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  • library/doc/html/chmat_8h_source.html

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    6669<a name="l00014"></a>00014 <span class="preprocessor"></span><span class="preprocessor">#define CHMAT_H</span> 
    6770<a name="l00015"></a>00015 <span class="preprocessor"></span> 
    68 <a name="l00016"></a>00016  
    69 <a name="l00017"></a>00017 <span class="preprocessor">#include "<a class="code" href="square__mat_8h.html" title="Matrices in decomposed forms (LDL&amp;#39;, LU, UDU&amp;#39;, etc).">square_mat.h</a>"</span> 
     71<a name="l00016"></a>00016 <span class="preprocessor">#include &quot;../bdmerror.h&quot;</span> 
     72<a name="l00017"></a>00017 <span class="preprocessor">#include &quot;<a class="code" href="square__mat_8h.html" title="Matrices in decomposed forms (LDL&amp;#39;, LU, UDU&amp;#39;, etc).">square_mat.h</a>&quot;</span> 
    7073<a name="l00018"></a>00018  
    71 <a name="l00024"></a><a class="code" href="classchmat.html">00024</a> <span class="keyword">class </span><a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> : <span class="keyword">public</span> <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> { 
    72 <a name="l00025"></a>00025 <span class="keyword">protected</span>: 
    73 <a name="l00027"></a><a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c">00027</a>         mat <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>; 
    74 <a name="l00028"></a>00028 <span class="keyword">public</span>: 
    75 <a name="l00029"></a>00029  
    76 <a name="l00030"></a>00030         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#bbc2d98d7455b1f38828907d442836bf">opupdt</a> ( <span class="keyword">const</span> vec &amp;v, <span class="keywordtype">double</span> w ); 
    77 <a name="l00031"></a>00031         mat <a class="code" href="classchmat.html#045addd685f8d978efda232d7dcb070e" title="Conversion to full matrix.">to_mat</a>() <span class="keyword">const</span>; 
    78 <a name="l00032"></a>00032         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#66f509f92b0ccf020e2a2a32566e0777" title="Inplace symmetric multiplication by a SQUARE matrix , i.e. .">mult_sym</a> ( <span class="keyword">const</span> mat &amp;C ); 
    79 <a name="l00033"></a>00033         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#66f509f92b0ccf020e2a2a32566e0777" title="Inplace symmetric multiplication by a SQUARE matrix , i.e. .">mult_sym</a> ( <span class="keyword">const</span> mat &amp;C , <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;U ) <span class="keyword">const</span>; 
    80 <a name="l00034"></a>00034         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#07f50d1332b901eee962e8b1913102f7" title="Inplace symmetric multiplication by a SQUARE transpose of matrix , i.e. .">mult_sym_t</a> ( <span class="keyword">const</span> mat &amp;C ); 
    81 <a name="l00035"></a>00035         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#07f50d1332b901eee962e8b1913102f7" title="Inplace symmetric multiplication by a SQUARE transpose of matrix , i.e. .">mult_sym_t</a> ( <span class="keyword">const</span> mat &amp;C, <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;U ) <span class="keyword">const</span>; 
    82 <a name="l00036"></a>00036         <span class="keywordtype">double</span> <a class="code" href="classchmat.html#b504ca818203b13e667cb3c503980382" title="Logarithm of a determinant.">logdet</a>() <span class="keyword">const</span>; 
    83 <a name="l00037"></a>00037         vec <a class="code" href="classchmat.html#b22aa239dbaca33e3fb93b4f674d7051" title="Multiplies square root of  by vector .">sqrt_mult</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
    84 <a name="l00038"></a>00038         <span class="keywordtype">double</span> <a class="code" href="classchmat.html#6807737c7ffdb7041256b51db7592248" title="Evaluates quadratic form ;.">qform</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
    85 <a name="l00039"></a>00039         <span class="keywordtype">double</span> <a class="code" href="classchmat.html#b49427cff186c62f5df3724e5d2c34b4" title="Evaluates quadratic form ;.">invqform</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
    86 <a name="l00040"></a>00040         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#d0a995d312ecc11d3b43693f5e224ba9" title="Clearing matrix so that it corresponds to zeros.">clear</a>(); 
