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<li class="navelem"><a class="el" href="namespace_quant_lib.html">QuantLib</a></li><li class="navelem"><a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a></li> </ul>
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<p>Matrix used in linear algebra.
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<p><code>#include <ql/math/matrix.hpp></code></p>
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<img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Matrix:</div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td colspan="2"><div class="groupHeader">Constructors, destructor, and assignment</div></td></tr>
<tr class="memitem:a3aede62f513da27e6f61ae7a972b4f96"><td class="memItemLeft" align="right" valign="top"><a id="a3aede62f513da27e6f61ae7a972b4f96"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#a3aede62f513da27e6f61ae7a972b4f96">Matrix</a> ()</td></tr>
<tr class="memdesc:a3aede62f513da27e6f61ae7a972b4f96"><td class="mdescLeft"> </td><td class="mdescRight">creates a null matrix <br /></td></tr>
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<tr class="memitem:a701a8e8f62aed6b7496b48e1f57db824"><td class="memItemLeft" align="right" valign="top"><a id="a701a8e8f62aed6b7496b48e1f57db824"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#a701a8e8f62aed6b7496b48e1f57db824">Matrix</a> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> rows, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> columns)</td></tr>
<tr class="memdesc:a701a8e8f62aed6b7496b48e1f57db824"><td class="mdescLeft"> </td><td class="mdescRight">creates a matrix with the given dimensions <br /></td></tr>
<tr class="separator:a701a8e8f62aed6b7496b48e1f57db824"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a87bcdd5b5f33ccbcde36aa1d237af97c"><td class="memItemLeft" align="right" valign="top"><a id="a87bcdd5b5f33ccbcde36aa1d237af97c"></a>
 </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#a87bcdd5b5f33ccbcde36aa1d237af97c">Matrix</a> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> rows, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> columns, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> value)</td></tr>
<tr class="memdesc:a87bcdd5b5f33ccbcde36aa1d237af97c"><td class="mdescLeft"> </td><td class="mdescRight">creates the matrix and fills it with <code>value</code> <br /></td></tr>
<tr class="separator:a87bcdd5b5f33ccbcde36aa1d237af97c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a4aff113d85809ff7f25218ef8724bb9d"><td class="memTemplParams" colspan="2">template<class Iterator > </td></tr>
<tr class="memitem:a4aff113d85809ff7f25218ef8724bb9d"><td class="memTemplItemLeft" align="right" valign="top"> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_matrix.html#a4aff113d85809ff7f25218ef8724bb9d">Matrix</a> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> rows, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> columns, Iterator begin, Iterator end)</td></tr>
<tr class="memdesc:a4aff113d85809ff7f25218ef8724bb9d"><td class="mdescLeft"> </td><td class="mdescRight">creates the matrix and fills it with data from a range. <a href="class_quant_lib_1_1_matrix.html#a4aff113d85809ff7f25218ef8724bb9d">More...</a><br /></td></tr>
<tr class="separator:a4aff113d85809ff7f25218ef8724bb9d"><td class="memSeparator" colspan="2"> </td></tr>
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 </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>
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 </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>
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<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>
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<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 class="separator:a81096f71e82f047e98c5117c5868f70d"><td class="memSeparator" colspan="2"> </td></tr>
<tr><td colspan="2"><div class="groupHeader">Iterator access</div></td></tr>
<tr class="memitem:a3dece4c106f934e6135985fdad30c0c8"><td class="memItemLeft" align="right" valign="top"><a id="a3dece4c106f934e6135985fdad30c0c8"></a>
const_iterator </td><td class="memItemRight" valign="bottom"><b>begin</b> () const</td></tr>
<tr class="separator:a3dece4c106f934e6135985fdad30c0c8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a5cd4a3c124542ff7e6a327775fe733cb"><td class="memItemLeft" align="right" valign="top"><a id="a5cd4a3c124542ff7e6a327775fe733cb"></a>
iterator </td><td class="memItemRight" valign="bottom"><b>begin</b> ()</td></tr>
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<tr class="memitem:a82a59cb80a1b5eed6e558cf220b24cc9"><td class="memItemLeft" align="right" valign="top"><a id="a82a59cb80a1b5eed6e558cf220b24cc9"></a>
const_iterator </td><td class="memItemRight" valign="bottom"><b>end</b> () const</td></tr>
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<tr class="memitem:a38d30f37dbda21e5685bd4c8f8a04b54"><td class="memItemLeft" align="right" valign="top"><a id="a38d30f37dbda21e5685bd4c8f8a04b54"></a>
iterator </td><td class="memItemRight" valign="bottom"><b>end</b> ()</td></tr>
<tr class="separator:a38d30f37dbda21e5685bd4c8f8a04b54"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ad47ab89f8e6a2ed24f4e62c6ca121efb"><td class="memItemLeft" align="right" valign="top"><a id="ad47ab89f8e6a2ed24f4e62c6ca121efb"></a>
const_reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rbegin</b> () const</td></tr>
<tr class="separator:ad47ab89f8e6a2ed24f4e62c6ca121efb"><td class="memSeparator" colspan="2"> </td></tr>
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reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rbegin</b> ()</td></tr>
<tr class="separator:a6373cc711367ba1881bfe5d3f13ea40f"><td class="memSeparator" colspan="2"> </td></tr>
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const_reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rend</b> () const</td></tr>
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reverse_iterator </td><td class="memItemRight" valign="bottom"><b>rend</b> ()</td></tr>
