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61	<h1>Matrix Decompositions<br>
62	<small>
63	[<a class="el" href="group__algebra.html">Linear Algebra</a>]</small>
64	</h1><table border="0" cellpadding="0" cellspacing="0">
65	<tr><td></td></tr>
66	<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
67	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g4d631e12d5d0079f7f75ee4f6451043e">itpp::chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &F)</td></tr>
68
69	<tr><td class="mdescLeft"> </td><td class="mdescRight">Cholesky factorisation of real symmetric and positive definite matrix. <a href="#g4d631e12d5d0079f7f75ee4f6451043e"></a><br></td></tr>
70	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g8aa42136e884519422d4f2dd95e51cb5">itpp::chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
71
72	<tr><td class="mdescLeft"> </td><td class="mdescRight">Cholesky factorisation of real symmetric and positive definite matrix. <a href="#g8aa42136e884519422d4f2dd95e51cb5"></a><br></td></tr>
73	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g217ccba3338767ac64ad1b2465b76029">itpp::chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &F)</td></tr>
74
75	<tr><td class="mdescLeft"> </td><td class="mdescRight">Cholesky factorisation of complex hermitian and positive-definite matrix. <a href="#g217ccba3338767ac64ad1b2465b76029"></a><br></td></tr>
76	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g976aa7781da316c23ea0aad3af2511d8">itpp::chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
77
78	<tr><td class="mdescLeft"> </td><td class="mdescRight">Cholesky factorisation of complex hermitian and positive-definite matrix. <a href="#g976aa7781da316c23ea0aad3af2511d8"></a><br></td></tr>
79	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g05eced45f3e27b8f60ffa422f02856df">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &d, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &V)</td></tr>
80
81	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues and eigenvectors of a symmetric real matrix. <a href="#g05eced45f3e27b8f60ffa422f02856df"></a><br></td></tr>
82	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g282eeffd56bf6ac0fb3e8efedb755cee">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &d)</td></tr>
83
84	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a symmetric real matrix. <a href="#g282eeffd56bf6ac0fb3e8efedb755cee"></a><br></td></tr>
85	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gebf551d77c5738033d081e35e7cd9cb6">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A)</td></tr>
86
87	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a symmetric real matrix. <a href="#gebf551d77c5738033d081e35e7cd9cb6"></a><br></td></tr>
88	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g40bacb19d51c45a59837ab38f04dabef">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &d, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &V)</td></tr>
89
90	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues and eigenvectors of a hermitian complex matrix. <a href="#g40bacb19d51c45a59837ab38f04dabef"></a><br></td></tr>
91	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g89faa81cc5408f5e1452d5fec9fea473">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &d)</td></tr>
92
93	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a hermitian complex matrix. <a href="#g89faa81cc5408f5e1452d5fec9fea473"></a><br></td></tr>
94	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g6dc61c925d40d736effa9dcbe7912df1">itpp::eig_sym</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A)</td></tr>
95
96	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a hermitian complex matrix. <a href="#g6dc61c925d40d736effa9dcbe7912df1"></a><br></td></tr>
97	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gdc7223ef54536dfc36d3e183468297b8">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &d, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &V)</td></tr>
98
99	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues and eigenvectors of a real non-symmetric matrix. <a href="#gdc7223ef54536dfc36d3e183468297b8"></a><br></td></tr>
100	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#ga4e8c2f66e19625dc7c1d15a04cf9e63">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &d)</td></tr>
101
102	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a real non-symmetric matrix. <a href="#ga4e8c2f66e19625dc7c1d15a04cf9e63"></a><br></td></tr>
103	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g7c9a5795e0c4e8e406977a95525557ba">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A)</td></tr>
104
105	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a real non-symmetric matrix. <a href="#g7c9a5795e0c4e8e406977a95525557ba"></a><br></td></tr>
106	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g8be5168b8699ab6772d2c24c183b5b44">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &d, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &V)</td></tr>
107
108	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix. <a href="#g8be5168b8699ab6772d2c24c183b5b44"></a><br></td></tr>
109	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gb874193ee0377616736ba5895a13dcab">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &d)</td></tr>
110
111	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a complex non-hermitian matrix. <a href="#gb874193ee0377616736ba5895a13dcab"></a><br></td></tr>
112	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gffe65e88bce986d9ff527b06d573e4b7">itpp::eig</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A)</td></tr>
113
114	<tr><td class="mdescLeft"> </td><td class="mdescRight">Calculates the eigenvalues of a complex non-hermitian matrix. <a href="#gffe65e88bce986d9ff527b06d573e4b7"></a><br></td></tr>
115	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g470eed4741289d81759d441e316f92f0">itpp::lu</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &L, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, <a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> &p)</td></tr>
116
117	<tr><td class="mdescLeft"> </td><td class="mdescRight">LU factorisation of real matrix. <a href="#g470eed4741289d81759d441e316f92f0"></a><br></td></tr>
118	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g9912a15ea024f75442720c1bf3b5dac1">itpp::lu</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &L, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &U, <a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> &p)</td></tr>
119
120	<tr><td class="mdescLeft"> </td><td class="mdescRight">LU factorisation of real matrix. <a href="#g9912a15ea024f75442720c1bf3b5dac1"></a><br></td></tr>
121	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="g2d3af51d172dd39a7f8a631a17120057"></a><!-- doxytag: member="matrixdecomp::interchange_permutations" ref="g2d3af51d172dd39a7f8a631a17120057" args="(vec &b, const ivec &p)" -->
122	void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g2d3af51d172dd39a7f8a631a17120057">itpp::interchange_permutations</a> (<a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, const <a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> &p)</td></tr>
123
124	<tr><td class="mdescLeft"> </td><td class="mdescRight">Makes swapping of vector b according to the interchange permutation vector p. <br></td></tr>
125	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="gb6e7ba47c63173084cf0cb6bebbff508"></a><!-- doxytag: member="matrixdecomp::permutation_matrix" ref="gb6e7ba47c63173084cf0cb6bebbff508" args="(const ivec &p)" -->
126	<a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gb6e7ba47c63173084cf0cb6bebbff508">itpp::permutation_matrix</a> (const <a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> &p)</td></tr>
127
128	<tr><td class="mdescLeft"> </td><td class="mdescRight">Make permutation matrix P from the interchange permutation vector p. <br></td></tr>
129	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g9e565beb0ca5841655a5ac3700821e2c">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &Q, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &R)</td></tr>
130
131	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of real matrix. <a href="#g9e565beb0ca5841655a5ac3700821e2c"></a><br></td></tr>
132	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gbd50eeb4508aaf4b7296f3a904458886">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &R)</td></tr>
133
134	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of real matrix with suppressed evaluation of Q. <a href="#gbd50eeb4508aaf4b7296f3a904458886"></a><br></td></tr>
135	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g83c28d9b53d73b1d9527cf14341637ff">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &Q, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &R, <a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> &P)</td></tr>
136
137	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of real matrix with pivoting. <a href="#g83c28d9b53d73b1d9527cf14341637ff"></a><br></td></tr>
138	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g321c23bad4ec43d1111f405587a9ffa2">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &Q, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &R)</td></tr>
139
140	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of a complex matrix. <a href="#g321c23bad4ec43d1111f405587a9ffa2"></a><br></td></tr>
141	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g1a880a8a274c14e51482293181b1a10e">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &R)</td></tr>
142
143	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of complex matrix with suppressed evaluation of Q. <a href="#g1a880a8a274c14e51482293181b1a10e"></a><br></td></tr>