    87 <a name="l00042"></a><a class="code" href="classchmat.html#f3921e3e5e31337cdbda40a3a5467257">00042</a>         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#f3921e3e5e31337cdbda40a3a5467257" title="add another chmat A2 with weight w.">add</a> ( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2, <span class="keywordtype">double</span> w=1.0 ) { 
    88 <a name="l00043"></a>00043                 it_assert_debug(<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>==A2.<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>,<span class="stringliteral">"Matrices of unequal dimension"</span>); 
    89 <a name="l00044"></a>00044                 mat pre=concat_vertical(<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>,sqrt(w)*A2.<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>);  
    90 <a name="l00045"></a>00045                 mat post=zeros(pre.rows(),pre.cols());  
    91 <a name="l00046"></a>00046                 <span class="keywordflow">if</span>(!qr(pre,post)) {it_warning(<span class="stringliteral">"Unstable QR in chmat add"</span>);} 
    92 <a name="l00047"></a>00047                 <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>=post(0,<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>-1,0,<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>-1); 
    93 <a name="l00048"></a>00048         }; 
    94 <a name="l00050"></a><a class="code" href="classchmat.html#5ce4e21a9012a4e98c1f0ed1ca5669bd">00050</a>         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#5ce4e21a9012a4e98c1f0ed1ca5669bd" title="Inversion in the same form, i.e. cholesky.">inv</a> ( <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;Inv )<span class="keyword"> const   </span>{ ( Inv.<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ) = itpp::inv ( <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ).T();}; <span class="comment">//Fixme: can be more efficient</span> 
    95 <a name="l00051"></a>00051         ; 
    96 <a name="l00052"></a>00052 <span class="comment">//      void inv ( mat &amp;Inv );</span> 
    97 <a name="l00053"></a>00053  
    98 <a name="l00055"></a><a class="code" href="classchmat.html#ba62fbf7cb8e065a4f3d24457824e89b">00055</a>         <span class="keyword">virtual</span> <a class="code" href="classchmat.html#ba62fbf7cb8e065a4f3d24457824e89b" title="Destructor for future use;.">~chmat</a>() {}; 
    99 <a name="l00057"></a>00057         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> ( ) : <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> (),<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ( ) {}; 
    100 <a name="l00059"></a><a class="code" href="classchmat.html#fdd73b0c596161637fd25bdf2c670c39">00059</a>         <a class="code" href="classchmat.html#fdd73b0c596161637fd25bdf2c670c39" title="Default constructor.">chmat</a> ( <span class="keyword">const</span> <span class="keywordtype">int</span> dim0 ) : <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( dim0 ),<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ( dim0,dim0 ) {}; 
    101 <a name="l00061"></a><a class="code" href="classchmat.html#d4f0a94e81279295e60e72812130f9d4">00061</a>         <a class="code" href="classchmat.html#d4f0a94e81279295e60e72812130f9d4" title="Default constructor.">chmat</a> ( <span class="keyword">const</span> vec &amp;v) : <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( v.length() ),<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ( diag(sqrt(v)) ) {}; 
    102 <a name="l00063"></a><a class="code" href="classchmat.html#d92f3bd9a727b8c88a8c7385feb3449a">00063</a>         <a class="code" href="classchmat.html#d92f3bd9a727b8c88a8c7385feb3449a" title="Copy constructor.">chmat</a> ( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;Ch0) : <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( Ch0.<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>),<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ( Ch0.<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>,Ch0.<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a> ) {<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>=Ch0.<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>;}; 
