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61	<h1>Solving Linear Equation Systems<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__linearequations.html#gd681464dcc43a1dd566a047a8703d1b0">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
68
69	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by LU factorisation. <a href="#gd681464dcc43a1dd566a047a8703d1b0"></a><br></td></tr>
70	<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__linearequations.html#g2b851be69935d19a71af456172dcd66a">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
71
72	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by LU factorisation. <a href="#g2b851be69935d19a71af456172dcd66a"></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__linearequations.html#g0e8044324a0dab0ab034bb7d969d3545">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
74
75	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve multiple linear equations by LU factorisation. <a href="#g0e8044324a0dab0ab034bb7d969d3545"></a><br></td></tr>
76	<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__linearequations.html#g5eeed005edd07d42bdac76efb95a10ef">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B)</td></tr>
77
78	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve multiple linear equations by LU factorisation. <a href="#g5eeed005edd07d42bdac76efb95a10ef"></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__linearequations.html#gf659f99b6d978e99a6109a4c4737d5e0">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &x)</td></tr>
80
81	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by LU factorisation. <a href="#gf659f99b6d978e99a6109a4c4737d5e0"></a><br></td></tr>
82	<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__linearequations.html#g79433271fb193f777f1527680a1f1f47">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b)</td></tr>
83
84	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by LU factorisation. <a href="#g79433271fb193f777f1527680a1f1f47"></a><br></td></tr>
85	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gdc73f49e6f97f745b446a217801e8e76">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
86
87	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve multiple linear equations by LU factorisation. <a href="#gdc73f49e6f97f745b446a217801e8e76"></a><br></td></tr>
88	<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__linearequations.html#g66c689c7c7dd59dcc617297e9e09674c">itpp::ls_solve</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B)</td></tr>
89
90	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve multiple linear equations by LU factorisation. <a href="#g66c689c7c7dd59dcc617297e9e09674c"></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__linearequations.html#g79c944eae1622c51102e29c710f599a6">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
92
93	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#g79c944eae1622c51102e29c710f599a6"></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__linearequations.html#ga46b244841f3ec438f1e41191757be39">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
95
96	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#ga46b244841f3ec438f1e41191757be39"></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__linearequations.html#gbeee00983a1f1f68cd998aaebe32b1d2">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
98
99	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#gbeee00983a1f1f68cd998aaebe32b1d2"></a><br></td></tr>
100	<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__linearequations.html#g7bdc6bb93ecfe978d4a422fa94c05156">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B)</td></tr>
101
102	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#g7bdc6bb93ecfe978d4a422fa94c05156"></a><br></td></tr>
103	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g6a49b9cd956395fd93c5c4f550c2b1d6">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &x)</td></tr>
104
105	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#g6a49b9cd956395fd93c5c4f550c2b1d6"></a><br></td></tr>
106	<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__linearequations.html#gc19522b8a7120792c41acce0f3436893">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b)</td></tr>
107
108	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#gc19522b8a7120792c41acce0f3436893"></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__linearequations.html#g114a7fea819005a29739d244fd5a5a55">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
110
111	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#g114a7fea819005a29739d244fd5a5a55"></a><br></td></tr>
112	<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__linearequations.html#g682ef1051b2386ed6e47c328617f46d1">itpp::ls_solve_chol</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B)</td></tr>
113
114	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solve linear equation system by Cholesky factorisation. <a href="#g682ef1051b2386ed6e47c328617f46d1"></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__linearequations.html#g618ea65fa1f15fd2e09c61765da06fac">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
116
117	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g618ea65fa1f15fd2e09c61765da06fac"></a><br></td></tr>
118	<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__linearequations.html#g635550ec883953a711dd5f658a164671">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
119
120	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g635550ec883953a711dd5f658a164671"></a><br></td></tr>
121	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gfa445fa4f699c7ca17b7b6475d40969d">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
122
123	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#gfa445fa4f699c7ca17b7b6475d40969d"></a><br></td></tr>
124	<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__linearequations.html#gd93074c8c7c9e3b98b2888365abe7fca">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B)</td></tr>
125
126	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#gd93074c8c7c9e3b98b2888365abe7fca"></a><br></td></tr>
127	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g23ed5ee5dee16412e2751e9bcedb449d">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &x)</td></tr>
128
129	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g23ed5ee5dee16412e2751e9bcedb449d"></a><br></td></tr>
130	<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__linearequations.html#g221d32bcf3790e81bbc73001fb3c7d1c">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b)</td></tr>
131
132	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g221d32bcf3790e81bbc73001fb3c7d1c"></a><br></td></tr>
133	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g4beeb59f1d32fc7c19b04ad3d7d5c210">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
134
135	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g4beeb59f1d32fc7c19b04ad3d7d5c210"></a><br></td></tr>
136	<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__linearequations.html#g60f41335126f7c70973f95ff8147fbfd">itpp::ls_solve_od</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B)</td></tr>
137
138	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g60f41335126f7c70973f95ff8147fbfd"></a><br></td></tr>
139	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gec926319b4d7faf913e1cf034af1899c">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
140
141	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#gec926319b4d7faf913e1cf034af1899c"></a><br></td></tr>
142	<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__linearequations.html#g70cd3ada0cecc2d675638a51ea0eee0d">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
143
144	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g70cd3ada0cecc2d675638a51ea0eee0d"></a><br></td></tr>
145	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gf24d2c5baba027d772c2fbe4958a34ca">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
146
147	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#gf24d2c5baba027d772c2fbe4958a34ca"></a><br></td></tr>
148	<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__linearequations.html#gd47cbd81c624acfc5715f6292dfd9cd4">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B)</td></tr>
149
150	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#gd47cbd81c624acfc5715f6292dfd9cd4"></a><br></td></tr>
151	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g90a505b0fd80f7aa15d869a3176549ec">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &x)</td></tr>
152
153	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#g90a505b0fd80f7aa15d869a3176549ec"></a><br></td></tr>
154	<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__linearequations.html#g126eb1902b5853564750c86339183586">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b)</td></tr>
155
156	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves overdetermined linear equation systems. <a href="#g126eb1902b5853564750c86339183586"></a><br></td></tr>
157	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g5a070b09b70e0cbf95a72c76f0b4f975">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
158
159	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#g5a070b09b70e0cbf95a72c76f0b4f975"></a><br></td></tr>
160	<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__linearequations.html#g67f1f4ffa7b7ea7bdb0c2d8276b58988">itpp::ls_solve_ud</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B)</td></tr>
161
162	<tr><td class="mdescLeft"> </td><td class="mdescRight">Solves underdetermined linear equation systems. <a href="#g67f1f4ffa7b7ea7bdb0c2d8276b58988"></a><br></td></tr>
163	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g523a45a9e50832ea218e34fff1a55db0">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
164
165	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g523a45a9e50832ea218e34fff1a55db0"></a><br></td></tr>
166	<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__linearequations.html#gc93ca026801d8de27ec8378f01b06eda">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
167
168	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#gc93ca026801d8de27ec8378f01b06eda"></a><br></td></tr>
169	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g254891271fb32587592d21b6b771ad85">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &X)</td></tr>
170
171	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g254891271fb32587592d21b6b771ad85"></a><br></td></tr>
172	<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__linearequations.html#g0554bdde3c5e93abef3a11d45235d3da">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &B)</td></tr>
173
174	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g0554bdde3c5e93abef3a11d45235d3da"></a><br></td></tr>
175	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gaf8574970ef18e0c12c3150303010dd1">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &x)</td></tr>
176
177	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#gaf8574970ef18e0c12c3150303010dd1"></a><br></td></tr>
178	<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__linearequations.html#g2d0093ec5378e5e71136e7085a81b75f">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &b)</td></tr>
