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69<h1>ldmat Class Reference<br>
70<small>
71[<a class="el" href="group__math.html">Auxiliary math functions</a>]</small>
72</h1><!-- doxytag: class="ldmat" --><!-- doxytag: inherits="sqmat" --><code>#include &lt;<a class="el" href="libDC_8h-source.html">libDC.h</a>&gt;</code>
73<p>
74<div class="dynheader">
75Inheritance diagram for ldmat:</div>
76<div class="dynsection">
77
78<p><center><img src="classldmat.png" usemap="#ldmat_map" border="0" alt=""></center>
79<map name="ldmat_map">
80<area href="classsqmat.html" alt="sqmat" shape="rect" coords="0,0,43,24">
81</map>
82</div>
83
84<p>
85<a href="classldmat-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
86Matrix stored in LD form, (commonly known as UD).
87<p>
88Matrix is decomposed as follows: <p class="formulaDsp">
89<img class="formulaDsp" alt="\[M = L'DL\]" src="form_5.png">
90<p>
91 where only <img class="formulaInl" alt="$L$" src="form_21.png"> and <img class="formulaInl" alt="$D$" src="form_22.png"> matrices are stored. All inplace operations modifies only these and the need to compose and decompose the matrix is avoided. <table border="0" cellpadding="0" cellspacing="0">
92<tr><td></td></tr>
93<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="968113788422e858da23a477e98fd3a1"></a><!-- doxytag: member="ldmat::ldmat" ref="968113788422e858da23a477e98fd3a1" args="(const mat &amp;L, const vec &amp;D)" -->
95&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#968113788422e858da23a477e98fd3a1">ldmat</a> (const mat &amp;<a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a>, const vec &amp;<a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a>)</td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by copy of L and D. <br></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5f21785358072d36892d538eed1d1ea5"></a><!-- doxytag: member="ldmat::ldmat" ref="5f21785358072d36892d538eed1d1ea5" args="(const mat &amp;V)" -->
99&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f21785358072d36892d538eed1d1ea5">ldmat</a> (const mat &amp;V)</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by decomposition of full matrix V. <br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8e88c818f9605bc726e52c4136c71cc5"></a><!-- doxytag: member="ldmat::ldmat" ref="8e88c818f9605bc726e52c4136c71cc5" args="(const ldmat &amp;V0, const ivec &amp;perm)" -->
103&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#8e88c818f9605bc726e52c4136c71cc5">ldmat</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;V0, const ivec &amp;perm)</td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by restructuring of V0 accordint to permutation vector perm. <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abe16e0f86668ef61a9a4896c8565dee"></a><!-- doxytag: member="ldmat::ldmat" ref="abe16e0f86668ef61a9a4896c8565dee" args="(vec D0)" -->
107&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#abe16e0f86668ef61a9a4896c8565dee">ldmat</a> (vec D0)</td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct diagonal matrix with diagonal D0. <br></td></tr>
110<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a12dda6f529580b0377cc45226b43303"></a><!-- doxytag: member="ldmat::ldmat" ref="a12dda6f529580b0377cc45226b43303" args="()" -->
111&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a12dda6f529580b0377cc45226b43303">ldmat</a> ()</td></tr>
112
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
114<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="163ee002a7858d104da1c59dd11f016d"></a><!-- doxytag: member="ldmat::ldmat" ref="163ee002a7858d104da1c59dd11f016d" args="(const int dim0)" -->
115&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#163ee002a7858d104da1c59dd11f016d">ldmat</a> (const int dim0)</td></tr>
116
117<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default initialization with proper size. <br></td></tr>
118<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1e2734c0164ce5233c4d709679555138"></a><!-- doxytag: member="ldmat::~ldmat" ref="1e2734c0164ce5233c4d709679555138" args="()" -->
119virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#1e2734c0164ce5233c4d709679555138">~ldmat</a> ()</td></tr>
120
121<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor for future use;. <br></td></tr>