    103 <a name="l00065"></a><a class="code" href="classchmat.html#8334a00f30f0a05f893c2aeec395ef10">00065</a>         <a class="code" href="classchmat.html#8334a00f30f0a05f893c2aeec395ef10" title="Default constructor (m3k:cholform).">chmat</a> ( <span class="keyword">const</span> mat &amp;M ) : <a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( M.<a class="code" href="classsqmat.html#071e80ced9cc3b8cbb360fa7462eb646" title="Reimplementing common functions of mat: rows().">rows</a>() ),<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a> ( M.<a class="code" href="classsqmat.html#071e80ced9cc3b8cbb360fa7462eb646" title="Reimplementing common functions of mat: rows().">rows</a>(),M.<a class="code" href="classsqmat.html#ecc2e2540f95a04f4449842588170f5b" title="Reimplementing common functions of mat: cols().">cols</a>() ) { 
    104 <a name="l00066"></a>00066                 mat Q; 
    105 <a name="l00067"></a>00067                 it_assert_debug ( M.rows() ==M.cols(),<span class="stringliteral">"chmat:: input matrix must be square!"</span> ); 
    106 <a name="l00068"></a>00068                 <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>=chol ( M ); 
    107 <a name="l00069"></a>00069         }; 
    108 <a name="l00071"></a><a class="code" href="classchmat.html#24de7f42e0a86bb270588cd0dd9d60b4">00071</a>         <a class="code" href="classchmat.html#24de7f42e0a86bb270588cd0dd9d60b4" title="Constructor.">chmat</a> ( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;M, <span class="keyword">const</span> ivec &amp;perm ):<a class="code" href="classsqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a>(M.<a class="code" href="classsqmat.html#071e80ced9cc3b8cbb360fa7462eb646" title="Reimplementing common functions of mat: rows().">rows</a>()){it_error(<span class="stringliteral">"not implemneted"</span>);}; 
    109 <a name="l00073"></a><a class="code" href="classchmat.html#9c50d31c999d85d8e9d8cf2b69b6ac8c">00073</a>         mat &amp; <a class="code" href="classchmat.html#9c50d31c999d85d8e9d8cf2b69b6ac8c" title="Access function.">_Ch</a>() {<span class="keywordflow">return</span> <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>;} 
    110 <a name="l00075"></a><a class="code" href="classchmat.html#0e2982a88febb5e604f96505ea40bd95">00075</a>         <span class="keyword">const</span> mat &amp; <a class="code" href="classchmat.html#0e2982a88febb5e604f96505ea40bd95" title="Access function.">_Ch</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>;} 
    111 <a name="l00077"></a><a class="code" href="classchmat.html#a4fc7f9b0539b97c414442a22f3db6e8">00077</a>         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#a4fc7f9b0539b97c414442a22f3db6e8" title="Access functions.">setD</a> ( <span class="keyword">const</span> vec &amp;nD ) {<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>=diag ( sqrt(nD) );} 
    112 <a name="l00079"></a><a class="code" href="classchmat.html#4c8b321967b14ed2616a2abb9498a979">00079</a>         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#4c8b321967b14ed2616a2abb9498a979" title="Access functions.">setCh</a> ( <span class="keyword">const</span> vec &amp;chQ ) { 
    113 <a name="l00080"></a>00080                 it_assert_debug(chQ.length()==<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>*<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>,<span class="stringliteral">""</span>);  
    114 <a name="l00081"></a>00081                 copy_vector(dim*dim, chQ._data(), <a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>._data());  
    115 <a name="l00082"></a>00082         } 
    116 <a name="l00084"></a><a class="code" href="classchmat.html#4b9271097d8317d9514c5d0d62cccb39">00084</a>         <span class="keywordtype">void</span> <a class="code" href="classchmat.html#4b9271097d8317d9514c5d0d62cccb39" title="Access functions.">setD</a> ( <span class="keyword">const</span> vec &amp;nD, <span class="keywordtype">int</span> i ) {<span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j=i;j&lt;nD.length();j++ ) {<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>( j,j ) =sqrt(nD ( j-i ));}} <span class="comment">//Fixme can be more general</span> 
    117 <a name="l00085"></a>00085  
    118 <a name="l00087"></a>00087         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classchmat.html#6a8b39fe3a28d2c8e3fc0d74141229fb" title="Operators.">operator += </a>( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 ); 