144	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gdb3c49c28626013e0679b2ce088b8d70">itpp::qr</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &Q, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &R, <a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> &P)</td></tr>
145
146	<tr><td class="mdescLeft"> </td><td class="mdescRight">QR factorisation of a complex matrix with pivoting. <a href="#gdb3c49c28626013e0679b2ce088b8d70"></a><br></td></tr>
147	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#ga0c6711c11ece9641878d3ab19f39d33">itpp::schur</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &T)</td></tr>
148
149	<tr><td class="mdescLeft"> </td><td class="mdescRight">Schur decomposition of a real matrix. <a href="#ga0c6711c11ece9641878d3ab19f39d33"></a><br></td></tr>
150	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g5a511c9baeb36e803a006b3172848800">itpp::schur</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A)</td></tr>
151
152	<tr><td class="mdescLeft"> </td><td class="mdescRight">Schur decomposition of a real matrix. <a href="#g5a511c9baeb36e803a006b3172848800"></a><br></td></tr>
153	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gcdfbe918727616dbc8eda854c4bf0cc4">itpp::schur</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &U, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &T)</td></tr>
154
155	<tr><td class="mdescLeft"> </td><td class="mdescRight">Schur decomposition of a complex matrix. <a href="#gcdfbe918727616dbc8eda854c4bf0cc4"></a><br></td></tr>
156	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#gd1d1f3ad1c35dee4ded80cc86c5961cc">itpp::schur</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A)</td></tr>
157
158	<tr><td class="mdescLeft"> </td><td class="mdescRight">Schur decomposition of a complex matrix. <a href="#gd1d1f3ad1c35dee4ded80cc86c5961cc"></a><br></td></tr>
159	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g9fcc7191c3cee4db65e51d93123c7fba">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &s)</td></tr>
160
161	<tr><td class="mdescLeft"> </td><td class="mdescRight">Get singular values <code>s</code> of a real matrix <code>A</code> using SVD. <a href="#g9fcc7191c3cee4db65e51d93123c7fba"></a><br></td></tr>
162	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g92dd138100c619c71ba24b3dae0dec72">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &s)</td></tr>
163
164	<tr><td class="mdescLeft"> </td><td class="mdescRight">Get singular values <code>s</code> of a complex matrix <code>A</code> using SVD. <a href="#g92dd138100c619c71ba24b3dae0dec72"></a><br></td></tr>
165	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#ge3b83ff6532c19ec15ffe76450b70e2c">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A)</td></tr>
166
167	<tr><td class="mdescLeft"> </td><td class="mdescRight">Return singular values of a real matrix <code>A</code> using SVD. <a href="#ge3b83ff6532c19ec15ffe76450b70e2c"></a><br></td></tr>
168	<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#ga53763a60632139d71957ea7cf0080c9">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A)</td></tr>
169
170	<tr><td class="mdescLeft"> </td><td class="mdescRight">Return singular values of a complex matrix <code>A</code> using SVD. <a href="#ga53763a60632139d71957ea7cf0080c9"></a><br></td></tr>
171	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g908131485c5c53ed2e84e2f0a258db8c">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &s, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &V)</td></tr>
172
173	<tr><td class="mdescLeft"> </td><td class="mdescRight">Perform Singular Value Decomposition (SVD) of a real matrix <code>A</code>. <a href="#g908131485c5c53ed2e84e2f0a258db8c"></a><br></td></tr>
174	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__matrixdecomp.html#g98a4dc87128a758f82ed05d7b060958b">itpp::svd</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &U, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &s, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &V)</td></tr>
175
176	<tr><td class="mdescLeft"> </td><td class="mdescRight">Perform Singular Value Decomposition (SVD) of a complex matrix <code>A</code>. <a href="#g98a4dc87128a758f82ed05d7b060958b"></a><br></td></tr>
177	</table>
178	<hr><h2>Function Documentation</h2>
179	<a class="anchor" name="g976aa7781da316c23ea0aad3af2511d8"></a><!-- doxytag: member="itpp::chol" ref="g976aa7781da316c23ea0aad3af2511d8" args="(const cmat &X)" -->
180	<div class="memitem">
181	<div class="memproto">
182	<table class="memname">
183	<tr>
184	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::chol </td>
185	<td>(</td>
186	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
187	<td class="paramname"> <em>X</em> </td>
188	<td> ) </td>
189	<td></td>
190	</tr>
191	</table>
192	</div>
193	<div class="memdoc">
194
195	<p>
196	Cholesky factorisation of complex hermitian and positive-definite matrix.
197	<p>
198	The Cholesky factorisation of a hermitian positive-definite matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
199	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{F}^H \mathbf{F} \]" src="form_129.png">
200	<p>
201	where <img class="formulaInl" alt="$\mathbf{F}$" src="form_128.png"> is an upper triangular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix.
202	<p>References <a class="el" href="cholesky_8cpp-source.html#l00111">itpp::chol()</a>, and <a class="el" href="itassert_8h-source.html#l00173">it_warning</a>.</p>
203
204	</div>
205	</div><p>
206	<a class="anchor" name="g217ccba3338767ac64ad1b2465b76029"></a><!-- doxytag: member="itpp::chol" ref="g217ccba3338767ac64ad1b2465b76029" args="(const cmat &X, cmat &F)" -->
207	<div class="memitem">
208	<div class="memproto">
209	<table class="memname">
210	<tr>
211	<td class="memname">bool itpp::chol </td>
212	<td>(</td>
213	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
214	<td class="paramname"> <em>X</em>, </td>
215	</tr>
216	<tr>
217	<td class="paramkey"></td>
218	<td></td>
219	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
220	<td class="paramname"> <em>F</em></td><td> </td>
221	</tr>
222	<tr>
223	<td></td>
224	<td>)</td>
225	<td></td><td></td><td></td>
226	</tr>
227	</table>
228	</div>
229	<div class="memdoc">
230
231	<p>
232	Cholesky factorisation of complex hermitian and positive-definite matrix.
233	<p>
234	The Cholesky factorisation of a hermitian positive-definite matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
235	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{F}^H \mathbf{F} \]" src="form_129.png">
236	<p>
237	where <img class="formulaInl" alt="$\mathbf{F}$" src="form_128.png"> is an upper triangular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix.<p>
238	Returns true if calculation succeeded. False otherwise.<p>
239	If <code>X</code> is positive definite, true is returned and <code>F=chol</code>(X) produces an upper triangular <code>F</code>. If also <code>X</code> is symmetric then <code>F'*F</code> = X. If <code>X</code> is not positive definite, false is returned.
240	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
241
242	</div>
243	</div><p>
244	<a class="anchor" name="g8aa42136e884519422d4f2dd95e51cb5"></a><!-- doxytag: member="itpp::chol" ref="g8aa42136e884519422d4f2dd95e51cb5" args="(const mat &X)" -->
245	<div class="memitem">
246	<div class="memproto">
247	<table class="memname">
248	<tr>
249	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::chol </td>
250	<td>(</td>
251	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
252	<td class="paramname"> <em>X</em> </td>
253	<td> ) </td>
254	<td></td>
255	</tr>
256	</table>
257	</div>
258	<div class="memdoc">
259
260	<p>
261	Cholesky factorisation of real symmetric and positive definite matrix.
262	<p>
263	The Cholesky factorisation of a real symmetric positive-definite matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
264	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{F}^T \mathbf{F} \]" src="form_127.png">
265	<p>
266	where <img class="formulaInl" alt="$\mathbf{F}$" src="form_128.png"> is an upper triangular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix.
267	<p>References <a class="el" href="itassert_8h-source.html#l00173">it_warning</a>.</p>
268
269	<p>Referenced by <a class="el" href="chmat_8h-source.html#l00059">chmat::chmat()</a>, <a class="el" href="cholesky_8cpp-source.html#l00101">itpp::chol()</a>, <a class="el" href="libDC_8cpp-source.html#l00046">ldmat::ldmat()</a>, and <a class="el" href="libDC_8h-source.html#l00159">fsqmat::sqrt_mult()</a>.</p>
270
271	</div>
272	</div><p>
273	<a class="anchor" name="g4d631e12d5d0079f7f75ee4f6451043e"></a><!-- doxytag: member="itpp::chol" ref="g4d631e12d5d0079f7f75ee4f6451043e" args="(const mat &X, mat &F)" -->
274	<div class="memitem">
275	<div class="memproto">
276	<table class="memname">
277	<tr>
278	<td class="memname">bool itpp::chol </td>
279	<td>(</td>
280	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
281	<td class="paramname"> <em>X</em>, </td>
282	</tr>
283	<tr>
284	<td class="paramkey"></td>
285	<td></td>
286	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
287	<td class="paramname"> <em>F</em></td><td> </td>
288	</tr>
289	<tr>
290	<td></td>
291	<td>)</td>
292	<td></td><td></td><td></td>
293	</tr>
294	</table>
295	</div>
296	<div class="memdoc">
297
298	<p>
299	Cholesky factorisation of real symmetric and positive definite matrix.
300	<p>
301	The Cholesky factorisation of a real symmetric positive-definite matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
302	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{F}^T \mathbf{F} \]" src="form_127.png">
303	<p>
304	where <img class="formulaInl" alt="$\mathbf{F}$" src="form_128.png"> is an upper triangular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix.<p>
