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68<h1>ldmat Class Reference</h1><!-- doxytag: class="ldmat" --><!-- doxytag: inherits="sqmat" -->Matrix stored in LD form, (commonly known as UD). 
69<a href="#_details">More...</a>
70<p>
71<code>#include &lt;<a class="el" href="square__mat_8h_source.html">square_mat.h</a>&gt;</code>
72<p>
73
74<p>
75<a href="classldmat-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
76<tr><td></td></tr>
77<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
78<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)" -->
79&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>
80
81<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by copy of L and D. <br></td></tr>
82<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)" -->
83&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f21785358072d36892d538eed1d1ea5">ldmat</a> (const mat &amp;V)</td></tr>
84
85<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by decomposition of full matrix V. <br></td></tr>
86<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)" -->
87&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>
88
89<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct by restructuring of V0 accordint to permutation vector perm. <br></td></tr>
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abe16e0f86668ef61a9a4896c8565dee"></a><!-- doxytag: member="ldmat::ldmat" ref="abe16e0f86668ef61a9a4896c8565dee" args="(vec D0)" -->
91&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#abe16e0f86668ef61a9a4896c8565dee">ldmat</a> (vec D0)</td></tr>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Construct diagonal matrix with diagonal D0. <br></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a12dda6f529580b0377cc45226b43303"></a><!-- doxytag: member="ldmat::ldmat" ref="a12dda6f529580b0377cc45226b43303" args="()" -->
95&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#a12dda6f529580b0377cc45226b43303">ldmat</a> ()</td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
98<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)" -->
99&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#163ee002a7858d104da1c59dd11f016d">ldmat</a> (const int dim0)</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default initialization with proper size. <br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1e2734c0164ce5233c4d709679555138"></a><!-- doxytag: member="ldmat::~ldmat" ref="1e2734c0164ce5233c4d709679555138" args="()" -->
103virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#1e2734c0164ce5233c4d709679555138">~ldmat</a> ()</td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor for future use;. <br></td></tr>
106<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>
107
108<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2c1ebc071de4bafbba55b80afd8a7e8e"></a><!-- doxytag: member="ldmat::to_mat" ref="2c1ebc071de4bafbba55b80afd8a7e8e" args="() const " -->
109mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2c1ebc071de4bafbba55b80afd8a7e8e">to_mat</a> () const </td></tr>
110
111<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conversion to full matrix. <br></td></tr>
112<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>
113
114<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>
115<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>
116
117<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>
118<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)" -->
119void&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>
120
121<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add another matrix in LD form with weight w. <br></td></tr>
122<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2b42750ba4962d439aa52a77ae12949b"></a><!-- doxytag: member="ldmat::logdet" ref="2b42750ba4962d439aa52a77ae12949b" args="() const " -->
123double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#2b42750ba4962d439aa52a77ae12949b">logdet</a> () const </td></tr>
124
125<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of a determinant. <br></td></tr>
126<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 " -->
127double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d64f331b781903e913cb2ee836886f3f">qform</a> (const vec &amp;v) const </td></tr>
128
129<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>
130<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 " -->
131double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#d876c5f83e02b3e809b35c9de5068f14">invqform</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="$x= v'*inv(V)*v$" src="form_57.png">;. <br></td></tr>
134<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d6e401de9607332305c27e67972a07a"></a><!-- doxytag: member="ldmat::clear" ref="4d6e401de9607332305c27e67972a07a" args="()" -->
135void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4d6e401de9607332305c27e67972a07a">clear</a> ()</td></tr>
136
137<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Clearing matrix so that it corresponds to zeros. <br></td></tr>
138<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>
139
140<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>
141<tr><td class="memItemLeft" nowrap align="right" valign="top">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>
142
143<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix inversion preserving the chosen form.  <a href="#2c160cb123c1102face7a50ec566a031"></a><br></td></tr>
144<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>
145
146<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>
147<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>
148
149<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>
150<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>
151
152<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>
153<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)" -->