179
180	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g2d0093ec5378e5e71136e7085a81b75f"></a><br></td></tr>
181	<tr><td class="memItemLeft" nowrap align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g797859ceb64d2233c41520836b91a983">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &X)</td></tr>
182
183	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g797859ceb64d2233c41520836b91a983"></a><br></td></tr>
184	<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__linearequations.html#g3d33801c6488e98ad4b9e0842909644f">itpp::backslash</a> (const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &B)</td></tr>
185
186	<tr><td class="mdescLeft"> </td><td class="mdescRight">A general linear equation system solver. <a href="#g3d33801c6488e98ad4b9e0842909644f"></a><br></td></tr>
187	<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__linearequations.html#g06f1de8cabe1784c5a6d8e0704762421">itpp::forward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &L, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
188
189	<tr><td class="mdescLeft"> </td><td class="mdescRight">Forward substitution of square matrix. <a href="#g06f1de8cabe1784c5a6d8e0704762421"></a><br></td></tr>
190	<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gc7c3161dea713d70d5d599a835b0638f">itpp::forward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &L, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
191
192	<tr><td class="mdescLeft"> </td><td class="mdescRight">Forward substitution of square matrix. <a href="#gc7c3161dea713d70d5d599a835b0638f"></a><br></td></tr>
193	<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__linearequations.html#g118cc3706a66f4627206d889bfa8db82">itpp::forward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &L, int p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
194
195	<tr><td class="mdescLeft"> </td><td class="mdescRight">Forward substitution of band matrices. <a href="#g118cc3706a66f4627206d889bfa8db82"></a><br></td></tr>
196	<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g8c7d440ecb34fd3d1c6f015fe4877ff7">itpp::forward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &L, int p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
197
198	<tr><td class="mdescLeft"> </td><td class="mdescRight">Forward substitution of band matrices. <a href="#g8c7d440ecb34fd3d1c6f015fe4877ff7"></a><br></td></tr>
199	<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__linearequations.html#g4fe9c0b4ef9b22132956d99ccedd804d">itpp::backward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
200
201	<tr><td class="mdescLeft"> </td><td class="mdescRight">Backward substitution of square matrix. <a href="#g4fe9c0b4ef9b22132956d99ccedd804d"></a><br></td></tr>
202	<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#gcd34872e3a3b23f4cd20647a348bbe22">itpp::backward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
203
204	<tr><td class="mdescLeft"> </td><td class="mdescRight">Backward substitution of square matrix. <a href="#gcd34872e3a3b23f4cd20647a348bbe22"></a><br></td></tr>
205	<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__linearequations.html#g4d266602981eb46a9f733c55dc1fd7a2">itpp::backward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, int q, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b)</td></tr>
206
207	<tr><td class="mdescLeft"> </td><td class="mdescRight">Backward substitution of band matrix. <a href="#g4d266602981eb46a9f733c55dc1fd7a2"></a><br></td></tr>
208	<tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__linearequations.html#g4dc8a32c721296c2480fd991b8a570d1">itpp::backward_substitution</a> (const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &U, int q, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &x)</td></tr>
209
210	<tr><td class="mdescLeft"> </td><td class="mdescRight">Backward substitution of band matrix. <a href="#g4dc8a32c721296c2480fd991b8a570d1"></a><br></td></tr>
211	</table>
212	<hr><h2>Function Documentation</h2>
213	<a class="anchor" name="g3d33801c6488e98ad4b9e0842909644f"></a><!-- doxytag: member="itpp::backslash" ref="g3d33801c6488e98ad4b9e0842909644f" args="(const cmat &A, const cmat &B)" -->
214	<div class="memitem">
215	<div class="memproto">
216	<table class="memname">
217	<tr>
218	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::backslash </td>
219	<td>(</td>
220	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
221	<td class="paramname"> <em>A</em>, </td>
222	</tr>
223	<tr>
224	<td class="paramkey"></td>
225	<td></td>
226	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
227	<td class="paramname"> <em>B</em></td><td> </td>
228	</tr>
229	<tr>
230	<td></td>
231	<td>)</td>
232	<td></td><td></td><td></td>
233	</tr>
234	</table>
235	</div>
236	<div class="memdoc">
237
238	<p>
239	A general linear equation system solver.
240	<p>
241	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B), ls_solve_od(A,B), or ls_solve_ud(A,B).
242	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
243
244	<p>Referenced by <a class="el" href="filter__design_8cpp-source.html#l00228">itpp::arma_estimator()</a>, <a class="el" href="ls__solve_8cpp-source.html#l00667">itpp::backslash()</a>, and <a class="el" href="filter__design_8cpp-source.html#l00197">itpp::modified_yule_walker()</a>.</p>
245
246	</div>
247	</div><p>
248	<a class="anchor" name="g797859ceb64d2233c41520836b91a983"></a><!-- doxytag: member="itpp::backslash" ref="g797859ceb64d2233c41520836b91a983" args="(const cmat &A, const cmat &B, cmat &X)" -->
249	<div class="memitem">
250	<div class="memproto">
251	<table class="memname">
252	<tr>
253	<td class="memname">bool itpp::backslash </td>
254	<td>(</td>
255	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
256	<td class="paramname"> <em>A</em>, </td>
257	</tr>
258	<tr>
259	<td class="paramkey"></td>
260	<td></td>
261	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
262	<td class="paramname"> <em>B</em>, </td>
263	</tr>
264	<tr>
265	<td class="paramkey"></td>
266	<td></td>
267	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
268	<td class="paramname"> <em>X</em></td><td> </td>
269	</tr>
270	<tr>
271	<td></td>
272	<td>)</td>
273	<td></td><td></td><td></td>
274	</tr>
275	</table>
276	</div>
277	<div class="memdoc">
278
279	<p>
280	A general linear equation system solver.
281	<p>
282	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B,X), ls_solve_od(A,B,X), or ls_solve_ud(A,B,X).
283	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>, <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
284
285	</div>
286	</div><p>
287	<a class="anchor" name="g2d0093ec5378e5e71136e7085a81b75f"></a><!-- doxytag: member="itpp::backslash" ref="g2d0093ec5378e5e71136e7085a81b75f" args="(const cmat &A, const cvec &b)" -->
288	<div class="memitem">
289	<div class="memproto">
290	<table class="memname">
291	<tr>
292	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::backslash </td>
293	<td>(</td>
294	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
295	<td class="paramname"> <em>A</em>, </td>
296	</tr>
297	<tr>
298	<td class="paramkey"></td>
299	<td></td>
300	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
301	<td class="paramname"> <em>b</em></td><td> </td>
302	</tr>
303	<tr>
304	<td></td>
305	<td>)</td>
306	<td></td><td></td><td></td>
307	</tr>
308	</table>
309	</div>
310	<div class="memdoc">
311
312	<p>
313	A general linear equation system solver.
314	<p>
315	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b), ls_solve_od(A,b) or ls_solve_ud(A,b)
316	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00744">itpp::backslash()</a>, and <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
317
318	</div>
319	</div><p>
320	<a class="anchor" name="gaf8574970ef18e0c12c3150303010dd1"></a><!-- doxytag: member="itpp::backslash" ref="gaf8574970ef18e0c12c3150303010dd1" args="(const cmat &A, const cvec &b, cvec &x)" -->
321	<div class="memitem">
322	<div class="memproto">
323	<table class="memname">
324	<tr>
325	<td class="memname">bool itpp::backslash </td>
326	<td>(</td>
327	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
328	<td class="paramname"> <em>A</em>, </td>
329	</tr>
330	<tr>
331	<td class="paramkey"></td>
332	<td></td>
333	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
334	<td class="paramname"> <em>b</em>, </td>
335	</tr>
336	<tr>
337	<td class="paramkey"></td>
338	<td></td>
339	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
340	<td class="paramname"> <em>x</em></td><td> </td>
341	</tr>
342	<tr>
343	<td></td>
344	<td>)</td>
345	<td></td><td></td><td></td>
346	</tr>
347	</table>
348	</div>
349	<div class="memdoc">
350
351	<p>
352	A general linear equation system solver.
353	<p>
354	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b,x), ls_solve_od(A,b,x) or ls_solve_ud(A,b,x)
355	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>, <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
356
357	</div>
358	</div><p>
359	<a class="anchor" name="g0554bdde3c5e93abef3a11d45235d3da"></a><!-- doxytag: member="itpp::backslash" ref="g0554bdde3c5e93abef3a11d45235d3da" args="(const mat &A, const mat &B)" -->
360	<div class="memitem">
361	<div class="memproto">
362	<table class="memname">
363	<tr>
364	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::backslash </td>
365	<td>(</td>
366	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
367	<td class="paramname"> <em>A</em>, </td>
368	</tr>
369	<tr>
370	<td class="paramkey"></td>
371	<td></td>
372	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
373	<td class="paramname"> <em>B</em></td><td> </td>
374	</tr>
375	<tr>
376	<td></td>
377	<td>)</td>
378	<td></td><td></td><td></td>
379	</tr>
380	</table>
381	</div>
382	<div class="memdoc">
383
384	<p>
385	A general linear equation system solver.
386	<p>
387	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B), ls_solve_od(A,B), or ls_solve_ud(A,B).
388	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00744">itpp::backslash()</a>, and <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
389
390	</div>
391	</div><p>
392	<a class="anchor" name="g254891271fb32587592d21b6b771ad85"></a><!-- doxytag: member="itpp::backslash" ref="g254891271fb32587592d21b6b771ad85" args="(const mat &A, const mat &B, mat &X)" -->
393	<div class="memitem">
394	<div class="memproto">
395	<table class="memname">
396	<tr>
397	<td class="memname">bool itpp::backslash </td>
398	<td>(</td>
399	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
400	<td class="paramname"> <em>A</em>, </td>
401	</tr>
402	<tr>
403	<td class="paramkey"></td>
404	<td></td>
405	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
406	<td class="paramname"> <em>B</em>, </td>
407	</tr>
408	<tr>
409	<td class="paramkey"></td>
410	<td></td>
411	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
412	<td class="paramname"> <em>X</em></td><td> </td>
413	</tr>
414	<tr>
415	<td></td>
416	<td>)</td>
417	<td></td><td></td><td></td>
418	</tr>
419	</table>
420	</div>
421	<div class="memdoc">
422
423	<p>
424	A general linear equation system solver.
425	<p>
426	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B,X), ls_solve_od(A,B,X), or ls_solve_ud(A,B,X).
