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3<title>mixpp: ldmat Class Reference</title>
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23<h1>ldmat Class Reference</h1><!-- doxytag: class="ldmat" --><!-- doxytag: inherits="sqmat" -->Matrix stored in LD form, (typically known as UD). 
24<a href="#_details">More...</a>
25<p>
26<code>#include &lt;<a class="el" href="libDC_8h-source.html">libDC.h</a>&gt;</code>
27<p>
28<div class="dynheader">
29Inheritance diagram for ldmat:</div>
30<div class="dynsection">
31<p><center><img src="classldmat__inherit__graph.png" border="0" usemap="#ldmat__inherit__map" alt="Inheritance graph"></center>
32<map name="ldmat__inherit__map">
33<area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="5,7,67,33"></map>
34<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
35<div class="dynheader">
36Collaboration diagram for ldmat:</div>
37<div class="dynsection">
38<p><center><img src="classldmat__coll__graph.png" border="0" usemap="#ldmat__coll__map" alt="Collaboration graph"></center>
39<map name="ldmat__coll__map">
40<area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="5,7,67,33"></map>
41<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
42
43<p>
44<a href="classldmat-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
45<tr><td></td></tr>
46<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
47<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)" -->
48&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>
49
50<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by copy of L and D. <br></td></tr>
51<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)" -->
52&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f21785358072d36892d538eed1d1ea5">ldmat</a> (const mat &amp;V)</td></tr>
53
54<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by decomposition of full matrix V. <br></td></tr>
55<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abe16e0f86668ef61a9a4896c8565dee"></a><!-- doxytag: member="ldmat::ldmat" ref="abe16e0f86668ef61a9a4896c8565dee" args="(vec D0)" -->
56&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#abe16e0f86668ef61a9a4896c8565dee">ldmat</a> (vec D0)</td></tr>
57
58<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct diagonal matrix with diagonal D0. <br></td></tr>
59<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a12dda6f529580b0377cc45226b43303"></a><!-- doxytag: member="ldmat::ldmat" ref="a12dda6f529580b0377cc45226b43303" args="()" -->
60&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a12dda6f529580b0377cc45226b43303">ldmat</a> ()</td></tr>
61
62<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
63<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)" -->
64&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#163ee002a7858d104da1c59dd11f016d">ldmat</a> (const int dim0)</td></tr>
65
66<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default initialization with proper size. <br></td></tr>
67<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1e2734c0164ce5233c4d709679555138"></a><!-- doxytag: member="ldmat::~ldmat" ref="1e2734c0164ce5233c4d709679555138" args="()" -->
68virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#1e2734c0164ce5233c4d709679555138">~ldmat</a> ()</td></tr>
69
70<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor for future use;. <br></td></tr>
71<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>
72
73<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5b0515da8dc2293d9e4360b74cc26c9e"></a><!-- doxytag: member="ldmat::to_mat" ref="5b0515da8dc2293d9e4360b74cc26c9e" args="()" -->
74mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5b0515da8dc2293d9e4360b74cc26c9e">to_mat</a> ()</td></tr>
75
76<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conversion to full matrix. <br></td></tr>
77<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>
78
79<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>
80<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>
81
82<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>
83<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)" -->
84void&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>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add another matrix in LD form with weight w. <br></td></tr>
87<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2b42750ba4962d439aa52a77ae12949b"></a><!-- doxytag: member="ldmat::logdet" ref="2b42750ba4962d439aa52a77ae12949b" args="() const " -->
88double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2b42750ba4962d439aa52a77ae12949b">logdet</a> () const </td></tr>
89
90<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of a determinant. <br></td></tr>
91<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 " -->
92double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d64f331b781903e913cb2ee836886f3f">qform</a> (const vec &amp;v) const </td></tr>
93
94<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>
95<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 " -->
96double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d876c5f83e02b3e809b35c9de5068f14">invqform</a> (const vec &amp;v) const </td></tr>
