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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a></div>
<h1>Matrix Class Reference</h1><!-- doxytag: class="QuantLib::Matrix" --><code>#include <ql/Math/matrix.hpp></code>
<p>
Inheritance diagram for Matrix:<p><center><img src="class_quant_lib_1_1_matrix__inherit__graph.png" border="0" usemap="#_matrix__inherit__map" alt="Inheritance graph"></center>
<map name="_matrix__inherit__map">
<area href="class_quant_lib_1_1_disposable.html" shape="rect" coords="6,81,246,105" alt="">
</map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_matrix-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Matrix used in linear algebra.
<p>
This class implements the concept of <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> as used in linear algebra. As such, it is <b>not</b> meant to be used as a container.
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Constructors, destructor, and assignment</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3aede62f513da27e6f61ae7a972b4f96"></a><!-- doxytag: member="QuantLib::Matrix::Matrix" ref="3aede62f513da27e6f61ae7a972b4f96" args="()" -->
</td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#3aede62f513da27e6f61ae7a972b4f96">Matrix</a> ()</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">creates a null matrix <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="701a8e8f62aed6b7496b48e1f57db824"></a><!-- doxytag: member="QuantLib::Matrix::Matrix" ref="701a8e8f62aed6b7496b48e1f57db824" args="(Size rows, Size columns)" -->
</td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#701a8e8f62aed6b7496b48e1f57db824">Matrix</a> (Size rows, Size columns)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">creates a matrix with the given dimensions <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87bcdd5b5f33ccbcde36aa1d237af97c"></a><!-- doxytag: member="QuantLib::Matrix::Matrix" ref="87bcdd5b5f33ccbcde36aa1d237af97c" args="(Size rows, Size columns, Real value)" -->
</td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#87bcdd5b5f33ccbcde36aa1d237af97c">Matrix</a> (Size rows, Size columns, Real value)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">creates the matrix and fills it with <code>value</code> <br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="db458d0a51fee7c80c34482e88b84de7"></a><!-- doxytag: member="QuantLib::Matrix::Matrix" ref="db458d0a51fee7c80c34482e88b84de7" args="(const Matrix &)" -->
</td><td class="memItemRight" valign="bottom"><b>Matrix</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18559c34691fddf02fe9024ce196cb09"></a><!-- doxytag: member="QuantLib::Matrix::Matrix" ref="18559c34691fddf02fe9024ce196cb09" args="(const Disposable< Matrix > &)" -->
</td><td class="memItemRight" valign="bottom"><b>Matrix</b> (const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="be73cd0177a33a456bb5ab08b1855344"></a><!-- doxytag: member="QuantLib::Matrix::operator=" ref="be73cd0177a33a456bb5ab08b1855344" args="(const Matrix &)" -->
<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="81096f71e82f047e98c5117c5868f70d"></a><!-- doxytag: member="QuantLib::Matrix::operator=" ref="81096f71e82f047e98c5117c5868f70d" args="(const Disposable< Matrix > &)" -->
<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator=</b> (const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > &)</td></tr>
<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2fea9c8bdadaab95246ddd3547b79652"></a><!-- doxytag: member="QuantLib::Matrix::iterator" ref="2fea9c8bdadaab95246ddd3547b79652" args="" -->
typedef Real * </td><td class="memItemRight" valign="bottom"><b>iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0282fb9d40dbac6ced245bd67c194257"></a><!-- doxytag: member="QuantLib::Matrix::const_iterator" ref="0282fb9d40dbac6ced245bd67c194257" args="" -->
typedef const Real * </td><td class="memItemRight" valign="bottom"><b>const_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f460725d447791acfd9f7b85856c0b91"></a><!-- doxytag: member="QuantLib::Matrix::reverse_iterator" ref="f460725d447791acfd9f7b85856c0b91" args="" -->
typedef boost::reverse_iterator<<br>
iterator > </td><td class="memItemRight" valign="bottom"><b>reverse_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1902a26c330085fea93accc4cc10d5fe"></a><!-- doxytag: member="QuantLib::Matrix::const_reverse_iterator" ref="1902a26c330085fea93accc4cc10d5fe" args="" -->
typedef boost::reverse_iterator<<br>