    119 <a name="l00088"></a>00088         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classchmat.html#a8c3628a8c15eb0009e57c66fcac1a76" title="mapping of negative add operation to operators">operator -= </a>( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 ); 
    120 <a name="l00089"></a>00089         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; operator * ( <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;d ){<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>*sqrt(d); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}; 
    121 <a name="l00090"></a>00090         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; operator = ( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 ){<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>=A2.<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>;<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>=A2.<a class="code" href="classsqmat.html#0abed904bdc0882373ba9adba919689d" title="dimension of the square matrix">dim</a>;<span class="keywordflow">return</span> *<span class="keyword">this</span>;} 
    122 <a name="l00091"></a>00091         <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; operator *= ( <span class="keywordtype">double</span> x ){<a class="code" href="classchmat.html#95158bb150f5e7f939168abcd577fd9c" title="Upper triangle of the cholesky matrix.">Ch</a>*=sqrt(x); <span class="keywordflow">return</span> *<span class="keyword">this</span>;}; 
    123 <a name="l00092"></a>00092 }; 
    124 <a name="l00093"></a>00093  
    125 <a name="l00094"></a>00094  
    126 <a name="l00097"></a><a class="code" href="classchmat.html#6a8b39fe3a28d2c8e3fc0d74141229fb">00097</a> <span class="keyword">inline</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classchmat.html#6a8b39fe3a28d2c8e3fc0d74141229fb" title="Operators.">chmat::operator += </a>( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 )  {this-&gt;<a class="code" href="classchmat.html#f3921e3e5e31337cdbda40a3a5467257" title="add another chmat A2 with weight w.">add</a> ( A2 );<span class="keywordflow">return</span> *<span class="keyword">this</span>;} 
    127 <a name="l00099"></a><a class="code" href="classchmat.html#a8c3628a8c15eb0009e57c66fcac1a76">00099</a> <span class="keyword">inline</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classchmat.html#a8c3628a8c15eb0009e57c66fcac1a76" title="mapping of negative add operation to operators">chmat::operator -= </a>( <span class="keyword">const</span> <a class="code" href="classchmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 )  {this-&gt;<a class="code" href="classchmat.html#f3921e3e5e31337cdbda40a3a5467257" title="add another chmat A2 with weight w.">add</a> ( A2,-1.0 );<span class="keywordflow">return</span> *<span class="keyword">this</span>;} 
    128 <a name="l00100"></a>00100  
    129 <a name="l00101"></a>00101 <span class="preprocessor">#endif // CHMAT_H</span> 
     74<a name="l00019"></a>00019 <span class="keyword">namespace </span>bdm 
     75<a name="l00020"></a>00020 { 
     76<a name="l00021"></a>00021  
     77<a name="l00027"></a><a class="code" href="classbdm_1_1chmat.html">00027</a> <span class="keyword">class </span><a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> : <span class="keyword">public</span> <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> { 
     78<a name="l00028"></a>00028 <span class="keyword">protected</span>: 
     79<a name="l00030"></a><a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223">00030</a>         mat <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>; 
     80<a name="l00031"></a>00031 <span class="keyword">public</span>: 
     81<a name="l00032"></a>00032  
     82<a name="l00033"></a>00033         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#abea30d9ae395363e5aef36f6359b15fd">opupdt</a> ( <span class="keyword">const</span> vec &amp;v, <span class="keywordtype">double</span> w ); 
     83<a name="l00034"></a>00034         mat <a class="code" href="classbdm_1_1chmat.html#a4b4c5d4dbb8a3d585b68d936cb6df31b" title="Conversion to full matrix.">to_mat</a>() <span class="keyword">const</span>; 
     84<a name="l00035"></a>00035         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a832d1a18bbf33ee7681adf01d5d08e21" title="Inplace symmetric multiplication by a SQUARE matrix , i.e. .">mult_sym</a> ( <span class="keyword">const</span> mat &amp;C ); 