97
98<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>
99<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d6e401de9607332305c27e67972a07a"></a><!-- doxytag: member="ldmat::clear" ref="4d6e401de9607332305c27e67972a07a" args="()" -->
100void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4d6e401de9607332305c27e67972a07a">clear</a> ()</td></tr>
101
102<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Clearing matrix so that it corresponds to zeros. <br></td></tr>
103<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0fceb6b5b637cec89bb0a3d2e6be1306"></a><!-- doxytag: member="ldmat::cols" ref="0fceb6b5b637cec89bb0a3d2e6be1306" args="() const " -->
104int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0fceb6b5b637cec89bb0a3d2e6be1306">cols</a> () const </td></tr>
105
106<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="96dfb21865db4f5bd36fa70f9b0b1163"></a><!-- doxytag: member="ldmat::rows" ref="96dfb21865db4f5bd36fa70f9b0b1163" args="() const " -->
108int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#96dfb21865db4f5bd36fa70f9b0b1163">rows</a> () const </td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
111<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>
112
113<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>
114<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>
115
116<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix inversion preserving the chosen form.  <a href="#2c160cb123c1102face7a50ec566a031"></a><br></td></tr>
117<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>
118
119<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>
120<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>
121
122<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>
123<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>
124
125<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>
126<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)" -->
127void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0884a613b94fde61bfc84288e73ce57f">setD</a> (const vec &amp;nD)</td></tr>
128
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
130<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)" -->
131void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#7619922b4de18830ce5351c6b5667e60">setD</a> (const vec &amp;nD, int i)</td></tr>
132
133<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
134<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)" -->
135void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#32ff66296627ff5341d7c0b973249614">setL</a> (const vec &amp;nL)</td></tr>
136
137<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
138<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="classldmat.html#ca445ee152a56043af946ea095b2d8f8">operator+=</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;ldA)</td></tr>
139
140<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">add another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix  <a href="#ca445ee152a56043af946ea095b2d8f8"></a><br></td></tr>
141<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="classldmat.html#e3f4d2d85ab1ba384c852329aa31d0fb">operator-=</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;ldA)</td></tr>
142
143<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">subtract another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix  <a href="#e3f4d2d85ab1ba384c852329aa31d0fb"></a><br></td></tr>
144<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="16871b2d54be6e5dc73f78b8cb90771c"></a><!-- doxytag: member="ldmat::operator *=" ref="16871b2d54be6e5dc73f78b8cb90771c" args="(double x)" -->
145<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#16871b2d54be6e5dc73f78b8cb90771c">operator *=</a> (double x)</td></tr>
146
147<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">multiply by a scalar <br></td></tr>
148<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
149<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4cce04824539c4a8d062d9a36d6e014e"></a><!-- doxytag: member="ldmat::D" ref="4cce04824539c4a8d062d9a36d6e014e" args="" -->
150vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a></td></tr>
151
152<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Positive vector <img class="formulaInl" alt="$D$" src="form_22.png">. <br></td></tr>
153<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f74a64b99fe58a75ebd37bb679e121ea"></a><!-- doxytag: member="ldmat::L" ref="f74a64b99fe58a75ebd37bb679e121ea" args="" -->
154mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a></td></tr>
155
156<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower-triangular matrix <img class="formulaInl" alt="$L$" src="form_21.png">. <br></td></tr>
157<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
158<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)" -->
159std::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>
160
161<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">print both <code>L</code> and <code>D</code> <br></td></tr>
162</table>
163<hr><a name="_details"></a><h2>Detailed Description</h2>
164Matrix stored in LD form, (typically known as UD).