122<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0f0f6e083e6d947cf58097ffce3ccd1a">opupdt</a> (const vec &amp;v, double w)</td></tr>
123
124<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2c1ebc071de4bafbba55b80afd8a7e8e"></a><!-- doxytag: member="ldmat::to_mat" ref="2c1ebc071de4bafbba55b80afd8a7e8e" args="() const " -->
125mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2c1ebc071de4bafbba55b80afd8a7e8e">to_mat</a> () const </td></tr>
126
127<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conversion to full matrix. <br></td></tr>
128<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#e967b9425007f0cb6cd59b845f9756d8">mult_sym</a> (const mat &amp;C)</td></tr>
129
130<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Inplace symmetric multiplication by a SQUARE matrix <img class="formulaInl" alt="$C$" src="form_24.png">, i.e. <img class="formulaInl" alt="$V = C*V*C'$" src="form_25.png">.  <a href="#e967b9425007f0cb6cd59b845f9756d8"></a><br></td></tr>
131<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4fd155f38eb6dd5af4bdf9c98a7999a9">mult_sym_t</a> (const mat &amp;C)</td></tr>
132
133<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Inplace symmetric multiplication by a SQUARE transpose of matrix <img class="formulaInl" alt="$C$" src="form_24.png">, i.e. <img class="formulaInl" alt="$V = C'*V*C$" src="form_26.png">.  <a href="#4fd155f38eb6dd5af4bdf9c98a7999a9"></a><br></td></tr>
134<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a60f2c7e4f3c6a7738eaaaab81ffad20"></a><!-- doxytag: member="ldmat::add" ref="a60f2c7e4f3c6a7738eaaaab81ffad20" args="(const ldmat &amp;ld2, double w=1.0)" -->
135void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a60f2c7e4f3c6a7738eaaaab81ffad20">add</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;ld2, double w=1.0)</td></tr>
136
137<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add another matrix in LD form with weight w. <br></td></tr>
138<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2b42750ba4962d439aa52a77ae12949b"></a><!-- doxytag: member="ldmat::logdet" ref="2b42750ba4962d439aa52a77ae12949b" args="() const " -->
139double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2b42750ba4962d439aa52a77ae12949b">logdet</a> () const </td></tr>
140
141<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of a determinant. <br></td></tr>
142<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d64f331b781903e913cb2ee836886f3f"></a><!-- doxytag: member="ldmat::qform" ref="d64f331b781903e913cb2ee836886f3f" args="(const vec &amp;v) const " -->
143double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d64f331b781903e913cb2ee836886f3f">qform</a> (const vec &amp;v) const </td></tr>
144
145<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluates quadratic form <img class="formulaInl" alt="$x= v'*V*v$" src="form_29.png">;. <br></td></tr>
146<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d876c5f83e02b3e809b35c9de5068f14"></a><!-- doxytag: member="ldmat::invqform" ref="d876c5f83e02b3e809b35c9de5068f14" args="(const vec &amp;v) const " -->
147double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d876c5f83e02b3e809b35c9de5068f14">invqform</a> (const vec &amp;v) const </td></tr>
148
149<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluates quadratic form <img class="formulaInl" alt="$x= v'*inv(V)*v$" src="form_30.png">;. <br></td></tr>
150<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d6e401de9607332305c27e67972a07a"></a><!-- doxytag: member="ldmat::clear" ref="4d6e401de9607332305c27e67972a07a" args="()" -->
151void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4d6e401de9607332305c27e67972a07a">clear</a> ()</td></tr>
152
153<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Clearing matrix so that it corresponds to zeros. <br></td></tr>
154<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g0fceb6b5b637cec89bb0a3d2e6be1306"></a><!-- doxytag: member="ldmat::cols" ref="g0fceb6b5b637cec89bb0a3d2e6be1306" args="() const " -->
155int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#g0fceb6b5b637cec89bb0a3d2e6be1306">cols</a> () const </td></tr>
156
157<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
