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61<h1>Special Matrices<br>
62<small>
63[<a class="el" href="group__base.html">Base 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"><a class="anchor" name="gd48c030f898e4bfdbc21592664481f7d"></a><!-- doxytag: member="specmat::ones" ref="gd48c030f898e4bfdbc21592664481f7d" args="(int size)" -->
68<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#gd48c030f898e4bfdbc21592664481f7d">itpp::ones</a> (int size)</td></tr>
69
70<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A float vector of ones. <br></td></tr>
71<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g47db04faa5626794d635f23000be8c73"></a><!-- doxytag: member="specmat::ones_b" ref="g47db04faa5626794d635f23000be8c73" args="(int size)" -->
72<a class="el" href="classitpp_1_1Vec.html#e10151f44bbabf17b670a9493d8088cf">bvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g47db04faa5626794d635f23000be8c73">itpp::ones_b</a> (int size)</td></tr>
73
74<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Binary vector of ones. <br></td></tr>
75<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g42a431a8a221e1eae1749d6eb4321869"></a><!-- doxytag: member="specmat::ones_i" ref="g42a431a8a221e1eae1749d6eb4321869" args="(int size)" -->
76<a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g42a431a8a221e1eae1749d6eb4321869">itpp::ones_i</a> (int size)</td></tr>
77
78<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Int vector of ones. <br></td></tr>
79<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g7fd779aadee0c88b61d85245b960f7e1"></a><!-- doxytag: member="specmat::ones_c" ref="g7fd779aadee0c88b61d85245b960f7e1" args="(int size)" -->
80<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g7fd779aadee0c88b61d85245b960f7e1">itpp::ones_c</a> (int size)</td></tr>
81
82<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A float Complex vector of ones. <br></td></tr>
83<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gdc0f3edbf58bced9e82d8b260d395cac"></a><!-- doxytag: member="specmat::ones" ref="gdc0f3edbf58bced9e82d8b260d395cac" args="(int rows, int cols)" -->
84<a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#gdc0f3edbf58bced9e82d8b260d395cac">itpp::ones</a> (int rows, int cols)</td></tr>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A float (rows,cols)-matrix of ones. <br></td></tr>
87<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g8bbe1bc019c73f32dc796b276ed7aa2e"></a><!-- doxytag: member="specmat::ones_b" ref="g8bbe1bc019c73f32dc796b276ed7aa2e" args="(int rows, int cols)" -->
88<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g8bbe1bc019c73f32dc796b276ed7aa2e">itpp::ones_b</a> (int rows, int cols)</td></tr>
89
90<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Binary (rows,cols)-matrix of ones. <br></td></tr>
91<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g7c2c02190b4aa222cc692641cc3a73c7"></a><!-- doxytag: member="specmat::ones_i" ref="g7c2c02190b4aa222cc692641cc3a73c7" args="(int rows, int cols)" -->
92<a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g7c2c02190b4aa222cc692641cc3a73c7">itpp::ones_i</a> (int rows, int cols)</td></tr>
93
94<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Int (rows,cols)-matrix of ones. <br></td></tr>
95<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g593a539551f14bd6241701910a106b16"></a><!-- doxytag: member="specmat::ones_c" ref="g593a539551f14bd6241701910a106b16" args="(int rows, int cols)" -->
96<a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g593a539551f14bd6241701910a106b16">itpp::ones_c</a> (int rows, int cols)</td></tr>
97
98<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double Complex (rows,cols)-matrix of ones. <br></td></tr>
99<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g4c206300055f51390d03770ea5600da3"></a><!-- doxytag: member="specmat::zeros" ref="g4c206300055f51390d03770ea5600da3" args="(int size)" -->
100<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g4c206300055f51390d03770ea5600da3">itpp::zeros</a> (int size)</td></tr>
101
102<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double vector of zeros. <br></td></tr>
103<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g23556708b3ff63238ef07f68f3698301"></a><!-- doxytag: member="specmat::zeros_b" ref="g23556708b3ff63238ef07f68f3698301" args="(int size)" -->
104<a class="el" href="classitpp_1_1Vec.html#e10151f44bbabf17b670a9493d8088cf">bvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g23556708b3ff63238ef07f68f3698301">itpp::zeros_b</a> (int size)</td></tr>
105
106<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Binary vector of zeros. <br></td></tr>
