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26<h1>ldmat Class Reference</h1><!-- doxytag: class="ldmat" --><!-- doxytag: inherits="sqmat" -->Matrix stored in LD form, (typically known as UD). 
27<a href="#_details">More...</a>
28<p>
29<code>#include &lt;<a class="el" href="libDC_8h-source.html">libDC.h</a>&gt;</code>
30<p>
31<div class="dynheader">
32Inheritance diagram for ldmat:</div>
33<div class="dynsection">
34<p><center><img src="classldmat__inherit__graph.png" border="0" usemap="#ldmat__inherit__map" alt="Inheritance graph"></center>
35<map name="ldmat__inherit__map">
36<area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="5,7,61,31"></map>
37<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
38<div class="dynheader">
39Collaboration diagram for ldmat:</div>
40<div class="dynsection">
41<p><center><img src="classldmat__coll__graph.png" border="0" usemap="#ldmat__coll__map" alt="Collaboration graph"></center>
42<map name="ldmat__coll__map">
43<area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="5,7,61,31"></map>
44<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
45
46<p>
47<a href="classldmat-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
48<tr><td></td></tr>
49<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
50<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)" -->
51&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>
52
53<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by copy of L and D. <br></td></tr>
54<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)" -->
55&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f21785358072d36892d538eed1d1ea5">ldmat</a> (const mat &amp;V)</td></tr>
56
57<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by decomposition of full matrix V. <br></td></tr>
58<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abe16e0f86668ef61a9a4896c8565dee"></a><!-- doxytag: member="ldmat::ldmat" ref="abe16e0f86668ef61a9a4896c8565dee" args="(vec D0)" -->
59&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#abe16e0f86668ef61a9a4896c8565dee">ldmat</a> (vec D0)</td></tr>
60
61<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct diagonal matrix with diagonal D0. <br></td></tr>
62<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a12dda6f529580b0377cc45226b43303"></a><!-- doxytag: member="ldmat::ldmat" ref="a12dda6f529580b0377cc45226b43303" args="()" -->
63&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a12dda6f529580b0377cc45226b43303">ldmat</a> ()</td></tr>
64
65<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
66<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)" -->
67&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#163ee002a7858d104da1c59dd11f016d">ldmat</a> (const int dim0)</td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default initialization with proper size. <br></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1e2734c0164ce5233c4d709679555138"></a><!-- doxytag: member="ldmat::~ldmat" ref="1e2734c0164ce5233c4d709679555138" args="()" -->
71virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#1e2734c0164ce5233c4d709679555138">~ldmat</a> ()</td></tr>
72
73<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor for future use;. <br></td></tr>
74<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>
75
76<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5b0515da8dc2293d9e4360b74cc26c9e"></a><!-- doxytag: member="ldmat::to_mat" ref="5b0515da8dc2293d9e4360b74cc26c9e" args="()" -->
77mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5b0515da8dc2293d9e4360b74cc26c9e">to_mat</a> ()</td></tr>
78
79<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conversion to full matrix. <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#e967b9425007f0cb6cd59b845f9756d8">mult_sym</a> (const mat &amp;C)</td></tr>
81
82<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>
83<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>
84
85<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>
86<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)" -->
87void&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>
88
89<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add another matrix in LD form with weight w. <br></td></tr>
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2b42750ba4962d439aa52a77ae12949b"></a><!-- doxytag: member="ldmat::logdet" ref="2b42750ba4962d439aa52a77ae12949b" args="() const " -->
91double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2b42750ba4962d439aa52a77ae12949b">logdet</a> () const </td></tr>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of a determinant. <br></td></tr>
94<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 " -->
95double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d64f331b781903e913cb2ee836886f3f">qform</a> (const vec &amp;v) const </td></tr>
96
97<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>
98<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 " -->
99double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d876c5f83e02b3e809b35c9de5068f14">invqform</a> (const vec &amp;v) const </td></tr>
100
101<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>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d6e401de9607332305c27e67972a07a"></a><!-- doxytag: member="ldmat::clear" ref="4d6e401de9607332305c27e67972a07a" args="()" -->
103void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4d6e401de9607332305c27e67972a07a">clear</a> ()</td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Clearing matrix so that it corresponds to zeros. <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0fceb6b5b637cec89bb0a3d2e6be1306"></a><!-- doxytag: member="ldmat::cols" ref="0fceb6b5b637cec89bb0a3d2e6be1306" args="() const " -->