158<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g96dfb21865db4f5bd36fa70f9b0b1163"></a><!-- doxytag: member="ldmat::rows" ref="g96dfb21865db4f5bd36fa70f9b0b1163" args="() const " -->
159int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#g96dfb21865db4f5bd36fa70f9b0b1163">rows</a> () const </td></tr>
160
161<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
162<tr><td class="memItemLeft" nowrap align="right" valign="top">vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#fc380626ced6f9244fb58c5f0231174d">sqrt_mult</a> (const vec &amp;v) const </td></tr>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Multiplies square root of <img class="formulaInl" alt="$V$" src="form_27.png"> by vector <img class="formulaInl" alt="$x$" src="form_28.png">.  <a href="#fc380626ced6f9244fb58c5f0231174d"></a><br></td></tr>
165<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2c160cb123c1102face7a50ec566a031">inv</a> (<a class="el" href="classldmat.html">ldmat</a> &amp;Inv) const </td></tr>
166
167<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix inversion preserving the chosen form.  <a href="#2c160cb123c1102face7a50ec566a031"></a><br></td></tr>
168<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#e7207748909325bb0f99b43f090a2b7e">mult_sym</a> (const mat &amp;C, <a class="el" href="classldmat.html">ldmat</a> &amp;U) const </td></tr>
169
170<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_31.png"> by a general matrix <img class="formulaInl" alt="$C$" src="form_24.png">, result of which is stored in the current class.  <a href="#e7207748909325bb0f99b43f090a2b7e"></a><br></td></tr>
171<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f94dc3a233f3d40fc853d8d4ac3b8eab">mult_sym_t</a> (const mat &amp;C, <a class="el" href="classldmat.html">ldmat</a> &amp;U) const </td></tr>
172
173<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_31.png"> by a transpose of a general matrix <img class="formulaInl" alt="$C$" src="form_24.png">, result of which is stored in the current class.  <a href="#f94dc3a233f3d40fc853d8d4ac3b8eab"></a><br></td></tr>
174<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f291faa073e7bc8dfafc7ae93daa2506">ldform</a> (const mat &amp;A, const vec &amp;D0)</td></tr>
175
176<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_32.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_33.png">.  <a href="#f291faa073e7bc8dfafc7ae93daa2506"></a><br></td></tr>
177<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0884a613b94fde61bfc84288e73ce57f"></a><!-- doxytag: member="ldmat::setD" ref="0884a613b94fde61bfc84288e73ce57f" args="(const vec &amp;nD)" -->
178void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0884a613b94fde61bfc84288e73ce57f">setD</a> (const vec &amp;nD)</td></tr>
179
180<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
181<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7619922b4de18830ce5351c6b5667e60"></a><!-- doxytag: member="ldmat::setD" ref="7619922b4de18830ce5351c6b5667e60" args="(const vec &amp;nD, int i)" -->
182void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#7619922b4de18830ce5351c6b5667e60">setD</a> (const vec &amp;nD, int i)</td></tr>
183
184<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
185<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="32ff66296627ff5341d7c0b973249614"></a><!-- doxytag: member="ldmat::setL" ref="32ff66296627ff5341d7c0b973249614" args="(const vec &amp;nL)" -->
186void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#32ff66296627ff5341d7c0b973249614">setL</a> (const vec &amp;nL)</td></tr>
187
188<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
189<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="282c879f50aa9ef934e7f46d86881582"></a><!-- doxytag: member="ldmat::_D" ref="282c879f50aa9ef934e7f46d86881582" args="() const " -->
190const vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#282c879f50aa9ef934e7f46d86881582">_D</a> () const </td></tr>
191
192<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
193<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5f44f100248c6627314afaa653b9e5bd"></a><!-- doxytag: member="ldmat::_L" ref="5f44f100248c6627314afaa653b9e5bd" args="() const " -->
194const mat &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f44f100248c6627314afaa653b9e5bd">_L</a> () const </td></tr>
195