305	Returns true if calculation succeeded. False otherwise.
306	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
307
308	</div>
309	</div><p>
310	<a class="anchor" name="gffe65e88bce986d9ff527b06d573e4b7"></a><!-- doxytag: member="itpp::eig" ref="gffe65e88bce986d9ff527b06d573e4b7" args="(const cmat &A)" -->
311	<div class="memitem">
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315	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::eig </td>
316	<td>(</td>
317	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
318	<td class="paramname"> <em>A</em> </td>
319	<td> ) </td>
320	<td></td>
321	</tr>
322	</table>
323	</div>
324	<div class="memdoc">
325
326	<p>
327	Calculates the eigenvalues of a complex non-hermitian matrix.
328	<p>
329	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
330	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
331	<p>
332	<p>
333	Uses the LAPACK routine ZGEEV.
334	<p>Referenced by <a class="el" href="eigen_8cpp-source.html#l00318">itpp::eig()</a>, and <a class="el" href="poly_8cpp-source.html#l00066">itpp::roots()</a>.</p>
335
336	</div>
337	</div><p>
338	<a class="anchor" name="gb874193ee0377616736ba5895a13dcab"></a><!-- doxytag: member="itpp::eig" ref="gb874193ee0377616736ba5895a13dcab" args="(const cmat &A, cvec &d)" -->
339	<div class="memitem">
340	<div class="memproto">
341	<table class="memname">
342	<tr>
343	<td class="memname">bool itpp::eig </td>
344	<td>(</td>
345	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
346	<td class="paramname"> <em>A</em>, </td>
347	</tr>
348	<tr>
349	<td class="paramkey"></td>
350	<td></td>
351	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
352	<td class="paramname"> <em>d</em></td><td> </td>
353	</tr>
354	<tr>
355	<td></td>
356	<td>)</td>
357	<td></td><td></td><td></td>
358	</tr>
359	</table>
360	</div>
361	<div class="memdoc">
362
363	<p>
364	Calculates the eigenvalues of a complex non-hermitian matrix.
365	<p>
366	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
367	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
368	<p>
369	True is returned if the calculation was successful. Otherwise false.<p>
370	Uses the LAPACK routine ZGEEV.
371	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
372
373	</div>
374	</div><p>
375	<a class="anchor" name="g8be5168b8699ab6772d2c24c183b5b44"></a><!-- doxytag: member="itpp::eig" ref="g8be5168b8699ab6772d2c24c183b5b44" args="(const cmat &A, cvec &d, cmat &V)" -->
376	<div class="memitem">
377	<div class="memproto">
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379	<tr>
380	<td class="memname">bool itpp::eig </td>
381	<td>(</td>
382	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
383	<td class="paramname"> <em>A</em>, </td>
384	</tr>
385	<tr>
386	<td class="paramkey"></td>
387	<td></td>
388	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
389	<td class="paramname"> <em>d</em>, </td>
390	</tr>
391	<tr>
392	<td class="paramkey"></td>
393	<td></td>
394	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
395	<td class="paramname"> <em>V</em></td><td> </td>
396	</tr>
397	<tr>
398	<td></td>
399	<td>)</td>
400	<td></td><td></td><td></td>
401	</tr>
402	</table>
403	</div>
404	<div class="memdoc">
405
406	<p>
407	Calculates the eigenvalues and eigenvectors of a complex non-hermitian matrix.
408	<p>
409	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
410	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
411	<p>
412	The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false.<p>
413	Uses the LAPACK routine ZGEEV.
414	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
415
416	</div>
417	</div><p>
418	<a class="anchor" name="g7c9a5795e0c4e8e406977a95525557ba"></a><!-- doxytag: member="itpp::eig" ref="g7c9a5795e0c4e8e406977a95525557ba" args="(const mat &A)" -->
419	<div class="memitem">
420	<div class="memproto">
421	<table class="memname">
422	<tr>
423	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::eig </td>
424	<td>(</td>
425	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
426	<td class="paramname"> <em>A</em> </td>
427	<td> ) </td>
428	<td></td>
429	</tr>
430	</table>
431	</div>
432	<div class="memdoc">
433
434	<p>
435	Calculates the eigenvalues of a real non-symmetric matrix.
436	<p>
437	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
438	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
439	<p>
440	<p>
441	Uses the LAPACK routine DGEEV.
442	<p>References <a class="el" href="eigen_8cpp-source.html#l00325">itpp::eig()</a>.</p>
443
444	</div>
445	</div><p>
446	<a class="anchor" name="ga4e8c2f66e19625dc7c1d15a04cf9e63"></a><!-- doxytag: member="itpp::eig" ref="ga4e8c2f66e19625dc7c1d15a04cf9e63" args="(const mat &A, cvec &d)" -->
447	<div class="memitem">
448	<div class="memproto">
449	<table class="memname">
450	<tr>
451	<td class="memname">bool itpp::eig </td>
452	<td>(</td>
453	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
454	<td class="paramname"> <em>A</em>, </td>
455	</tr>
456	<tr>
457	<td class="paramkey"></td>
458	<td></td>
459	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
460	<td class="paramname"> <em>d</em></td><td> </td>
461	</tr>
462	<tr>
463	<td></td>
464	<td>)</td>
465	<td></td><td></td><td></td>
466	</tr>
467	</table>
468	</div>
469	<div class="memdoc">
470
471	<p>
472	Calculates the eigenvalues of a real non-symmetric matrix.
473	<p>
474	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
475	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
476	<p>
477	True is returned if the calculation was successful. Otherwise false.<p>
478	Uses the LAPACK routine DGEEV.
479	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
480
481	</div>
482	</div><p>
483	<a class="anchor" name="gdc7223ef54536dfc36d3e183468297b8"></a><!-- doxytag: member="itpp::eig" ref="gdc7223ef54536dfc36d3e183468297b8" args="(const mat &A, cvec &d, cmat &V)" -->
484	<div class="memitem">
485	<div class="memproto">
486	<table class="memname">
487	<tr>
488	<td class="memname">bool itpp::eig </td>
489	<td>(</td>
490	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
491	<td class="paramname"> <em>A</em>, </td>
492	</tr>
493	<tr>
494	<td class="paramkey"></td>
495	<td></td>
496	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
497	<td class="paramname"> <em>d</em>, </td>
498	</tr>
499	<tr>
500	<td class="paramkey"></td>
501	<td></td>
502	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
503	<td class="paramname"> <em>V</em></td><td> </td>
504	</tr>
505	<tr>
506	<td></td>
507	<td>)</td>
508	<td></td><td></td><td></td>
509	</tr>
510	</table>
511	</div>
512	<div class="memdoc">
513
514	<p>
515	Calculates the eigenvalues and eigenvectors of a real non-symmetric matrix.
516	<p>
517	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
518	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
519	<p>
520	The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false.<p>
521	Uses the LAPACK routine DGEEV.
522	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
523
524	</div>
525	</div><p>
526	<a class="anchor" name="g6dc61c925d40d736effa9dcbe7912df1"></a><!-- doxytag: member="itpp::eig_sym" ref="g6dc61c925d40d736effa9dcbe7912df1" args="(const cmat &A)" -->
527	<div class="memitem">
528	<div class="memproto">
529	<table class="memname">
530	<tr>
531	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::eig_sym </td>
532	<td>(</td>
533	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
534	<td class="paramname"> <em>A</em> </td>
535	<td> ) </td>
536	<td></td>
537	</tr>
538	</table>
539	</div>
540	<div class="memdoc">
541
542	<p>
543	Calculates the eigenvalues of a hermitian complex matrix.
544	<p>
545	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex and hermitian <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
546	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
547	<p>
548	<p>
549	Uses the LAPACK routine ZHEEV.
550	<p>Referenced by <a class="el" href="eigen_8cpp-source.html#l00303">itpp::eig_sym()</a>.</p>
551
552	</div>
553	</div><p>
554	<a class="anchor" name="g89faa81cc5408f5e1452d5fec9fea473"></a><!-- doxytag: member="itpp::eig_sym" ref="g89faa81cc5408f5e1452d5fec9fea473" args="(const cmat &A, vec &d)" -->
