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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" -->Matrix stored in LD form, (commonly known as UD). 
73<a href="#_details">More...</a>
74<p>
75<code>#include &lt;<a class="el" href="square__mat_8h-source.html">square_mat.h</a>&gt;</code>
76<p>
77
78<p>
79<a href="classldmat-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
80<tr><td></td></tr>
81<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
82<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)" -->
83&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>
84
85<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by copy of L and D. <br></td></tr>
86<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)" -->
87&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f21785358072d36892d538eed1d1ea5">ldmat</a> (const mat &amp;V)</td></tr>
88
89<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by decomposition of full matrix V. <br></td></tr>
90<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)" -->
91&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>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by restructuring of V0 accordint to permutation vector perm. <br></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abe16e0f86668ef61a9a4896c8565dee"></a><!-- doxytag: member="ldmat::ldmat" ref="abe16e0f86668ef61a9a4896c8565dee" args="(vec D0)" -->
95&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#abe16e0f86668ef61a9a4896c8565dee">ldmat</a> (vec D0)</td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct diagonal matrix with diagonal D0. <br></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a12dda6f529580b0377cc45226b43303"></a><!-- doxytag: member="ldmat::ldmat" ref="a12dda6f529580b0377cc45226b43303" args="()" -->
99&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a12dda6f529580b0377cc45226b43303">ldmat</a> ()</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
102<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)" -->
103&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#163ee002a7858d104da1c59dd11f016d">ldmat</a> (const int dim0)</td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default initialization with proper size. <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1e2734c0164ce5233c4d709679555138"></a><!-- doxytag: member="ldmat::~ldmat" ref="1e2734c0164ce5233c4d709679555138" args="()" -->
107virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#1e2734c0164ce5233c4d709679555138">~ldmat</a> ()</td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor for future use;. <br></td></tr>
110<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>
111
112<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2c1ebc071de4bafbba55b80afd8a7e8e"></a><!-- doxytag: member="ldmat::to_mat" ref="2c1ebc071de4bafbba55b80afd8a7e8e" args="() const " -->
113mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2c1ebc071de4bafbba55b80afd8a7e8e">to_mat</a> () const </td></tr>
114
115<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conversion to full matrix. <br></td></tr>
116<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>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Inplace symmetric multiplication by a SQUARE matrix <img class="formulaInl" alt="$C$" src="form_52.png">, i.e. <img class="formulaInl" alt="$V = C*V*C'$" src="form_53.png">.  <a href="#e967b9425007f0cb6cd59b845f9756d8"></a><br></td></tr>
119<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>
120
121<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_52.png">, i.e. <img class="formulaInl" alt="$V = C'*V*C$" src="form_54.png">.  <a href="#4fd155f38eb6dd5af4bdf9c98a7999a9"></a><br></td></tr>
122<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)" -->
123void&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>
124
125<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add another matrix in LD form with weight w. <br></td></tr>
126<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2b42750ba4962d439aa52a77ae12949b"></a><!-- doxytag: member="ldmat::logdet" ref="2b42750ba4962d439aa52a77ae12949b" args="() const " -->
127double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2b42750ba4962d439aa52a77ae12949b">logdet</a> () const </td></tr>
128
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of a determinant. <br></td></tr>
130<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 " -->
131double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d64f331b781903e913cb2ee836886f3f">qform</a> (const vec &amp;v) const </td></tr>
132
133<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluates quadratic form <img class="formulaInl" alt="$x= v'*V*v$" src="form_56.png">;. <br></td></tr>
134<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 " -->
135double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d876c5f83e02b3e809b35c9de5068f14">invqform</a> (const vec &amp;v) const </td></tr>
136
137<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluates quadratic form <img class="formulaInl" alt="$x= v'*inv(V)*v$" src="form_57.png">;. <br></td></tr>
138<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d6e401de9607332305c27e67972a07a"></a><!-- doxytag: member="ldmat::clear" ref="4d6e401de9607332305c27e67972a07a" args="()" -->
139void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4d6e401de9607332305c27e67972a07a">clear</a> ()</td></tr>
140
141<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Clearing matrix so that it corresponds to zeros. <br></td></tr>
142<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g0fceb6b5b637cec89bb0a3d2e6be1306"></a><!-- doxytag: member="ldmat::cols" ref="g0fceb6b5b637cec89bb0a3d2e6be1306" args="() const " -->