     85<a name="l00036"></a>00036         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a832d1a18bbf33ee7681adf01d5d08e21" title="Inplace symmetric multiplication by a SQUARE matrix , i.e. .">mult_sym</a> ( <span class="keyword">const</span> mat &amp;C , <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;U ) <span class="keyword">const</span>; 
     86<a name="l00037"></a>00037         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a7a4f54f1ea8b802f318de77a78f6ddb0" title="Inplace symmetric multiplication by a SQUARE transpose of matrix , i.e. .">mult_sym_t</a> ( <span class="keyword">const</span> mat &amp;C ); 
     87<a name="l00038"></a>00038         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a7a4f54f1ea8b802f318de77a78f6ddb0" title="Inplace symmetric multiplication by a SQUARE transpose of matrix , i.e. .">mult_sym_t</a> ( <span class="keyword">const</span> mat &amp;C, <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;U ) <span class="keyword">const</span>; 
     88<a name="l00039"></a>00039         <span class="keywordtype">double</span> <a class="code" href="classbdm_1_1chmat.html#a949ccd174ed19f9cfe36366cbd5c56a4" title="Logarithm of a determinant.">logdet</a>() <span class="keyword">const</span>; 
     89<a name="l00040"></a>00040         vec <a class="code" href="classbdm_1_1chmat.html#aec8d3a1cbf3b50183f246a858663c92d" title="Multiplies square root of  by vector .">sqrt_mult</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
     90<a name="l00041"></a>00041         <span class="keywordtype">double</span> <a class="code" href="classbdm_1_1chmat.html#a6e0aee9691909602d341fe5ebd1f1ca8" title="Evaluates quadratic form ;.">qform</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
     91<a name="l00042"></a>00042         <span class="keywordtype">double</span> <a class="code" href="classbdm_1_1chmat.html#a3ac8d00a14a22a21760a8374fe5c5757" title="Evaluates quadratic form ;.">invqform</a> ( <span class="keyword">const</span> vec &amp;v ) <span class="keyword">const</span>; 
     92<a name="l00043"></a>00043         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#abc753cb54aa8946ce41d95e82fc148b5" title="Clearing matrix so that it corresponds to zeros.">clear</a>(); 
     93<a name="l00045"></a><a class="code" href="classbdm_1_1chmat.html#a6b3d5b772f791fc7c5df544a418278c7">00045</a>         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a6b3d5b772f791fc7c5df544a418278c7" title="add another chmat A2 with weight w.">add</a> ( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2, <span class="keywordtype">double</span> w = 1.0 ) { 
     94<a name="l00046"></a>00046                 <a class="code" href="bdmerror_8h.html#a89a0f906b242b79c5d3d342291b2cab4" title="Throw std::runtime_exception if t is not true and NDEBUG is not defined.">bdm_assert_debug</a> ( <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> == A2.<a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a>, <span class="stringliteral">&quot;Matrices of unequal dimension&quot;</span> ); 
     95<a name="l00047"></a>00047                 mat pre = concat_vertical ( <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>, sqrt ( w ) * A2.<a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ); 
     96<a name="l00048"></a>00048                 mat post = zeros ( pre.rows(), pre.cols() ); 
     97<a name="l00049"></a>00049                 <span class="keywordflow">if</span> ( !qr ( pre, post ) ) { 
     98<a name="l00050"></a>00050                         <a class="code" href="bdmerror_8h.html#a59c5a63b3878ebcd6cc952fc2b47191c" title="Display a warning message.">bdm_warning</a> ( <span class="stringliteral">&quot;Unstable QR in chmat add&quot;</span> ); 
     99<a name="l00051"></a>00051                 } 
     100<a name="l00052"></a>00052                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> = post ( 0, <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> - 1, 0, <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> - 1 ); 
     101<a name="l00053"></a>00053         }; 
     102<a name="l00055"></a><a class="code" href="classbdm_1_1chmat.html#acbf3389db96dff41fb2e9532d59b13c0">00055</a>         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#acbf3389db96dff41fb2e9532d59b13c0" title="Inversion in the same form, i.e. cholesky.">inv</a> ( <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;Inv )<span class="keyword"> const   </span>{ 