555	<div class="memitem">
556	<div class="memproto">
557	<table class="memname">
558	<tr>
559	<td class="memname">bool itpp::eig_sym </td>
560	<td>(</td>
561	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
562	<td class="paramname"> <em>A</em>, </td>
563	</tr>
564	<tr>
565	<td class="paramkey"></td>
566	<td></td>
567	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
568	<td class="paramname"> <em>d</em></td><td> </td>
569	</tr>
570	<tr>
571	<td></td>
572	<td>)</td>
573	<td></td><td></td><td></td>
574	</tr>
575	</table>
576	</div>
577	<div class="memdoc">
578
579	<p>
580	Calculates the eigenvalues of a hermitian complex matrix.
581	<p>
582	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex and hermitian <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
583	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
584	<p>
585	True is returned if the calculation was successful. Otherwise false.<p>
586	Uses the LAPACK routine ZHEEV.
587	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
588
589	</div>
590	</div><p>
591	<a class="anchor" name="g40bacb19d51c45a59837ab38f04dabef"></a><!-- doxytag: member="itpp::eig_sym" ref="g40bacb19d51c45a59837ab38f04dabef" args="(const cmat &A, vec &d, cmat &V)" -->
592	<div class="memitem">
593	<div class="memproto">
594	<table class="memname">
595	<tr>
596	<td class="memname">bool itpp::eig_sym </td>
597	<td>(</td>
598	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
599	<td class="paramname"> <em>A</em>, </td>
600	</tr>
601	<tr>
602	<td class="paramkey"></td>
603	<td></td>
604	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
605	<td class="paramname"> <em>d</em>, </td>
606	</tr>
607	<tr>
608	<td class="paramkey"></td>
609	<td></td>
610	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
611	<td class="paramname"> <em>V</em></td><td> </td>
612	</tr>
613	<tr>
614	<td></td>
615	<td>)</td>
616	<td></td><td></td><td></td>
617	</tr>
618	</table>
619	</div>
620	<div class="memdoc">
621
622	<p>
623	Calculates the eigenvalues and eigenvectors of a hermitian complex matrix.
624	<p>
625	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the complex and hermitian <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
626	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
627	<p>
628	The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false.<p>
629	Uses the LAPACK routine ZHEEV.
630	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
631
632	</div>
633	</div><p>
634	<a class="anchor" name="gebf551d77c5738033d081e35e7cd9cb6"></a><!-- doxytag: member="itpp::eig_sym" ref="gebf551d77c5738033d081e35e7cd9cb6" args="(const mat &A)" -->
635	<div class="memitem">
636	<div class="memproto">
637	<table class="memname">
638	<tr>
639	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::eig_sym </td>
640	<td>(</td>
641	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
642	<td class="paramname"> <em>A</em> </td>
643	<td> ) </td>
644	<td></td>
645	</tr>
646	</table>
647	</div>
648	<div class="memdoc">
649
650	<p>
651	Calculates the eigenvalues of a symmetric real matrix.
652	<p>
653	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real and symmetric <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
654	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
655	<p>
656	<p>
657	Uses the LAPACK routine DSYEV.
658	<p>References <a class="el" href="eigen_8cpp-source.html#l00310">itpp::eig_sym()</a>.</p>
659
660	</div>
661	</div><p>
662	<a class="anchor" name="g282eeffd56bf6ac0fb3e8efedb755cee"></a><!-- doxytag: member="itpp::eig_sym" ref="g282eeffd56bf6ac0fb3e8efedb755cee" args="(const mat &A, vec &d)" -->
663	<div class="memitem">
664	<div class="memproto">
665	<table class="memname">
666	<tr>
667	<td class="memname">bool itpp::eig_sym </td>
668	<td>(</td>
669	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
670	<td class="paramname"> <em>A</em>, </td>
671	</tr>
672	<tr>
673	<td class="paramkey"></td>
674	<td></td>
675	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
676	<td class="paramname"> <em>d</em></td><td> </td>
677	</tr>
678	<tr>
679	<td></td>
680	<td>)</td>
681	<td></td><td></td><td></td>
682	</tr>
683	</table>
684	</div>
685	<div class="memdoc">
686
687	<p>
688	Calculates the eigenvalues of a symmetric real matrix.
689	<p>
690	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real and symmetric <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
691	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
692	<p>
693	True is returned if the calculation was successful. Otherwise false.<p>
694	Uses the LAPACK routine DSYEV.
695	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
696
697	</div>
698	</div><p>
699	<a class="anchor" name="g05eced45f3e27b8f60ffa422f02856df"></a><!-- doxytag: member="itpp::eig_sym" ref="g05eced45f3e27b8f60ffa422f02856df" args="(const mat &A, vec &d, mat &V)" -->
700	<div class="memitem">
701	<div class="memproto">
702	<table class="memname">
703	<tr>
704	<td class="memname">bool itpp::eig_sym </td>
705	<td>(</td>
706	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
707	<td class="paramname"> <em>A</em>, </td>
708	</tr>
709	<tr>
710	<td class="paramkey"></td>
711	<td></td>
712	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
713	<td class="paramname"> <em>d</em>, </td>
714	</tr>
715	<tr>
716	<td class="paramkey"></td>
717	<td></td>
718	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
719	<td class="paramname"> <em>V</em></td><td> </td>
720	</tr>
721	<tr>
722	<td></td>
723	<td>)</td>
724	<td></td><td></td><td></td>
725	</tr>
726	</table>
727	</div>
728	<div class="memdoc">
729
730	<p>
731	Calculates the eigenvalues and eigenvectors of a symmetric real matrix.
732	<p>
733	The Eigenvalues <img class="formulaInl" alt="$\mathbf{d}(d_0, d_1, \ldots, d_{n-1})$" src="form_132.png"> and the eigenvectors <img class="formulaInl" alt="$\mathbf{v}_i, \: i=0, \ldots, n-1$" src="form_133.png"> of the real and symmetric <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> satisfies <p class="formulaDsp">
734	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{v}_i = d_i \mathbf{v}_i\: i=0, \ldots, n-1. \]" src="form_135.png">
735	<p>
736	The eigenvectors are the columns of the matrix V. True is returned if the calculation was successful. Otherwise false.<p>
737	Uses the LAPACK routine DSYEV.
738	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
739
740	</div>
741	</div><p>
742	<a class="anchor" name="g9912a15ea024f75442720c1bf3b5dac1"></a><!-- doxytag: member="itpp::lu" ref="g9912a15ea024f75442720c1bf3b5dac1" args="(const cmat &X, cmat &L, cmat &U, ivec &p)" -->
743	<div class="memitem">
744	<div class="memproto">
745	<table class="memname">
746	<tr>
747	<td class="memname">bool itpp::lu </td>
748	<td>(</td>
749	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
750	<td class="paramname"> <em>X</em>, </td>
751	</tr>
752	<tr>
753	<td class="paramkey"></td>
754	<td></td>
755	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
756	<td class="paramname"> <em>L</em>, </td>
757	</tr>
758	<tr>
759	<td class="paramkey"></td>
760	<td></td>
761	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
762	<td class="paramname"> <em>U</em>, </td>
763	</tr>
764	<tr>
765	<td class="paramkey"></td>
766	<td></td>
767	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> & </td>
768	<td class="paramname"> <em>p</em></td><td> </td>
769	</tr>
770	<tr>
771	<td></td>
772	<td>)</td>
773	<td></td><td></td><td></td>
774	</tr>
775	</table>
776	</div>
777	<div class="memdoc">
778
779	<p>
780	LU factorisation of real matrix.
781	<p>
782	The LU factorization of the complex matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
783	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} , \]" src="form_143.png">
784	<p>
785	where <img class="formulaInl" alt="$\mathbf{L}$" src="form_144.png"> and <img class="formulaInl" alt="$\mathbf{U}$" src="form_145.png"> are lower and upper triangular matrices and <img class="formulaInl" alt="$\mathbf{P}$" src="form_146.png"> is a permutation matrix.<p>
786	The interchange permutation vector <em>p</em> is such that <em>k</em> and <em>p(k)</em> should be changed for all <em>k</em>. Given this vector a permutation matrix can be constructed using the function <div class="fragment"><pre class="fragment"> <a class="code" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69" title="bin matrix">bmat</a> <a class="code" href="group__matrixdecomp.html#gb6e7ba47c63173084cf0cb6bebbff508" title="Make permutation matrix P from the interchange permutation vector p.">permutation_matrix</a>(<span class="keyword">const</span> ivec &p)
787	</pre></div><p>
788	If <em>X</em> is an <em>n</em> by <em>n</em> matrix <em>lu(X,L,U,p)</em> computes the LU decomposition. <em>L</em> is a lower triangular, <em>U</em> an upper triangular matrix. <em>p</em> is the interchange permutation vector such that elements <em>k</em> and row <em>p(k)</em> should be interchanged.<p>