143int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#g0fceb6b5b637cec89bb0a3d2e6be1306">cols</a> () const </td></tr>
144
145<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
146<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g96dfb21865db4f5bd36fa70f9b0b1163"></a><!-- doxytag: member="ldmat::rows" ref="g96dfb21865db4f5bd36fa70f9b0b1163" args="() const " -->
147int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__math.html#g96dfb21865db4f5bd36fa70f9b0b1163">rows</a> () const </td></tr>
148
149<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
150<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>
151
152<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Multiplies square root of <img class="formulaInl" alt="$V$" src="form_55.png"> by vector <img class="formulaInl" alt="$x$" src="form_1.png">.  <a href="#fc380626ced6f9244fb58c5f0231174d"></a><br></td></tr>
153<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>
154
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix inversion preserving the chosen form.  <a href="#2c160cb123c1102face7a50ec566a031"></a><br></td></tr>
156<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>
157
158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_58.png"> by a general matrix <img class="formulaInl" alt="$C$" src="form_52.png">, result of which is stored in the current class.  <a href="#e7207748909325bb0f99b43f090a2b7e"></a><br></td></tr>
159<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>
160
161<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_58.png"> by a transpose of a general matrix <img class="formulaInl" alt="$C$" src="form_52.png">, result of which is stored in the current class.  <a href="#f94dc3a233f3d40fc853d8d4ac3b8eab"></a><br></td></tr>
162<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>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_59.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_60.png">.  <a href="#f291faa073e7bc8dfafc7ae93daa2506"></a><br></td></tr>
165<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)" -->
166void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0884a613b94fde61bfc84288e73ce57f">setD</a> (const vec &amp;nD)</td></tr>
167
168<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
169<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)" -->
170void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#7619922b4de18830ce5351c6b5667e60">setD</a> (const vec &amp;nD, int i)</td></tr>
171
172<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
173<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)" -->
174void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#32ff66296627ff5341d7c0b973249614">setL</a> (const vec &amp;nL)</td></tr>
175
176<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
177<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="282c879f50aa9ef934e7f46d86881582"></a><!-- doxytag: member="ldmat::_D" ref="282c879f50aa9ef934e7f46d86881582" args="() const " -->
178const vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#282c879f50aa9ef934e7f46d86881582">_D</a> () const </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="5f44f100248c6627314afaa653b9e5bd"></a><!-- doxytag: member="ldmat::_L" ref="5f44f100248c6627314afaa653b9e5bd" args="() const " -->
182const mat &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f44f100248c6627314afaa653b9e5bd">_L</a> () const </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="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>
186
187<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>
188<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>
189
190<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>
191<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="875b7e6dcf73ae7001329099019fdb1d"></a><!-- doxytag: member="ldmat::operator*=" ref="875b7e6dcf73ae7001329099019fdb1d" args="(double x)" -->
192<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>
193
194<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">multiply by a scalar <br></td></tr>
195<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
196<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4cce04824539c4a8d062d9a36d6e014e"></a><!-- doxytag: member="ldmat::D" ref="4cce04824539c4a8d062d9a36d6e014e" args="" -->
197vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a></td></tr>
198
199<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Positive vector <img class="formulaInl" alt="$D$" src="form_50.png">. <br></td></tr>
200<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f74a64b99fe58a75ebd37bb679e121ea"></a><!-- doxytag: member="ldmat::L" ref="f74a64b99fe58a75ebd37bb679e121ea" args="" -->
201mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a></td></tr>
202
203<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower-triangular matrix <img class="formulaInl" alt="$L$" src="form_49.png">. <br></td></tr>
204<tr><td colspan="2"><br><h2>Private Attributes</h2></td></tr>
205<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0abed904bdc0882373ba9adba919689d"></a><!-- doxytag: member="ldmat::dim" ref="0abed904bdc0882373ba9adba919689d" args="" -->
206int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classsqmat.html#0abed904bdc0882373ba9adba919689d">dim</a></td></tr>
207
208<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the square matrix <br></td></tr>
209<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
210<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)" -->
211std::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>
212
213<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">print both <code>L</code> and <code>D</code> <br></td></tr>
214</table>
215<hr><a name="_details"></a><h2>Detailed Description</h2>
216Matrix stored in LD form, (commonly known as UD).