107int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0fceb6b5b637cec89bb0a3d2e6be1306">cols</a> () const </td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
110<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="96dfb21865db4f5bd36fa70f9b0b1163"></a><!-- doxytag: member="ldmat::rows" ref="96dfb21865db4f5bd36fa70f9b0b1163" args="() const " -->
111int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#96dfb21865db4f5bd36fa70f9b0b1163">rows</a> () const </td></tr>
112
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
114<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>
115
116<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>
117<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>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix inversion preserving the chosen form.  <a href="#2c160cb123c1102face7a50ec566a031"></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#e7207748909325bb0f99b43f090a2b7e">mult_sym</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 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>
123<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>
124
125<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>
126<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>
127
128<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>
129<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)" -->
130void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0884a613b94fde61bfc84288e73ce57f">setD</a> (const vec &amp;nD)</td></tr>
131
132<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
133<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)" -->
134void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#7619922b4de18830ce5351c6b5667e60">setD</a> (const vec &amp;nD, int i)</td></tr>
135
136<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
137<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)" -->
138void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#32ff66296627ff5341d7c0b973249614">setL</a> (const vec &amp;nL)</td></tr>
139
140<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <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#ca445ee152a56043af946ea095b2d8f8">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">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>
144<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>
145
146<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>
147<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="875b7e6dcf73ae7001329099019fdb1d"></a><!-- doxytag: member="ldmat::operator*=" ref="875b7e6dcf73ae7001329099019fdb1d" args="(double x)" -->
148<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>
149
150<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">multiply by a scalar <br></td></tr>
151<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
152<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4cce04824539c4a8d062d9a36d6e014e"></a><!-- doxytag: member="ldmat::D" ref="4cce04824539c4a8d062d9a36d6e014e" args="" -->
153vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a></td></tr>
154
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Positive vector <img class="formulaInl" alt="$D$" src="form_22.png">. <br></td></tr>
156<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f74a64b99fe58a75ebd37bb679e121ea"></a><!-- doxytag: member="ldmat::L" ref="f74a64b99fe58a75ebd37bb679e121ea" args="" -->
157mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a></td></tr>
158
159<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower-triangular matrix <img class="formulaInl" alt="$L$" src="form_21.png">. <br></td></tr>
160<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
161<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)" -->
162std::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>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">print both <code>L</code> and <code>D</code> <br></td></tr>
165</table>
166<hr><a name="_details"></a><h2>Detailed Description</h2>
167Matrix stored in LD form, (typically known as UD).
168<p>
169Matrix is decomposed as follows: <p class="formulaDsp">
170<img class="formulaDsp" alt="\[M = L'DL\]" src="form_5.png">
171<p>
172 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>
173<a class="anchor" name="0f0f6e083e6d947cf58097ffce3ccd1a"></a><!-- doxytag: member="ldmat::opupdt" ref="0f0f6e083e6d947cf58097ffce3ccd1a" args="(const vec &amp;v, double w)" -->
174<div class="memitem">
175<div class="memproto">
176      <table class="memname">
177        <tr>
178          <td class="memname">void ldmat::opupdt           </td>
179          <td>(</td>
180          <td class="paramtype">const vec &amp;&nbsp;</td>
181          <td class="paramname"> <em>v</em>, </td>
182        </tr>
183        <tr>
184          <td class="paramkey"></td>
185          <td></td>
186          <td class="paramtype">double&nbsp;</td>
187          <td class="paramname"> <em>w</em></td><td>&nbsp;</td>
188        </tr>
189        <tr>
190          <td></td>
191          <td>)</td>
192          <td></td><td></td><td width="100%"><code> [virtual]</code></td>
193        </tr>
194      </table>
195</div>
196<div class="memdoc">
197
198<p>
199Perfroms 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>
200  <table border="0" cellspacing="2" cellpadding="0">
201    <tr><td valign="top"></td><td valign="top"><em>v</em>&nbsp;</td><td>Vector forming the outer product to be added </td></tr>
202    <tr><td valign="top"></td><td valign="top"><em>w</em>&nbsp;</td><td>weight of updating; can be negative</td></tr>
203  </table>
204</dl>
205BLAS-2b operation.