154void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#0884a613b94fde61bfc84288e73ce57f">setD</a> (const vec &amp;nD)</td></tr>
155
156<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
157<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)" -->
158void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#7619922b4de18830ce5351c6b5667e60">setD</a> (const vec &amp;nD, int i)</td></tr>
159
160<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
161<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)" -->
162void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#32ff66296627ff5341d7c0b973249614">setL</a> (const vec &amp;nL)</td></tr>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access functions. <br></td></tr>
165<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="282c879f50aa9ef934e7f46d86881582"></a><!-- doxytag: member="ldmat::_D" ref="282c879f50aa9ef934e7f46d86881582" args="() const " -->
166const vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#282c879f50aa9ef934e7f46d86881582">_D</a> () const </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="5f44f100248c6627314afaa653b9e5bd"></a><!-- doxytag: member="ldmat::_L" ref="5f44f100248c6627314afaa653b9e5bd" args="() const " -->
170const mat &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#5f44f100248c6627314afaa653b9e5bd">_L</a> () const </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="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>
174
175<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="#ca445ee152a56043af946ea095b2d8f8"></a><br></td></tr>
176<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>
177
178<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="#e3f4d2d85ab1ba384c852329aa31d0fb"></a><br></td></tr>
179<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="875b7e6dcf73ae7001329099019fdb1d"></a><!-- doxytag: member="ldmat::operator*=" ref="875b7e6dcf73ae7001329099019fdb1d" args="(double x)" -->
180<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>
181
182<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">multiply by a scalar <br></td></tr>
183<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ecc2e2540f95a04f4449842588170f5b"></a><!-- doxytag: member="ldmat::cols" ref="ecc2e2540f95a04f4449842588170f5b" args="() const " -->
184int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classsqmat.html#ecc2e2540f95a04f4449842588170f5b">cols</a> () const </td></tr>
185
186<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Reimplementing common functions of mat: <a class="el" href="classsqmat.html#ecc2e2540f95a04f4449842588170f5b" title="Reimplementing common functions of mat: cols().">cols()</a>. <br></td></tr>
187<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="071e80ced9cc3b8cbb360fa7462eb646"></a><!-- doxytag: member="ldmat::rows" ref="071e80ced9cc3b8cbb360fa7462eb646" args="() const " -->
188int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classsqmat.html#071e80ced9cc3b8cbb360fa7462eb646">rows</a> () const </td></tr>
189
190<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Reimplementing common functions of mat: <a class="el" href="classsqmat.html#071e80ced9cc3b8cbb360fa7462eb646" title="Reimplementing common functions of mat: rows().">rows()</a>. <br></td></tr>
191<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
192<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4cce04824539c4a8d062d9a36d6e014e"></a><!-- doxytag: member="ldmat::D" ref="4cce04824539c4a8d062d9a36d6e014e" args="" -->
193vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#4cce04824539c4a8d062d9a36d6e014e">D</a></td></tr>
194
195<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Positive vector <img class="formulaInl" alt="$D$" src="form_50.png">. <br></td></tr>
196<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f74a64b99fe58a75ebd37bb679e121ea"></a><!-- doxytag: member="ldmat::L" ref="f74a64b99fe58a75ebd37bb679e121ea" args="" -->
197mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classldmat.html#f74a64b99fe58a75ebd37bb679e121ea">L</a></td></tr>
198
199<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower-triangular matrix <img class="formulaInl" alt="$L$" src="form_49.png">. <br></td></tr>
200<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0abed904bdc0882373ba9adba919689d"></a><!-- doxytag: member="ldmat::dim" ref="0abed904bdc0882373ba9adba919689d" args="" -->
201int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classsqmat.html#0abed904bdc0882373ba9adba919689d">dim</a></td></tr>
202
203<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the square matrix <br></td></tr>
204<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
205<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)" -->
206std::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>
207
208<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">print both <code>L</code> and <code>D</code> <br></td></tr>
209</table>
210<hr><a name="_details"></a><h2>Detailed Description</h2>
211Matrix stored in LD form, (commonly known as UD).
212<p>
213Matrix is decomposed as follows: <p class="formulaDsp">
214<img class="formulaDsp" alt="\[M = L'DL\]" src="form_48.png">
215<p>
216 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>
217<a class="anchor" name="2c160cb123c1102face7a50ec566a031"></a><!-- doxytag: member="ldmat::inv" ref="2c160cb123c1102face7a50ec566a031" args="(ldmat &amp;Inv) const " -->
218<div class="memitem">
219<div class="memproto">
220      <table class="memname">
221        <tr>
222          <td class="memname">void ldmat::inv           </td>
223          <td>(</td>
224          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
225          <td class="paramname"> <em>Inv</em>          </td>
226          <td>&nbsp;)&nbsp;</td>
227          <td> const</td>
228        </tr>
229      </table>
230</div>
231<div class="memdoc">
232
233<p>
234Matrix inversion preserving the chosen form.