217<p>
218Matrix is decomposed as follows: <p class="formulaDsp">
219<img class="formulaDsp" alt="\[M = L'DL\]" src="form_48.png">
220<p>
221 where only <img class="formulaInl" alt="$L$" src="form_49.png"> and <img class="formulaInl" alt="$D$" src="form_50.png"> matrices are stored. All inplace operations modifies only these and the need to compose and decompose the matrix is avoided. <hr><h2>Member Function Documentation</h2>
222<a class="anchor" name="2c160cb123c1102face7a50ec566a031"></a><!-- doxytag: member="ldmat::inv" ref="2c160cb123c1102face7a50ec566a031" args="(ldmat &amp;Inv) const " -->
223<div class="memitem">
224<div class="memproto">
225      <table class="memname">
226        <tr>
227          <td class="memname">void ldmat::inv           </td>
228          <td>(</td>
229          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
230          <td class="paramname"> <em>Inv</em>          </td>
231          <td>&nbsp;)&nbsp;</td>
232          <td> const<code> [virtual]</code></td>
233        </tr>
234      </table>
235</div>
236<div class="memdoc">
237
238<p>
239Matrix inversion preserving the chosen form.
240<p>
241<dl compact><dt><b>Parameters:</b></dt><dd>
242  <table border="0" cellspacing="2" cellpadding="0">
243    <tr><td valign="top"></td><td valign="top"><em>Inv</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
244  </table>
245</dl>
246
247<p>References <a class="el" href="square__mat_8cpp-source.html#l00116">clear()</a>, <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00277">L</a>, <a class="el" href="square__mat_8cpp-source.html#l00200">ldform()</a>, and <a class="el" href="square__mat_8cpp-source.html#l00298">ltuinv()</a>.</p>
248
249<p>Referenced by <a class="el" href="exp__family_8cpp-source.html#l00124">bdm::egiw::variance()</a>.</p>
250
251</div>
252</div><p>
253<a class="anchor" name="f291faa073e7bc8dfafc7ae93daa2506"></a><!-- doxytag: member="ldmat::ldform" ref="f291faa073e7bc8dfafc7ae93daa2506" args="(const mat &amp;A, const vec &amp;D0)" -->
254<div class="memitem">
255<div class="memproto">
256      <table class="memname">
257        <tr>
258          <td class="memname">void ldmat::ldform           </td>
259          <td>(</td>
260          <td class="paramtype">const mat &amp;&nbsp;</td>
261          <td class="paramname"> <em>A</em>, </td>
262        </tr>
263        <tr>
264          <td class="paramkey"></td>
265          <td></td>
266          <td class="paramtype">const vec &amp;&nbsp;</td>
267          <td class="paramname"> <em>D0</em></td><td>&nbsp;</td>
268        </tr>
269        <tr>
270          <td></td>
271          <td>)</td>
272          <td></td><td></td><td></td>
273        </tr>
274      </table>
275</div>
276<div class="memdoc">
277
278<p>
279Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_59.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_60.png">.
280<p>
281The new decomposition fullfills: <img class="formulaInl" alt="$A'*diag(D)*A = self.L'*diag(self.D)*self.L$" src="form_61.png"> <dl compact><dt><b>Parameters:</b></dt><dd>
282  <table border="0" cellspacing="2" cellpadding="0">
283    <tr><td valign="top"></td><td valign="top"><em>A</em>&nbsp;</td><td>general matrix </td></tr>
284    <tr><td valign="top"></td><td valign="top"><em>D0</em>&nbsp;</td><td>general vector </td></tr>
285  </table>
286</dl>
287
288<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00107">sqmat::dim</a>, and <a class="el" href="square__mat_8h-source.html#l00277">L</a>.</p>
289
290<p>Referenced by <a class="el" href="square__mat_8cpp-source.html#l00118">inv()</a>, <a class="el" href="square__mat_8cpp-source.html#l00046">ldmat()</a>, <a class="el" href="square__mat_8cpp-source.html#l00125">mult_sym()</a>, and <a class="el" href="square__mat_8cpp-source.html#l00130">mult_sym_t()</a>.</p>
291
292</div>
293</div><p>
294<a class="anchor" name="e7207748909325bb0f99b43f090a2b7e"></a><!-- doxytag: member="ldmat::mult_sym" ref="e7207748909325bb0f99b43f090a2b7e" args="(const mat &amp;C, ldmat &amp;U) const " -->
295<div class="memitem">
296<div class="memproto">
297      <table class="memname">
298        <tr>
299          <td class="memname">void ldmat::mult_sym           </td>
300          <td>(</td>
301          <td class="paramtype">const mat &amp;&nbsp;</td>
302          <td class="paramname"> <em>C</em>, </td>
303        </tr>
304        <tr>
305          <td class="paramkey"></td>
306          <td></td>
307          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
308          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
309        </tr>
310        <tr>
311          <td></td>
312          <td>)</td>
313          <td></td><td></td><td> const</td>
314        </tr>
315      </table>
316</div>
317<div class="memdoc">
318
319<p>
320Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_58.png"> by a general matrix <img class="formulaInl" alt="$C$" src="form_52.png">, result of which is stored in the current class.