196<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
197<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#gca445ee152a56043af946ea095b2d8f8">operator+=</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;ldA)</td></tr>
198
199<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">add another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD).">ldmat</a> matrix  <a href="group__math.html#gca445ee152a56043af946ea095b2d8f8"></a><br></td></tr>
200<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#ge3f4d2d85ab1ba384c852329aa31d0fb">operator-=</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;ldA)</td></tr>
201
202<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">subtract another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD).">ldmat</a> matrix  <a href="group__math.html#ge3f4d2d85ab1ba384c852329aa31d0fb"></a><br></td></tr>
203<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="875b7e6dcf73ae7001329099019fdb1d"></a><!-- doxytag: member="ldmat::operator*=" ref="875b7e6dcf73ae7001329099019fdb1d" args="(double x)" -->
204<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#875b7e6dcf73ae7001329099019fdb1d">operator*=</a> (double x)</td></tr>
205
206<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">multiply by a scalar <br></td></tr>
207<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
208<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4cce04824539c4a8d062d9a36d6e014e"></a><!-- doxytag: member="ldmat::D" ref="4cce04824539c4a8d062d9a36d6e014e" args="" -->
209vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a></td></tr>
210
211<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Positive vector <img class="formulaInl" alt="$D$" src="form_22.png">. <br></td></tr>
212<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f74a64b99fe58a75ebd37bb679e121ea"></a><!-- doxytag: member="ldmat::L" ref="f74a64b99fe58a75ebd37bb679e121ea" args="" -->
213mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a></td></tr>
214
215<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower-triangular matrix <img class="formulaInl" alt="$L$" src="form_21.png">. <br></td></tr>
216<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
217<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="eaaa0baa6026b84cfcbced41c84599d1"></a><!-- doxytag: member="ldmat::operator&lt;&lt;" ref="eaaa0baa6026b84cfcbced41c84599d1" args="(std::ostream &amp;os, const ldmat &amp;sq)" -->
218std::ostream &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#eaaa0baa6026b84cfcbced41c84599d1">operator&lt;&lt;</a> (std::ostream &amp;os, const <a class="el" href="classldmat.html">ldmat</a> &amp;sq)</td></tr>
219
220<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">print both <code>L</code> and <code>D</code> <br></td></tr>
221</table>
222<hr><h2>Member Function Documentation</h2>
223<a class="anchor" name="0f0f6e083e6d947cf58097ffce3ccd1a"></a><!-- doxytag: member="ldmat::opupdt" ref="0f0f6e083e6d947cf58097ffce3ccd1a" args="(const vec &amp;v, double w)" -->
224<div class="memitem">
225<div class="memproto">
226      <table class="memname">
227        <tr>
228          <td class="memname">void ldmat::opupdt           </td>
229          <td>(</td>
230          <td class="paramtype">const vec &amp;&nbsp;</td>
231          <td class="paramname"> <em>v</em>, </td>
232        </tr>
233        <tr>
234          <td class="paramkey"></td>
235          <td></td>
236          <td class="paramtype">double&nbsp;</td>
237          <td class="paramname"> <em>w</em></td><td>&nbsp;</td>
238        </tr>
239        <tr>
240          <td></td>
241          <td>)</td>
242          <td></td><td></td><td><code> [virtual]</code></td>
243        </tr>
244      </table>
245</div>
246<div class="memdoc">
247
248<p>
249Perfroms a rank-1 update by outer product of vectors: <img class="formulaInl" alt="$V = V + w v v'$" src="form_23.png">. <dl compact><dt><b>Parameters:</b></dt><dd>
250  <table border="0" cellspacing="2" cellpadding="0">
251    <tr><td valign="top"></td><td valign="top"><em>v</em>&nbsp;</td><td>Vector forming the outer product to be added </td></tr>
252    <tr><td valign="top"></td><td valign="top"><em>w</em>&nbsp;</td><td>weight of updating; can be negative</td></tr>
253  </table>
254</dl>
255BLAS-2b operation.