     103<a name="l00056"></a>00056                 ( Inv.<a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ) = itpp::inv ( <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ).T(); 
     104<a name="l00057"></a>00057         }; <span class="comment">//Fixme: can be more efficient</span> 
     105<a name="l00058"></a>00058         ; 
     106<a name="l00059"></a>00059 <span class="comment">//      void inv ( mat &amp;Inv );</span> 
     107<a name="l00060"></a>00060  
     108<a name="l00062"></a><a class="code" href="classbdm_1_1chmat.html#aa888e866a163bffe94b51e58af65901b">00062</a>         <span class="keyword">virtual</span> <a class="code" href="classbdm_1_1chmat.html#aa888e866a163bffe94b51e58af65901b" title="Destructor for future use;.">~chmat</a>() {}; 
     109<a name="l00064"></a>00064         <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> ( ) : <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> (), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( ) {}; 
     110<a name="l00066"></a><a class="code" href="classbdm_1_1chmat.html#a947c52c64022ef364d8ef17c94a65ef1">00066</a>         <a class="code" href="classbdm_1_1chmat.html#a947c52c64022ef364d8ef17c94a65ef1" title="Default constructor.">chmat</a> ( <span class="keyword">const</span> <span class="keywordtype">int</span> dim0 ) : <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( dim0 ), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( dim0, dim0 ) {}; 
     111<a name="l00068"></a><a class="code" href="classbdm_1_1chmat.html#aae4dd65ff29d7d951b18903b100bd39d">00068</a>         <a class="code" href="classbdm_1_1chmat.html#aae4dd65ff29d7d951b18903b100bd39d" title="Default constructor.">chmat</a> ( <span class="keyword">const</span> vec &amp;v ) : <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( v.length() ), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( diag ( sqrt ( v ) ) ) {}; 
     112<a name="l00070"></a><a class="code" href="classbdm_1_1chmat.html#a57513fca80f91194faf90297f2ab2b24">00070</a>         <a class="code" href="classbdm_1_1chmat.html#a57513fca80f91194faf90297f2ab2b24" title="Copy constructor.">chmat</a> ( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;Ch0 ) : <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( Ch0.<a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> ), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( Ch0.<a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a>, Ch0.<a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> ) { 
     113<a name="l00071"></a>00071                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> = Ch0.<a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>; 
     114<a name="l00072"></a>00072         } 
     115<a name="l00073"></a>00073  
     116<a name="l00075"></a><a class="code" href="classbdm_1_1chmat.html#a796ee52e1343bc53d278f17c55bb1cc7">00075</a>         <a class="code" href="classbdm_1_1chmat.html#a796ee52e1343bc53d278f17c55bb1cc7" title="Default constructor (m3k:cholform).">chmat</a> ( <span class="keyword">const</span> mat &amp;M ) : <a class="code" href="classbdm_1_1sqmat.html" title="Abstract class for representation of double symmetric matrices in square-root form...">sqmat</a> ( M.<a class="code" href="classbdm_1_1sqmat.html#a73e639221343dcce76c3305524d67590" title="Reimplementing common functions of mat: rows().">rows</a>() ), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( M.<a class="code" href="classbdm_1_1sqmat.html#a73e639221343dcce76c3305524d67590" title="Reimplementing common functions of mat: rows().">rows</a>(), M.<a class="code" href="classbdm_1_1sqmat.html#a445ef762cf5d2d6cfdf53c72942363cf" title="Reimplementing common functions of mat: cols().">cols</a>() ) { 
     117<a name="l00076"></a>00076                 mat Q; 
     118<a name="l00077"></a>00077                 <a class="code" href="bdmerror_8h.html#a89a0f906b242b79c5d3d342291b2cab4" title="Throw std::runtime_exception if t is not true and NDEBUG is not defined.">bdm_assert_debug</a> ( M.rows() == M.cols(), <span class="stringliteral">&quot;chmat:: input matrix must be square!&quot;</span> ); 