321<p>
322<dl compact><dt><b>Parameters:</b></dt><dd>
323  <table border="0" cellspacing="2" cellpadding="0">
324    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
325    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
326  </table>
327</dl>
328
329<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00277">L</a>, and <a class="el" href="square__mat_8cpp-source.html#l00200">ldform()</a>.</p>
330
331</div>
332</div><p>
333<a class="anchor" name="e967b9425007f0cb6cd59b845f9756d8"></a><!-- doxytag: member="ldmat::mult_sym" ref="e967b9425007f0cb6cd59b845f9756d8" args="(const mat &amp;C)" -->
334<div class="memitem">
335<div class="memproto">
336      <table class="memname">
337        <tr>
338          <td class="memname">void ldmat::mult_sym           </td>
339          <td>(</td>
340          <td class="paramtype">const mat &amp;&nbsp;</td>
341          <td class="paramname"> <em>C</em>          </td>
342          <td>&nbsp;)&nbsp;</td>
343          <td><code> [virtual]</code></td>
344        </tr>
345      </table>
346</div>
347<div class="memdoc">
348
349<p>
350Inplace symmetric multiplication by a SQUARE matrix <img class="formulaInl" alt="$C$" src="form_52.png">, i.e. <img class="formulaInl" alt="$V = C*V*C'$" src="form_53.png">.
351<p>
352<dl compact><dt><b>Parameters:</b></dt><dd>
353  <table border="0" cellspacing="2" cellpadding="0">
354    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
355  </table>
356</dl>
357
358<p>Implements <a class="el" href="classsqmat.html#60fbbfa9e483b8187c135f787ee53afa">sqmat</a>.</p>
359
360<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00277">L</a>, and <a class="el" href="square__mat_8cpp-source.html#l00200">ldform()</a>.</p>
361
362</div>
363</div><p>
364<a class="anchor" name="f94dc3a233f3d40fc853d8d4ac3b8eab"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="f94dc3a233f3d40fc853d8d4ac3b8eab" args="(const mat &amp;C, ldmat &amp;U) const " -->
365<div class="memitem">
366<div class="memproto">
367      <table class="memname">
368        <tr>
369          <td class="memname">void ldmat::mult_sym_t           </td>
370          <td>(</td>
371          <td class="paramtype">const mat &amp;&nbsp;</td>
372          <td class="paramname"> <em>C</em>, </td>
373        </tr>
374        <tr>
375          <td class="paramkey"></td>
376          <td></td>
377          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
378          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
379        </tr>
380        <tr>
381          <td></td>
382          <td>)</td>
383          <td></td><td></td><td> const</td>
384        </tr>
385      </table>
386</div>
387<div class="memdoc">
388
389<p>
390Symmetric multiplication of <img class="formulaInl" alt="$U$" src="form_58.png"> by a transpose of a general matrix <img class="formulaInl" alt="$C$" src="form_52.png">, result of which is stored in the current class.
391<p>
392<dl compact><dt><b>Parameters:</b></dt><dd>
393  <table border="0" cellspacing="2" cellpadding="0">
394    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
395    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
396  </table>
397</dl>
398
399<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00277">L</a>, and <a class="el" href="square__mat_8cpp-source.html#l00200">ldform()</a>.</p>
400
401</div>
402</div><p>
403<a class="anchor" name="4fd155f38eb6dd5af4bdf9c98a7999a9"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="4fd155f38eb6dd5af4bdf9c98a7999a9" args="(const mat &amp;C)" -->
404<div class="memitem">
405<div class="memproto">
406      <table class="memname">
407        <tr>
408          <td class="memname">void ldmat::mult_sym_t           </td>
409          <td>(</td>
410          <td class="paramtype">const mat &amp;&nbsp;</td>
411          <td class="paramname"> <em>C</em>          </td>
412          <td>&nbsp;)&nbsp;</td>
413          <td><code> [virtual]</code></td>
414        </tr>
415      </table>
416</div>
417<div class="memdoc">
418
419<p>
420Inplace symmetric multiplication by a SQUARE transpose of matrix <img class="formulaInl" alt="$C$" src="form_52.png">, i.e. <img class="formulaInl" alt="$V = C'*V*C$" src="form_54.png">.