789	Returns true is calculation succeeds. False otherwise.
790	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
791
792	<p>Referenced by <a class="el" href="det_8cpp-source.html#l00043">itpp::det()</a>.</p>
793
794	</div>
795	</div><p>
796	<a class="anchor" name="g470eed4741289d81759d441e316f92f0"></a><!-- doxytag: member="itpp::lu" ref="g470eed4741289d81759d441e316f92f0" args="(const mat &X, mat &L, mat &U, ivec &p)" -->
797	<div class="memitem">
798	<div class="memproto">
799	<table class="memname">
800	<tr>
801	<td class="memname">bool itpp::lu </td>
802	<td>(</td>
803	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
804	<td class="paramname"> <em>X</em>, </td>
805	</tr>
806	<tr>
807	<td class="paramkey"></td>
808	<td></td>
809	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
810	<td class="paramname"> <em>L</em>, </td>
811	</tr>
812	<tr>
813	<td class="paramkey"></td>
814	<td></td>
815	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
816	<td class="paramname"> <em>U</em>, </td>
817	</tr>
818	<tr>
819	<td class="paramkey"></td>
820	<td></td>
821	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#b03757d874926a9be91535e71af1656e">ivec</a> & </td>
822	<td class="paramname"> <em>p</em></td><td> </td>
823	</tr>
824	<tr>
825	<td></td>
826	<td>)</td>
827	<td></td><td></td><td></td>
828	</tr>
829	</table>
830	</div>
831	<div class="memdoc">
832
833	<p>
834	LU factorisation of real matrix.
835	<p>
836	The LU factorization of the real matrix <img class="formulaInl" alt="$\mathbf{X}$" src="form_125.png"> of size <img class="formulaInl" alt="$n \times n$" src="form_126.png"> is given by <p class="formulaDsp">
837	<img class="formulaDsp" alt="\[ \mathbf{X} = \mathbf{P}^T \mathbf{L} \mathbf{U} , \]" src="form_143.png">
838	<p>
839	where <img class="formulaInl" alt="$\mathbf{L}$" src="form_144.png"> and <img class="formulaInl" alt="$\mathbf{U}$" src="form_145.png"> are lower and upper triangular matrices and <img class="formulaInl" alt="$\mathbf{P}$" src="form_146.png"> is a permutation matrix.<p>
840	The interchange permutation vector <em>p</em> is such that <em>k</em> and <em>p(k)</em> should be changed for all <em>k</em>. Given this vector a permutation matrix can be constructed using the function <div class="fragment"><pre class="fragment"> <a class="code" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69" title="bin matrix">bmat</a> <a class="code" href="group__matrixdecomp.html#gb6e7ba47c63173084cf0cb6bebbff508" title="Make permutation matrix P from the interchange permutation vector p.">permutation_matrix</a>(<span class="keyword">const</span> ivec &p)
841	</pre></div><p>
842	If <em>X</em> is an <em>n</em> by <em>n</em> matrix <em>lu(X,L,U,p)</em> computes the LU decomposition. <em>L</em> is a lower triangular, <em>U</em> an upper triangular matrix. <em>p</em> is the interchange permutation vector such that <em>k</em> and <em>p(k)</em> should be changed for all <em>k</em>.<p>
843	Returns true is calculation succeeds. False otherwise.
844	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
845
846	</div>
847	</div><p>
848	<a class="anchor" name="gdb3c49c28626013e0679b2ce088b8d70"></a><!-- doxytag: member="itpp::qr" ref="gdb3c49c28626013e0679b2ce088b8d70" args="(const cmat &A, cmat &Q, cmat &R, bmat &P)" -->
849	<div class="memitem">
850	<div class="memproto">
851	<table class="memname">
852	<tr>
853	<td class="memname">bool itpp::qr </td>
854	<td>(</td>
855	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
856	<td class="paramname"> <em>A</em>, </td>
857	</tr>
858	<tr>
859	<td class="paramkey"></td>
860	<td></td>
861	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
862	<td class="paramname"> <em>Q</em>, </td>
863	</tr>
864	<tr>
865	<td class="paramkey"></td>
866	<td></td>
867	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
868	<td class="paramname"> <em>R</em>, </td>
869	</tr>
870	<tr>
871	<td class="paramkey"></td>
872	<td></td>
873	<td class="paramtype"><a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> & </td>
874	<td class="paramname"> <em>P</em></td><td> </td>
875	</tr>
876	<tr>
877	<td></td>
878	<td>)</td>
879	<td></td><td></td><td></td>
880	</tr>
881	</table>
882	</div>
883	<div class="memdoc">
884
885	<p>
886	QR factorisation of a complex matrix with pivoting.
887	<p>
888	The QR factorization of the complex matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> of size <img class="formulaInl" alt="$m \times n$" src="form_140.png"> is given by <p class="formulaDsp">
889	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} , \]" src="form_153.png">
890	<p>
891	where <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> is an <img class="formulaInl" alt="$m \times m$" src="form_149.png"> unitary matrix, <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> is an <img class="formulaInl" alt="$m \times n$" src="form_140.png"> upper triangular matrix and <img class="formulaInl" alt="$\mathbf{P}$" src="form_146.png"> is an <img class="formulaInl" alt="$n \times n$" src="form_126.png"> permutation matrix.<p>
892	Returns true is calculation succeeds. False otherwise. Uses the LAPACK routines ZGEQP3 and ZUNGQR.
893	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
894
895	<p>Referenced by <a class="el" href="libKF_8cpp-source.html#l00199">bdm::EKFCh::bayes()</a>, <a class="el" href="libKF_8cpp-source.html#l00130">bdm::KalmanCh::bayes()</a>, and <a class="el" href="chmat_8cpp-source.html#l00007">chmat::opupdt()</a>.</p>
896
897	</div>
898	</div><p>
899	<a class="anchor" name="g1a880a8a274c14e51482293181b1a10e"></a><!-- doxytag: member="itpp::qr" ref="g1a880a8a274c14e51482293181b1a10e" args="(const cmat &A, cmat &R)" -->
900	<div class="memitem">
901	<div class="memproto">
902	<table class="memname">
903	<tr>
904	<td class="memname">bool itpp::qr </td>
905	<td>(</td>
906	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
907	<td class="paramname"> <em>A</em>, </td>
908	</tr>
909	<tr>
910	<td class="paramkey"></td>
911	<td></td>
912	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
913	<td class="paramname"> <em>R</em></td><td> </td>
914	</tr>
915	<tr>
916	<td></td>
917	<td>)</td>
918	<td></td><td></td><td></td>
919	</tr>
920	</table>
921	</div>
922	<div class="memdoc">
923
924	<p>
925	QR factorisation of complex matrix with suppressed evaluation of Q.
926	<p>
927	For certain type of applications only the <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> matrix of full QR factorization of the complex matrix <img class="formulaInl" alt="$\mathbf{A}=\mathbf{Q}\mathbf{R}$" src="form_151.png"> is needed. These situations arise typically in designs of square-root algorithms where it is required that <img class="formulaInl" alt="$\mathbf{A}^{H}\mathbf{A}=\mathbf{R}^{H}\mathbf{R}$" src="form_154.png">. In such cases, evaluation of <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> can be skipped.<p>
928	Modification of qr(A,Q,R).<p>
929	<dl class="author" compact><dt><b>Author:</b></dt><dd>Vasek Smidl </dd></dl>
930
931	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
932
933	</div>
934	</div><p>
935	<a class="anchor" name="g321c23bad4ec43d1111f405587a9ffa2"></a><!-- doxytag: member="itpp::qr" ref="g321c23bad4ec43d1111f405587a9ffa2" args="(const cmat &A, cmat &Q, cmat &R)" -->