165<p>
166Matrix is decomposed as follows: <p class="formulaDsp">
167<img class="formulaDsp" alt="\[M = L'DL\]" src="form_5.png">
168<p>
169 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. <hr><h2>Member Function Documentation</h2>
170<a class="anchor" name="0f0f6e083e6d947cf58097ffce3ccd1a"></a><!-- doxytag: member="ldmat::opupdt" ref="0f0f6e083e6d947cf58097ffce3ccd1a" args="(const vec &amp;v, double w)" -->
171<div class="memitem">
172<div class="memproto">
173      <table class="memname">
174        <tr>
175          <td class="memname">void ldmat::opupdt           </td>
176          <td>(</td>
177          <td class="paramtype">const vec &amp;&nbsp;</td>
178          <td class="paramname"> <em>v</em>, </td>
179        </tr>
180        <tr>
181          <td class="paramkey"></td>
182          <td></td>
183          <td class="paramtype">double&nbsp;</td>
184          <td class="paramname"> <em>w</em></td><td>&nbsp;</td>
185        </tr>
186        <tr>
187          <td></td>
188          <td>)</td>
189          <td></td><td></td><td width="100%"><code> [virtual]</code></td>
190        </tr>
191      </table>
192</div>
193<div class="memdoc">
194
195<p>
196Perfroms 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>
197  <table border="0" cellspacing="2" cellpadding="0">
198    <tr><td valign="top"></td><td valign="top"><em>v</em>&nbsp;</td><td>Vector forming the outer product to be added </td></tr>
199    <tr><td valign="top"></td><td valign="top"><em>w</em>&nbsp;</td><td>weight of updating; can be negative</td></tr>
200  </table>
201</dl>
202BLAS-2b operation.
203<p>Implements <a class="el" href="classsqmat.html#b223484796661f2dadb5607a86ce0581">sqmat</a>.</p>
204
205</div>
206</div><p>
207<a class="anchor" name="e967b9425007f0cb6cd59b845f9756d8"></a><!-- doxytag: member="ldmat::mult_sym" ref="e967b9425007f0cb6cd59b845f9756d8" args="(const mat &amp;C)" -->
208<div class="memitem">
209<div class="memproto">
210      <table class="memname">
211        <tr>
212          <td class="memname">void ldmat::mult_sym           </td>
213          <td>(</td>
214          <td class="paramtype">const mat &amp;&nbsp;</td>
215          <td class="paramname"> <em>C</em>          </td>
216          <td>&nbsp;)&nbsp;</td>
217          <td width="100%"><code> [virtual]</code></td>
218        </tr>
219      </table>
220</div>
221<div class="memdoc">
222
223<p>
224Inplace 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">.
225<p>
226<dl compact><dt><b>Parameters:</b></dt><dd>
227  <table border="0" cellspacing="2" cellpadding="0">
228    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
229  </table>
230</dl>
231
232<p>Implements <a class="el" href="classsqmat.html#60fbbfa9e483b8187c135f787ee53afa">sqmat</a>.</p>
233
234</div>
235</div><p>
236<a class="anchor" name="4fd155f38eb6dd5af4bdf9c98a7999a9"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="4fd155f38eb6dd5af4bdf9c98a7999a9" args="(const mat &amp;C)" -->
237<div class="memitem">
238<div class="memproto">
239      <table class="memname">
240        <tr>
241          <td class="memname">void ldmat::mult_sym_t           </td>
242          <td>(</td>
243          <td class="paramtype">const mat &amp;&nbsp;</td>
244          <td class="paramname"> <em>C</em>          </td>
245          <td>&nbsp;)&nbsp;</td>
246          <td width="100%"><code> [virtual]</code></td>
247        </tr>
248      </table>
249</div>
250<div class="memdoc">
251
252<p>
253Inplace 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">.