256<p>Implements <a class="el" href="classsqmat.html#b223484796661f2dadb5607a86ce0581">sqmat</a>.</p>
257
258<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00107">sqmat::dim</a>, <a class="el" href="libDC_8cpp-source.html#l00319">dydr()</a>, and <a class="el" href="libDC_8h-source.html#l00277">L</a>.</p>
259
260<p>Referenced by <a class="el" href="libDC_8cpp-source.html#l00104">add()</a>, <a class="el" href="bdm_2estim_2arx_8cpp-source.html#l00005">bdm::ARX::bayes()</a>, and <a class="el" href="bdm_2estim_2arx_8cpp-source.html#l00025">bdm::ARX::logpred()</a>.</p>
261
262</div>
263</div><p>
264<a class="anchor" name="e967b9425007f0cb6cd59b845f9756d8"></a><!-- doxytag: member="ldmat::mult_sym" ref="e967b9425007f0cb6cd59b845f9756d8" args="(const mat &amp;C)" -->
265<div class="memitem">
266<div class="memproto">
267      <table class="memname">
268        <tr>
269          <td class="memname">void ldmat::mult_sym           </td>
270          <td>(</td>
271          <td class="paramtype">const mat &amp;&nbsp;</td>
272          <td class="paramname"> <em>C</em>          </td>
273          <td>&nbsp;)&nbsp;</td>
274          <td><code> [virtual]</code></td>
275        </tr>
276      </table>
277</div>
278<div class="memdoc">
279
280<p>
281Inplace symmetric multiplication by a SQUARE matrix <img class="formulaInl" alt="$C$" src="form_24.png">, i.e. <img class="formulaInl" alt="$V = C*V*C'$" src="form_25.png">.
282<p>
283<dl compact><dt><b>Parameters:</b></dt><dd>
284  <table border="0" cellspacing="2" cellpadding="0">
285    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
286  </table>
287</dl>
288
289<p>Implements <a class="el" href="classsqmat.html#60fbbfa9e483b8187c135f787ee53afa">sqmat</a>.</p>
290
291<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00277">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00200">ldform()</a>.</p>
292
293</div>
294</div><p>
295<a class="anchor" name="4fd155f38eb6dd5af4bdf9c98a7999a9"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="4fd155f38eb6dd5af4bdf9c98a7999a9" args="(const mat &amp;C)" -->
296<div class="memitem">
297<div class="memproto">
298      <table class="memname">
299        <tr>
300          <td class="memname">void ldmat::mult_sym_t           </td>
301          <td>(</td>
302          <td class="paramtype">const mat &amp;&nbsp;</td>
303          <td class="paramname"> <em>C</em>          </td>
304          <td>&nbsp;)&nbsp;</td>
305          <td><code> [virtual]</code></td>
306        </tr>
307      </table>
308</div>
309<div class="memdoc">
310
311<p>
312Inplace symmetric multiplication by a SQUARE transpose of matrix <img class="formulaInl" alt="$C$" src="form_24.png">, i.e. <img class="formulaInl" alt="$V = C'*V*C$" src="form_26.png">.
313<p>
314<dl compact><dt><b>Parameters:</b></dt><dd>
315  <table border="0" cellspacing="2" cellpadding="0">
316    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
317  </table>
318</dl>
319
320<p>Implements <a class="el" href="classsqmat.html#6909e906da17725b1b80f3cae7cf3325">sqmat</a>.</p>
321
322<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00277">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00200">ldform()</a>.</p>
323
324</div>
325</div><p>
326<a class="anchor" name="fc380626ced6f9244fb58c5f0231174d"></a><!-- doxytag: member="ldmat::sqrt_mult" ref="fc380626ced6f9244fb58c5f0231174d" args="(const vec &amp;v) const " -->
327<div class="memitem">
328<div class="memproto">
329      <table class="memname">
330        <tr>
331          <td class="memname">vec ldmat::sqrt_mult           </td>
332          <td>(</td>
333          <td class="paramtype">const vec &amp;&nbsp;</td>
334          <td class="paramname"> <em>v</em>          </td>
335          <td>&nbsp;)&nbsp;</td>
336          <td> const<code> [virtual]</code></td>
337        </tr>
338      </table>
339</div>
340<div class="memdoc">
341
342<p>
343Multiplies square root of <img class="formulaInl" alt="$V$" src="form_27.png"> by vector <img class="formulaInl" alt="$x$" src="form_28.png">.