235<p>
236<dl compact><dt><b>Parameters:</b></dt><dd>
237  <table border="0" cellspacing="2" cellpadding="0">
238    <tr><td valign="top"></td><td valign="top"><em>Inv</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
239  </table>
240</dl>
241
242<p>References <a class="el" href="square__mat_8cpp_source.html#l00116">clear()</a>, <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00270">L</a>, and <a class="el" href="square__mat_8cpp_source.html#l00200">ldform()</a>.</p>
243
244<p>Referenced by <a class="el" href="exp__family_8cpp_source.html#l00124">bdm::egiw::variance()</a>.</p>
245
246</div>
247</div><p>
248<a class="anchor" name="f291faa073e7bc8dfafc7ae93daa2506"></a><!-- doxytag: member="ldmat::ldform" ref="f291faa073e7bc8dfafc7ae93daa2506" args="(const mat &amp;A, const vec &amp;D0)" -->
249<div class="memitem">
250<div class="memproto">
251      <table class="memname">
252        <tr>
253          <td class="memname">void ldmat::ldform           </td>
254          <td>(</td>
255          <td class="paramtype">const mat &amp;&nbsp;</td>
256          <td class="paramname"> <em>A</em>, </td>
257        </tr>
258        <tr>
259          <td class="paramkey"></td>
260          <td></td>
261          <td class="paramtype">const vec &amp;&nbsp;</td>
262          <td class="paramname"> <em>D0</em></td><td>&nbsp;</td>
263        </tr>
264        <tr>
265          <td></td>
266          <td>)</td>
267          <td></td><td></td><td></td>
268        </tr>
269      </table>
270</div>
271<div class="memdoc">
272
273<p>
274Transforms general <img class="formulaInl" alt="$A'D0 A$" src="form_59.png"> into pure <img class="formulaInl" alt="$L'DL$" src="form_60.png">.
275<p>
276The 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>
277  <table border="0" cellspacing="2" cellpadding="0">
278    <tr><td valign="top"></td><td valign="top"><em>A</em>&nbsp;</td><td>general matrix </td></tr>
279    <tr><td valign="top"></td><td valign="top"><em>D0</em>&nbsp;</td><td>general vector </td></tr>
280  </table>
281</dl>
282
283<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00102">sqmat::dim</a>, and <a class="el" href="square__mat_8h_source.html#l00270">L</a>.</p>
284
285<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>
286
287</div>
288</div><p>
289<a class="anchor" name="e7207748909325bb0f99b43f090a2b7e"></a><!-- doxytag: member="ldmat::mult_sym" ref="e7207748909325bb0f99b43f090a2b7e" args="(const mat &amp;C, ldmat &amp;U) const " -->
290<div class="memitem">
291<div class="memproto">
292      <table class="memname">
293        <tr>
294          <td class="memname">void ldmat::mult_sym           </td>
295          <td>(</td>
296          <td class="paramtype">const mat &amp;&nbsp;</td>
297          <td class="paramname"> <em>C</em>, </td>
298        </tr>
299        <tr>
300          <td class="paramkey"></td>
301          <td></td>
302          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
303          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
304        </tr>
305        <tr>
306          <td></td>
307          <td>)</td>
308          <td></td><td></td><td> const</td>
309        </tr>
310      </table>
311</div>
312<div class="memdoc">
313
314<p>
315Symmetric 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.
316<p>
317<dl compact><dt><b>Parameters:</b></dt><dd>
318  <table border="0" cellspacing="2" cellpadding="0">
319    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
320    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
321  </table>
322</dl>
323
324<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00270">L</a>, and <a class="el" href="square__mat_8cpp_source.html#l00200">ldform()</a>.</p>
325
326</div>
327</div><p>
328<a class="anchor" name="e967b9425007f0cb6cd59b845f9756d8"></a><!-- doxytag: member="ldmat::mult_sym" ref="e967b9425007f0cb6cd59b845f9756d8" args="(const mat &amp;C)" -->
329<div class="memitem">
330<div class="memproto">
331      <table class="memname">
332        <tr>
333          <td class="memname">void ldmat::mult_sym           </td>
334          <td>(</td>
335          <td class="paramtype">const mat &amp;&nbsp;</td>
336          <td class="paramname"> <em>C</em>          </td>
337          <td>&nbsp;)&nbsp;</td>
338          <td><code> [virtual]</code></td>
339        </tr>
340      </table>
341</div>
342<div class="memdoc">
343
344<p>
345Inplace 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">.