const_iterator > </td><td class="memItemRight" valign="bottom"><b>const_reverse_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9b1ce1ec83276b70eae647b0b2b28910"></a><!-- doxytag: member="QuantLib::Matrix::row_iterator" ref="9b1ce1ec83276b70eae647b0b2b28910" args="" -->
typedef Real * </td><td class="memItemRight" valign="bottom"><b>row_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ffee08e33e5d41deaff785910ac653ca"></a><!-- doxytag: member="QuantLib::Matrix::const_row_iterator" ref="ffee08e33e5d41deaff785910ac653ca" args="" -->
typedef const Real * </td><td class="memItemRight" valign="bottom"><b>const_row_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d46c9d05f90a19ddab72f0bbc4260023"></a><!-- doxytag: member="QuantLib::Matrix::reverse_row_iterator" ref="d46c9d05f90a19ddab72f0bbc4260023" args="" -->
typedef boost::reverse_iterator<<br>
row_iterator > </td><td class="memItemRight" valign="bottom"><b>reverse_row_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e1c1bc28c3d8abe06f7749edf787502a"></a><!-- doxytag: member="QuantLib::Matrix::const_reverse_row_iterator" ref="e1c1bc28c3d8abe06f7749edf787502a" args="" -->
typedef boost::reverse_iterator<<br>
const_row_iterator > </td><td class="memItemRight" valign="bottom"><b>const_reverse_row_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c3d8a5c7f0147d2d76feb480361d7d5a"></a><!-- doxytag: member="QuantLib::Matrix::column_iterator" ref="c3d8a5c7f0147d2d76feb480361d7d5a" args="" -->
typedef <a class="el" href="class_quant_lib_1_1step__iterator.html">step_iterator</a>< iterator > </td><td class="memItemRight" valign="bottom"><b>column_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c6d572f54173d49c75740a22c9c36609"></a><!-- doxytag: member="QuantLib::Matrix::const_column_iterator" ref="c6d572f54173d49c75740a22c9c36609" args="" -->
typedef <a class="el" href="class_quant_lib_1_1step__iterator.html">step_iterator</a>< const_iterator > </td><td class="memItemRight" valign="bottom"><b>const_column_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0172813d0237da300d91ed8930f20a61"></a><!-- doxytag: member="QuantLib::Matrix::reverse_column_iterator" ref="0172813d0237da300d91ed8930f20a61" args="" -->
typedef boost::reverse_iterator<<br>
<a class="el" href="class_quant_lib_1_1step__iterator.html">column_iterator</a> > </td><td class="memItemRight" valign="bottom"><b>reverse_column_iterator</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="51b452fec445b4d94800582fd8c9e463"></a><!-- doxytag: member="QuantLib::Matrix::const_reverse_column_iterator" ref="51b452fec445b4d94800582fd8c9e463" args="" -->
typedef boost::reverse_iterator<<br>
<a class="el" href="class_quant_lib_1_1step__iterator.html">const_column_iterator</a> > </td><td class="memItemRight" valign="bottom"><b>const_reverse_column_iterator</b></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Algebraic operators</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#f9e9ef3ae7410799e5d1ac6b6d74dc68">operator+=</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5fe157d2a6b00251b2b7d4a0cbc059c8"></a><!-- doxytag: member="QuantLib::Matrix::operator-=" ref="5fe157d2a6b00251b2b7d4a0cbc059c8" args="(const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator-=</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d082a71b46fee43f34636a7c23b6c37e"></a><!-- doxytag: member="QuantLib::Matrix::operator *=" ref="d082a71b46fee43f34636a7c23b6c37e" args="(Real)" -->
const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator *=</b> (Real)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1560f8a2756a34d48eadac60ecb72c9e"></a><!-- doxytag: member="QuantLib::Matrix::operator/=" ref="1560f8a2756a34d48eadac60ecb72c9e" args="(Real)" -->
const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator/=</b> (Real)</td></tr>
<tr><td colspan="2"><div class="groupHeader">Iterator access</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3dece4c106f934e6135985fdad30c0c8"></a><!-- doxytag: member="QuantLib::Matrix::begin" ref="3dece4c106f934e6135985fdad30c0c8" args="() const" -->
const_iterator </td><td class="memItemRight" valign="bottom"><b>begin</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5cd4a3c124542ff7e6a327775fe733cb"></a><!-- doxytag: member="QuantLib::Matrix::begin" ref="5cd4a3c124542ff7e6a327775fe733cb" args="()" -->
iterator </td><td class="memItemRight" valign="bottom"><b>begin</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="82a59cb80a1b5eed6e558cf220b24cc9"></a><!-- doxytag: member="QuantLib::Matrix::end" ref="82a59cb80a1b5eed6e558cf220b24cc9" args="() const" -->