427	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>, <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
428
429	</div>
430	</div><p>
431	<a class="anchor" name="gc93ca026801d8de27ec8378f01b06eda"></a><!-- doxytag: member="itpp::backslash" ref="gc93ca026801d8de27ec8378f01b06eda" args="(const mat &A, const vec &b)" -->
432	<div class="memitem">
433	<div class="memproto">
434	<table class="memname">
435	<tr>
436	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::backslash </td>
437	<td>(</td>
438	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
439	<td class="paramname"> <em>A</em>, </td>
440	</tr>
441	<tr>
442	<td class="paramkey"></td>
443	<td></td>
444	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
445	<td class="paramname"> <em>b</em></td><td> </td>
446	</tr>
447	<tr>
448	<td></td>
449	<td>)</td>
450	<td></td><td></td><td></td>
451	</tr>
452	</table>
453	</div>
454	<div class="memdoc">
455
456	<p>
457	A general linear equation system solver.
458	<p>
459	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b), ls_solve_od(A,b) or ls_solve_ud(A,b)
460	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00744">itpp::backslash()</a>, and <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
461
462	</div>
463	</div><p>
464	<a class="anchor" name="g523a45a9e50832ea218e34fff1a55db0"></a><!-- doxytag: member="itpp::backslash" ref="g523a45a9e50832ea218e34fff1a55db0" args="(const mat &A, const vec &b, vec &x)" -->
465	<div class="memitem">
466	<div class="memproto">
467	<table class="memname">
468	<tr>
469	<td class="memname">bool itpp::backslash </td>
470	<td>(</td>
471	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
472	<td class="paramname"> <em>A</em>, </td>
473	</tr>
474	<tr>
475	<td class="paramkey"></td>
476	<td></td>
477	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
478	<td class="paramname"> <em>b</em>, </td>
479	</tr>
480	<tr>
481	<td class="paramkey"></td>
482	<td></td>
483	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
484	<td class="paramname"> <em>x</em></td><td> </td>
485	</tr>
486	<tr>
487	<td></td>
488	<td>)</td>
489	<td></td><td></td><td></td>
490	</tr>
491	</table>
492	</div>
493	<div class="memdoc">
494
495	<p>
496	A general linear equation system solver.
497	<p>
498	Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b,x), ls_solve_od(A,b,x) or ls_solve_ud(A,b,x)
499	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>, <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
500
501	</div>
502	</div><p>
503	<a class="anchor" name="g4dc8a32c721296c2480fd991b8a570d1"></a><!-- doxytag: member="itpp::backward_substitution" ref="g4dc8a32c721296c2480fd991b8a570d1" args="(const mat &U, int q, const vec &b, vec &x)" -->
504	<div class="memitem">
505	<div class="memproto">
506	<table class="memname">
507	<tr>
508	<td class="memname">void itpp::backward_substitution </td>
509	<td>(</td>
510	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
511	<td class="paramname"> <em>U</em>, </td>
512	</tr>
513	<tr>
514	<td class="paramkey"></td>
515	<td></td>
516	<td class="paramtype">int </td>
517	<td class="paramname"> <em>q</em>, </td>
518	</tr>
519	<tr>
520	<td class="paramkey"></td>
521	<td></td>
522	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
523	<td class="paramname"> <em>b</em>, </td>
524	</tr>
525	<tr>
526	<td class="paramkey"></td>
527	<td></td>
528	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
529	<td class="paramname"> <em>x</em></td><td> </td>
530	</tr>
531	<tr>
532	<td></td>
533	<td>)</td>
534	<td></td><td></td><td></td>
535	</tr>
536	</table>
537	</div>
538	<div class="memdoc">
539
540	<p>
541	Backward substitution of band matrix.
542	<p>
543	Solves Ux=b, where U is a upper triangular n by n matrix band-matrix with upper bandwidth q. Assumes that U is nonsingular. Requires about 2nq flops (if n >> q). Uses Alg. 4.3.3 in Golub & van Loan "Matrix computations", 3rd ed., p. 153.
544	<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, and <a class="el" href="tcp_8h-source.html#l00117">itpp::max()</a>.</p>
545
546	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00813">itpp::backward_substitution()</a>, <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="libDC_8cpp-source.html#l00168">ldmat::invqform()</a>.</p>
547
548	</div>
549	</div><p>
550	<a class="anchor" name="g4d266602981eb46a9f733c55dc1fd7a2"></a><!-- doxytag: member="itpp::backward_substitution" ref="g4d266602981eb46a9f733c55dc1fd7a2" args="(const mat &U, int q, const vec &b)" -->
551	<div class="memitem">
552	<div class="memproto">
553	<table class="memname">
554	<tr>
555	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::backward_substitution </td>
556	<td>(</td>
557	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
558	<td class="paramname"> <em>U</em>, </td>
559	</tr>
560	<tr>
561	<td class="paramkey"></td>
562	<td></td>
563	<td class="paramtype">int </td>
564	<td class="paramname"> <em>q</em>, </td>
565	</tr>
566	<tr>
567	<td class="paramkey"></td>
568	<td></td>
569	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
570	<td class="paramname"> <em>b</em></td><td> </td>
571	</tr>
572	<tr>
573	<td></td>
574	<td>)</td>
575	<td></td><td></td><td></td>
576	</tr>
577	</table>
578	</div>
579	<div class="memdoc">
580
581	<p>
582	Backward substitution of band matrix.
583	<p>
584	Solves Ux=b, where U is a upper triangular n by n matrix band-matrix with upper bandwidth q. Assumes that U is nonsingular. Requires about 2nq flops (if n >> q). Uses Alg. 4.3.3 in Golub & van Loan "Matrix computations", 3rd ed., p. 153.
585	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00850">itpp::backward_substitution()</a>.</p>
586
587	</div>
588	</div><p>
589	<a class="anchor" name="gcd34872e3a3b23f4cd20647a348bbe22"></a><!-- doxytag: member="itpp::backward_substitution" ref="gcd34872e3a3b23f4cd20647a348bbe22" args="(const mat &U, const vec &b, vec &x)" -->
590	<div class="memitem">
591	<div class="memproto">
592	<table class="memname">
593	<tr>
594	<td class="memname">void itpp::backward_substitution </td>
595	<td>(</td>
596	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
597	<td class="paramname"> <em>U</em>, </td>
598	</tr>
599	<tr>
600	<td class="paramkey"></td>
601	<td></td>
602	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
603	<td class="paramname"> <em>b</em>, </td>
604	</tr>
605	<tr>
606	<td class="paramkey"></td>
607	<td></td>
608	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
609	<td class="paramname"> <em>x</em></td><td> </td>
610	</tr>
611	<tr>
612	<td></td>
613	<td>)</td>
614	<td></td><td></td><td></td>
615	</tr>
616	</table>
617	</div>
618	<div class="memdoc">
619
620	<p>
621	Backward substitution of square matrix.
622	<p>
623	Solves Ux=b, where U is a upper triangular n by n matrix. Assumes that U is nonsingular. Requires n^2 flops. Uses Alg. 3.1.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 89.
624	<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>.</p>
625
626	</div>
627	</div><p>
628	<a class="anchor" name="g4fe9c0b4ef9b22132956d99ccedd804d"></a><!-- doxytag: member="itpp::backward_substitution" ref="g4fe9c0b4ef9b22132956d99ccedd804d" args="(const mat &U, const vec &b)" -->
629	<div class="memitem">
630	<div class="memproto">
631	<table class="memname">
632	<tr>
633	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::backward_substitution </td>
634	<td>(</td>
635	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
636	<td class="paramname"> <em>U</em>, </td>
637	</tr>
638	<tr>
639	<td class="paramkey"></td>
640	<td></td>
641	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
642	<td class="paramname"> <em>b</em></td><td> </td>
643	</tr>
644	<tr>
645	<td></td>
646	<td>)</td>
647	<td></td><td></td><td></td>
648	</tr>
649	</table>
650	</div>
651	<div class="memdoc">
652
653	<p>
654	Backward substitution of square matrix.
655	<p>
656	Solves Ux=b, where U is a upper triangular n by n matrix. Assumes that U is nonsingular. Requires n^2 flops. Uses Alg. 3.1.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 89.