107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9c37bc66992f8d3d29d8c3aef6a5a514"></a><!-- doxytag: member="specmat::zeros_i" ref="g9c37bc66992f8d3d29d8c3aef6a5a514" args="(int size)" -->
108<a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g9c37bc66992f8d3d29d8c3aef6a5a514">itpp::zeros_i</a> (int size)</td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Int vector of zeros. <br></td></tr>
111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g96c974bd8909ccdcdafcdcdd1f406876"></a><!-- doxytag: member="specmat::zeros_c" ref="g96c974bd8909ccdcdafcdcdd1f406876" args="(int size)" -->
112<a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g96c974bd8909ccdcdafcdcdd1f406876">itpp::zeros_c</a> (int size)</td></tr>
113
114<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double Complex vector of zeros. <br></td></tr>
115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g10723ecada06221cbe64fe2736a59de1"></a><!-- doxytag: member="specmat::zeros" ref="g10723ecada06221cbe64fe2736a59de1" args="(int rows, int cols)" -->
116<a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g10723ecada06221cbe64fe2736a59de1">itpp::zeros</a> (int rows, int cols)</td></tr>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double (rows,cols)-matrix of zeros. <br></td></tr>
119<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g8f5e0472807d1f2b4296594e7fd01027"></a><!-- doxytag: member="specmat::zeros_b" ref="g8f5e0472807d1f2b4296594e7fd01027" args="(int rows, int cols)" -->
120<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g8f5e0472807d1f2b4296594e7fd01027">itpp::zeros_b</a> (int rows, int cols)</td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Binary (rows,cols)-matrix of zeros. <br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g9df9aa3553b6a5c07924954b85466cec"></a><!-- doxytag: member="specmat::zeros_i" ref="g9df9aa3553b6a5c07924954b85466cec" args="(int rows, int cols)" -->
124<a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g9df9aa3553b6a5c07924954b85466cec">itpp::zeros_i</a> (int rows, int cols)</td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Int (rows,cols)-matrix of zeros. <br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g7850aa51041a98644ed191017f101340"></a><!-- doxytag: member="specmat::zeros_c" ref="g7850aa51041a98644ed191017f101340" args="(int rows, int cols)" -->
128<a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g7850aa51041a98644ed191017f101340">itpp::zeros_c</a> (int rows, int cols)</td></tr>
129
130<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double Complex (rows,cols)-matrix of zeros. <br></td></tr>
131<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g19f45f6a0e37b06cd1213bbe995853af"></a><!-- doxytag: member="specmat::eye" ref="g19f45f6a0e37b06cd1213bbe995853af" args="(int size)" -->
132<a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g19f45f6a0e37b06cd1213bbe995853af">itpp::eye</a> (int size)</td></tr>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double (size,size) unit matrix. <br></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gbbde61be8b986fd19ad1c9dc792e10e2"></a><!-- doxytag: member="specmat::eye_b" ref="gbbde61be8b986fd19ad1c9dc792e10e2" args="(int size)" -->
136<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#gbbde61be8b986fd19ad1c9dc792e10e2">itpp::eye_b</a> (int size)</td></tr>
137
138<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Binary (size,size) unit matrix. <br></td></tr>
139<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g31d445a0a63bcf661f18f900062d5110"></a><!-- doxytag: member="specmat::eye_i" ref="g31d445a0a63bcf661f18f900062d5110" args="(int size)" -->
140<a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g31d445a0a63bcf661f18f900062d5110">itpp::eye_i</a> (int size)</td></tr>
141
142<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Int (size,size) unit matrix. <br></td></tr>
143<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gfc47b09fb906e391212e488b009e6fdf"></a><!-- doxytag: member="specmat::eye_c" ref="gfc47b09fb906e391212e488b009e6fdf" args="(int size)" -->
144<a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#gfc47b09fb906e391212e488b009e6fdf">itpp::eye_c</a> (int size)</td></tr>
145
146<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A Double Complex (size,size) unit matrix. <br></td></tr>
147<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="gbfc73e72a56769280cd9fda812367196"></a><!-- doxytag: member="specmat::eye" ref="gbfc73e72a56769280cd9fda812367196" args="(int size, Mat&lt; T &gt; &amp;m)" -->
148template&lt;class T &gt; </td></tr>
149<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__specmat.html#gbfc73e72a56769280cd9fda812367196">itpp::eye</a> (int size, Mat&lt; T &gt; &amp;m)</td></tr>
150
151<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A non-copying version of the eye function. <br></td></tr>