344<p>
345Used e.g. in generating normal samples.
346<p>Implements <a class="el" href="classsqmat.html#6b79438b5d7544a9c8e110a145355d8f">sqmat</a>.</p>
347
348<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00107">sqmat::dim</a>, and <a class="el" href="libDC_8h-source.html#l00277">L</a>.</p>
349
350</div>
351</div><p>
352<a class="anchor" name="2c160cb123c1102face7a50ec566a031"></a><!-- doxytag: member="ldmat::inv" ref="2c160cb123c1102face7a50ec566a031" args="(ldmat &amp;Inv) const " -->
353<div class="memitem">
354<div class="memproto">
355      <table class="memname">
356        <tr>
357          <td class="memname">void ldmat::inv           </td>
358          <td>(</td>
359          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
360          <td class="paramname"> <em>Inv</em>          </td>
361          <td>&nbsp;)&nbsp;</td>
362          <td> const<code> [virtual]</code></td>
363        </tr>
364      </table>
365</div>
366<div class="memdoc">
367
368<p>
369Matrix inversion preserving the chosen form.
370<p>
371<dl compact><dt><b>Parameters:</b></dt><dd>
372  <table border="0" cellspacing="2" cellpadding="0">
373    <tr><td valign="top"></td><td valign="top"><em>Inv</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
374  </table>
375</dl>
376
377<p>References <a class="el" href="libDC_8cpp-source.html#l00116">clear()</a>, <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00277">L</a>, <a class="el" href="libDC_8cpp-source.html#l00200">ldform()</a>, and <a class="el" href="libDC_8cpp-source.html#l00298">ltuinv()</a>.</p>
378
379<p>Referenced by <a class="el" href="libEF_8cpp-source.html#l00090">bdm::egiw::variance()</a>.</p>
380
381</div>
382</div><p>
383<a class="anchor" name="e7207748909325bb0f99b43f090a2b7e"></a><!-- doxytag: member="ldmat::mult_sym" ref="e7207748909325bb0f99b43f090a2b7e" args="(const mat &amp;C, ldmat &amp;U) const " -->
384<div class="memitem">
385<div class="memproto">
386      <table class="memname">
387        <tr>
388          <td class="memname">void ldmat::mult_sym           </td>
389          <td>(</td>
390          <td class="paramtype">const mat &amp;&nbsp;</td>
391          <td class="paramname"> <em>C</em>, </td>
392        </tr>
393        <tr>
394          <td class="paramkey"></td>
395          <td></td>
396          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
397          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
398        </tr>
399        <tr>
400          <td></td>
401          <td>)</td>
402          <td></td><td></td><td> const</td>
403        </tr>
404      </table>
405</div>
406<div class="memdoc">
407
408<p>
409Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_31.png"> by a general matrix <img class="formulaInl" alt="$C$" src="form_24.png">, result of which is stored in the current class.