657	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00850">itpp::backward_substitution()</a>.</p>
658
659	</div>
660	</div><p>
661	<a class="anchor" name="g8c7d440ecb34fd3d1c6f015fe4877ff7"></a><!-- doxytag: member="itpp::forward_substitution" ref="g8c7d440ecb34fd3d1c6f015fe4877ff7" args="(const mat &L, int p, const vec &b, vec &x)" -->
662	<div class="memitem">
663	<div class="memproto">
664	<table class="memname">
665	<tr>
666	<td class="memname">void itpp::forward_substitution </td>
667	<td>(</td>
668	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
669	<td class="paramname"> <em>L</em>, </td>
670	</tr>
671	<tr>
672	<td class="paramkey"></td>
673	<td></td>
674	<td class="paramtype">int </td>
675	<td class="paramname"> <em>p</em>, </td>
676	</tr>
677	<tr>
678	<td class="paramkey"></td>
679	<td></td>
680	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
681	<td class="paramname"> <em>b</em>, </td>
682	</tr>
683	<tr>
684	<td class="paramkey"></td>
685	<td></td>
686	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
687	<td class="paramname"> <em>x</em></td><td> </td>
688	</tr>
689	<tr>
690	<td></td>
691	<td>)</td>
692	<td></td><td></td><td></td>
693	</tr>
694	</table>
695	</div>
696	<div class="memdoc">
697
698	<p>
699	Forward substitution of band matrices.
700	<p>
701	Solves Lx=b, where L is a lower triangular n by n band-matrix with lower bandwidth p. Assumes that L is nonsingular. Requires about 2np flops (if n >> p). Uses Alg. 4.3.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 153.
702	<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>, and <a class="el" href="tcp_8h-source.html#l00115">itpp::min()</a>.</p>
703
704	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00756">itpp::forward_substitution()</a>, and <a class="el" href="chmat_8cpp-source.html#l00040">chmat::invqform()</a>.</p>
705
706	</div>
707	</div><p>
708	<a class="anchor" name="g118cc3706a66f4627206d889bfa8db82"></a><!-- doxytag: member="itpp::forward_substitution" ref="g118cc3706a66f4627206d889bfa8db82" args="(const mat &L, int p, const vec &b)" -->
709	<div class="memitem">
710	<div class="memproto">
711	<table class="memname">
712	<tr>
713	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::forward_substitution </td>
714	<td>(</td>
715	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
716	<td class="paramname"> <em>L</em>, </td>
717	</tr>
718	<tr>
719	<td class="paramkey"></td>
720	<td></td>
721	<td class="paramtype">int </td>
722	<td class="paramname"> <em>p</em>, </td>
723	</tr>
724	<tr>
725	<td class="paramkey"></td>
726	<td></td>
727	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
728	<td class="paramname"> <em>b</em></td><td> </td>
729	</tr>
730	<tr>
731	<td></td>
732	<td>)</td>
733	<td></td><td></td><td></td>
734	</tr>
735	</table>
736	</div>
737	<div class="memdoc">
738
739	<p>
740	Forward substitution of band matrices.
741	<p>
742	Solves Lx=b, where L is a lower triangular n by n band-matrix with lower bandwidth p. Assumes that L is nonsingular. Requires about 2np flops (if n >> p). Uses Alg. 4.3.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 153.
743	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00797">itpp::forward_substitution()</a>.</p>
744
745	</div>
746	</div><p>
747	<a class="anchor" name="gc7c3161dea713d70d5d599a835b0638f"></a><!-- doxytag: member="itpp::forward_substitution" ref="gc7c3161dea713d70d5d599a835b0638f" args="(const mat &L, const vec &b, vec &x)" -->
748	<div class="memitem">
749	<div class="memproto">
750	<table class="memname">
751	<tr>
752	<td class="memname">void itpp::forward_substitution </td>
753	<td>(</td>
754	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
755	<td class="paramname"> <em>L</em>, </td>
756	</tr>
757	<tr>
758	<td class="paramkey"></td>
759	<td></td>
760	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
761	<td class="paramname"> <em>b</em>, </td>
762	</tr>
763	<tr>
764	<td class="paramkey"></td>
765	<td></td>
766	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
767	<td class="paramname"> <em>x</em></td><td> </td>
768	</tr>
769	<tr>
770	<td></td>
771	<td>)</td>
772	<td></td><td></td><td></td>
773	</tr>
774	</table>
775	</div>
776	<div class="memdoc">
777
778	<p>
779	Forward substitution of square matrix.
780	<p>
781	Solves Lx=b, where L is a lower triangular n by n matrix. Assumes that L is nonsingular. Requires n^2 flops. Uses Alg. 3.1.1 in Golub & van Loan "Matrix computations", 3rd ed., p. 89.
782	<p>References <a class="el" href="itassert_8h-source.html#l00094">it_assert</a>.</p>
783
784	</div>
785	</div><p>
786	<a class="anchor" name="g06f1de8cabe1784c5a6d8e0704762421"></a><!-- doxytag: member="itpp::forward_substitution" ref="g06f1de8cabe1784c5a6d8e0704762421" args="(const mat &L, const vec &b)" -->
787	<div class="memitem">
788	<div class="memproto">
789	<table class="memname">
790	<tr>
791	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::forward_substitution </td>
792	<td>(</td>
793	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
794	<td class="paramname"> <em>L</em>, </td>
795	</tr>
796	<tr>
797	<td class="paramkey"></td>
798	<td></td>
799	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
800	<td class="paramname"> <em>b</em></td><td> </td>
801	</tr>
802	<tr>
803	<td></td>
804	<td>)</td>
805	<td></td><td></td><td></td>
806	</tr>
807	</table>
808	</div>
809	<div class="memdoc">
810
811	<p>
812	Forward substitution of square matrix.
813	<p>
814	Solves Lx=b, where L is a lower triangular n by n matrix. Assumes that L is nonsingular. Requires n^2 flops. Uses Alg. 3.1.1 in Golub & van Loan "Matrix computations", 3rd ed., p. 89.
815	<p>References <a class="el" href="ls__solve_8cpp-source.html#l00797">itpp::forward_substitution()</a>.</p>
816
817	</div>
818	</div><p>
819	<a class="anchor" name="g66c689c7c7dd59dcc617297e9e09674c"></a><!-- doxytag: member="itpp::ls_solve" ref="g66c689c7c7dd59dcc617297e9e09674c" args="(const cmat &A, const cmat &B)" -->
820	<div class="memitem">
821	<div class="memproto">
822	<table class="memname">
823	<tr>
824	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::ls_solve </td>
825	<td>(</td>
826	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
827	<td class="paramname"> <em>A</em>, </td>
828	</tr>
829	<tr>
830	<td class="paramkey"></td>
831	<td></td>
832	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
833	<td class="paramname"> <em>B</em></td><td> </td>
834	</tr>
835	<tr>
836	<td></td>
837	<td>)</td>
838	<td></td><td></td><td></td>
839	</tr>
840	</table>
841	</div>
842	<div class="memdoc">
843
844	<p>
845	Solve multiple linear equations by LU factorisation.
846	<p>
847	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">. Here <img class="formulaInl" alt="$A$" src="form_138.png"> is a nonsingular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZGESV.
848	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
849
850	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00651">itpp::backslash()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00294">itpp::ls_solve()</a>.</p>
851
852	</div>
853	</div><p>
854	<a class="anchor" name="gdc73f49e6f97f745b446a217801e8e76"></a><!-- doxytag: member="itpp::ls_solve" ref="gdc73f49e6f97f745b446a217801e8e76" args="(const cmat &A, const cmat &B, cmat &X)" -->
855	<div class="memitem">
856	<div class="memproto">
857	<table class="memname">
858	<tr>
859	<td class="memname">bool itpp::ls_solve </td>
860	<td>(</td>
861	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
862	<td class="paramname"> <em>A</em>, </td>
863	</tr>
864	<tr>
865	<td class="paramkey"></td>
866	<td></td>
867	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
868	<td class="paramname"> <em>B</em>, </td>
869	</tr>
870	<tr>
871	<td class="paramkey"></td>
872	<td></td>
873	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
874	<td class="paramname"> <em>X</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	Solve multiple linear equations by LU factorisation.
887	<p>
888	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">. Here <img class="formulaInl" alt="$A$" src="form_138.png"> is a nonsingular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZGESV.
889	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
890
891	</div>
892	</div><p>
893	<a class="anchor" name="g79433271fb193f777f1527680a1f1f47"></a><!-- doxytag: member="itpp::ls_solve" ref="g79433271fb193f777f1527680a1f1f47" args="(const cmat &A, const cvec &b)" -->
894	<div class="memitem">
895	<div class="memproto">
896	<table class="memname">
897	<tr>
898	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::ls_solve </td>
899	<td>(</td>
900	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
901	<td class="paramname"> <em>A</em>, </td>
902	</tr>
903	<tr>
904	<td class="paramkey"></td>
905	<td></td>
906	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
907	<td class="paramname"> <em>b</em></td><td> </td>
908	</tr>
909	<tr>
910	<td></td>
911	<td>)</td>
912	<td></td><td></td><td></td>
913	</tr>
914	</table>
915	</div>
916	<div class="memdoc">
917
918	<p>
919	Solve linear equation system by LU factorisation.
920	<p>
921	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZGESV.