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const_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_begin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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row_iterator </td><td class="memItemRight" valign="bottom"><b>row_begin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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const_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_end</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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row_iterator </td><td class="memItemRight" valign="bottom"><b>row_end</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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const_reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rbegin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rbegin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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const_reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rend</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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reverse_row_iterator </td><td class="memItemRight" valign="bottom"><b>row_rend</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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<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> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<a class="el" href="class_quant_lib_1_1step__iterator.html">column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_begin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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<tr class="memitem:aafbc5e6c85dc09c1b61bb98d9337e37c"><td class="memItemLeft" align="right" valign="top"><a id="aafbc5e6c85dc09c1b61bb98d9337e37c"></a>
<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> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<a class="el" href="class_quant_lib_1_1step__iterator.html">column_iterator</a> </td><td class="memItemRight" valign="bottom"><b>column_end</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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const_reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rbegin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rbegin</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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<tr class="memitem:a424962464e508cfa1ea0b5a75eb1c795"><td class="memItemLeft" align="right" valign="top"><a id="a424962464e508cfa1ea0b5a75eb1c795"></a>
const_reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rend</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i) const</td></tr>
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<tr class="memitem:a9c049aca593b7236c024f4ddd9edabbf"><td class="memItemLeft" align="right" valign="top"><a id="a9c049aca593b7236c024f4ddd9edabbf"></a>
reverse_column_iterator </td><td class="memItemRight" valign="bottom"><b>column_rend</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i)</td></tr>
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<tr><td colspan="2"><div class="groupHeader">Element access</div></td></tr>
<tr class="memitem:abe8a2be18f9ad4c8d4a776ca57f0d149"><td class="memItemLeft" align="right" valign="top"><a id="abe8a2be18f9ad4c8d4a776ca57f0d149"></a>
const_row_iterator </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a>) const</td></tr>
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const_row_iterator </td><td class="memItemRight" valign="bottom"><b>at</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a>) const</td></tr>
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row_iterator </td><td class="memItemRight" valign="bottom"><b>operator[]</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a>)</td></tr>
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<tr class="memitem:acab29082cda83fa27661e845fea8af2a"><td class="memItemLeft" align="right" valign="top"><a id="acab29082cda83fa27661e845fea8af2a"></a>
row_iterator </td><td class="memItemRight" valign="bottom"><b>at</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a>)</td></tr>
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<tr class="memitem:a29955fdae23efc58809c738645467c63"><td class="memItemLeft" align="right" valign="top"><a id="a29955fdae23efc58809c738645467c63"></a>
<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> () const</td></tr>
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<tr class="memitem:a9d034edcc5c2a6e02741b26ef10effea"><td class="memItemLeft" align="right" valign="top"><a id="a9d034edcc5c2a6e02741b26ef10effea"></a>
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> & </td><td class="memItemRight" valign="bottom"><b>operator()</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> i, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> j) const</td></tr>
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<tr><td colspan="2"><div class="groupHeader">Inspectors</div></td></tr>
<tr class="memitem:a74da223ed3bde38f5e9f6822f6cacfbe"><td class="memItemLeft" align="right" valign="top"><a id="a74da223ed3bde38f5e9f6822f6cacfbe"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>rows</b> () const</td></tr>
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<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>columns</b> () const</td></tr>
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bool </td><td class="memItemRight" valign="bottom"><b>empty</b> () const</td></tr>
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<tr class="memitem:a3f935d7e989ec6a7161736d7912f8071"><td class="memItemLeft" align="right" valign="top"><a id="a3f935d7e989ec6a7161736d7912f8071"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>size1</b> () const</td></tr>
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<tr class="memitem:a258283c8309d2cfc9d07e6f48228f273"><td class="memItemLeft" align="right" valign="top"><a id="a258283c8309d2cfc9d07e6f48228f273"></a>
<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td><td class="memItemRight" valign="bottom"><b>size2</b> () const</td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="related"></a>
