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67<h1>poly.h File Reference</h1>Polynomial functions. 
68<a href="#_details">More...</a>
69<p>
70<code>#include &lt;<a class="el" href="vec_8h-source.html">itpp/base/vec.h</a>&gt;</code><br>
71
72<p>
73<a href="poly_8h-source.html">Go to the source code of this file.</a><table border="0" cellpadding="0" cellspacing="0">
74<tr><td></td></tr>
75<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
76<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#g8de86444d21f007b0eb2f43730a9d693">itpp::cheb</a> (int n, double x)</td></tr>
77
78<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
79Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
80<img class="formulaDsp" alt="\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),&amp; |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),&amp; x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),&amp; x < -1 \end{array} \right. \]" src="form_355.png">
81<p>
82.  <a href="group__poly.html#g8de86444d21f007b0eb2f43730a9d693"></a><br></td></tr>
83<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#g5a2bb27c029a001ea07977fc0b2ad084">itpp::cheb</a> (int n, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
84
85<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
86Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
87<img class="formulaDsp" alt="\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),&amp; |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),&amp; x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),&amp; x < -1 \end{array} \right. \]" src="form_355.png">
88<p>
89.  <a href="group__poly.html#g5a2bb27c029a001ea07977fc0b2ad084"></a><br></td></tr>
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#gdc7b40bdfa59f4690108b0af6032a28e">itpp::cheb</a> (int n, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;x)</td></tr>
91
92<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
93Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
94<img class="formulaDsp" alt="\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),&amp; |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),&amp; x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),&amp; x < -1 \end{array} \right. \]" src="form_355.png">
95<p>
96.  <a href="group__poly.html#gdc7b40bdfa59f4690108b0af6032a28e"></a><br></td></tr>
97<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gab3633500ff808dd810c8c4ed982b8a3"></a><!-- doxytag: member="poly.h::poly" ref="gab3633500ff808dd810c8c4ed982b8a3" args="(const vec &amp;r, vec &amp;p)" -->
99void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#gab3633500ff808dd810c8c4ed982b8a3">itpp::poly</a> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;r, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;p)</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Create a polynomial of the given roots<p>
102Create a polynomial <code>p</code> with roots <code>r</code>. <br></td></tr>
103<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gb62c0f2cb5cb5151c79a575891693316"></a><!-- doxytag: member="poly.h::poly" ref="gb62c0f2cb5cb5151c79a575891693316" args="(const vec &amp;r)" -->
104<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::poly</b> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;r)</td></tr>
105
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g976038e6562ce114820cd05478249e68"></a><!-- doxytag: member="poly.h::poly" ref="g976038e6562ce114820cd05478249e68" args="(const cvec &amp;r, cvec &amp;p)" -->
107void&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::poly</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;r, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;p)</td></tr>
108
109<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g21cfb2107f66b8b55bc398a020856377"></a><!-- doxytag: member="poly.h::poly" ref="g21cfb2107f66b8b55bc398a020856377" args="(const cvec &amp;r)" -->
110<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::poly</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;r)</td></tr>
111
112<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
113<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gf849a0862dc9bcd2e429732e577fe006"></a><!-- doxytag: member="poly.h::roots" ref="gf849a0862dc9bcd2e429732e577fe006" args="(const vec &amp;p, cvec &amp;r)" -->
114void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#gf849a0862dc9bcd2e429732e577fe006">itpp::roots</a> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;p, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;r)</td></tr>
115
116<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Calculate the roots of the polynomial<p>
117Calculate the roots <code>r</code> of the polynomial <code>p</code>. <br></td></tr>
118<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9f52ae9ce005cea38fc6172ed4322213"></a><!-- doxytag: member="poly.h::roots" ref="g9f52ae9ce005cea38fc6172ed4322213" args="(const vec &amp;p)" -->
119<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::roots</b> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;p)</td></tr>
120
121<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g7032851d6d528bc2cf86e6efd338185b"></a><!-- doxytag: member="poly.h::roots" ref="g7032851d6d528bc2cf86e6efd338185b" args="(const cvec &amp;p, cvec &amp;r)" -->
122void&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::roots</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;p, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;r)</td></tr>
123
124<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g740d31b3bf4bb8604864e4b6ac85b87c"></a><!-- doxytag: member="poly.h::roots" ref="g740d31b3bf4bb8604864e4b6ac85b87c" args="(const cvec &amp;p)" -->
125<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::roots</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;p)</td></tr>
126
127<tr><td colspan="2"><div class="groupHeader"></div></td></tr>
128<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g59f5bb49a251bf31f40538f5fca4b9b2"></a><!-- doxytag: member="poly.h::polyval" ref="g59f5bb49a251bf31f40538f5fca4b9b2" args="(const vec &amp;p, const vec &amp;x)" -->
129<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__poly.html#g59f5bb49a251bf31f40538f5fca4b9b2">itpp::polyval</a> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
130
131<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate polynomial<p>
132Evaluate the polynomial <code>p</code> (of length <img class="formulaInl" alt="$N+1$" src="form_353.png"> at the points <code>x</code> The output is given by <p class="formulaDsp">
133<img class="formulaDsp" alt="\[ p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]" src="form_354.png">
134<p>
135. <br></td></tr>
136<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g34523a27f81ea97aa996bbcb898f4858"></a><!-- doxytag: member="poly.h::polyval" ref="g34523a27f81ea97aa996bbcb898f4858" args="(const vec &amp;p, const cvec &amp;x)" -->
137<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::polyval</b> (const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;p, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
138
139<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g2b96f640c406de26b21d9c17a6500f80"></a><!-- doxytag: member="poly.h::polyval" ref="g2b96f640c406de26b21d9c17a6500f80" args="(const cvec &amp;p, const vec &amp;x)" -->
140<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::polyval</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
141
142<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9bdf5c1688d8df8155d3ff8d86302838"></a><!-- doxytag: member="poly.h::polyval" ref="g9bdf5c1688d8df8155d3ff8d86302838" args="(const cvec &amp;p, const cvec &amp;x)" -->
143<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>itpp::polyval</b> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;p, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
144
145</table>
146<hr><a name="_details"></a><h2>Detailed Description</h2>
147Polynomial functions.
148<p>
149<dl class="author" compact><dt><b>Author:</b></dt><dd>Tony Ottosson, Kumar Appaiah and Adam Piatyszek</dd></dl>
150-------------------------------------------------------------------------<p>
151Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)<p>
152This file is part of IT++ - a C++ library of mathematical, signal processing, speech processing, and communications classes and functions.<p>
153IT++ is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.<p>
154IT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.<p>
155You should have received a copy of the GNU General Public License along with IT++. If not, see &lt;<a href="http://www.gnu.org/licenses/">http://www.gnu.org/licenses/</a>&gt;.<p>
156------------------------------------------------------------------------- </div>
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