922	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>.</p>
923
924	</div>
925	</div><p>
926	<a class="anchor" name="gf659f99b6d978e99a6109a4c4737d5e0"></a><!-- doxytag: member="itpp::ls_solve" ref="gf659f99b6d978e99a6109a4c4737d5e0" args="(const cmat &A, const cvec &b, cvec &x)" -->
927	<div class="memitem">
928	<div class="memproto">
929	<table class="memname">
930	<tr>
931	<td class="memname">bool itpp::ls_solve </td>
932	<td>(</td>
933	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
934	<td class="paramname"> <em>A</em>, </td>
935	</tr>
936	<tr>
937	<td class="paramkey"></td>
938	<td></td>
939	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
940	<td class="paramname"> <em>b</em>, </td>
941	</tr>
942	<tr>
943	<td class="paramkey"></td>
944	<td></td>
945	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
946	<td class="paramname"> <em>x</em></td><td> </td>
947	</tr>
948	<tr>
949	<td></td>
950	<td>)</td>
951	<td></td><td></td><td></td>
952	</tr>
953	</table>
954	</div>
955	<div class="memdoc">
956
957	<p>
958	Solve linear equation system by LU factorisation.
959	<p>
960	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZGESV.
961	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
962
963	</div>
964	</div><p>
965	<a class="anchor" name="g5eeed005edd07d42bdac76efb95a10ef"></a><!-- doxytag: member="itpp::ls_solve" ref="g5eeed005edd07d42bdac76efb95a10ef" args="(const mat &A, const mat &B)" -->
966	<div class="memitem">
967	<div class="memproto">
968	<table class="memname">
969	<tr>
970	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::ls_solve </td>
971	<td>(</td>
972	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
973	<td class="paramname"> <em>A</em>, </td>
974	</tr>
975	<tr>
976	<td class="paramkey"></td>
977	<td></td>
978	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
979	<td class="paramname"> <em>B</em></td><td> </td>
980	</tr>
981	<tr>
982	<td></td>
983	<td>)</td>
984	<td></td><td></td><td></td>
985	</tr>
986	</table>
987	</div>
988	<div class="memdoc">
989
990	<p>
991	Solve multiple linear equations by LU factorisation.
992	<p>
993	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">. Here <img class="formulaInl" alt="$A$" src="form_138.png"> is a nonsingular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DGESV.
994	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>.</p>
995
996	</div>
997	</div><p>
998	<a class="anchor" name="g0e8044324a0dab0ab034bb7d969d3545"></a><!-- doxytag: member="itpp::ls_solve" ref="g0e8044324a0dab0ab034bb7d969d3545" args="(const mat &A, const mat &B, mat &X)" -->
999	<div class="memitem">
1000	<div class="memproto">
1001	<table class="memname">
1002	<tr>
1003	<td class="memname">bool itpp::ls_solve </td>
1004	<td>(</td>
1005	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1006	<td class="paramname"> <em>A</em>, </td>
1007	</tr>
1008	<tr>
1009	<td class="paramkey"></td>
1010	<td></td>
1011	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1012	<td class="paramname"> <em>B</em>, </td>
1013	</tr>
1014	<tr>
1015	<td class="paramkey"></td>
1016	<td></td>
1017	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1018	<td class="paramname"> <em>X</em></td><td> </td>
1019	</tr>
1020	<tr>
1021	<td></td>
1022	<td>)</td>
1023	<td></td><td></td><td></td>
1024	</tr>
1025	</table>
1026	</div>
1027	<div class="memdoc">
1028
1029	<p>
1030	Solve multiple linear equations by LU factorisation.
1031	<p>
1032	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">. Here <img class="formulaInl" alt="$A$" src="form_138.png"> is a nonsingular <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DGESV.
1033	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1034
1035	</div>
1036	</div><p>
1037	<a class="anchor" name="g2b851be69935d19a71af456172dcd66a"></a><!-- doxytag: member="itpp::ls_solve" ref="g2b851be69935d19a71af456172dcd66a" args="(const mat &A, const vec &b)" -->
1038	<div class="memitem">
1039	<div class="memproto">
1040	<table class="memname">
1041	<tr>
1042	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::ls_solve </td>
1043	<td>(</td>
1044	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1045	<td class="paramname"> <em>A</em>, </td>
1046	</tr>
1047	<tr>
1048	<td class="paramkey"></td>
1049	<td></td>
1050	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1051	<td class="paramname"> <em>b</em></td><td> </td>
1052	</tr>
1053	<tr>
1054	<td></td>
1055	<td>)</td>
1056	<td></td><td></td><td></td>
1057	</tr>
1058	</table>
1059	</div>
1060	<div class="memdoc">
1061
1062	<p>
1063	Solve linear equation system by LU factorisation.
1064	<p>
1065	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DGESV.
1066	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00321">itpp::ls_solve()</a>.</p>
1067
1068	</div>
1069	</div><p>
1070	<a class="anchor" name="gd681464dcc43a1dd566a047a8703d1b0"></a><!-- doxytag: member="itpp::ls_solve" ref="gd681464dcc43a1dd566a047a8703d1b0" args="(const mat &A, const vec &b, vec &x)" -->
1071	<div class="memitem">
1072	<div class="memproto">
1073	<table class="memname">
1074	<tr>
1075	<td class="memname">bool itpp::ls_solve </td>
1076	<td>(</td>
1077	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1078	<td class="paramname"> <em>A</em>, </td>
1079	</tr>
1080	<tr>
1081	<td class="paramkey"></td>
1082	<td></td>
1083	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1084	<td class="paramname"> <em>b</em>, </td>
1085	</tr>
1086	<tr>
1087	<td class="paramkey"></td>
1088	<td></td>
1089	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1090	<td class="paramname"> <em>x</em></td><td> </td>
1091	</tr>
1092	<tr>
1093	<td></td>
1094	<td>)</td>
1095	<td></td><td></td><td></td>
1096	</tr>
1097	</table>
1098	</div>
1099	<div class="memdoc">
1100
1101	<p>
1102	Solve linear equation system by LU factorisation.
1103	<p>
1104	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DGESV.
1105	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1106
1107	</div>
1108	</div><p>
1109	<a class="anchor" name="g682ef1051b2386ed6e47c328617f46d1"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="g682ef1051b2386ed6e47c328617f46d1" args="(const cmat &A, const cmat &B)" -->
1110	<div class="memitem">
1111	<div class="memproto">
1112	<table class="memname">
1113	<tr>
1114	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::ls_solve_chol </td>
1115	<td>(</td>
1116	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1117	<td class="paramname"> <em>A</em>, </td>
1118	</tr>
1119	<tr>
1120	<td class="paramkey"></td>
1121	<td></td>
1122	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1123	<td class="paramname"> <em>B</em></td><td> </td>
1124	</tr>
1125	<tr>
1126	<td></td>
1127	<td>)</td>
1128	<td></td><td></td><td></td>
1129	</tr>
1130	</table>
1131	</div>
1132	<div class="memdoc">
1133
1134	<p>
1135	Solve linear equation system by Cholesky factorisation.
1136	<p>
1137	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a Hermitian positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZPOSV.
1138	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
1139
1140	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00154">itpp::ls_solve_chol()</a>.</p>
1141
1142	</div>
1143	</div><p>
1144	<a class="anchor" name="g114a7fea819005a29739d244fd5a5a55"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="g114a7fea819005a29739d244fd5a5a55" args="(const cmat &A, const cmat &B, cmat &X)" -->
1145	<div class="memitem">
1146	<div class="memproto">
1147	<table class="memname">
1148	<tr>
1149	<td class="memname">bool itpp::ls_solve_chol </td>
1150	<td>(</td>
1151	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1152	<td class="paramname"> <em>A</em>, </td>
1153	</tr>
1154	<tr>
1155	<td class="paramkey"></td>
1156	<td></td>
1157	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1158	<td class="paramname"> <em>B</em>, </td>
1159	</tr>
1160	<tr>
1161	<td class="paramkey"></td>
1162	<td></td>
1163	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1164	<td class="paramname"> <em>X</em></td><td> </td>
1165	</tr>
1166	<tr>
1167	<td></td>
1168	<td>)</td>
1169	<td></td><td></td><td></td>
1170	</tr>
1171	</table>
1172	</div>
1173	<div class="memdoc">
1174
1175	<p>
1176	Solve linear equation system by Cholesky factorisation.
1177	<p>
1178	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a Hermitian positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZPOSV.
1179	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1180
1181	</div>
1182	</div><p>
1183	<a class="anchor" name="gc19522b8a7120792c41acce0f3436893"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="gc19522b8a7120792c41acce0f3436893" args="(const cmat &A, const cvec &b)" -->
1184	<div class="memitem">
1185	<div class="memproto">
1186	<table class="memname">
1187	<tr>
1188	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::ls_solve_chol </td>
1189	<td>(</td>
1190	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1191	<td class="paramname"> <em>A</em>, </td>
1192	</tr>
1193	<tr>
1194	<td class="paramkey"></td>
1195	<td></td>
1196	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1197	<td class="paramname"> <em>b</em></td><td> </td>
1198	</tr>
1199	<tr>
1200	<td></td>
1201	<td>)</td>
1202	<td></td><td></td><td></td>
1203	</tr>
1204	</table>
1205	</div>
1206	<div class="memdoc">
1207
1208	<p>
1209	Solve linear equation system by Cholesky factorisation.
1210	<p>
1211	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a Hermitian positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZPOSV.