Related Functions</h2></td></tr>
<tr><td class="ititle" colspan="2"><p>(Note that these are not member functions.) </p>
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<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>
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<tr class="memitem:a9e487c70c0d5d812575f22581853850d"><td class="memItemLeft" align="right" valign="top"><a id="a9e487c70c0d5d812575f22581853850d"></a>
<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>
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<tr class="memitem:a4f8ba3054dc2cde44875bd9390459e43"><td class="memItemLeft" align="right" valign="top"><a id="a4f8ba3054dc2cde44875bd9390459e43"></a>
<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> &, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)</td></tr>
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<tr class="memitem:ae0d84c1fcb55e2d2b09a9bcdfe073c22"><td class="memItemLeft" align="right" valign="top"><a id="ae0d84c1fcb55e2d2b09a9bcdfe073c22"></a>
<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> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>, const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
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<tr class="memitem:a3713b783d128e8e98a66cb198797e169"><td class="memItemLeft" align="right" valign="top"><a id="a3713b783d128e8e98a66cb198797e169"></a>
<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> &, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)</td></tr>
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<tr class="memitem:a4c828aca6d7e61c2b68a20834d2234ed"><td class="memItemLeft" align="right" valign="top"><a id="a4c828aca6d7e61c2b68a20834d2234ed"></a>
<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>
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<tr class="memitem:a5fd624f86387e8fffe348a747a73f28d"><td class="memItemLeft" align="right" valign="top"><a id="a5fd624f86387e8fffe348a747a73f28d"></a>
<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>
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<tr class="memitem:a59f5d426bdf004ad93fa962fc7cbe385"><td class="memItemLeft" align="right" valign="top"><a id="a59f5d426bdf004ad93fa962fc7cbe385"></a>
<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>
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<tr class="memitem:a4b7aa0bda7534f7e2a7708a7f0be628c"><td class="memItemLeft" align="right" valign="top"><a id="a4b7aa0bda7534f7e2a7708a7f0be628c"></a>
<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>
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<tr class="memitem:a30cc235798876a57b09e1338e8db34ea"><td class="memItemLeft" align="right" valign="top"><a id="a30cc235798876a57b09e1338e8db34ea"></a>
<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>
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template<class Iterator1 , class Iterator2 > </td></tr>
<tr class="memitem:a72610cea5fb83ff91bde7fcf8c2ee94a"><td class="memTemplItemLeft" align="right" valign="top"><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>
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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>
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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>
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<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>inverse</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &m)</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>determinant</b> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &m)</td></tr>
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<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>
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<tr class="memitem:aac6e1b8e2666440c95b38c2b672dd10f"><td class="memItemLeft" align="right" valign="top"><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#aac6e1b8e2666440c95b38c2b672dd10f">pseudoSqrt</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, SalvagingAlgorithm::Type=SalvagingAlgorithm::None)</td></tr>
<tr class="memdesc:aac6e1b8e2666440c95b38c2b672dd10f"><td class="mdescLeft"> </td><td class="mdescRight">Returns the pseudo square root of a real symmetric matrix. <a href="class_quant_lib_1_1_matrix.html#aac6e1b8e2666440c95b38c2b672dd10f">More...</a><br /></td></tr>
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<tr class="memitem:ae874444cc115097ecd8c0deec4394750"><td class="memItemLeft" align="right" valign="top"><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#ae874444cc115097ecd8c0deec4394750">rankReducedSqrt</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> maxRank, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> componentRetainedPercentage, SalvagingAlgorithm::Type)</td></tr>
<tr class="memdesc:ae874444cc115097ecd8c0deec4394750"><td class="mdescLeft"> </td><td class="mdescRight">Returns the rank-reduced pseudo square root of a real symmetric matrix. <a href="class_quant_lib_1_1_matrix.html#ae874444cc115097ecd8c0deec4394750">More...</a><br /></td></tr>
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Algebraic operators</h2></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> * </td><td class="memItemRight" valign="bottom"><b>iterator</b></td></tr>
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typedef const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> * </td><td class="memItemRight" valign="bottom"><b>const_iterator</b></td></tr>
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typedef boost::reverse_iterator< iterator > </td><td class="memItemRight" valign="bottom"><b>reverse_iterator</b></td></tr>
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typedef boost::reverse_iterator< const_iterator > </td><td class="memItemRight" valign="bottom"><b>const_reverse_iterator</b></td></tr>
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typedef <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> * </td><td class="memItemRight" valign="bottom"><b>row_iterator</b></td></tr>