     119<a name="l00078"></a>00078                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> = chol ( M ); 
     120<a name="l00079"></a>00079         } 
     121<a name="l00080"></a>00080  
     122<a name="l00085"></a><a class="code" href="classbdm_1_1chmat.html#a3c4e675e7efd91f78faa3dcf23aec153">00085</a>         <a class="code" href="classbdm_1_1chmat.html#a3c4e675e7efd91f78faa3dcf23aec153">chmat</a> ( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;M, <span class="keyword">const</span> ivec &amp;perm ) { 
     123<a name="l00086"></a>00086                 <a class="code" href="bdmerror_8h.html#a7c43f3a72afe68ab0c85663a1bb3521a" title="Unconditionally throw std::runtime_error.">bdm_error</a> ( <span class="stringliteral">&quot;not implemented&quot;</span> ); 
     124<a name="l00087"></a>00087         } 
     125<a name="l00088"></a>00088  
     126<a name="l00090"></a><a class="code" href="classbdm_1_1chmat.html#a17daa8c5c5914bd3194cb3053c5793a5">00090</a>         mat &amp; <a class="code" href="classbdm_1_1chmat.html#a17daa8c5c5914bd3194cb3053c5793a5" title="Access function.">_Ch</a>() { 
     127<a name="l00091"></a>00091                 <span class="keywordflow">return</span> <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>; 
     128<a name="l00092"></a>00092         } 
     129<a name="l00094"></a><a class="code" href="classbdm_1_1chmat.html#a3e9e137c1a6f46d13c2b6790cfddaa92">00094</a>         <span class="keyword">const</span> mat &amp; <a class="code" href="classbdm_1_1chmat.html#a3e9e137c1a6f46d13c2b6790cfddaa92" title="Access function.">_Ch</a>()<span class="keyword"> const </span>{ 
     130<a name="l00095"></a>00095                 <span class="keywordflow">return</span> <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>; 
     131<a name="l00096"></a>00096         } 
     132<a name="l00098"></a><a class="code" href="classbdm_1_1chmat.html#ab192df5b54b173ba9bc6922ee9983bc9">00098</a>         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#ab192df5b54b173ba9bc6922ee9983bc9" title="Access functions.">setD</a> ( <span class="keyword">const</span> vec &amp;nD ) { 
     133<a name="l00099"></a>00099                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> = diag ( sqrt ( nD ) ); 
     134<a name="l00100"></a>00100         } 
     135<a name="l00102"></a><a class="code" href="classbdm_1_1chmat.html#ab8fd18754b0e5e0463f818cd16c710c8">00102</a>         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#ab8fd18754b0e5e0463f818cd16c710c8" title="Access functions.">setCh</a> ( <span class="keyword">const</span> vec &amp;chQ ) { 
     136<a name="l00103"></a>00103                 <a class="code" href="bdmerror_8h.html#a89a0f906b242b79c5d3d342291b2cab4" title="Throw std::runtime_exception if t is not true and NDEBUG is not defined.">bdm_assert_debug</a> ( chQ.length() == <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> * <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a>, <span class="stringliteral">&quot;wrong length&quot;</span> ); 
     137<a name="l00104"></a>00104                 copy_vector ( dim*dim, chQ._data(), <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>._data() ); 
     138<a name="l00105"></a>00105         } 
     139<a name="l00106"></a>00106  
     140<a name="l00108"></a><a class="code" href="classbdm_1_1chmat.html#a18f4b97bde650086fe5e3d9461a13514">00108</a>         <span class="keywordtype">void</span> <a class="code" href="classbdm_1_1chmat.html#a18f4b97bde650086fe5e3d9461a13514" title="Access functions.">setD</a> ( <span class="keyword">const</span> vec &amp;nD, <span class="keywordtype">int</span> i ) { 
     141<a name="l00109"></a>00109                 <span class="keywordflow">for</span> ( <span class="keywordtype">int</span> j = i; j &lt; nD.length(); j++ ) { 
     142<a name="l00110"></a>00110                         <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> ( j, j ) = sqrt ( nD ( j - i ) );    <span class="comment">//Fixme can be more general</span> 
     143<a name="l00111"></a>00111                 } 
     144<a name="l00112"></a>00112         } 
     145<a name="l00113"></a>00113  
     146<a name="l00115"></a>00115         <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classbdm_1_1chmat.html#a029a0997afc656fde0c73bbf7724aca9" title="Operators.">operator += </a>( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 ); 