const_iterator </td><td class="memItemRight" valign="bottom"><b>end</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="38d30f37dbda21e5685bd4c8f8a04b54"></a><!-- doxytag: member="QuantLib::Matrix::end" ref="38d30f37dbda21e5685bd4c8f8a04b54" args="()" -->
iterator </td><td class="memItemRight" valign="bottom"><b>end</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d47ab89f8e6a2ed24f4e62c6ca121efb"></a><!-- doxytag: member="QuantLib::Matrix::rbegin" ref="d47ab89f8e6a2ed24f4e62c6ca121efb" args="() const" -->
const_reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rbegin</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6373cc711367ba1881bfe5d3f13ea40f"></a><!-- doxytag: member="QuantLib::Matrix::rbegin" ref="6373cc711367ba1881bfe5d3f13ea40f" args="()" -->
reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rbegin</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="276cdf4dfa735784145fa56de702f534"></a><!-- doxytag: member="QuantLib::Matrix::rend" ref="276cdf4dfa735784145fa56de702f534" args="() const" -->
const_reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rend</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c0615a909a24d4e71460cabbf59794a2"></a><!-- doxytag: member="QuantLib::Matrix::rend" ref="c0615a909a24d4e71460cabbf59794a2" args="()" -->
reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rend</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="11f377032b07193b43fd3c164567120b"></a><!-- doxytag: member="QuantLib::Matrix::row_begin" ref="11f377032b07193b43fd3c164567120b" args="(Size i) const" -->
const_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_begin</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0ba8451fef9b8e764408a0806b159235"></a><!-- doxytag: member="QuantLib::Matrix::row_begin" ref="0ba8451fef9b8e764408a0806b159235" args="(Size i)" -->
row_iterator </td><td class="memItemRight" valign="bottom"><b>row_begin</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9a7d3e55243a1695cd6b0ae6249ad068"></a><!-- doxytag: member="QuantLib::Matrix::row_end" ref="9a7d3e55243a1695cd6b0ae6249ad068" args="(Size i) const" -->
const_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_end</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="619c3165548ec37e1dc529f248b49415"></a><!-- doxytag: member="QuantLib::Matrix::row_end" ref="619c3165548ec37e1dc529f248b49415" args="(Size i)" -->
row_iterator </td><td class="memItemRight" valign="bottom"><b>row_end</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3c2e832cac1665f051c745fea500500f"></a><!-- doxytag: member="QuantLib::Matrix::row_rbegin" ref="3c2e832cac1665f051c745fea500500f" args="(Size i) const" -->
const_reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rbegin</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cd9c3b4faa2fa1c7fe0a39eeb12e890a"></a><!-- doxytag: member="QuantLib::Matrix::row_rbegin" ref="cd9c3b4faa2fa1c7fe0a39eeb12e890a" args="(Size i)" -->
reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rbegin</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="83cb27d16a58bb3ebfded604083cd712"></a><!-- doxytag: member="QuantLib::Matrix::row_rend" ref="83cb27d16a58bb3ebfded604083cd712" args="(Size i) const" -->
const_reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rend</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b2f057a3df14d6e9501f9d03fd758d49"></a><!-- doxytag: member="QuantLib::Matrix::row_rend" ref="b2f057a3df14d6e9501f9d03fd758d49" args="(Size i)" -->
reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rend</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="894a41169df8af177e2f82db24f4f611"></a><!-- doxytag: member="QuantLib::Matrix::column_begin" ref="894a41169df8af177e2f82db24f4f611" args="(Size i) const" -->
<a class="el" href="class_quant_lib_1_1step__iterator.html">const_column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_begin</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="12daadbc027a549e80230721ee4a4cfa"></a><!-- doxytag: member="QuantLib::Matrix::column_begin" ref="12daadbc027a549e80230721ee4a4cfa" args="(Size i)" -->
<a class="el" href="class_quant_lib_1_1step__iterator.html">column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_begin</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="afbc5e6c85dc09c1b61bb98d9337e37c"></a><!-- doxytag: member="QuantLib::Matrix::column_end" ref="afbc5e6c85dc09c1b61bb98d9337e37c" args="(Size i) const" -->
