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61<h1>Polynomial Functions<br>
62<small>
63[<a class="el" href="group__signal.html">Signal Processing (SP) Module</a>]</small>
64</h1><table border="0" cellpadding="0" cellspacing="0">
65<tr><td></td></tr>
66<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
67<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>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
70Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
71<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">
72<p>
73.  <a href="#g8de86444d21f007b0eb2f43730a9d693"></a><br></td></tr>
74<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>
75
76<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
77Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
78<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">
79<p>
80.  <a href="#g5a2bb27c029a001ea07977fc0b2ad084"></a><br></td></tr>
81<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>
82
83<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Chebyshev polynomial of the first kind<p>
84Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
85<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">
86<p>
87.  <a href="#gdc7b40bdfa59f4690108b0af6032a28e"></a><br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gab3633500ff808dd810c8c4ed982b8a3"></a><!-- doxytag: member="poly::poly" ref="gab3633500ff808dd810c8c4ed982b8a3" args="(const vec &amp;r, vec &amp;p)" -->
89void&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>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Create a polynomial of the given roots<p>
92Create a polynomial <code>p</code> with roots <code>r</code>. <br></td></tr>
93<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g976038e6562ce114820cd05478249e68"></a><!-- doxytag: member="poly::poly" ref="g976038e6562ce114820cd05478249e68" args="(const cvec &amp;r, cvec &amp;p)" -->
94void&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>
95
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gb62c0f2cb5cb5151c79a575891693316"></a><!-- doxytag: member="poly::poly" ref="gb62c0f2cb5cb5151c79a575891693316" args="(const vec &amp;r)" -->
97<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>
98
99<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g21cfb2107f66b8b55bc398a020856377"></a><!-- doxytag: member="poly::poly" ref="g21cfb2107f66b8b55bc398a020856377" args="(const cvec &amp;r)" -->
100<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>
101
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gf849a0862dc9bcd2e429732e577fe006"></a><!-- doxytag: member="poly::roots" ref="gf849a0862dc9bcd2e429732e577fe006" args="(const vec &amp;p, cvec &amp;r)" -->
103void&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>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Calculate the roots of the polynomial<p>
106Calculate the roots <code>r</code> of the polynomial <code>p</code>. <br></td></tr>
107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g7032851d6d528bc2cf86e6efd338185b"></a><!-- doxytag: member="poly::roots" ref="g7032851d6d528bc2cf86e6efd338185b" args="(const cvec &amp;p, cvec &amp;r)" -->
108void&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>
109
110<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9f52ae9ce005cea38fc6172ed4322213"></a><!-- doxytag: member="poly::roots" ref="g9f52ae9ce005cea38fc6172ed4322213" args="(const vec &amp;p)" -->
111<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>
112
113<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g740d31b3bf4bb8604864e4b6ac85b87c"></a><!-- doxytag: member="poly::roots" ref="g740d31b3bf4bb8604864e4b6ac85b87c" args="(const cvec &amp;p)" -->
114<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>
115
116<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g59f5bb49a251bf31f40538f5fca4b9b2"></a><!-- doxytag: member="poly::polyval" ref="g59f5bb49a251bf31f40538f5fca4b9b2" args="(const vec &amp;p, const vec &amp;x)" -->
117<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>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate polynomial<p>
120Evaluate 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">
121<img class="formulaDsp" alt="\[ p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]" src="form_354.png">
122<p>
123. <br></td></tr>
124<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g34523a27f81ea97aa996bbcb898f4858"></a><!-- doxytag: member="poly::polyval" ref="g34523a27f81ea97aa996bbcb898f4858" args="(const vec &amp;p, const cvec &amp;x)" -->
125<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>
126
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g2b96f640c406de26b21d9c17a6500f80"></a><!-- doxytag: member="poly::polyval" ref="g2b96f640c406de26b21d9c17a6500f80" args="(const cvec &amp;p, const vec &amp;x)" -->
128<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>
129
130<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9bdf5c1688d8df8155d3ff8d86302838"></a><!-- doxytag: member="poly::polyval" ref="g9bdf5c1688d8df8155d3ff8d86302838" args="(const cvec &amp;p, const cvec &amp;x)" -->
131<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>
132
133</table>
134<hr><h2>Function Documentation</h2>
135<a class="anchor" name="gdc7b40bdfa59f4690108b0af6032a28e"></a><!-- doxytag: member="itpp::cheb" ref="gdc7b40bdfa59f4690108b0af6032a28e" args="(int n, const mat &amp;x)" -->
136<div class="memitem">
137<div class="memproto">
138      <table class="memname">
139        <tr>
140          <td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::cheb           </td>
141          <td>(</td>
142          <td class="paramtype">int&nbsp;</td>
143          <td class="paramname"> <em>n</em>, </td>
144        </tr>
145        <tr>
146          <td class="paramkey"></td>
147          <td></td>
148          <td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;&nbsp;</td>
149          <td class="paramname"> <em>x</em></td><td>&nbsp;</td>
150        </tr>
151        <tr>
152          <td></td>
153          <td>)</td>
154          <td></td><td></td><td></td>
155        </tr>
156      </table>
157</div>
158<div class="memdoc">
159
160<p>
161Chebyshev polynomial of the first kind<p>
162Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
163<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">
164<p>
165.