206<p>Implements <a class="el" href="classsqmat.html#b223484796661f2dadb5607a86ce0581">sqmat</a>.</p>
207
208<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00099">sqmat::dim</a>, and <a class="el" href="libDC_8h-source.html#l00262">L</a>.</p>
209
210<p>Referenced by <a class="el" href="libDC_8cpp-source.html#l00104">add()</a>, and <a class="el" href="libDC_8cpp-source.html#l00118">inv()</a>.</p>
211
212</div>
213</div><p>
214<a class="anchor" name="e967b9425007f0cb6cd59b845f9756d8"></a><!-- doxytag: member="ldmat::mult_sym" ref="e967b9425007f0cb6cd59b845f9756d8" args="(const mat &amp;C)" -->
215<div class="memitem">
216<div class="memproto">
217      <table class="memname">
218        <tr>
219          <td class="memname">void ldmat::mult_sym           </td>
220          <td>(</td>
221          <td class="paramtype">const mat &amp;&nbsp;</td>
222          <td class="paramname"> <em>C</em>          </td>
223          <td>&nbsp;)&nbsp;</td>
224          <td width="100%"><code> [virtual]</code></td>
225        </tr>
226      </table>
227</div>
228<div class="memdoc">
229
230<p>
231Inplace 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">.
232<p>
233<dl compact><dt><b>Parameters:</b></dt><dd>
234  <table border="0" cellspacing="2" cellpadding="0">
235    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
236  </table>
237</dl>
238
239<p>Implements <a class="el" href="classsqmat.html#60fbbfa9e483b8187c135f787ee53afa">sqmat</a>.</p>
240
241<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00262">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00209">ldform()</a>.</p>
242
243</div>
244</div><p>
245<a class="anchor" name="4fd155f38eb6dd5af4bdf9c98a7999a9"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="4fd155f38eb6dd5af4bdf9c98a7999a9" args="(const mat &amp;C)" -->
246<div class="memitem">
247<div class="memproto">
248      <table class="memname">
249        <tr>
250          <td class="memname">void ldmat::mult_sym_t           </td>
251          <td>(</td>
252          <td class="paramtype">const mat &amp;&nbsp;</td>
253          <td class="paramname"> <em>C</em>          </td>
254          <td>&nbsp;)&nbsp;</td>
255          <td width="100%"><code> [virtual]</code></td>
256        </tr>
257      </table>
258</div>
259<div class="memdoc">
260
261<p>
262Inplace 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">.
263<p>
264<dl compact><dt><b>Parameters:</b></dt><dd>
265  <table border="0" cellspacing="2" cellpadding="0">
266    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
267  </table>
268</dl>
269
270<p>Implements <a class="el" href="classsqmat.html#6909e906da17725b1b80f3cae7cf3325">sqmat</a>.</p>
271
272<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00262">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00209">ldform()</a>.</p>
273
274</div>
275</div><p>
276<a class="anchor" name="fc380626ced6f9244fb58c5f0231174d"></a><!-- doxytag: member="ldmat::sqrt_mult" ref="fc380626ced6f9244fb58c5f0231174d" args="(const vec &amp;v) const " -->
277<div class="memitem">
278<div class="memproto">
279      <table class="memname">
280        <tr>
281          <td class="memname">vec ldmat::sqrt_mult           </td>
282          <td>(</td>
283          <td class="paramtype">const vec &amp;&nbsp;</td>
284          <td class="paramname"> <em>v</em>          </td>
285          <td>&nbsp;)&nbsp;</td>
286          <td width="100%"> const<code> [virtual]</code></td>
287        </tr>
288      </table>
289</div>
290<div class="memdoc">
291
292<p>
293Multiplies square root of <img class="formulaInl" alt="$V$" src="form_27.png"> by vector <img class="formulaInl" alt="$x$" src="form_28.png">.