<a class="el" href="class_quant_lib_1_1step__iterator.html">const_column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_end</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4797c1371f55c7aacbe45229a57b294e"></a><!-- doxytag: member="QuantLib::Matrix::column_end" ref="4797c1371f55c7aacbe45229a57b294e" args="(Size i)" -->
<a class="el" href="class_quant_lib_1_1step__iterator.html">column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_end</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c3e18fbf519c4425fd9fc3ea50743ee1"></a><!-- doxytag: member="QuantLib::Matrix::column_rbegin" ref="c3e18fbf519c4425fd9fc3ea50743ee1" args="(Size i) const" -->
const_reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rbegin</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="be56132398da3b7df80e868e46606115"></a><!-- doxytag: member="QuantLib::Matrix::column_rbegin" ref="be56132398da3b7df80e868e46606115" args="(Size i)" -->
reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rbegin</b> (Size i)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="424962464e508cfa1ea0b5a75eb1c795"></a><!-- doxytag: member="QuantLib::Matrix::column_rend" ref="424962464e508cfa1ea0b5a75eb1c795" args="(Size i) const" -->
const_reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rend</b> (Size i) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9c049aca593b7236c024f4ddd9edabbf"></a><!-- doxytag: member="QuantLib::Matrix::column_rend" ref="9c049aca593b7236c024f4ddd9edabbf" args="(Size i)" -->
reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rend</b> (Size i)</td></tr>
<tr><td colspan="2"><div class="groupHeader">Element access</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="be8a2be18f9ad4c8d4a776ca57f0d149"></a><!-- doxytag: member="QuantLib::Matrix::operator[]" ref="be8a2be18f9ad4c8d4a776ca57f0d149" args="(Size) const" -->
const_row_iterator </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (Size) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c5fbc1f823e94a8d3dc9258ecfe35cfc"></a><!-- doxytag: member="QuantLib::Matrix::at" ref="c5fbc1f823e94a8d3dc9258ecfe35cfc" args="(Size) const" -->
const_row_iterator </td><td class="memItemRight" valign="bottom"><b>at</b> (Size) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a81ad20c93d236084fa25efd9ca92337"></a><!-- doxytag: member="QuantLib::Matrix::operator[]" ref="a81ad20c93d236084fa25efd9ca92337" args="(Size)" -->
row_iterator </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (Size)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cab29082cda83fa27661e845fea8af2a"></a><!-- doxytag: member="QuantLib::Matrix::at" ref="cab29082cda83fa27661e845fea8af2a" args="(Size)" -->
row_iterator </td><td class="memItemRight" valign="bottom"><b>at</b> (Size)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="31468541cacc7047b8a0abfec0a17be1"></a><!-- doxytag: member="QuantLib::Matrix::diagonal" ref="31468541cacc7047b8a0abfec0a17be1" args="(void) const" -->
<a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><b>diagonal</b> (void) const</td></tr>
<tr><td colspan="2"><div class="groupHeader">Inspectors</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="74da223ed3bde38f5e9f6822f6cacfbe"></a><!-- doxytag: member="QuantLib::Matrix::rows" ref="74da223ed3bde38f5e9f6822f6cacfbe" args="() const" -->
Size </td><td class="memItemRight" valign="bottom"><b>rows</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="86a771d47cf764c4ef43aab250442fda"></a><!-- doxytag: member="QuantLib::Matrix::columns" ref="86a771d47cf764c4ef43aab250442fda" args="() const" -->
Size </td><td class="memItemRight" valign="bottom"><b>columns</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="644718bb2fb240de962dc3c9a1fdf0dc"></a><!-- doxytag: member="QuantLib::Matrix::empty" ref="644718bb2fb240de962dc3c9a1fdf0dc" args="() const" -->
bool </td><td class="memItemRight" valign="bottom"><b>empty</b> () const</td></tr>
<tr><td colspan="2"><div class="groupHeader">Utilities</div></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8b6bd270cf6df33aeb61928ecfd88dee"></a><!-- doxytag: member="QuantLib::Matrix::swap" ref="8b6bd270cf6df33aeb61928ecfd88dee" args="(Matrix &)" -->
void </td><td class="memItemRight" valign="bottom"><b>swap</b> (<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td colspan="2"><br><h2>Related Functions</h2></td></tr>