     147<a name="l00116"></a>00116         <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classbdm_1_1chmat.html#af1d0180fb795d38b8c352df2686ec5ba" title="mapping of negative add operation to operators">operator -= </a>( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp;A2 ); 
     148<a name="l00117"></a>00117         <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; operator * ( <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;d ) { 
     149<a name="l00118"></a>00118                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a>*sqrt ( d ); 
     150<a name="l00119"></a>00119                 <span class="keywordflow">return</span> *<span class="keyword">this</span>; 
     151<a name="l00120"></a>00120         }; 
     152<a name="l00121"></a>00121         chmat&amp; operator = ( <span class="keyword">const</span> chmat &amp;A2 ) { 
     153<a name="l00122"></a>00122                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> = A2.Ch; 
     154<a name="l00123"></a>00123                 <a class="code" href="classbdm_1_1sqmat.html#a05111b5744a494880e62cb0f3d42293f" title="dimension of the square matrix">dim</a> = A2.dim; 
     155<a name="l00124"></a>00124                 <span class="keywordflow">return</span> *<span class="keyword">this</span>; 
     156<a name="l00125"></a>00125         } 
     157<a name="l00126"></a>00126         chmat&amp; operator *= ( <span class="keywordtype">double</span> x ) { 
     158<a name="l00127"></a>00127                 <a class="code" href="classbdm_1_1chmat.html#a3e4f39b1895a0a870f8db98329635223" title="Upper triangle of the cholesky matrix.">Ch</a> *= sqrt ( x ); 
     159<a name="l00128"></a>00128                 <span class="keywordflow">return</span> *<span class="keyword">this</span>; 
     160<a name="l00129"></a>00129         }; 
     161<a name="l00130"></a>00130 }; 
     162<a name="l00131"></a>00131  
     163<a name="l00132"></a>00132  
     164<a name="l00135"></a><a class="code" href="classbdm_1_1chmat.html#a029a0997afc656fde0c73bbf7724aca9">00135</a> <span class="keyword">inline</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classbdm_1_1chmat.html#a029a0997afc656fde0c73bbf7724aca9" title="Operators.">chmat::operator += </a>( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp; A2 )  { 
     165<a name="l00136"></a>00136         this-&gt;<a class="code" href="classbdm_1_1chmat.html#a6b3d5b772f791fc7c5df544a418278c7" title="add another chmat A2 with weight w.">add</a> ( A2 ); 
     166<a name="l00137"></a>00137         <span class="keywordflow">return</span> *<span class="keyword">this</span>; 
     167<a name="l00138"></a>00138 } 
     168<a name="l00140"></a><a class="code" href="classbdm_1_1chmat.html#af1d0180fb795d38b8c352df2686ec5ba">00140</a> <span class="keyword">inline</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a>&amp; <a class="code" href="classbdm_1_1chmat.html#af1d0180fb795d38b8c352df2686ec5ba" title="mapping of negative add operation to operators">chmat::operator -= </a>( <span class="keyword">const</span> <a class="code" href="classbdm_1_1chmat.html" title="Symmetric matrix stored in square root decomposition using upper cholesky.">chmat</a> &amp; A2 )  { 
     169<a name="l00141"></a>00141         this-&gt;<a class="code" href="classbdm_1_1chmat.html#a6b3d5b772f791fc7c5df544a418278c7" title="add another chmat A2 with weight w.">add</a> ( A2, -1.0 ); 
     170<a name="l00142"></a>00142         <span class="keywordflow">return</span> *<span class="keyword">this</span>; 
     171<a name="l00143"></a>00143 } 
     172<a name="l00144"></a>00144  
     173<a name="l00145"></a>00145 } 
     174<a name="l00146"></a>00146  
     175<a name="l00147"></a>00147 <span class="preprocessor">#endif // CHMAT_H</span> 
    130176</pre></div></div> 
    131 <hr size="1"><address style="text-align: right;"><small>Generated on Wed Aug 5 00:06:46 2009 for mixpp by&nbsp; 
     177<hr size="1"/><address style="text-align: right;"><small>Generated on Sun Aug 30 22:10:49 2009 for mixpp by&nbsp; 
    132178<a href="http://www.doxygen.org/index.html"> 
    133 <img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.9 </small></address> 
     179<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.6.1 </small></address> 
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