936	<div class="memitem">
937	<div class="memproto">
938	<table class="memname">
939	<tr>
940	<td class="memname">bool itpp::qr </td>
941	<td>(</td>
942	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
943	<td class="paramname"> <em>A</em>, </td>
944	</tr>
945	<tr>
946	<td class="paramkey"></td>
947	<td></td>
948	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
949	<td class="paramname"> <em>Q</em>, </td>
950	</tr>
951	<tr>
952	<td class="paramkey"></td>
953	<td></td>
954	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
955	<td class="paramname"> <em>R</em></td><td> </td>
956	</tr>
957	<tr>
958	<td></td>
959	<td>)</td>
960	<td></td><td></td><td></td>
961	</tr>
962	</table>
963	</div>
964	<div class="memdoc">
965
966	<p>
967	QR factorisation of a complex matrix.
968	<p>
969	The QR factorization of the complex matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> of size <img class="formulaInl" alt="$m \times n$" src="form_140.png"> is given by <p class="formulaDsp">
970	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{Q} \mathbf{R} , \]" src="form_147.png">
971	<p>
972	where <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> is an <img class="formulaInl" alt="$m \times m$" src="form_149.png"> unitary matrix and <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> is an <img class="formulaInl" alt="$m \times n$" src="form_140.png"> upper triangular matrix.<p>
973	Returns true is calculation succeeds. False otherwise. Uses the LAPACK routines ZGEQRF and ZUNGQR.
974	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
975
976	</div>
977	</div><p>
978	<a class="anchor" name="g83c28d9b53d73b1d9527cf14341637ff"></a><!-- doxytag: member="itpp::qr" ref="g83c28d9b53d73b1d9527cf14341637ff" args="(const mat &A, mat &Q, mat &R, bmat &P)" -->
979	<div class="memitem">
980	<div class="memproto">
981	<table class="memname">
982	<tr>
983	<td class="memname">bool itpp::qr </td>
984	<td>(</td>
985	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
986	<td class="paramname"> <em>A</em>, </td>
987	</tr>
988	<tr>
989	<td class="paramkey"></td>
990	<td></td>
991	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
992	<td class="paramname"> <em>Q</em>, </td>
993	</tr>
994	<tr>
995	<td class="paramkey"></td>
996	<td></td>
997	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
998	<td class="paramname"> <em>R</em>, </td>
999	</tr>
1000	<tr>
1001	<td class="paramkey"></td>
1002	<td></td>
1003	<td class="paramtype"><a class="el" href="mat_8h.html#f90acd1af41bf2d1d8a4bb23662fff69">bmat</a> & </td>
1004	<td class="paramname"> <em>P</em></td><td> </td>
1005	</tr>
1006	<tr>
1007	<td></td>
1008	<td>)</td>
1009	<td></td><td></td><td></td>
1010	</tr>
1011	</table>
1012	</div>
1013	<div class="memdoc">
1014
1015	<p>
1016	QR factorisation of real matrix with pivoting.
1017	<p>
1018	The QR factorization of the real matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> of size <img class="formulaInl" alt="$m \times n$" src="form_140.png"> is given by <p class="formulaDsp">
1019	<img class="formulaDsp" alt="\[ \mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} , \]" src="form_153.png">
1020	<p>
1021	where <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> is an <img class="formulaInl" alt="$m \times m$" src="form_149.png"> orthogonal matrix, <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> is an <img class="formulaInl" alt="$m \times n$" src="form_140.png"> upper triangular matrix and <img class="formulaInl" alt="$\mathbf{P}$" src="form_146.png"> is an <img class="formulaInl" alt="$n \times n$" src="form_126.png"> permutation matrix.<p>
1022	Returns true is calculation succeeds. False otherwise. Uses the LAPACK routines DGEQP3 and DORGQR.
1023	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1024
1025	</div>
1026	</div><p>
1027	<a class="anchor" name="gbd50eeb4508aaf4b7296f3a904458886"></a><!-- doxytag: member="itpp::qr" ref="gbd50eeb4508aaf4b7296f3a904458886" args="(const mat &A, mat &R)" -->
1028	<div class="memitem">
1029	<div class="memproto">
1030	<table class="memname">
1031	<tr>
1032	<td class="memname">bool itpp::qr </td>
1033	<td>(</td>
1034	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1035	<td class="paramname"> <em>A</em>, </td>
1036	</tr>
1037	<tr>
1038	<td class="paramkey"></td>
1039	<td></td>
1040	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1041	<td class="paramname"> <em>R</em></td><td> </td>
1042	</tr>
1043	<tr>
1044	<td></td>
1045	<td>)</td>
1046	<td></td><td></td><td></td>
1047	</tr>
1048	</table>
1049	</div>
1050	<div class="memdoc">
1051
1052	<p>
1053	QR factorisation of real matrix with suppressed evaluation of Q.
1054	<p>
1055	For certain type of applications only the <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> matrix of full QR factorization of the real matrix <img class="formulaInl" alt="$\mathbf{A}=\mathbf{Q}\mathbf{R}$" src="form_151.png"> is needed. These situations arise typically in designs of square-root algorithms where it is required that <img class="formulaInl" alt="$\mathbf{A}^{T}\mathbf{A}=\mathbf{R}^{T}\mathbf{R}$" src="form_152.png">. In such cases, evaluation of <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> can be skipped.<p>
1056	Modification of qr(A,Q,R).<p>
1057	<dl class="author" compact><dt><b>Author:</b></dt><dd>Vasek Smidl </dd></dl>
1058
1059	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1060
1061	</div>
1062	</div><p>
1063	<a class="anchor" name="g9e565beb0ca5841655a5ac3700821e2c"></a><!-- doxytag: member="itpp::qr" ref="g9e565beb0ca5841655a5ac3700821e2c" args="(const mat &A, mat &Q, mat &R)" -->
1064	<div class="memitem">
1065	<div class="memproto">
1066	<table class="memname">
1067	<tr>
1068	<td class="memname">bool itpp::qr </td>
1069	<td>(</td>
1070	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1071	<td class="paramname"> <em>A</em>, </td>
1072	</tr>
1073	<tr>
1074	<td class="paramkey"></td>
1075	<td></td>
1076	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1077	<td class="paramname"> <em>Q</em>, </td>
1078	</tr>
1079	<tr>
1080	<td class="paramkey"></td>
1081	<td></td>
1082	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1083	<td class="paramname"> <em>R</em></td><td> </td>
1084	</tr>
1085	<tr>
1086	<td></td>
1087	<td>)</td>
1088	<td></td><td></td><td></td>
1089	</tr>
1090	</table>
1091	</div>
1092	<div class="memdoc">
1093
1094	<p>
1095	QR factorisation of real matrix.
1096	<p>
1097	The QR factorization of the real matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> of size <img class="formulaInl" alt="$m \times n$" src="form_140.png"> is given by <p class="formulaDsp">
1098	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{Q} \mathbf{R} , \]" src="form_147.png">
1099	<p>
1100	where <img class="formulaInl" alt="$\mathbf{Q}$" src="form_148.png"> is an <img class="formulaInl" alt="$m \times m$" src="form_149.png"> orthogonal matrix and <img class="formulaInl" alt="$\mathbf{R}$" src="form_150.png"> is an <img class="formulaInl" alt="$m \times n$" src="form_140.png"> upper triangular matrix.<p>
1101	Returns true is calculation succeeds. False otherwise. Uses the LAPACK routine DGEQRF and DORGQR.
1102	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1103
1104	</div>
1105	</div><p>
1106	<a class="anchor" name="gd1d1f3ad1c35dee4ded80cc86c5961cc"></a><!-- doxytag: member="itpp::schur" ref="gd1d1f3ad1c35dee4ded80cc86c5961cc" args="(const cmat &A)" -->
1107	<div class="memitem">
1108	<div class="memproto">
1109	<table class="memname">
1110	<tr>
1111	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::schur </td>
1112	<td>(</td>
1113	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1114	<td class="paramname"> <em>A</em> </td>
1115	<td> ) </td>
1116	<td></td>
1117	</tr>
1118	</table>
1119	</div>
1120	<div class="memdoc">
1121
1122	<p>
1123	Schur decomposition of a complex matrix.
1124	<p>
1125	This function computes the Schur form of a square complex matrix <img class="formulaInl" alt="$ \mathbf{A} $" src="form_155.png">. The Schur decomposition satisfies the following equation: <p class="formulaDsp">
1126	<img class="formulaDsp" alt="\[ \mathbf{U} \mathbf{T} \mathbf{U}^{H} = \mathbf{A} \]" src="form_161.png">
1127	<p>
1128	where: <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> is a unitary, <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"> is upper triangular, and <img class="formulaInl" alt="$ \mathbf{U}^{H} $" src="form_162.png"> is the Hermitian transposition of the <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> matrix.<p>
1129	<dl class="return" compact><dt><b>Returns:</b></dt><dd>Complex Schur matrix <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"></dd></dl>