152<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g69cec3c441dfa7b6e9627b485b0b80d7"></a><!-- doxytag: member="specmat::impulse" ref="g69cec3c441dfa7b6e9627b485b0b80d7" args="(int size)" -->
153<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g69cec3c441dfa7b6e9627b485b0b80d7">itpp::impulse</a> (int size)</td></tr>
154
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Impulse vector. <br></td></tr>
156<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ge5632baa525e231b015f3d45f3503cac"></a><!-- doxytag: member="specmat::linspace" ref="ge5632baa525e231b015f3d45f3503cac" args="(double from, double to, int length=100)" -->
157<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#ge5632baa525e231b015f3d45f3503cac">itpp::linspace</a> (double from, double to, int length=100)</td></tr>
158
159<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Linspace (works in the same way as the matlab version). <br></td></tr>
160<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__specmat.html#g81e638d011c3be35eb900db4691ac663">itpp::zigzag_space</a> (double t0, double t1, int K=5)</td></tr>
161
162<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Zig-zag space function (variation on linspace).  <a href="#g81e638d011c3be35eb900db4691ac663"></a><br></td></tr>
163<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g10afe3456dd34b57639dee69e8f7d06f">itpp::hadamard</a> (int size)</td></tr>
164
165<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Hadamard matrix.  <a href="#g10afe3456dd34b57639dee69e8f7d06f"></a><br></td></tr>
166<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#g36320b9a2493b5c4c3ff3d048fdd5390">itpp::jacobsthal</a> (int p)</td></tr>
167
168<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Jacobsthal matrix.  <a href="#g36320b9a2493b5c4c3ff3d048fdd5390"></a><br></td></tr>
169<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__specmat.html#gaedb7979abc426d27338c49372338b8d">itpp::conference</a> (int n)</td></tr>
170
171<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conference matrix.  <a href="#gaedb7979abc426d27338c49372338b8d"></a><br></td></tr>
172<tr><td class="memTemplParams" nowrap colspan="2">template&lt;typename Num_T &gt; </td></tr>
173<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">const Mat&lt; Num_T &gt;&nbsp;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__specmat.html#gdceb476e87115118925d84cc35f3904c">itpp::toeplitz</a> (const Vec&lt; Num_T &gt; &amp;c, const Vec&lt; Num_T &gt; &amp;r)</td></tr>
174
175<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Generate Toeplitz matrix from two vectors <code>c</code> and <code>r</code>.  <a href="#gdceb476e87115118925d84cc35f3904c"></a><br></td></tr>
176<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="g3ab0fe843dd23ee39f2b16e31d8db975"></a><!-- doxytag: member="specmat::toeplitz" ref="g3ab0fe843dd23ee39f2b16e31d8db975" args="(const Vec&lt; Num_T &gt; &amp;c)" -->
177template&lt;typename Num_T &gt; </td></tr>
178<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">const Mat&lt; Num_T &gt;&nbsp;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__specmat.html#g3ab0fe843dd23ee39f2b16e31d8db975">itpp::toeplitz</a> (const Vec&lt; Num_T &gt; &amp;c)</td></tr>
179
180<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Generate symmetric Toeplitz matrix from vector <code>c</code>. <br></td></tr>
181<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="g8b9843c19113d494cef6bd0f12e5d454"></a><!-- doxytag: member="specmat::toeplitz" ref="g8b9843c19113d494cef6bd0f12e5d454" args="(const cvec &amp;c)" -->
182template&lt;&gt; </td></tr>
183<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="group__specmat.html#g8b9843c19113d494cef6bd0f12e5d454">itpp::toeplitz</a> (const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;c)</td></tr>
184
185<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Generate symmetric Toeplitz matrix from vector <code>c</code> (complex valued). <br></td></tr>
186</table>
187<hr><h2>Function Documentation</h2>
188<a class="anchor" name="gaedb7979abc426d27338c49372338b8d"></a><!-- doxytag: member="itpp::conference" ref="gaedb7979abc426d27338c49372338b8d" args="(int n)" -->
189<div class="memitem">
190<div class="memproto">
191      <table class="memname">
192        <tr>
193          <td class="memname"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a> itpp::conference           </td>
194          <td>(</td>
195          <td class="paramtype">int&nbsp;</td>
196          <td class="paramname"> <em>n</em>          </td>
197          <td>&nbsp;)&nbsp;</td>
198          <td></td>
199        </tr>
200      </table>
201</div>
202<div class="memdoc">
203
204<p>
205Conference matrix.