254<p>
255<dl compact><dt><b>Parameters:</b></dt><dd>
256  <table border="0" cellspacing="2" cellpadding="0">
257    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
258  </table>
259</dl>
260
261<p>Implements <a class="el" href="classsqmat.html#6909e906da17725b1b80f3cae7cf3325">sqmat</a>.</p>
262
263</div>
264</div><p>
265<a class="anchor" name="fc380626ced6f9244fb58c5f0231174d"></a><!-- doxytag: member="ldmat::sqrt_mult" ref="fc380626ced6f9244fb58c5f0231174d" args="(const vec &amp;v) const " -->
266<div class="memitem">
267<div class="memproto">
268      <table class="memname">
269        <tr>
270          <td class="memname">vec ldmat::sqrt_mult           </td>
271          <td>(</td>
272          <td class="paramtype">const vec &amp;&nbsp;</td>
273          <td class="paramname"> <em>v</em>          </td>
274          <td>&nbsp;)&nbsp;</td>
275          <td width="100%"> const<code> [virtual]</code></td>
276        </tr>
277      </table>
278</div>
279<div class="memdoc">
280
281<p>
282Multiplies square root of <img class="formulaInl" alt="$V$" src="form_27.png"> by vector <img class="formulaInl" alt="$x$" src="form_28.png">.
283<p>
284Used e.g. in generating normal samples.
285<p>Implements <a class="el" href="classsqmat.html#6b79438b5d7544a9c8e110a145355d8f">sqmat</a>.</p>
286
287</div>
288</div><p>
289<a class="anchor" name="2c160cb123c1102face7a50ec566a031"></a><!-- doxytag: member="ldmat::inv" ref="2c160cb123c1102face7a50ec566a031" args="(ldmat &amp;Inv) const " -->
290<div class="memitem">
291<div class="memproto">
292      <table class="memname">
293        <tr>
294          <td class="memname">void ldmat::inv           </td>
295          <td>(</td>
296          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
297          <td class="paramname"> <em>Inv</em>          </td>
298          <td>&nbsp;)&nbsp;</td>
299          <td width="100%"> const<code> [virtual]</code></td>
300        </tr>
301      </table>
302</div>
303<div class="memdoc">
304
305<p>
306Matrix inversion preserving the chosen form.
307<p>
308<dl compact><dt><b>Parameters:</b></dt><dd>
309  <table border="0" cellspacing="2" cellpadding="0">
310    <tr><td valign="top"></td><td valign="top"><em>Inv</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
311  </table>
312</dl>
313
314</div>
315</div><p>
316<a class="anchor" name="e7207748909325bb0f99b43f090a2b7e"></a><!-- doxytag: member="ldmat::mult_sym" ref="e7207748909325bb0f99b43f090a2b7e" args="(const mat &amp;C, ldmat &amp;U) const " -->
317<div class="memitem">
318<div class="memproto">
319      <table class="memname">
320        <tr>
321          <td class="memname">void ldmat::mult_sym           </td>
322          <td>(</td>
323          <td class="paramtype">const mat &amp;&nbsp;</td>
324          <td class="paramname"> <em>C</em>, </td>
325        </tr>
326        <tr>
327          <td class="paramkey"></td>
328          <td></td>
329          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
330          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
331        </tr>
332        <tr>
333          <td></td>
334          <td>)</td>
335          <td></td><td></td><td width="100%"> const</td>
336        </tr>
337      </table>
338</div>
339<div class="memdoc">
340
341<p>
342Symmetric 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.
343<p>
344<dl compact><dt><b>Parameters:</b></dt><dd>
345  <table border="0" cellspacing="2" cellpadding="0">
346    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
347    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
348  </table>
349</dl>
350
351</div>
352</div><p>
353<a class="anchor" name="f94dc3a233f3d40fc853d8d4ac3b8eab"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="f94dc3a233f3d40fc853d8d4ac3b8eab" args="(const mat &amp;C, ldmat &amp;U) const " -->
354<div class="memitem">
355<div class="memproto">
356      <table class="memname">
357        <tr>
358          <td class="memname">void ldmat::mult_sym_t           </td>
359          <td>(</td>
360          <td class="paramtype">const mat &amp;&nbsp;</td>
361          <td class="paramname"> <em>C</em>, </td>
362        </tr>
363        <tr>
364          <td class="paramkey"></td>
365          <td></td>
366          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
367          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
368        </tr>
369        <tr>
370          <td></td>
371          <td>)</td>
372          <td></td><td></td><td width="100%"> const</td>
373        </tr>
374      </table>
375</div>
376<div class="memdoc">
377
378<p>
379Symmetric 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.