294<p>
295Used e.g. in generating normal samples.
296<p>Implements <a class="el" href="classsqmat.html#6b79438b5d7544a9c8e110a145355d8f">sqmat</a>.</p>
297
298<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00099">sqmat::dim</a>, and <a class="el" href="libDC_8h-source.html#l00262">L</a>.</p>
299
300</div>
301</div><p>
302<a class="anchor" name="2c160cb123c1102face7a50ec566a031"></a><!-- doxytag: member="ldmat::inv" ref="2c160cb123c1102face7a50ec566a031" args="(ldmat &amp;Inv) const " -->
303<div class="memitem">
304<div class="memproto">
305      <table class="memname">
306        <tr>
307          <td class="memname">void ldmat::inv           </td>
308          <td>(</td>
309          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
310          <td class="paramname"> <em>Inv</em>          </td>
311          <td>&nbsp;)&nbsp;</td>
312          <td width="100%"> const<code> [virtual]</code></td>
313        </tr>
314      </table>
315</div>
316<div class="memdoc">
317
318<p>
319Matrix inversion preserving the chosen form.
320<p>
321<dl compact><dt><b>Parameters:</b></dt><dd>
322  <table border="0" cellspacing="2" cellpadding="0">
323    <tr><td valign="top"></td><td valign="top"><em>Inv</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
324  </table>
325</dl>
326
327<p>References <a class="el" href="libDC_8cpp-source.html#l00116">clear()</a>, <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00099">sqmat::dim</a>, <a class="el" href="libDC_8h-source.html#l00262">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00058">opupdt()</a>.</p>
328
329</div>
330</div><p>
331<a class="anchor" name="e7207748909325bb0f99b43f090a2b7e"></a><!-- doxytag: member="ldmat::mult_sym" ref="e7207748909325bb0f99b43f090a2b7e" args="(const mat &amp;C, ldmat &amp;U) const " -->
332<div class="memitem">
333<div class="memproto">
334      <table class="memname">
335        <tr>
336          <td class="memname">void ldmat::mult_sym           </td>
337          <td>(</td>
338          <td class="paramtype">const mat &amp;&nbsp;</td>
339          <td class="paramname"> <em>C</em>, </td>
340        </tr>
341        <tr>
342          <td class="paramkey"></td>
343          <td></td>
344          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
345          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
346        </tr>
347        <tr>
348          <td></td>
349          <td>)</td>
350          <td></td><td></td><td width="100%"> const</td>
351        </tr>
352      </table>
353</div>
354<div class="memdoc">
355
356<p>
357Symmetric 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.
358<p>
359<dl compact><dt><b>Parameters:</b></dt><dd>
360  <table border="0" cellspacing="2" cellpadding="0">
361    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
362    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
363  </table>
364</dl>
365
366<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00262">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00209">ldform()</a>.</p>
367
368</div>
369</div><p>
370<a class="anchor" name="f94dc3a233f3d40fc853d8d4ac3b8eab"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="f94dc3a233f3d40fc853d8d4ac3b8eab" args="(const mat &amp;C, ldmat &amp;U) const " -->
371<div class="memitem">
372<div class="memproto">
373      <table class="memname">
374        <tr>
375          <td class="memname">void ldmat::mult_sym_t           </td>
376          <td>(</td>
377          <td class="paramtype">const mat &amp;&nbsp;</td>
378          <td class="paramname"> <em>C</em>, </td>
379        </tr>
380        <tr>
381          <td class="paramkey"></td>
382          <td></td>
383          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
384          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
385        </tr>
386        <tr>
387          <td></td>
388          <td>)</td>
389          <td></td><td></td><td width="100%"> const</td>
390        </tr>
391      </table>
392</div>
393<div class="memdoc">
394
395<p>
396Symmetric 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.