166<p>
167<dl compact><dt><b>Parameters:</b></dt><dd>
168  <table border="0" cellspacing="2" cellpadding="0">
169    <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>order of the Chebyshev polynomial </td></tr>
170    <tr><td valign="top"></td><td valign="top"><em>x</em>&nbsp;</td><td>matrix of values at which the Chebyshev polynomial is to be evaluated </td></tr>
171  </table>
172</dl>
173<dl class="return" compact><dt><b>Returns:</b></dt><dd>values of the Chebyshev polynomial evaluated for each element in <code>x</code>.</dd></dl>
174<dl class="author" compact><dt><b>Author:</b></dt><dd>Kumar Appaiah, Adam Piatyszek (code review) </dd></dl>
175
176<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
177
178<p>Referenced by <a class="el" href="poly_8cpp-source.html#l00209">itpp::cheb()</a>, and <a class="el" href="window_8cpp-source.html#l00119">itpp::chebwin()</a>.</p>
179
180</div>
181</div><p>
182<a class="anchor" name="g5a2bb27c029a001ea07977fc0b2ad084"></a><!-- doxytag: member="itpp::cheb" ref="g5a2bb27c029a001ea07977fc0b2ad084" args="(int n, const vec &amp;x)" -->
183<div class="memitem">
184<div class="memproto">
185      <table class="memname">
186        <tr>
187          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::cheb           </td>
188          <td>(</td>
189          <td class="paramtype">int&nbsp;</td>
190          <td class="paramname"> <em>n</em>, </td>
191        </tr>
192        <tr>
193          <td class="paramkey"></td>
194          <td></td>
195          <td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;&nbsp;</td>
196          <td class="paramname"> <em>x</em></td><td>&nbsp;</td>
197        </tr>
198        <tr>
199          <td></td>
200          <td>)</td>
201          <td></td><td></td><td></td>
202        </tr>
203      </table>
204</div>
205<div class="memdoc">
206
207<p>
208Chebyshev polynomial of the first kind<p>
209Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
210<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">
211<p>
212.
213<p>
214<dl compact><dt><b>Parameters:</b></dt><dd>
215  <table border="0" cellspacing="2" cellpadding="0">
216    <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>order of the Chebyshev polynomial </td></tr>
217    <tr><td valign="top"></td><td valign="top"><em>x</em>&nbsp;</td><td>vector of values at which the Chebyshev polynomial is to be evaluated </td></tr>
218  </table>
219</dl>
220<dl class="return" compact><dt><b>Returns:</b></dt><dd>values of the Chebyshev polynomial evaluated for each element of <code>x</code> </dd></dl>
221<dl class="author" compact><dt><b>Author:</b></dt><dd>Kumar Appaiah, Adam Piatyszek (code review) </dd></dl>
222
223<p>References <a class="el" href="poly_8cpp-source.html#l00220">itpp::cheb()</a>, and <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
224
225</div>
226</div><p>
227<a class="anchor" name="g8de86444d21f007b0eb2f43730a9d693"></a><!-- doxytag: member="itpp::cheb" ref="g8de86444d21f007b0eb2f43730a9d693" args="(int n, double x)" -->
228<div class="memitem">
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232          <td class="memname">double itpp::cheb           </td>
233          <td>(</td>
234          <td class="paramtype">int&nbsp;</td>
235          <td class="paramname"> <em>n</em>, </td>
236        </tr>
237        <tr>
238          <td class="paramkey"></td>
239          <td></td>
240          <td class="paramtype">double&nbsp;</td>
241          <td class="paramname"> <em>x</em></td><td>&nbsp;</td>
242        </tr>
243        <tr>
244          <td></td>
245          <td>)</td>
246          <td></td><td></td><td></td>
247        </tr>
248      </table>
249</div>
250<div class="memdoc">
251
252<p>
253Chebyshev polynomial of the first kind<p>
254Chebyshev polynomials of the first kind can be defined as follows: <p class="formulaDsp">
255<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">
256<p>
257.
258<p>
259<dl compact><dt><b>Parameters:</b></dt><dd>
260  <table border="0" cellspacing="2" cellpadding="0">
261    <tr><td valign="top"></td><td valign="top"><em>n</em>&nbsp;</td><td>order of the Chebyshev polynomial </td></tr>
262    <tr><td valign="top"></td><td valign="top"><em>x</em>&nbsp;</td><td>value at which the Chebyshev polynomial is to be evaluated</td></tr>
263  </table>
264</dl>
265<dl class="author" compact><dt><b>Author:</b></dt><dd>Kumar Appaiah, Adam Piatyszek (code review) </dd></dl>
266
267<p>References <a class="el" href="trig__hyp_8h-source.html#l00073">itpp::acos()</a>, <a class="el" href="trig__hyp_8h-source.html#l00108">itpp::acosh()</a>, <a class="el" href="trig__hyp_8h-source.html#l00061">itpp::cos()</a>, <a class="el" href="trig__hyp_8h-source.html#l00096">itpp::cosh()</a>, <a class="el" href="misc_8h-source.html#l00122">itpp::is_even()</a>, and <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>.</p>
268
269</div>
270</div><p>
271</div>
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