206<p>
207Constructs an n by n matrix C, where n=p^m+1=2 (mod 4) and p is a odd prime (not checked). This code only work with m=1, that is n=p+1 and p odd prime. The valid sizes of n is then n=6, 14, 18, 30, 38, ... (and not 10, 26, ...). C has the property that C*C'=(n-1)I, that is it has orthogonal rows and columns in the same way as Hadamard matricies. However, one element in each row (on the diagonal) is zeros. The others are {-1,+1}.<p>
208For more details see pp. 55-58 in MacWilliams &amp; Sloane "The theory of error correcting codes", North-Holland, 1977.
209<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="specmat_8cpp-source.html#l00179">itpp::jacobsthal()</a>.</p>
210
211</div>
212</div><p>
213<a class="anchor" name="g10afe3456dd34b57639dee69e8f7d06f"></a><!-- doxytag: member="itpp::hadamard" ref="g10afe3456dd34b57639dee69e8f7d06f" args="(int size)" -->
214<div class="memitem">
215<div class="memproto">
216      <table class="memname">
217        <tr>
218          <td class="memname"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a> itpp::hadamard           </td>
219          <td>(</td>
220          <td class="paramtype">int&nbsp;</td>
221          <td class="paramname"> <em>size</em>          </td>
222          <td>&nbsp;)&nbsp;</td>
223          <td></td>
224        </tr>
225      </table>
226</div>
227<div class="memdoc">
228
229<p>
230Hadamard matrix.
231<p>
232This function constructs a <em>size</em> by <em>size</em> Hadammard matrix, where <em>size</em> is a power of 2.
233<p>References <a class="el" href="group__convertfunc.html#g0f093b7797b4e80006219f0dee101ecf">itpp::ceil_i()</a>, <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="log__exp_8h-source.html#l00247">itpp::log2()</a>, <a class="el" href="log__exp_8h-source.html#l00204">itpp::pow2()</a>, and <a class="el" href="log__exp_8h-source.html#l00053">itpp::pow2i()</a>.</p>
234
235</div>
236</div><p>
237<a class="anchor" name="g36320b9a2493b5c4c3ff3d048fdd5390"></a><!-- doxytag: member="itpp::jacobsthal" ref="g36320b9a2493b5c4c3ff3d048fdd5390" args="(int p)" -->
238<div class="memitem">
239<div class="memproto">
240      <table class="memname">
241        <tr>
242          <td class="memname"><a class="el" href="classitpp_1_1Mat.html#9e0dd2f635e4bd0b28c09685d9c4f3bb">imat</a> itpp::jacobsthal           </td>
243          <td>(</td>
244          <td class="paramtype">int&nbsp;</td>
245          <td class="paramname"> <em>p</em>          </td>
246          <td>&nbsp;)&nbsp;</td>
247          <td></td>
248        </tr>
249      </table>
250</div>
251<div class="memdoc">
252
253<p>
254Jacobsthal matrix.
255<p>
256Constructs an p by p matrix Q where p is a prime (not checked). The elements in Q {qij} is given by qij=X(j-i), where X(x) is the Legendre symbol given as:<p>
257<ul>
258<li>
259X(x)=0 if x is a multiple of p,  </li>
260<li>
261X(x)=1 if x is a quadratic residue modulo p,  </li>
262<li>
263X(x)=-1 if x is a quadratic nonresidue modulo p.  </li>
264</ul>
265<p>
266See Wicker "Error Control Systems for digital communication and storage", p. 134 for more information on these topics. Do not check that p is a prime.
267<p>Referenced by <a class="el" href="specmat_8cpp-source.html#l00203">itpp::conference()</a>.</p>
268
269</div>
270</div><p>
271<a class="anchor" name="gdceb476e87115118925d84cc35f3904c"></a><!-- doxytag: member="itpp::toeplitz" ref="gdceb476e87115118925d84cc35f3904c" args="(const Vec&lt; Num_T &gt; &amp;c, const Vec&lt; Num_T &gt; &amp;r)" -->
272<div class="memitem">
273<div class="memproto">
274<div class="memtemplate">
275template&lt;typename Num_T &gt; </div>
276      <table class="memname">
277        <tr>
278          <td class="memname">const Mat&lt;Num_T&gt; itpp::toeplitz           </td>
279          <td>(</td>
280          <td class="paramtype">const Vec&lt; Num_T &gt; &amp;&nbsp;</td>
281          <td class="paramname"> <em>c</em>, </td>
282        </tr>
283        <tr>
284          <td class="paramkey"></td>
285          <td></td>
286          <td class="paramtype">const Vec&lt; Num_T &gt; &amp;&nbsp;</td>
287          <td class="paramname"> <em>r</em></td><td>&nbsp;</td>
288        </tr>
289        <tr>
290          <td></td>
291          <td>)</td>
292          <td></td><td></td><td><code> [inline]</code></td>
293        </tr>
294      </table>
295</div>
296<div class="memdoc">
297
298<p>
299Generate Toeplitz matrix from two vectors <code>c</code> and <code>r</code>.