397<p>
398<dl compact><dt><b>Parameters:</b></dt><dd>
399  <table border="0" cellspacing="2" cellpadding="0">
400    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
401    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
402  </table>
403</dl>
404
405<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00262">L</a>, and <a class="el" href="libDC_8cpp-source.html#l00209">ldform()</a>.</p>
406
407</div>
408</div><p>
409<a class="anchor" name="f291faa073e7bc8dfafc7ae93daa2506"></a><!-- doxytag: member="ldmat::ldform" ref="f291faa073e7bc8dfafc7ae93daa2506" args="(const mat &amp;A, const vec &amp;D0)" -->
410<div class="memitem">
411<div class="memproto">
412      <table class="memname">
413        <tr>
414          <td class="memname">void ldmat::ldform           </td>
415          <td>(</td>
416          <td class="paramtype">const mat &amp;&nbsp;</td>
417          <td class="paramname"> <em>A</em>, </td>
418        </tr>
419        <tr>
420          <td class="paramkey"></td>
421          <td></td>
422          <td class="paramtype">const vec &amp;&nbsp;</td>
423          <td class="paramname"> <em>D0</em></td><td>&nbsp;</td>
424        </tr>
425        <tr>
426          <td></td>
427          <td>)</td>
428          <td></td><td></td><td width="100%"></td>
429        </tr>
430      </table>
431</div>
432<div class="memdoc">
433
434<p>
435Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_32.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_33.png">.
436<p>
437The 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>
438  <table border="0" cellspacing="2" cellpadding="0">
439    <tr><td valign="top"></td><td valign="top"><em>A</em>&nbsp;</td><td>general matrix </td></tr>
440    <tr><td valign="top"></td><td valign="top"><em>D0</em>&nbsp;</td><td>general vector </td></tr>
441  </table>
442</dl>
443
444<p>References <a class="el" href="libDC_8h-source.html#l00260">D</a>, <a class="el" href="libDC_8h-source.html#l00099">sqmat::dim</a>, and <a class="el" href="libDC_8h-source.html#l00262">L</a>.</p>
445
446<p>Referenced by <a class="el" href="libDC_8cpp-source.html#l00046">ldmat()</a>, <a class="el" href="libDC_8cpp-source.html#l00130">mult_sym()</a>, and <a class="el" href="libDC_8cpp-source.html#l00135">mult_sym_t()</a>.</p>
447
448</div>
449</div><p>
450<a class="anchor" name="ca445ee152a56043af946ea095b2d8f8"></a><!-- doxytag: member="ldmat::operator+=" ref="ca445ee152a56043af946ea095b2d8f8" args="(const ldmat &amp;ldA)" -->
451<div class="memitem">
452<div class="memproto">
453      <table class="memname">
454        <tr>
455          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator+=           </td>
456          <td>(</td>
457          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
458          <td class="paramname"> <em>ldA</em>          </td>
459          <td>&nbsp;)&nbsp;</td>
460          <td width="100%"><code> [inline]</code></td>
461        </tr>
462      </table>
463</div>
464<div class="memdoc">
465
466<p>
467add another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix
468<p>
469Operations: mapping of add operation to operators
470</div>
471</div><p>
472<a class="anchor" name="e3f4d2d85ab1ba384c852329aa31d0fb"></a><!-- doxytag: member="ldmat::operator-=" ref="e3f4d2d85ab1ba384c852329aa31d0fb" args="(const ldmat &amp;ldA)" -->
473<div class="memitem">
474<div class="memproto">
475      <table class="memname">
476        <tr>
477          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator-=           </td>
478          <td>(</td>
479          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
480          <td class="paramname"> <em>ldA</em>          </td>
481          <td>&nbsp;)&nbsp;</td>
482          <td width="100%"><code> [inline]</code></td>
483        </tr>
484      </table>
485</div>
486<div class="memdoc">
487
488<p>
489subtract another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD).">ldmat</a> matrix
490<p>
491mapping of negative add operation to operators
492</div>
493</div><p>
494<hr>The documentation for this class was generated from the following files:<ul>
495<li>work/mixpp/bdm/math/<a class="el" href="libDC_8h-source.html">libDC.h</a><li>work/mixpp/bdm/math/libDC.cpp</ul>
496</div>
497<hr size="1"><address style="text-align: right;"><small>Generated on Tue Apr 29 20:46:52 2008 for mixpp by&nbsp;
498<a href="http://www.doxygen.org/index.html">
499<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.5 </small></address>
500</body>
501</html>
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