1130	Uses the LAPACK routine ZGEES.
1131	<p>Referenced by <a class="el" href="schur_8cpp-source.html#l00119">itpp::schur()</a>.</p>
1132
1133	</div>
1134	</div><p>
1135	<a class="anchor" name="gcdfbe918727616dbc8eda854c4bf0cc4"></a><!-- doxytag: member="itpp::schur" ref="gcdfbe918727616dbc8eda854c4bf0cc4" args="(const cmat &A, cmat &U, cmat &T)" -->
1136	<div class="memitem">
1137	<div class="memproto">
1138	<table class="memname">
1139	<tr>
1140	<td class="memname">bool itpp::schur </td>
1141	<td>(</td>
1142	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1143	<td class="paramname"> <em>A</em>, </td>
1144	</tr>
1145	<tr>
1146	<td class="paramkey"></td>
1147	<td></td>
1148	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1149	<td class="paramname"> <em>U</em>, </td>
1150	</tr>
1151	<tr>
1152	<td class="paramkey"></td>
1153	<td></td>
1154	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1155	<td class="paramname"> <em>T</em></td><td> </td>
1156	</tr>
1157	<tr>
1158	<td></td>
1159	<td>)</td>
1160	<td></td><td></td><td></td>
1161	</tr>
1162	</table>
1163	</div>
1164	<div class="memdoc">
1165
1166	<p>
1167	Schur decomposition of a complex matrix.
1168	<p>
1169	This function computes the Schur form of a square complex matrix <img class="formulaInl" alt="$ \mathbf{A} $" src="form_155.png">. The Schur decomposition satisfies the following equation: <p class="formulaDsp">
1170	<img class="formulaDsp" alt="\[ \mathbf{U} \mathbf{T} \mathbf{U}^{H} = \mathbf{A} \]" src="form_161.png">
1171	<p>
1172	where: <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> is a unitary, <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"> is upper triangular, and <img class="formulaInl" alt="$ \mathbf{U}^{H} $" src="form_162.png"> is the Hermitian transposition of the <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> matrix.<p>
1173	Uses the LAPACK routine ZGEES.
1174	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1175
1176	</div>
1177	</div><p>
1178	<a class="anchor" name="g5a511c9baeb36e803a006b3172848800"></a><!-- doxytag: member="itpp::schur" ref="g5a511c9baeb36e803a006b3172848800" args="(const mat &A)" -->
1179	<div class="memitem">
1180	<div class="memproto">
1181	<table class="memname">
1182	<tr>
1183	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::schur </td>
1184	<td>(</td>
1185	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1186	<td class="paramname"> <em>A</em> </td>
1187	<td> ) </td>
1188	<td></td>
1189	</tr>
1190	</table>
1191	</div>
1192	<div class="memdoc">
1193
1194	<p>
1195	Schur decomposition of a real matrix.
1196	<p>
1197	This function computes the Schur form of a square real matrix <img class="formulaInl" alt="$ \mathbf{A} $" src="form_155.png">. The Schur decomposition satisfies the following equation: <p class="formulaDsp">
1198	<img class="formulaDsp" alt="\[ \mathbf{U} \mathbf{T} \mathbf{U}^{T} = \mathbf{A} \]" src="form_156.png">
1199	<p>
1200	where: <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> is a unitary, <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"> is upper quasi-triangular, and <img class="formulaInl" alt="$ \mathbf{U}^{T} $" src="form_159.png"> is the transposed <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> matrix.<p>
1201	The upper quasi-triangular matrix may have <img class="formulaInl" alt="$ 2 \times 2 $" src="form_160.png"> blocks on its diagonal.<p>
1202	<dl class="return" compact><dt><b>Returns:</b></dt><dd>Real Schur matrix <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"></dd></dl>
1203	uses the LAPACK routine DGEES.
1204	<p>References <a class="el" href="schur_8cpp-source.html#l00127">itpp::schur()</a>.</p>
1205
1206	</div>
1207	</div><p>
1208	<a class="anchor" name="ga0c6711c11ece9641878d3ab19f39d33"></a><!-- doxytag: member="itpp::schur" ref="ga0c6711c11ece9641878d3ab19f39d33" args="(const mat &A, mat &U, mat &T)" -->
1209	<div class="memitem">
1210	<div class="memproto">
1211	<table class="memname">
1212	<tr>
1213	<td class="memname">bool itpp::schur </td>
1214	<td>(</td>
1215	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1216	<td class="paramname"> <em>A</em>, </td>
1217	</tr>
1218	<tr>
1219	<td class="paramkey"></td>
1220	<td></td>
1221	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1222	<td class="paramname"> <em>U</em>, </td>
1223	</tr>
1224	<tr>
1225	<td class="paramkey"></td>
1226	<td></td>
1227	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1228	<td class="paramname"> <em>T</em></td><td> </td>
1229	</tr>
1230	<tr>
1231	<td></td>
1232	<td>)</td>
1233	<td></td><td></td><td></td>
1234	</tr>
1235	</table>
1236	</div>
1237	<div class="memdoc">
1238
1239	<p>
1240	Schur decomposition of a real matrix.
1241	<p>
1242	This function computes the Schur form of a square real matrix <img class="formulaInl" alt="$ \mathbf{A} $" src="form_155.png">. The Schur decomposition satisfies the following equation: <p class="formulaDsp">
1243	<img class="formulaDsp" alt="\[ \mathbf{U} \mathbf{T} \mathbf{U}^{T} = \mathbf{A} \]" src="form_156.png">
1244	<p>
1245	where: <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> is a unitary, <img class="formulaInl" alt="$ \mathbf{T} $" src="form_158.png"> is upper quasi-triangular, and <img class="formulaInl" alt="$ \mathbf{U}^{T} $" src="form_159.png"> is the transposed <img class="formulaInl" alt="$ \mathbf{U} $" src="form_157.png"> matrix.<p>
1246	The upper quasi-triangular matrix may have <img class="formulaInl" alt="$ 2 \times 2 $" src="form_160.png"> blocks on its diagonal.<p>
1247	Uses the LAPACK routine DGEES.
1248	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1249
1250	</div>
1251	</div><p>
1252	<a class="anchor" name="g98a4dc87128a758f82ed05d7b060958b"></a><!-- doxytag: member="itpp::svd" ref="g98a4dc87128a758f82ed05d7b060958b" args="(const cmat &A, cmat &U, vec &s, cmat &V)" -->
1253	<div class="memitem">
1254	<div class="memproto">
1255	<table class="memname">
1256	<tr>
1257	<td class="memname">bool itpp::svd </td>
1258	<td>(</td>
1259	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1260	<td class="paramname"> <em>A</em>, </td>
1261	</tr>
1262	<tr>
1263	<td class="paramkey"></td>
1264	<td></td>
1265	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1266	<td class="paramname"> <em>U</em>, </td>
1267	</tr>
1268	<tr>
1269	<td class="paramkey"></td>
1270	<td></td>
1271	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1272	<td class="paramname"> <em>s</em>, </td>
1273	</tr>
1274	<tr>
1275	<td class="paramkey"></td>
1276	<td></td>
1277	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1278	<td class="paramname"> <em>V</em></td><td> </td>