300<p>
301Returns the Toeplitz matrix constructed given the first column C, and (optionally) the first row R. If the first element of C is not the same as the first element of R, the first element of C is used. If the second argument is omitted, the first row is taken to be the same as the first column and a symmetric (Hermitian) Toeplitz matrix is created.<p>
302An example square Toeplitz matrix has the form: <div class="fragment"><pre class="fragment">
303 *       c(0)    r(1)     r(2)   ...   r(n)
304 *       c(1)    c(0)     r(1)        r(n-1)
305 *       c(2)    c(1)     c(0)        r(n-2)
306 *        .                             .
307 *        .                             .
308 *        .                             .
309 *
310 *       c(n)   c(n-1)   c(n-2)  ...   c(0)
311 * </pre></div><p>
312<dl class="author" compact><dt><b>Author:</b></dt><dd>Adam Piatyszek </dd></dl>
313
314<p>References <a class="el" href="tcp_8h-source.html#l00115">itpp::min()</a>, and <a class="el" href="vec_8h-source.html#l00277">itpp::Vec&lt; Num_T &gt;::size()</a>.</p>
315
316</div>
317</div><p>
318<a class="anchor" name="g81e638d011c3be35eb900db4691ac663"></a><!-- doxytag: member="itpp::zigzag_space" ref="g81e638d011c3be35eb900db4691ac663" args="(double t0, double t1, int K=5)" -->
319<div class="memitem">
320<div class="memproto">
321      <table class="memname">
322        <tr>
323          <td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::zigzag_space           </td>
324          <td>(</td>
325          <td class="paramtype">double&nbsp;</td>
326          <td class="paramname"> <em>t0</em>, </td>
327        </tr>
328        <tr>
329          <td class="paramkey"></td>
330          <td></td>
331          <td class="paramtype">double&nbsp;</td>
332          <td class="paramname"> <em>t1</em>, </td>
333        </tr>
334        <tr>
335          <td class="paramkey"></td>
336          <td></td>
337          <td class="paramtype">int&nbsp;</td>
338          <td class="paramname"> <em>K</em> = <code>5</code></td><td>&nbsp;</td>
339        </tr>
340        <tr>
341          <td></td>
342          <td>)</td>
343          <td></td><td></td><td></td>
344        </tr>
345      </table>
346</div>
347<div class="memdoc">
348
349<p>
350Zig-zag space function (variation on linspace).
351<p>
352This function is a variation on <a class="el" href="group__specmat.html#ge5632baa525e231b015f3d45f3503cac" title="Linspace (works in the same way as the matlab version).">linspace()</a>. It traverses the points in different order. For example <div class="fragment"><pre class="fragment"><a class="code" href="group__specmat.html#g81e638d011c3be35eb900db4691ac663" title="Zig-zag space function (variation on linspace).">zigzag_space</a>(-5,5,3)
353</pre></div> gives the vector <div class="fragment"><pre class="fragment">[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75]
354</pre></div> and <div class="fragment"><pre class="fragment"><a class="code" href="group__specmat.html#g81e638d011c3be35eb900db4691ac663" title="Zig-zag space function (variation on linspace).">zigzag_space</a>(-5,5,4)
355</pre></div> gives the vector <div class="fragment"><pre class="fragment">[-5 5 0 -2.5 2.5 -3.75 -1.25 1.25 3.75 -4.375 -3.125 -1.875 -0.625 0.625 1.875 3.125 4.375]
356</pre></div> and so on.<p>
357I.e. the function samples the interval [t0,t1] with finer and finer density and with points uniformly distributed over the interval, rather than from left to right (as does linspace).<p>
358The result is a vector of length 1+2^K.
359<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, <a class="el" href="matfunc_8h-source.html#l00051">itpp::length()</a>, <a class="el" href="specmat_8cpp-source.html#l00114">itpp::linspace()</a>, and <a class="el" href="group__specmat.html#g10723ecada06221cbe64fe2736a59de1">itpp::zeros()</a>.</p>
360
361</div>
362</div><p>
363</div>
364<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:14 2009 for mixpp by&nbsp;
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