421<p>
422<dl compact><dt><b>Parameters:</b></dt><dd>
423  <table border="0" cellspacing="2" cellpadding="0">
424    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
425  </table>
426</dl>
427
428<p>Implements <a class="el" href="classsqmat.html#6909e906da17725b1b80f3cae7cf3325">sqmat</a>.</p>
429
430<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00277">L</a>, and <a class="el" href="square__mat_8cpp-source.html#l00200">ldform()</a>.</p>
431
432</div>
433</div><p>
434<a class="anchor" name="0f0f6e083e6d947cf58097ffce3ccd1a"></a><!-- doxytag: member="ldmat::opupdt" ref="0f0f6e083e6d947cf58097ffce3ccd1a" args="(const vec &amp;v, double w)" -->
435<div class="memitem">
436<div class="memproto">
437      <table class="memname">
438        <tr>
439          <td class="memname">void ldmat::opupdt           </td>
440          <td>(</td>
441          <td class="paramtype">const vec &amp;&nbsp;</td>
442          <td class="paramname"> <em>v</em>, </td>
443        </tr>
444        <tr>
445          <td class="paramkey"></td>
446          <td></td>
447          <td class="paramtype">double&nbsp;</td>
448          <td class="paramname"> <em>w</em></td><td>&nbsp;</td>
449        </tr>
450        <tr>
451          <td></td>
452          <td>)</td>
453          <td></td><td></td><td><code> [virtual]</code></td>
454        </tr>
455      </table>
456</div>
457<div class="memdoc">
458
459<p>
460Perfroms a rank-1 update by outer product of vectors: <img class="formulaInl" alt="$V = V + w v v'$" src="form_51.png">. <dl compact><dt><b>Parameters:</b></dt><dd>
461  <table border="0" cellspacing="2" cellpadding="0">
462    <tr><td valign="top"></td><td valign="top"><em>v</em>&nbsp;</td><td>Vector forming the outer product to be added </td></tr>
463    <tr><td valign="top"></td><td valign="top"><em>w</em>&nbsp;</td><td>weight of updating; can be negative</td></tr>
464  </table>
465</dl>
466BLAS-2b operation.
467<p>Implements <a class="el" href="classsqmat.html#b223484796661f2dadb5607a86ce0581">sqmat</a>.</p>
468
469<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00107">sqmat::dim</a>, <a class="el" href="square__mat_8cpp-source.html#l00319">dydr()</a>, and <a class="el" href="square__mat_8h-source.html#l00277">L</a>.</p>
470
471<p>Referenced by <a class="el" href="square__mat_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>
472
473</div>
474</div><p>
475<a class="anchor" name="fc380626ced6f9244fb58c5f0231174d"></a><!-- doxytag: member="ldmat::sqrt_mult" ref="fc380626ced6f9244fb58c5f0231174d" args="(const vec &amp;v) const " -->
476<div class="memitem">
477<div class="memproto">
478      <table class="memname">
479        <tr>
480          <td class="memname">vec ldmat::sqrt_mult           </td>
481          <td>(</td>
482          <td class="paramtype">const vec &amp;&nbsp;</td>
483          <td class="paramname"> <em>v</em>          </td>
484          <td>&nbsp;)&nbsp;</td>
485          <td> const<code> [virtual]</code></td>
486        </tr>
487      </table>
488</div>
489<div class="memdoc">
490
491<p>
492Multiplies square root of <img class="formulaInl" alt="$V$" src="form_55.png"> by vector <img class="formulaInl" alt="$x$" src="form_1.png">.
493<p>
494Used e.g. in generating normal samples.
495<p>Implements <a class="el" href="classsqmat.html#6b79438b5d7544a9c8e110a145355d8f">sqmat</a>.</p>
496
497<p>References <a class="el" href="square__mat_8h-source.html#l00275">D</a>, <a class="el" href="square__mat_8h-source.html#l00107">sqmat::dim</a>, and <a class="el" href="square__mat_8h-source.html#l00277">L</a>.</p>
498
499</div>
500</div><p>
501<hr>The documentation for this class was generated from the following files:<ul>
502<li><a class="el" href="square__mat_8h-source.html">square_mat.h</a><li>square_mat.cpp</ul>
503</div>
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506<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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