1279	</tr>
1280	<tr>
1281	<td></td>
1282	<td>)</td>
1283	<td></td><td></td><td></td>
1284	</tr>
1285	</table>
1286	</div>
1287	<div class="memdoc">
1288
1289	<p>
1290	Perform Singular Value Decomposition (SVD) of a complex matrix <code>A</code>.
1291	<p>
1292	This function returns two orthonormal matrices <img class="formulaInl" alt="$U$" src="form_32.png"> and <img class="formulaInl" alt="$V$" src="form_29.png"> and a vector of singular values <img class="formulaInl" alt="$s$" src="form_163.png">. The SVD algorithm computes the decomposition of a complex <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1293	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^H \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_168.png">
1294	<p>
1295	where the elements of <img class="formulaInl" alt="$\mathbf{s}$" src="form_170.png">, <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1296	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^H \]" src="form_169.png">
1297	<p>
1298	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1299	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1300
1301	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1302
1303	</div>
1304	</div><p>
1305	<a class="anchor" name="g908131485c5c53ed2e84e2f0a258db8c"></a><!-- doxytag: member="itpp::svd" ref="g908131485c5c53ed2e84e2f0a258db8c" args="(const mat &A, mat &U, vec &s, mat &V)" -->
1306	<div class="memitem">
1307	<div class="memproto">
1308	<table class="memname">
1309	<tr>
1310	<td class="memname">bool itpp::svd </td>
1311	<td>(</td>
1312	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1313	<td class="paramname"> <em>A</em>, </td>
1314	</tr>
1315	<tr>
1316	<td class="paramkey"></td>
1317	<td></td>
1318	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1319	<td class="paramname"> <em>U</em>, </td>
1320	</tr>
1321	<tr>
1322	<td class="paramkey"></td>
1323	<td></td>
1324	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1325	<td class="paramname"> <em>s</em>, </td>
1326	</tr>
1327	<tr>
1328	<td class="paramkey"></td>
1329	<td></td>
1330	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1331	<td class="paramname"> <em>V</em></td><td> </td>
1332	</tr>
1333	<tr>
1334	<td></td>
1335	<td>)</td>
1336	<td></td><td></td><td></td>
1337	</tr>
1338	</table>
1339	</div>
1340	<div class="memdoc">
1341
1342	<p>
1343	Perform Singular Value Decomposition (SVD) of a real matrix <code>A</code>.
1344	<p>
1345	This function returns two orthonormal matrices <img class="formulaInl" alt="$U$" src="form_32.png"> and <img class="formulaInl" alt="$V$" src="form_29.png"> and a vector of singular values <img class="formulaInl" alt="$s$" src="form_163.png">. The SVD algorithm computes the decomposition of a real <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1346	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^T \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_164.png">
1347	<p>
1348	where the elements of <img class="formulaInl" alt="$\mathbf{s}$" src="form_170.png">, <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1349	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^T \]" src="form_166.png">
1350	<p>
1351	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1352	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1353
1354	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1355
1356	</div>
1357	</div><p>
1358	<a class="anchor" name="ga53763a60632139d71957ea7cf0080c9"></a><!-- doxytag: member="itpp::svd" ref="ga53763a60632139d71957ea7cf0080c9" args="(const cmat &A)" -->
1359	<div class="memitem">
1360	<div class="memproto">
1361	<table class="memname">
1362	<tr>
1363	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::svd </td>
1364	<td>(</td>
1365	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1366	<td class="paramname"> <em>A</em> </td>
1367	<td> ) </td>
1368	<td></td>
1369	</tr>
1370	</table>
1371	</div>
1372	<div class="memdoc">
1373
1374	<p>
1375	Return singular values of a complex matrix <code>A</code> using SVD.
1376	<p>
1377	This function returns singular values from the SVD decomposition of a complex matrix <img class="formulaInl" alt="$A$" src="form_138.png">. The SVD algorithm computes the decomposition of a complex <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1378	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^H \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_168.png">
1379	<p>
1380	where <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1381	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^H \]" src="form_169.png">
1382	<p>
1383	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1384	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1385
1386	<p>Referenced by <a class="el" href="misc__stat_8cpp-source.html#l00105">itpp::norm()</a>, <a class="el" href="matfunc_8h-source.html#l00493">itpp::rank()</a>, and <a class="el" href="svd_8cpp-source.html#l00211">itpp::svd()</a>.</p>
1387
1388	</div>
1389	</div><p>
1390	<a class="anchor" name="ge3b83ff6532c19ec15ffe76450b70e2c"></a><!-- doxytag: member="itpp::svd" ref="ge3b83ff6532c19ec15ffe76450b70e2c" args="(const mat &A)" -->
1391	<div class="memitem">
1392	<div class="memproto">
1393	<table class="memname">
1394	<tr>
1395	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::svd </td>
1396	<td>(</td>
1397	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1398	<td class="paramname"> <em>A</em> </td>
1399	<td> ) </td>
1400	<td></td>
1401	</tr>
1402	</table>
1403	</div>
1404	<div class="memdoc">
1405
1406	<p>
1407	Return singular values of a real matrix <code>A</code> using SVD.
1408	<p>
1409	This function returns singular values from the SVD decomposition of a real matrix <img class="formulaInl" alt="$A$" src="form_138.png">. The SVD algorithm computes the decomposition of a real <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1410	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^T \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_164.png">
1411	<p>
1412	where <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1413	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^T \]" src="form_166.png">
1414	<p>
1415	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1416	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1417
1418	<p>References <a class="el" href="svd_8cpp-source.html#l00218">itpp::svd()</a>.</p>
1419
1420	</div>
1421	</div><p>
1422	<a class="anchor" name="g92dd138100c619c71ba24b3dae0dec72"></a><!-- doxytag: member="itpp::svd" ref="g92dd138100c619c71ba24b3dae0dec72" args="(const cmat &A, vec &s)" -->
1423	<div class="memitem">
1424	<div class="memproto">
1425	<table class="memname">
1426	<tr>
1427	<td class="memname">bool itpp::svd </td>
1428	<td>(</td>
1429	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1430	<td class="paramname"> <em>A</em>, </td>
1431	</tr>
1432	<tr>
1433	<td class="paramkey"></td>
1434	<td></td>
1435	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1436	<td class="paramname"> <em>s</em></td><td> </td>
1437	</tr>
1438	<tr>
1439	<td></td>
1440	<td>)</td>
1441	<td></td><td></td><td></td>
1442	</tr>
1443	</table>
1444	</div>
1445	<div class="memdoc">
1446
1447	<p>
1448	Get singular values <code>s</code> of a complex matrix <code>A</code> using SVD.
1449	<p>
1450	This function calculates singular values <img class="formulaInl" alt="$s$" src="form_163.png"> from the SVD decomposition of a complex matrix <img class="formulaInl" alt="$A$" src="form_138.png">. The SVD algorithm computes the decomposition of a complex <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1451	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^H \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_168.png">
1452	<p>
1453	where <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1454	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^H \]" src="form_169.png">
1455	<p>
1456	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1457	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1458
1459	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1460
1461	</div>
1462	</div><p>
1463	<a class="anchor" name="g9fcc7191c3cee4db65e51d93123c7fba"></a><!-- doxytag: member="itpp::svd" ref="g9fcc7191c3cee4db65e51d93123c7fba" args="(const mat &A, vec &s)" -->
1464	<div class="memitem">
1465	<div class="memproto">
1466	<table class="memname">
1467	<tr>
1468	<td class="memname">bool itpp::svd </td>
1469	<td>(</td>
1470	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1471	<td class="paramname"> <em>A</em>, </td>
1472	</tr>
1473	<tr>
1474	<td class="paramkey"></td>
1475	<td></td>
1476	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1477	<td class="paramname"> <em>s</em></td><td> </td>
1478	</tr>
1479	<tr>
1480	<td></td>
1481	<td>)</td>
1482	<td></td><td></td><td></td>
1483	</tr>
1484	</table>
1485	</div>
1486	<div class="memdoc">
1487
1488	<p>
1489	Get singular values <code>s</code> of a real matrix <code>A</code> using SVD.
1490	<p>
1491	This function calculates singular values <img class="formulaInl" alt="$s$" src="form_163.png"> from the SVD decomposition of a real matrix <img class="formulaInl" alt="$A$" src="form_138.png">. The SVD algorithm computes the decomposition of a real <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png"> so that <p class="formulaDsp">
1492	<img class="formulaDsp" alt="\[ \mathrm{diag}(\mathbf{U}^T \mathbf{A} \mathbf{V}) = \mathbf{s} = \sigma_1, \ldots, \sigma_p \]" src="form_164.png">
1493	<p>
1494	where <img class="formulaInl" alt="$\sigma_1 \geq \sigma_2 \geq \ldots \sigma_p \geq 0$" src="form_165.png"> are the singular values of <img class="formulaInl" alt="$\mathbf{A}$" src="form_134.png">. Or put differently: <p class="formulaDsp">
1495	<img class="formulaDsp" alt="\[ \mathbf{A} = \mathbf{U} \mathbf{S} \mathbf{V}^T \]" src="form_166.png">
1496	<p>
1497	where <img class="formulaInl" alt="$ \mathrm{diag}(\mathbf{S}) = \mathbf{s} $" src="form_167.png"><p>
1498	<dl class="note" compact><dt><b>Note:</b></dt><dd>An external LAPACK library is required by this function. </dd></dl>
1499
1500	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1501
1502	</div>
1503	</div><p>
1504	</div>
1505	<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:14 2009 for mixpp by
1506	<a href="http://www.doxygen.org/index.html">
1507	<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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