346<p>
347<dl compact><dt><b>Parameters:</b></dt><dd>
348  <table border="0" cellspacing="2" cellpadding="0">
349    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
350  </table>
351</dl>
352
353<p>Implements <a class="el" href="classsqmat.html#60fbbfa9e483b8187c135f787ee53afa">sqmat</a>.</p>
354
355<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00270">L</a>, and <a class="el" href="square__mat_8cpp_source.html#l00200">ldform()</a>.</p>
356
357</div>
358</div><p>
359<a class="anchor" name="f94dc3a233f3d40fc853d8d4ac3b8eab"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="f94dc3a233f3d40fc853d8d4ac3b8eab" args="(const mat &amp;C, ldmat &amp;U) const " -->
360<div class="memitem">
361<div class="memproto">
362      <table class="memname">
363        <tr>
364          <td class="memname">void ldmat::mult_sym_t           </td>
365          <td>(</td>
366          <td class="paramtype">const mat &amp;&nbsp;</td>
367          <td class="paramname"> <em>C</em>, </td>
368        </tr>
369        <tr>
370          <td class="paramkey"></td>
371          <td></td>
372          <td class="paramtype"><a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
373          <td class="paramname"> <em>U</em></td><td>&nbsp;</td>
374        </tr>
375        <tr>
376          <td></td>
377          <td>)</td>
378          <td></td><td></td><td> const</td>
379        </tr>
380      </table>
381</div>
382<div class="memdoc">
383
384<p>
385Symmetric 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.
386<p>
387<dl compact><dt><b>Parameters:</b></dt><dd>
388  <table border="0" cellspacing="2" cellpadding="0">
389    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>matrix to multiply with </td></tr>
390    <tr><td valign="top"></td><td valign="top"><em>U</em>&nbsp;</td><td>a space where the inverse is stored. </td></tr>
391  </table>
392</dl>
393
394<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00270">L</a>, and <a class="el" href="square__mat_8cpp_source.html#l00200">ldform()</a>.</p>
395
396</div>
397</div><p>
398<a class="anchor" name="4fd155f38eb6dd5af4bdf9c98a7999a9"></a><!-- doxytag: member="ldmat::mult_sym_t" ref="4fd155f38eb6dd5af4bdf9c98a7999a9" args="(const mat &amp;C)" -->
399<div class="memitem">
400<div class="memproto">
401      <table class="memname">
402        <tr>
403          <td class="memname">void ldmat::mult_sym_t           </td>
404          <td>(</td>
405          <td class="paramtype">const mat &amp;&nbsp;</td>
406          <td class="paramname"> <em>C</em>          </td>
407          <td>&nbsp;)&nbsp;</td>
408          <td><code> [virtual]</code></td>
409        </tr>
410      </table>
411</div>
412<div class="memdoc">
413
414<p>
415Inplace 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">.
416<p>
417<dl compact><dt><b>Parameters:</b></dt><dd>
418  <table border="0" cellspacing="2" cellpadding="0">
419    <tr><td valign="top"></td><td valign="top"><em>C</em>&nbsp;</td><td>multiplying matrix, </td></tr>
420  </table>
421</dl>
422
423<p>Implements <a class="el" href="classsqmat.html#6909e906da17725b1b80f3cae7cf3325">sqmat</a>.</p>
424
425<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00270">L</a>, and <a class="el" href="square__mat_8cpp_source.html#l00200">ldform()</a>.</p>
426
427</div>
428</div><p>
429<a class="anchor" name="ca445ee152a56043af946ea095b2d8f8"></a><!-- doxytag: member="ldmat::operator+=" ref="ca445ee152a56043af946ea095b2d8f8" args="(const ldmat &amp;ldA)" -->
430<div class="memitem">
431<div class="memproto">
432      <table class="memname">
433        <tr>
434          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator+=           </td>
435          <td>(</td>
436          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
437          <td class="paramname"> <em>ldA</em>          </td>
438          <td>&nbsp;)&nbsp;</td>
439          <td><code> [inline]</code></td>
440        </tr>
441      </table>
442</div>
443<div class="memdoc">
444
445<p>
446add another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD).">ldmat</a> matrix
447<p>
448Operations: mapping of add operation to operators
449<p>References <a class="el" href="square__mat_8cpp_source.html#l00104">add()</a>.</p>
450
451</div>
452</div><p>
453<a class="anchor" name="e3f4d2d85ab1ba384c852329aa31d0fb"></a><!-- doxytag: member="ldmat::operator&#45;=" ref="e3f4d2d85ab1ba384c852329aa31d0fb" args="(const ldmat &amp;ldA)" -->