1212	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00181">itpp::ls_solve_chol()</a>.</p>
1213
1214	</div>
1215	</div><p>
1216	<a class="anchor" name="g6a49b9cd956395fd93c5c4f550c2b1d6"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="g6a49b9cd956395fd93c5c4f550c2b1d6" args="(const cmat &A, const cvec &b, cvec &x)" -->
1217	<div class="memitem">
1218	<div class="memproto">
1219	<table class="memname">
1220	<tr>
1221	<td class="memname">bool itpp::ls_solve_chol </td>
1222	<td>(</td>
1223	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1224	<td class="paramname"> <em>A</em>, </td>
1225	</tr>
1226	<tr>
1227	<td class="paramkey"></td>
1228	<td></td>
1229	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1230	<td class="paramname"> <em>b</em>, </td>
1231	</tr>
1232	<tr>
1233	<td class="paramkey"></td>
1234	<td></td>
1235	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1236	<td class="paramname"> <em>x</em></td><td> </td>
1237	</tr>
1238	<tr>
1239	<td></td>
1240	<td>)</td>
1241	<td></td><td></td><td></td>
1242	</tr>
1243	</table>
1244	</div>
1245	<div class="memdoc">
1246
1247	<p>
1248	Solve linear equation system by Cholesky factorisation.
1249	<p>
1250	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a Hermitian positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine ZPOSV.
1251	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1252
1253	</div>
1254	</div><p>
1255	<a class="anchor" name="g7bdc6bb93ecfe978d4a422fa94c05156"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="g7bdc6bb93ecfe978d4a422fa94c05156" args="(const mat &A, const mat &B)" -->
1256	<div class="memitem">
1257	<div class="memproto">
1258	<table class="memname">
1259	<tr>
1260	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::ls_solve_chol </td>
1261	<td>(</td>
1262	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1263	<td class="paramname"> <em>A</em>, </td>
1264	</tr>
1265	<tr>
1266	<td class="paramkey"></td>
1267	<td></td>
1268	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1269	<td class="paramname"> <em>B</em></td><td> </td>
1270	</tr>
1271	<tr>
1272	<td></td>
1273	<td>)</td>
1274	<td></td><td></td><td></td>
1275	</tr>
1276	</table>
1277	</div>
1278	<div class="memdoc">
1279
1280	<p>
1281	Solve linear equation system by Cholesky factorisation.
1282	<p>
1283	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a symmetric positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DPOSV.
1284	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00181">itpp::ls_solve_chol()</a>.</p>
1285
1286	</div>
1287	</div><p>
1288	<a class="anchor" name="gbeee00983a1f1f68cd998aaebe32b1d2"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="gbeee00983a1f1f68cd998aaebe32b1d2" args="(const mat &A, const mat &B, mat &X)" -->
1289	<div class="memitem">
1290	<div class="memproto">
1291	<table class="memname">
1292	<tr>
1293	<td class="memname">bool itpp::ls_solve_chol </td>
1294	<td>(</td>
1295	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1296	<td class="paramname"> <em>A</em>, </td>
1297	</tr>
1298	<tr>
1299	<td class="paramkey"></td>
1300	<td></td>
1301	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1302	<td class="paramname"> <em>B</em>, </td>
1303	</tr>
1304	<tr>
1305	<td class="paramkey"></td>
1306	<td></td>
1307	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1308	<td class="paramname"> <em>X</em></td><td> </td>
1309	</tr>
1310	<tr>
1311	<td></td>
1312	<td>)</td>
1313	<td></td><td></td><td></td>
1314	</tr>
1315	</table>
1316	</div>
1317	<div class="memdoc">
1318
1319	<p>
1320	Solve linear equation system by Cholesky factorisation.
1321	<p>
1322	Solves the linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a symmetric positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DPOSV.
1323	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1324
1325	</div>
1326	</div><p>
1327	<a class="anchor" name="ga46b244841f3ec438f1e41191757be39"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="ga46b244841f3ec438f1e41191757be39" args="(const mat &A, const vec &b)" -->
1328	<div class="memitem">
1329	<div class="memproto">
1330	<table class="memname">
1331	<tr>
1332	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::ls_solve_chol </td>
1333	<td>(</td>
1334	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1335	<td class="paramname"> <em>A</em>, </td>
1336	</tr>
1337	<tr>
1338	<td class="paramkey"></td>
1339	<td></td>
1340	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1341	<td class="paramname"> <em>b</em></td><td> </td>
1342	</tr>
1343	<tr>
1344	<td></td>
1345	<td>)</td>
1346	<td></td><td></td><td></td>
1347	</tr>
1348	</table>
1349	</div>
1350	<div class="memdoc">
1351
1352	<p>
1353	Solve linear equation system by Cholesky factorisation.
1354	<p>
1355	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a symmetric positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DPOSV.
1356	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00181">itpp::ls_solve_chol()</a>.</p>
1357
1358	</div>
1359	</div><p>
1360	<a class="anchor" name="g79c944eae1622c51102e29c710f599a6"></a><!-- doxytag: member="itpp::ls_solve_chol" ref="g79c944eae1622c51102e29c710f599a6" args="(const mat &A, const vec &b, vec &x)" -->
1361	<div class="memitem">
1362	<div class="memproto">
1363	<table class="memname">
1364	<tr>
1365	<td class="memname">bool itpp::ls_solve_chol </td>
1366	<td>(</td>
1367	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1368	<td class="paramname"> <em>A</em>, </td>
1369	</tr>
1370	<tr>
1371	<td class="paramkey"></td>
1372	<td></td>
1373	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1374	<td class="paramname"> <em>b</em>, </td>
1375	</tr>
1376	<tr>
1377	<td class="paramkey"></td>
1378	<td></td>
1379	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1380	<td class="paramname"> <em>x</em></td><td> </td>
1381	</tr>
1382	<tr>
1383	<td></td>
1384	<td>)</td>
1385	<td></td><td></td><td></td>
1386	</tr>
1387	</table>
1388	</div>
1389	<div class="memdoc">
1390
1391	<p>
1392	Solve linear equation system by Cholesky factorisation.
1393	<p>
1394	Solves the linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a symmetric positive definite <img class="formulaInl" alt="$n \times n$" src="form_126.png"> matrix. Uses the LAPACK routine DPOSV.
1395	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1396
1397	</div>
1398	</div><p>
1399	<a class="anchor" name="g60f41335126f7c70973f95ff8147fbfd"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g60f41335126f7c70973f95ff8147fbfd" args="(const cmat &A, const cmat &B)" -->
1400	<div class="memitem">
1401	<div class="memproto">
1402	<table class="memname">
1403	<tr>
1404	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::ls_solve_od </td>
1405	<td>(</td>
1406	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1407	<td class="paramname"> <em>A</em>, </td>
1408	</tr>
1409	<tr>
1410	<td class="paramkey"></td>
1411	<td></td>
1412	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1413	<td class="paramname"> <em>B</em></td><td> </td>
1414	</tr>
1415	<tr>
1416	<td></td>
1417	<td>)</td>
1418	<td></td><td></td><td></td>
1419	</tr>
1420	</table>
1421	</div>
1422	<div class="memdoc">
1423
1424	<p>
1425	Solves overdetermined linear equation systems.
1426	<p>
1427	Solves the overdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1428	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
1429
1430	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00651">itpp::backslash()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00450">itpp::ls_solve_od()</a>.</p>
1431
1432	</div>
1433	</div><p>
1434	<a class="anchor" name="g4beeb59f1d32fc7c19b04ad3d7d5c210"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g4beeb59f1d32fc7c19b04ad3d7d5c210" args="(const cmat &A, const cmat &B, cmat &X)" -->
1435	<div class="memitem">
1436	<div class="memproto">
1437	<table class="memname">
1438	<tr>
1439	<td class="memname">bool itpp::ls_solve_od </td>
1440	<td>(</td>
1441	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1442	<td class="paramname"> <em>A</em>, </td>
1443	</tr>
1444	<tr>
1445	<td class="paramkey"></td>
1446	<td></td>
1447	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1448	<td class="paramname"> <em>B</em>, </td>
1449	</tr>
1450	<tr>
1451	<td class="paramkey"></td>
1452	<td></td>
1453	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1454	<td class="paramname"> <em>X</em></td><td> </td>