<tr><td colspan="2">(Note that these are not member functions.) <br><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e99bf007dfbac44521a082ca343c4160"></a><!-- doxytag: member="QuantLib::Matrix::CholeskyDecomposition" ref="e99bf007dfbac44521a082ca343c4160" args="(const Matrix &m, bool flexible=false)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>CholeskyDecomposition</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &m, bool flexible=false)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1fe41a3027d4b54101228a2de063e329"></a><!-- doxytag: member="QuantLib::Matrix::operator+" ref="1fe41a3027d4b54101228a2de063e329" args="(const Matrix &, const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator+</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a43bca990eddf9cbce12bb42bb64ccff"></a><!-- doxytag: member="QuantLib::Matrix::operator-" ref="a43bca990eddf9cbce12bb42bb64ccff" args="(const Matrix &, const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator-</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dad492748c921db060b3834600eba090"></a><!-- doxytag: member="QuantLib::Matrix::operator *" ref="dad492748c921db060b3834600eba090" args="(const Matrix &, Real)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator *</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, Real)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8eee7bb2cc0fb6e7d0614d780aa8bfb0"></a><!-- doxytag: member="QuantLib::Matrix::operator *" ref="8eee7bb2cc0fb6e7d0614d780aa8bfb0" args="(Real, const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator *</b> (Real, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87bdcd1ea436e955114c491d050f272a"></a><!-- doxytag: member="QuantLib::Matrix::operator/" ref="87bdcd1ea436e955114c491d050f272a" args="(const Matrix &, Real)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator/</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, Real)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0de6479da2d8bc272b23206f46c98def"></a><!-- doxytag: member="QuantLib::Matrix::operator *" ref="0de6479da2d8bc272b23206f46c98def" args="(const Array &, const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><b>operator *</b> (const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a06784b3ab8ee66ab378f819c0709787"></a><!-- doxytag: member="QuantLib::Matrix::operator *" ref="a06784b3ab8ee66ab378f819c0709787" args="(const Matrix &, const Array &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_array.html">Array</a> > </td><td class="memItemRight" valign="bottom"><b>operator *</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ae2b3b7e202a8bb4db84958dd533c44d"></a><!-- doxytag: member="QuantLib::Matrix::operator *" ref="ae2b3b7e202a8bb4db84958dd533c44d" args="(const Matrix &, const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>operator *</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2dda6bd778bb64e7732fe6a6bbf8675d"></a><!-- doxytag: member="QuantLib::Matrix::transpose" ref="2dda6bd778bb64e7732fe6a6bbf8675d" args="(const Matrix &)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>transpose</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abd56590af05a9196bc52b253ef9b81d"></a><!-- doxytag: member="QuantLib::Matrix::outerProduct" ref="abd56590af05a9196bc52b253ef9b81d" args="(const Array &v1, const Array &v2)" -->
const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><b>outerProduct</b> (const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &v1, const <a class="el" href="class_quant_lib_1_1_array.html">Array</a> &v2)</td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="fd205249862d9dc22e86de30e612300a"></a><!-- doxytag: member="QuantLib::Matrix::outerProduct" ref="fd205249862d9dc22e86de30e612300a" args="(Iterator1 v1begin, Iterator1 v1end, Iterator2 v2begin, Iterator2 v2end)" -->
template<class Iterator1, class Iterator2> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memTemplItemRight" valign="bottom"><b>outerProduct</b> (Iterator1 v1begin, Iterator1 v1end, Iterator2 v2begin, Iterator2 v2end)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9df8756a7a5832acb371e2a6aaa9a89b"></a><!-- doxytag: member="QuantLib::Matrix::swap" ref="9df8756a7a5832acb371e2a6aaa9a89b" args="(Matrix &, Matrix &)" -->
void </td><td class="memItemRight" valign="bottom"><b>swap</b> (<a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f0d6a8b04f5a8094992e498ca5a71142"></a><!-- doxytag: member="QuantLib::Matrix::operator<<" ref="f0d6a8b04f5a8094992e498ca5a71142" args="(std::ostream &, const Matrix &)" -->
