS</a>, <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>, and <a class="el" href="polylib_8c-source.html#l00821">jacobfd()</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00711">Imgrjm()</a>. </td>
</tr>
</table>
<a name="a18" doxytag="polylib.c::hgrjp"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> double hgrjp </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">int </td>
<td class="mdname" nowrap> <em>i</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>z</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zgrj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>np</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Compute the value of the <em>i</em> th Lagrangian interpolant through the <em>np</em> Gauss-Radau-Jacobi points <em>zgrj</em> at the arbitrary location <em>z</em>. This routine assumes <em>zgrj</em> includes the point <em>+1</em>.
<p>
<ul>
<li><img align="top" src="form_5.png"> </li>
</ul>
<ul>
<li>Uses the defintion of the Lagrangian interpolant:<br>
<img align="top" src="form_8.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00610">610</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00009">EPS</a>, <a class="el" href="polylib_8c-source.html#l00921">jacobd()</a>, and <a class="el" href="polylib_8c-source.html#l00821">jacobfd()</a>.
<p>
Referenced by <a class="el" href="polylib_8c-source.html#l00738">Imgrjp()</a>. </td>
</tr>
</table>
<a name="a20" doxytag="polylib.c::Imgj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Imgj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>im</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zgj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zm</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>nz</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>mz</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Interpolation Operator from Gauss-Jacobi points to an arbitrary distrubtion at points <em>zm</em>.
<p>
<ul>
<li>Computes the one-dimensional interpolation matrix, <em>im</em>, to interpolate a function from at Gauss-Jacobi distribution of <em>nz</em> zeros <em>zgrj</em> to an arbitrary distribution of <em>mz</em> points <em>zm</em>, i.e.<br>
<img align="top" src="form_10.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00684">684</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00532">hgj()</a>. </td>
</tr>
</table>
<a name="a23" doxytag="polylib.c::Imglj"></a><p>
<table width="100%" cellpadding="2" cellspacing="0" border="0">
<tr>
<td class="md">
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td class="md" nowrap valign="top"> void Imglj </td>
<td class="md" valign="top">( </td>
<td class="md" nowrap valign="top">double * </td>
<td class="mdname" nowrap> <em>im</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zglj</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double * </td>
<td class="mdname" nowrap> <em>zm</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>nz</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>int </td>
<td class="mdname" nowrap> <em>mz</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>alpha</em>, </td>
</tr>
<tr>
<td></td>
<td></td>
<td class="md" nowrap>double </td>
<td class="mdname" nowrap> <em>beta</em></td>
</tr>
<tr>
<td></td>
<td class="md">) </td>
<td class="md" colspan="2"></td>
</tr>
</table>
</td>
</tr>
</table>
<table cellspacing=5 cellpadding=0 border=0>
<tr>
<td>
</td>
<td>
<p>
Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points <em>zm</em>.
<p>
<ul>
<li>Computes the one-dimensional interpolation matrix, <em>im</em>, to interpolate a function from at Gauss-Lobatto-Jacobi distribution of <em>nz</em> zeros <em>zgrj</em> (where <em>zgrj</em>[0]=-1) to an arbitrary distribution of <em>mz</em> points <em>zm</em>, i.e. <br>
<img align="top" src="form_10.png"> </li>
</ul>
<p>
Definition at line <a class="el" href="polylib_8c-source.html#l00766">766</a> of file <a class="el" href="polylib_8c-source.html">polylib.c</a>.
<p>
References <a class="el" href="polylib_8c-source.html#l00651">hglj()</a>. </td>
</tr>