1455	</tr>
1456	<tr>
1457	<td></td>
1458	<td>)</td>
1459	<td></td><td></td><td></td>
1460	</tr>
1461	</table>
1462	</div>
1463	<div class="memdoc">
1464
1465	<p>
1466	Solves overdetermined linear equation systems.
1467	<p>
1468	Solves the overdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1469	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1470
1471	</div>
1472	</div><p>
1473	<a class="anchor" name="g221d32bcf3790e81bbc73001fb3c7d1c"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g221d32bcf3790e81bbc73001fb3c7d1c" args="(const cmat &A, const cvec &b)" -->
1474	<div class="memitem">
1475	<div class="memproto">
1476	<table class="memname">
1477	<tr>
1478	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::ls_solve_od </td>
1479	<td>(</td>
1480	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1481	<td class="paramname"> <em>A</em>, </td>
1482	</tr>
1483	<tr>
1484	<td class="paramkey"></td>
1485	<td></td>
1486	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1487	<td class="paramname"> <em>b</em></td><td> </td>
1488	</tr>
1489	<tr>
1490	<td></td>
1491	<td>)</td>
1492	<td></td><td></td><td></td>
1493	</tr>
1494	</table>
1495	</div>
1496	<div class="memdoc">
1497
1498	<p>
1499	Solves overdetermined linear equation systems.
1500	<p>
1501	Solves the overdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1502	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>.</p>
1503
1504	</div>
1505	</div><p>
1506	<a class="anchor" name="g23ed5ee5dee16412e2751e9bcedb449d"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g23ed5ee5dee16412e2751e9bcedb449d" args="(const cmat &A, const cvec &b, cvec &x)" -->
1507	<div class="memitem">
1508	<div class="memproto">
1509	<table class="memname">
1510	<tr>
1511	<td class="memname">bool itpp::ls_solve_od </td>
1512	<td>(</td>
1513	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1514	<td class="paramname"> <em>A</em>, </td>
1515	</tr>
1516	<tr>
1517	<td class="paramkey"></td>
1518	<td></td>
1519	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1520	<td class="paramname"> <em>b</em>, </td>
1521	</tr>
1522	<tr>
1523	<td class="paramkey"></td>
1524	<td></td>
1525	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1526	<td class="paramname"> <em>x</em></td><td> </td>
1527	</tr>
1528	<tr>
1529	<td></td>
1530	<td>)</td>
1531	<td></td><td></td><td></td>
1532	</tr>
1533	</table>
1534	</div>
1535	<div class="memdoc">
1536
1537	<p>
1538	Solves overdetermined linear equation systems.
1539	<p>
1540	Solves the overdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and is built upon the LAPACK routine ZGELS.
1541	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1542
1543	</div>
1544	</div><p>
1545	<a class="anchor" name="gd93074c8c7c9e3b98b2888365abe7fca"></a><!-- doxytag: member="itpp::ls_solve_od" ref="gd93074c8c7c9e3b98b2888365abe7fca" args="(const mat &A, const mat &B)" -->
1546	<div class="memitem">
1547	<div class="memproto">
1548	<table class="memname">
1549	<tr>
1550	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::ls_solve_od </td>
1551	<td>(</td>
1552	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1553	<td class="paramname"> <em>A</em>, </td>
1554	</tr>
1555	<tr>
1556	<td class="paramkey"></td>
1557	<td></td>
1558	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1559	<td class="paramname"> <em>B</em></td><td> </td>
1560	</tr>
1561	<tr>
1562	<td></td>
1563	<td>)</td>
1564	<td></td><td></td><td></td>
1565	</tr>
1566	</table>
1567	</div>
1568	<div class="memdoc">
1569
1570	<p>
1571	Solves overdetermined linear equation systems.
1572	<p>
1573	Solves the overdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1574	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>.</p>
1575
1576	</div>
1577	</div><p>
1578	<a class="anchor" name="gfa445fa4f699c7ca17b7b6475d40969d"></a><!-- doxytag: member="itpp::ls_solve_od" ref="gfa445fa4f699c7ca17b7b6475d40969d" args="(const mat &A, const mat &B, mat &X)" -->
1579	<div class="memitem">
1580	<div class="memproto">
1581	<table class="memname">
1582	<tr>
1583	<td class="memname">bool itpp::ls_solve_od </td>
1584	<td>(</td>
1585	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1586	<td class="paramname"> <em>A</em>, </td>
1587	</tr>
1588	<tr>
1589	<td class="paramkey"></td>
1590	<td></td>
1591	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1592	<td class="paramname"> <em>B</em>, </td>
1593	</tr>
1594	<tr>
1595	<td class="paramkey"></td>
1596	<td></td>
1597	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1598	<td class="paramname"> <em>X</em></td><td> </td>
1599	</tr>
1600	<tr>
1601	<td></td>
1602	<td>)</td>
1603	<td></td><td></td><td></td>
1604	</tr>
1605	</table>
1606	</div>
1607	<div class="memdoc">
1608
1609	<p>
1610	Solves overdetermined linear equation systems.
1611	<p>
1612	Solves the overdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1613	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1614
1615	</div>
1616	</div><p>
1617	<a class="anchor" name="g635550ec883953a711dd5f658a164671"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g635550ec883953a711dd5f658a164671" args="(const mat &A, const vec &b)" -->
1618	<div class="memitem">
1619	<div class="memproto">
1620	<table class="memname">
1621	<tr>
1622	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::ls_solve_od </td>
1623	<td>(</td>
1624	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1625	<td class="paramname"> <em>A</em>, </td>
1626	</tr>
1627	<tr>
1628	<td class="paramkey"></td>
1629	<td></td>
1630	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1631	<td class="paramname"> <em>b</em></td><td> </td>
1632	</tr>
1633	<tr>
1634	<td></td>
1635	<td>)</td>
1636	<td></td><td></td><td></td>
1637	</tr>
1638	</table>
1639	</div>
1640	<div class="memdoc">
1641
1642	<p>
1643	Solves overdetermined linear equation systems.
1644	<p>
1645	Solves the overdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1646	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00477">itpp::ls_solve_od()</a>.</p>
1647
1648	</div>
1649	</div><p>
1650	<a class="anchor" name="g618ea65fa1f15fd2e09c61765da06fac"></a><!-- doxytag: member="itpp::ls_solve_od" ref="g618ea65fa1f15fd2e09c61765da06fac" args="(const mat &A, const vec &b, vec &x)" -->
1651	<div class="memitem">
1652	<div class="memproto">
1653	<table class="memname">
1654	<tr>
1655	<td class="memname">bool itpp::ls_solve_od </td>
1656	<td>(</td>
1657	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1658	<td class="paramname"> <em>A</em>, </td>
1659	</tr>
1660	<tr>
1661	<td class="paramkey"></td>
1662	<td></td>
1663	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1664	<td class="paramname"> <em>b</em>, </td>
1665	</tr>
1666	<tr>
1667	<td class="paramkey"></td>
1668	<td></td>
1669	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1670	<td class="paramname"> <em>x</em></td><td> </td>
1671	</tr>
1672	<tr>
1673	<td></td>
1674	<td>)</td>
1675	<td></td><td></td><td></td>
1676	</tr>
1677	</table>
1678	</div>
1679	<div class="memdoc">
1680
1681	<p>
1682	Solves overdetermined linear equation systems.
1683	<p>
1684	Solves the overdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \geq n$" src="form_141.png">. Uses QR-factorization and is built upon the LAPACK routine DGELS.
1685	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1686
1687	</div>
1688	</div><p>
1689	<a class="anchor" name="g67f1f4ffa7b7ea7bdb0c2d8276b58988"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="g67f1f4ffa7b7ea7bdb0c2d8276b58988" args="(const cmat &A, const cmat &B)" -->
1690	<div class="memitem">
1691	<div class="memproto">
1692	<table class="memname">
1693	<tr>
1694	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> itpp::ls_solve_ud </td>
1695	<td>(</td>
1696	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1697	<td class="paramname"> <em>A</em>, </td>
1698	</tr>
1699	<tr>
1700	<td class="paramkey"></td>
1701	<td></td>
1702	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1703	<td class="paramname"> <em>B</em></td><td> </td>