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typedef const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> * </td><td class="memItemRight" valign="bottom"><b>const_row_iterator</b></td></tr>
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typedef boost::reverse_iterator< row_iterator > </td><td class="memItemRight" valign="bottom"><b>reverse_row_iterator</b></td></tr>
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typedef boost::reverse_iterator< const_row_iterator > </td><td class="memItemRight" valign="bottom"><b>const_reverse_row_iterator</b></td></tr>
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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>
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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>
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typedef boost::reverse_iterator< <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>
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typedef boost::reverse_iterator< <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>
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<tr class="memitem:af9e9ef3ae7410799e5d1ac6b6d74dc68"><td class="memItemLeft" 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#af9e9ef3ae7410799e5d1ac6b6d74dc68">operator+=</a> (const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> &)</td></tr>
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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>
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const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator*=</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)</td></tr>
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const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td><td class="memItemRight" valign="bottom"><b>operator/=</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)</td></tr>
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Utilities</h2></td></tr>
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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>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Matrix used in linear algebra. </p>
<p>This class implements the concept of <a class="el" href="class_quant_lib_1_1_matrix.html" title="Matrix used in linear algebra.">Matrix</a> as used in linear algebra. As such, it is <b>not</b> meant to be used as a container. </p>
</div><h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a4aff113d85809ff7f25218ef8724bb9d">◆ </a></span>Matrix()</h2>
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<td class="memname"><a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> </td>
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<td class="paramname"><em>rows</em>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> </td>
<td class="paramname"><em>columns</em>, </td>
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<td class="paramtype">Iterator </td>
<td class="paramname"><em>begin</em>, </td>
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<p>creates the matrix and fills it with data from a range. </p>
<dl class="caveats"><dt><b><a class="el" href="caveats.html#_caveats000099">Warning:</a></b></dt><dd>if the range defined by [begin, end) is larger than the size of the matrix, a memory access violation might occur. It is up to the user to avoid this. </dd></dl>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#af9e9ef3ae7410799e5d1ac6b6d74dc68">◆ </a></span>operator+=()</h2>
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<td class="memname">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & operator+= </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_matrix.html">Matrix</a> & </td>
<td class="paramname"><em>m</em></td><td>)</td>
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<dl class="section pre"><dt>Precondition</dt><dd>all matrices involved in an algebraic expression must have the same size. </dd></dl>
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<h2 class="groupheader">Friends And Related Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#aac6e1b8e2666440c95b38c2b672dd10f">◆ </a></span>pseudoSqrt()</h2>
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<td class="memname"><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>
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<p>Returns the pseudo square root of a real symmetric matrix. </p>
<p>Given a matrix \( M \), the result \( S \) is defined as the matrix such that \( S S^T = M. \) 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>
<p>For more information see: R. Rebonato and P. Jäckel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, 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>
<p>Revised and extended in "Monte Carlo Methods in Finance", by Peter Jäckel, Chapter 6.</p>
<dl class="section pre"><dt>Precondition</dt><dd>the given matrix must be symmetric.</dd></dl>
<dl class="caveats"><dt><b><a class="el" href="caveats.html#_caveats000100">Warning:</a></b></dt><dd>Higham algorithm only works for correlation matrices.</dd></dl>
<dl class="test"><dt><b><a class="el" href="test.html#_test000054">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>
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<h2 class="memtitle"><span class="permalink"><a href="#ae874444cc115097ecd8c0deec4394750">◆ </a></span>rankReducedSqrt()</h2>
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<td class="memname"><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"><a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
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<td class="paramtype">SalvagingAlgorithm::Type </td>
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<p>Returns the rank-reduced pseudo square root of a real symmetric matrix. </p>
<p>The result matrix has rank<=maxRank. If maxRank>=size, then the specified percentage of eigenvalues out of the eigenvalues' sum is retained.</p>
<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="section pre"><dt>Precondition</dt><dd>the given matrix must be symmetric. </dd></dl>
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