410<p>
411<dl compact><dt><b>Parameters:</b></dt><dd>
412  <table border="0" cellspacing="2" cellpadding="0">
413    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
414    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
415  </table>
416</dl>
417
418<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00277">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00200">ldform()</a>.</p>
419
420</div>
421</div><p>
422<a class="anchor" name="f94dc3a233f3d40fc853d8d4ac3b8eab"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="f94dc3a233f3d40fc853d8d4ac3b8eab" args="(const mat &amp;C, ldmat &amp;U) const " -->
423<div class="memitem">
424<div class="memproto">
425      <table class="memname">
426        <tr>
427          <td class="memname">void ldmat::mult_sym_t           </td>
428          <td>(</td>
429          <td class="paramtype">const mat &amp;&nbsp;</td>
430          <td class="paramname"> <em>C</em>, </td>
431        </tr>
432        <tr>
433          <td class="paramkey"></td>
434          <td></td>
435          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
436          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
437        </tr>
438        <tr>
439          <td></td>
440          <td>)</td>
441          <td></td><td></td><td> const</td>
442        </tr>
443      </table>
444</div>
445<div class="memdoc">
446
447<p>
448Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_31.png"> by a transpose of a general matrix <img class="formulaInl" alt="$C$" src="form_24.png">, result of which is stored in the current class.
449<p>
450<dl compact><dt><b>Parameters:</b></dt><dd>
451  <table border="0" cellspacing="2" cellpadding="0">
452    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
453    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
454  </table>
455</dl>
456
457<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00277">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00200">ldform()</a>.</p>
458
459</div>
460</div><p>
461<a class="anchor" name="f291faa073e7bc8dfafc7ae93daa2506"></a><!-- doxytag: member="ldmat::ldform" ref="f291faa073e7bc8dfafc7ae93daa2506" args="(const mat &amp;A, const vec &amp;D0)" -->
462<div class="memitem">
463<div class="memproto">
464      <table class="memname">
465        <tr>
466          <td class="memname">void ldmat::ldform           </td>
467          <td>(</td>
468          <td class="paramtype">const mat &amp;&nbsp;</td>
469          <td class="paramname"> <em>A</em>, </td>
470        </tr>
471        <tr>
472          <td class="paramkey"></td>
473          <td></td>
474          <td class="paramtype">const vec &amp;&nbsp;</td>
475          <td class="paramname"> <em>D0</em></td><td>&nbsp;</td>
476        </tr>
477        <tr>
478          <td></td>
479          <td>)</td>
480          <td></td><td></td><td></td>
481        </tr>
482      </table>
483</div>
484<div class="memdoc">
485
486<p>
487Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_32.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_33.png">.
488<p>
489The new decomposition fullfills: <img class="formulaInl" alt="$A'*diag(D)*A = self.L'*diag(self.D)*self.L$" src="form_34.png"> <dl compact><dt><b>Parameters:</b></dt><dd>
490  <table border="0" cellspacing="2" cellpadding="0">
491    <tr><td valign="top"></td><td valign="top"><em>A</em>&nbsp;</td><td>general matrix </td></tr>
492    <tr><td valign="top"></td><td valign="top"><em>D0</em>&nbsp;</td><td>general vector </td></tr>
493  </table>
494</dl>
495
496<p>References <a class="el" href="libDC_8h-source.html#l00275">D</a>, <a class="el" href="libDC_8h-source.html#l00107">sqmat::dim</a>, and <a class="el" href="libDC_8h-source.html#l00277">L</a>.</p>
497
498<p>Referenced by <a class="el" href="libDC_8cpp-source.html#l00118">inv()</a>, <a class="el" href="libDC_8cpp-source.html#l00046">ldmat()</a>, <a class="el" href="libDC_8cpp-source.html#l00125">mult_sym()</a>, and <a class="el" href="libDC_8cpp-source.html#l00130">mult_sym_t()</a>.</p>
499
500</div>
501</div><p>
502<hr>The documentation for this class was generated from the following files:<ul>
503<li><a class="el" href="libDC_8h-source.html">libDC.h</a><li>libDC.cpp</ul>
504</div>
505<hr size="1"><address style="text-align: right;"><small>Generated on Sun Feb 15 23:09:30 2009 for mixpp by&nbsp;
506<a href="http://www.doxygen.org/index.html">
507<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
508</body>
509</html>
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