1704	</tr>
1705	<tr>
1706	<td></td>
1707	<td>)</td>
1708	<td></td><td></td><td></td>
1709	</tr>
1710	</table>
1711	</div>
1712	<div class="memdoc">
1713
1714	<p>
1715	Solves underdetermined linear equation systems.
1716	<p>
1717	Solves the underdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1718	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>.</p>
1719
1720	<p>Referenced by <a class="el" href="ls__solve_8cpp-source.html#l00651">itpp::backslash()</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00612">itpp::ls_solve_ud()</a>.</p>
1721
1722	</div>
1723	</div><p>
1724	<a class="anchor" name="g5a070b09b70e0cbf95a72c76f0b4f975"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="g5a070b09b70e0cbf95a72c76f0b4f975" args="(const cmat &A, const cmat &B, cmat &X)" -->
1725	<div class="memitem">
1726	<div class="memproto">
1727	<table class="memname">
1728	<tr>
1729	<td class="memname">bool itpp::ls_solve_ud </td>
1730	<td>(</td>
1731	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1732	<td class="paramname"> <em>A</em>, </td>
1733	</tr>
1734	<tr>
1735	<td class="paramkey"></td>
1736	<td></td>
1737	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1738	<td class="paramname"> <em>B</em>, </td>
1739	</tr>
1740	<tr>
1741	<td class="paramkey"></td>
1742	<td></td>
1743	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1744	<td class="paramname"> <em>X</em></td><td> </td>
1745	</tr>
1746	<tr>
1747	<td></td>
1748	<td>)</td>
1749	<td></td><td></td><td></td>
1750	</tr>
1751	</table>
1752	</div>
1753	<div class="memdoc">
1754
1755	<p>
1756	Solves underdetermined linear equation systems.
1757	<p>
1758	Solves the underdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1759	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1760
1761	</div>
1762	</div><p>
1763	<a class="anchor" name="g126eb1902b5853564750c86339183586"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="g126eb1902b5853564750c86339183586" args="(const cmat &A, const cvec &b)" -->
1764	<div class="memitem">
1765	<div class="memproto">
1766	<table class="memname">
1767	<tr>
1768	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> itpp::ls_solve_ud </td>
1769	<td>(</td>
1770	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1771	<td class="paramname"> <em>A</em>, </td>
1772	</tr>
1773	<tr>
1774	<td class="paramkey"></td>
1775	<td></td>
1776	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1777	<td class="paramname"> <em>b</em></td><td> </td>
1778	</tr>
1779	<tr>
1780	<td></td>
1781	<td>)</td>
1782	<td></td><td></td><td></td>
1783	</tr>
1784	</table>
1785	</div>
1786	<div class="memdoc">
1787
1788	<p>
1789	Solves overdetermined linear equation systems.
1790	<p>
1791	Solves the underdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine ZGELS.
1792	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
1793
1794	</div>
1795	</div><p>
1796	<a class="anchor" name="g90a505b0fd80f7aa15d869a3176549ec"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="g90a505b0fd80f7aa15d869a3176549ec" args="(const cmat &A, const cvec &b, cvec &x)" -->
1797	<div class="memitem">
1798	<div class="memproto">
1799	<table class="memname">
1800	<tr>
1801	<td class="memname">bool itpp::ls_solve_ud </td>
1802	<td>(</td>
1803	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> & </td>
1804	<td class="paramname"> <em>A</em>, </td>
1805	</tr>
1806	<tr>
1807	<td class="paramkey"></td>
1808	<td></td>
1809	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1810	<td class="paramname"> <em>b</em>, </td>
1811	</tr>
1812	<tr>
1813	<td class="paramkey"></td>
1814	<td></td>
1815	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> & </td>
1816	<td class="paramname"> <em>x</em></td><td> </td>
1817	</tr>
1818	<tr>
1819	<td></td>
1820	<td>)</td>
1821	<td></td><td></td><td></td>
1822	</tr>
1823	</table>
1824	</div>
1825	<div class="memdoc">
1826
1827	<p>
1828	Solves underdetermined linear equation systems.
1829	<p>
1830	Solves the underdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and is built upon the LAPACK routine ZGELS.
1831	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1832
1833	</div>
1834	</div><p>
1835	<a class="anchor" name="gd47cbd81c624acfc5715f6292dfd9cd4"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="gd47cbd81c624acfc5715f6292dfd9cd4" args="(const mat &A, const mat &B)" -->
1836	<div class="memitem">
1837	<div class="memproto">
1838	<table class="memname">
1839	<tr>
1840	<td class="memname"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> itpp::ls_solve_ud </td>
1841	<td>(</td>
1842	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1843	<td class="paramname"> <em>A</em>, </td>
1844	</tr>
1845	<tr>
1846	<td class="paramkey"></td>
1847	<td></td>
1848	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1849	<td class="paramname"> <em>B</em></td><td> </td>
1850	</tr>
1851	<tr>
1852	<td></td>
1853	<td>)</td>
1854	<td></td><td></td><td></td>
1855	</tr>
1856	</table>
1857	</div>
1858	<div class="memdoc">
1859
1860	<p>
1861	Solves underdetermined linear equation systems.
1862	<p>
1863	Solves the underdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1864	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
1865
1866	</div>
1867	</div><p>
1868	<a class="anchor" name="gf24d2c5baba027d772c2fbe4958a34ca"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="gf24d2c5baba027d772c2fbe4958a34ca" args="(const mat &A, const mat &B, mat &X)" -->
1869	<div class="memitem">
1870	<div class="memproto">
1871	<table class="memname">
1872	<tr>
1873	<td class="memname">bool itpp::ls_solve_ud </td>
1874	<td>(</td>
1875	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1876	<td class="paramname"> <em>A</em>, </td>
1877	</tr>
1878	<tr>
1879	<td class="paramkey"></td>
1880	<td></td>
1881	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1882	<td class="paramname"> <em>B</em>, </td>
1883	</tr>
1884	<tr>
1885	<td class="paramkey"></td>
1886	<td></td>
1887	<td class="paramtype"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1888	<td class="paramname"> <em>X</em></td><td> </td>
1889	</tr>
1890	<tr>
1891	<td></td>
1892	<td>)</td>
1893	<td></td><td></td><td></td>
1894	</tr>
1895	</table>
1896	</div>
1897	<div class="memdoc">
1898
1899	<p>
1900	Solves underdetermined linear equation systems.
1901	<p>
1902	Solves the underdetermined linear system <img class="formulaInl" alt="$AX=B$" src="form_139.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1903	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1904
1905	</div>
1906	</div><p>
1907	<a class="anchor" name="g70cd3ada0cecc2d675638a51ea0eee0d"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="g70cd3ada0cecc2d675638a51ea0eee0d" args="(const mat &A, const vec &b)" -->
1908	<div class="memitem">
1909	<div class="memproto">
1910	<table class="memname">
1911	<tr>
1912	<td class="memname"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> itpp::ls_solve_ud </td>
1913	<td>(</td>
1914	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1915	<td class="paramname"> <em>A</em>, </td>
1916	</tr>
1917	<tr>
1918	<td class="paramkey"></td>
1919	<td></td>
1920	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1921	<td class="paramname"> <em>b</em></td><td> </td>
1922	</tr>
1923	<tr>
1924	<td></td>
1925	<td>)</td>
1926	<td></td><td></td><td></td>
1927	</tr>
1928	</table>
1929	</div>
1930	<div class="memdoc">
1931
1932	<p>
1933	Solves overdetermined linear equation systems.
1934	<p>
1935	Solves the underdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and assumes that <img class="formulaInl" alt="$A$" src="form_138.png"> is full rank. Based on the LAPACK routine DGELS.
1936	<p>References <a class="el" href="itassert_8h-source.html#l00107">it_assert_debug</a>, and <a class="el" href="ls__solve_8cpp-source.html#l00639">itpp::ls_solve_ud()</a>.</p>
1937
1938	</div>
1939	</div><p>
1940	<a class="anchor" name="gec926319b4d7faf913e1cf034af1899c"></a><!-- doxytag: member="itpp::ls_solve_ud" ref="gec926319b4d7faf913e1cf034af1899c" args="(const mat &A, const vec &b, vec &x)" -->
1941	<div class="memitem">
1942	<div class="memproto">
1943	<table class="memname">
1944	<tr>
1945	<td class="memname">bool itpp::ls_solve_ud </td>
1946	<td>(</td>
1947	<td class="paramtype">const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> & </td>
1948	<td class="paramname"> <em>A</em>, </td>
1949	</tr>
1950	<tr>
1951	<td class="paramkey"></td>
1952	<td></td>
1953	<td class="paramtype">const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1954	<td class="paramname"> <em>b</em>, </td>
1955	</tr>
1956	<tr>
1957	<td class="paramkey"></td>
1958	<td></td>
1959	<td class="paramtype"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> & </td>
1960	<td class="paramname"> <em>x</em></td><td> </td>
1961	</tr>
1962	<tr>
1963	<td></td>
1964	<td>)</td>
1965	<td></td><td></td><td></td>
1966	</tr>
1967	</table>
1968	</div>
1969	<div class="memdoc">
1970
1971	<p>
1972	Solves underdetermined linear equation systems.
1973	<p>
1974	Solves the underdetermined linear system <img class="formulaInl" alt="$Ax=b$" src="form_137.png">, where <img class="formulaInl" alt="$A$" src="form_138.png"> is a <img class="formulaInl" alt="$m \times n$" src="form_140.png"> matrix and <img class="formulaInl" alt="$m \leq n$" src="form_142.png">. Uses LQ-factorization and is built upon the LAPACK routine DGELS.
1975	<p>References <a class="el" href="itassert_8h-source.html#l00126">it_error</a>.</p>
1976
1977	</div>
1978	</div><p>
1979	</div>
1980	<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:14 2009 for mixpp by
1981	<a href="http://www.doxygen.org/index.html">
1982	<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
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