std::ostream & </td><td class="memItemRight" valign="bottom"><b>operator<<</b> (std::ostream &, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#bbbd1fbdec84c274b421380416f9716a">pseudoSqrt</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, SalvagingAlgorithm::Type=SalvagingAlgorithm::None)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the pseudo square root of a real symmetric matrix. <a href="#bbbd1fbdec84c274b421380416f9716a"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#f4208d81b345ebe9f2defb4f839ede1f">rankReducedSqrt</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, Size maxRank, Real componentRetainedPercentage, SalvagingAlgorithm::Type)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Returns the rank-reduced pseudo square root of a real symmetric matrix. <a href="#f4208d81b345ebe9f2defb4f839ede1f"></a><br></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="f9e9ef3ae7410799e5d1ac6b6d74dc68"></a><!-- doxytag: member="QuantLib::Matrix::operator+=" ref="f9e9ef3ae7410799e5d1ac6b6d74dc68" args="(const Matrix &)" -->
<div class="memitem">
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<table class="memname">
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<td class="memname">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & operator+= </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td>
<td class="paramname"> </td>
<td> ) </td>
<td width="100%"></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>all matrices involved in an algebraic expression must have the same size. </dd></dl>
</div>
</div><p>
<hr><h2>Friends And Related Function Documentation</h2>
<a class="anchor" name="bbbd1fbdec84c274b421380416f9716a"></a><!-- doxytag: member="QuantLib::Matrix::pseudoSqrt" ref="bbbd1fbdec84c274b421380416f9716a" args="(const Matrix &, SalvagingAlgorithm::Type=SalvagingAlgorithm::None)" -->
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<td class="memname">const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > pseudoSqrt </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">SalvagingAlgorithm::Type </td>
<td class="paramname"> = <code>SalvagingAlgorithm::None</code></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [related]</code></td>
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</table>
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<div class="memdoc">
<p>
Returns the pseudo square root of a real symmetric matrix.
<p>
Given a matrix <img class="formulaInl" alt="$ M $" src="form_130.png">, the result <img class="formulaInl" alt="$ S $" src="form_135.png"> is defined as the matrix such that <img class="formulaInl" alt="$ S S^T = M. $" src="form_136.png"> If the matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.<p>
For more information see: "The most general methodology to create a valid correlation matrix for risk management and option pricing purposes", by R. Rebonato and P. Jckel. The Journal of Risk, 2(2), Winter 1999/2000 <a href="http://www.rebonato.com/correlationmatrix.pdf">http://www.rebonato.com/correlationmatrix.pdf</a><p>
Revised and extended in "Monte Carlo Methods in Finance", by Peter Jckel, Chapter 6.<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>the given matrix must be symmetric.</dd></dl>
<dl compact><dt><b><a class="el" href="todo.html#_todo000038">Todo:</a></b></dt><dd><ul>
<li>implement Higham algorithm: Higham "Computing the nearest correlation matrix"</li></ul>
</dd></dl>
<dl compact><dt><b><a class="el" href="test.html#_test000043">Tests:</a></b></dt><dd><ul>
<li>the correctness of the results is tested by reproducing known good data.</li><li>the correctness of the results is tested by checking returned values against numerical calculations. </li></ul>
</dd></dl>
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<td class="memname">const <a class="el" href="class_quant_lib_1_1_disposable.html">Disposable</a>< <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> > rankReducedSqrt </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td>
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<td class="paramtype">Size </td>
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<td class="paramtype">SalvagingAlgorithm::Type </td>
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<td></td><td></td><td width="100%"><code> [related]</code></td>
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<p>
Returns the rank-reduced pseudo square root of a real symmetric matrix.
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The result matrix has rank<=maxRank. If maxRank>=size, then the specified percentage of eigenvalues out of the eigenvalues' sum is retained.<p>
If the input matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.<p>
<dl class="pre" compact><dt><b>Precondition:</b></dt><dd>the given matrix must be symmetric. </dd></dl>
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