380<p>
381<dl compact><dt><b>Parameters:</b></dt><dd>
382  <table border="0" cellspacing="2" cellpadding="0">
383    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
384    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
385  </table>
386</dl>
387
388</div>
389</div><p>
390<a class="anchor" name="f291faa073e7bc8dfafc7ae93daa2506"></a><!-- doxytag: member="ldmat::ldform" ref="f291faa073e7bc8dfafc7ae93daa2506" args="(const mat &amp;A, const vec &amp;D0)" -->
391<div class="memitem">
392<div class="memproto">
393      <table class="memname">
394        <tr>
395          <td class="memname">void ldmat::ldform           </td>
396          <td>(</td>
397          <td class="paramtype">const mat &amp;&nbsp;</td>
398          <td class="paramname"> <em>A</em>, </td>
399        </tr>
400        <tr>
401          <td class="paramkey"></td>
402          <td></td>
403          <td class="paramtype">const vec &amp;&nbsp;</td>
404          <td class="paramname"> <em>D0</em></td><td>&nbsp;</td>
405        </tr>
406        <tr>
407          <td></td>
408          <td>)</td>
409          <td></td><td></td><td width="100%"></td>
410        </tr>
411      </table>
412</div>
413<div class="memdoc">
414
415<p>
416Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_32.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_33.png">.
417<p>
418The 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>
419  <table border="0" cellspacing="2" cellpadding="0">
420    <tr><td valign="top"></td><td valign="top"><em>A</em>&nbsp;</td><td>general matrix </td></tr>
421    <tr><td valign="top"></td><td valign="top"><em>D0</em>&nbsp;</td><td>general vector </td></tr>
422  </table>
423</dl>
424
425</div>
426</div><p>
427<a class="anchor" name="ca445ee152a56043af946ea095b2d8f8"></a><!-- doxytag: member="ldmat::operator+=" ref="ca445ee152a56043af946ea095b2d8f8" args="(const ldmat &amp;ldA)" -->
428<div class="memitem">
429<div class="memproto">
430      <table class="memname">
431        <tr>
432          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator+=           </td>
433          <td>(</td>
434          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
435          <td class="paramname"> <em>ldA</em>          </td>
436          <td>&nbsp;)&nbsp;</td>
437          <td width="100%"><code> [inline]</code></td>
438        </tr>
439      </table>
440</div>
441<div class="memdoc">
442
443<p>
444add another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix
445<p>
446Operations: mapping of add operation to operators
447</div>
448</div><p>
449<a class="anchor" name="e3f4d2d85ab1ba384c852329aa31d0fb"></a><!-- doxytag: member="ldmat::operator-=" ref="e3f4d2d85ab1ba384c852329aa31d0fb" args="(const ldmat &amp;ldA)" -->
450<div class="memitem">
451<div class="memproto">
452      <table class="memname">
453        <tr>
454          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator-=           </td>
455          <td>(</td>
456          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
457          <td class="paramname"> <em>ldA</em>          </td>
458          <td>&nbsp;)&nbsp;</td>
459          <td width="100%"><code> [inline]</code></td>
460        </tr>
461      </table>
462</div>
463<div class="memdoc">
464
465<p>
466subtract another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix
467<p>
468mapping of negative add operation to operators
469</div>
470</div><p>
471<hr>The documentation for this class was generated from the following files:<ul>
472<li>work/mixpp/bdm/math/<a class="el" href="libDC_8h-source.html">libDC.h</a><li>work/mixpp/bdm/math/libDC.cpp</ul>
473<hr size="1"><address style="text-align: right;"><small>Generated on Fri Apr 18 11:15:21 2008 for mixpp by&nbsp;
474<a href="http://www.doxygen.org/index.html">
475<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.3 </small></address>
476</body>
477</html>
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