454<div class="memitem">
455<div class="memproto">
456      <table class="memname">
457        <tr>
458          <td class="memname"><a class="el" href="classldmat.html">ldmat</a> &amp; ldmat::operator-=           </td>
459          <td>(</td>
460          <td class="paramtype">const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td>
461          <td class="paramname"> <em>ldA</em>          </td>
462          <td>&nbsp;)&nbsp;</td>
463          <td><code> [inline]</code></td>
464        </tr>
465      </table>
466</div>
467<div class="memdoc">
468
469<p>
470subtract another <a class="el" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD).">ldmat</a> matrix
471<p>
472mapping of negative add operation to operators
473<p>References <a class="el" href="square__mat_8cpp_source.html#l00104">add()</a>.</p>
474
475</div>
476</div><p>
477<a class="anchor" name="0f0f6e083e6d947cf58097ffce3ccd1a"></a><!-- doxytag: member="ldmat::opupdt" ref="0f0f6e083e6d947cf58097ffce3ccd1a" args="(const vec &amp;v, double w)" -->
478<div class="memitem">
479<div class="memproto">
480      <table class="memname">
481        <tr>
482          <td class="memname">void ldmat::opupdt           </td>
483          <td>(</td>
484          <td class="paramtype">const vec &amp;&nbsp;</td>
485          <td class="paramname"> <em>v</em>, </td>
486        </tr>
487        <tr>
488          <td class="paramkey"></td>
489          <td></td>
490          <td class="paramtype">double&nbsp;</td>
491          <td class="paramname"> <em>w</em></td><td>&nbsp;</td>
492        </tr>
493        <tr>
494          <td></td>
495          <td>)</td>
496          <td></td><td></td><td><code> [virtual]</code></td>
497        </tr>
498      </table>
499</div>
500<div class="memdoc">
501
502<p>
503Perfroms 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>
504  <table border="0" cellspacing="2" cellpadding="0">
505    <tr><td valign="top"></td><td valign="top"><em>v</em>&nbsp;</td><td>Vector forming the outer product to be added </td></tr>
506    <tr><td valign="top"></td><td valign="top"><em>w</em>&nbsp;</td><td>weight of updating; can be negative</td></tr>
507  </table>
508</dl>
509BLAS-2b operation.
510<p>Implements <a class="el" href="classsqmat.html#b223484796661f2dadb5607a86ce0581">sqmat</a>.</p>
511
512<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00102">sqmat::dim</a>, and <a class="el" href="square__mat_8h_source.html#l00270">L</a>.</p>
513
514<p>Referenced by <a class="el" href="square__mat_8cpp_source.html#l00104">add()</a>, <a class="el" href="arx_8cpp_source.html#l00005">bdm::ARX::bayes()</a>, and <a class="el" href="arx_8cpp_source.html#l00025">bdm::ARX::logpred()</a>.</p>
515
516</div>
517</div><p>
518<a class="anchor" name="fc380626ced6f9244fb58c5f0231174d"></a><!-- doxytag: member="ldmat::sqrt_mult" ref="fc380626ced6f9244fb58c5f0231174d" args="(const vec &amp;v) const " -->
519<div class="memitem">
520<div class="memproto">
521      <table class="memname">
522        <tr>
523          <td class="memname">vec ldmat::sqrt_mult           </td>
524          <td>(</td>
525          <td class="paramtype">const vec &amp;&nbsp;</td>
526          <td class="paramname"> <em>v</em>          </td>
527          <td>&nbsp;)&nbsp;</td>
528          <td> const<code> [virtual]</code></td>
529        </tr>
530      </table>
531</div>
532<div class="memdoc">
533
534<p>
535Multiplies square root of <img class="formulaInl" alt="$V$" src="form_55.png"> by vector <img class="formulaInl" alt="$x$" src="form_1.png">.
536<p>
537Used e.g. in generating normal samples.
538<p>Implements <a class="el" href="classsqmat.html#6b79438b5d7544a9c8e110a145355d8f">sqmat</a>.</p>
539
540<p>References <a class="el" href="square__mat_8h_source.html#l00268">D</a>, <a class="el" href="square__mat_8h_source.html#l00102">sqmat::dim</a>, and <a class="el" href="square__mat_8h_source.html#l00270">L</a>.</p>
541
542</div>
543</div><p>
544<hr>The documentation for this class was generated from the following files:<ul>
545<li><a class="el" href="square__mat_8h_source.html">square_mat.h</a><li>square_mat.cpp</ul>
546</div>
547<hr size="1"><address style="text-align: right;"><small>Generated on Wed Aug 5 00:06:53 2009 for mixpp by&nbsp;
548<a href="http://www.doxygen.org/index.html">
549<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.9 </small></address>
550</body>
551</html>
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