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67<h1>ls_solve.cpp File Reference</h1>Implementation of functions for solving linear equation systems. 
68<a href="#_details">More...</a>
69<p>
70<code>#include &lt;itpp/config.h&gt;</code><br>
71<code>#include &lt;<a class="el" href="ls__solve_8h-source.html">itpp/base/algebra/ls_solve.h</a>&gt;</code><br>
72<table border="0" cellpadding="0" cellspacing="0">
73<tr><td></td></tr>
74<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
75<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
76
77<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#g79c944eae1622c51102e29c710f599a6"></a><br></td></tr>
78<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
79
80<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#gbeee00983a1f1f68cd998aaebe32b1d2"></a><br></td></tr>
81<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
82
83<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#g6a49b9cd956395fd93c5c4f550c2b1d6"></a><br></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#g114a7fea819005a29739d244fd5a5a55"></a><br></td></tr>
87<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
88
89<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#ga46b244841f3ec438f1e41191757be39"></a><br></td></tr>
90<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B)</td></tr>
91
92<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#g7bdc6bb93ecfe978d4a422fa94c05156"></a><br></td></tr>
93<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b)</td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#gc19522b8a7120792c41acce0f3436893"></a><br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B)</td></tr>
97
98<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by Cholesky factorisation.  <a href="group__linearequations.html#g682ef1051b2386ed6e47c328617f46d1"></a><br></td></tr>
99<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by LU factorisation.  <a href="group__linearequations.html#gd681464dcc43a1dd566a047a8703d1b0"></a><br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
103
104<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve multiple linear equations by LU factorisation.  <a href="group__linearequations.html#g0e8044324a0dab0ab034bb7d969d3545"></a><br></td></tr>
105<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
106
107<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by LU factorisation.  <a href="group__linearequations.html#gf659f99b6d978e99a6109a4c4737d5e0"></a><br></td></tr>
108<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve multiple linear equations by LU factorisation.  <a href="group__linearequations.html#gdc73f49e6f97f745b446a217801e8e76"></a><br></td></tr>
111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
112
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by LU factorisation.  <a href="group__linearequations.html#g2b851be69935d19a71af456172dcd66a"></a><br></td></tr>
114<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B)</td></tr>
115
116<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve multiple linear equations by LU factorisation.  <a href="group__linearequations.html#g5eeed005edd07d42bdac76efb95a10ef"></a><br></td></tr>
117<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b)</td></tr>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve linear equation system by LU factorisation.  <a href="group__linearequations.html#g79433271fb193f777f1527680a1f1f47"></a><br></td></tr>
120<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B)</td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solve multiple linear equations by LU factorisation.  <a href="group__linearequations.html#g66c689c7c7dd59dcc617297e9e09674c"></a><br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
124
125<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g618ea65fa1f15fd2e09c61765da06fac"></a><br></td></tr>
126<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
127
128<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#gfa445fa4f699c7ca17b7b6475d40969d"></a><br></td></tr>
129<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
130
131<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g23ed5ee5dee16412e2751e9bcedb449d"></a><br></td></tr>
132<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g4beeb59f1d32fc7c19b04ad3d7d5c210"></a><br></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
136
137<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g635550ec883953a711dd5f658a164671"></a><br></td></tr>
138<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B)</td></tr>
139
140<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#gd93074c8c7c9e3b98b2888365abe7fca"></a><br></td></tr>
141<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b)</td></tr>
142
143<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g221d32bcf3790e81bbc73001fb3c7d1c"></a><br></td></tr>
144<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B)</td></tr>
145
146<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g60f41335126f7c70973f95ff8147fbfd"></a><br></td></tr>
147<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
148
149<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#gec926319b4d7faf913e1cf034af1899c"></a><br></td></tr>
150<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
151
152<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#gf24d2c5baba027d772c2fbe4958a34ca"></a><br></td></tr>
153<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
154
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#g90a505b0fd80f7aa15d869a3176549ec"></a><br></td></tr>
156<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
157
158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#g5a070b09b70e0cbf95a72c76f0b4f975"></a><br></td></tr>
159<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
160
161<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g70cd3ada0cecc2d675638a51ea0eee0d"></a><br></td></tr>
162<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B)</td></tr>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#gd47cbd81c624acfc5715f6292dfd9cd4"></a><br></td></tr>
165<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b)</td></tr>
166
167<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves overdetermined linear equation systems.  <a href="group__linearequations.html#g126eb1902b5853564750c86339183586"></a><br></td></tr>
168<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B)</td></tr>
169
170<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Solves underdetermined linear equation systems.  <a href="group__linearequations.html#g67f1f4ffa7b7ea7bdb0c2d8276b58988"></a><br></td></tr>
171<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
172
173<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g523a45a9e50832ea218e34fff1a55db0"></a><br></td></tr>
174<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
175
176<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#gc93ca026801d8de27ec8378f01b06eda"></a><br></td></tr>
177<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;X)</td></tr>
178
179<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g254891271fb32587592d21b6b771ad85"></a><br></td></tr>
180<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6bba394f181c76fda12759568986c613">mat</a> &amp;B)</td></tr>
181
182<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g0554bdde3c5e93abef3a11d45235d3da"></a><br></td></tr>
183<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;x)</td></tr>
184
185<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#gaf8574970ef18e0c12c3150303010dd1"></a><br></td></tr>
186<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Vec.html#e83c1408740e41a7e29c383b71d4d544">cvec</a> &amp;b)</td></tr>
187
188<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g2d0093ec5378e5e71136e7085a81b75f"></a><br></td></tr>
189<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B, <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;X)</td></tr>
190
191<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g797859ceb64d2233c41520836b91a983"></a><br></td></tr>
192<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a>&nbsp;</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> &amp;A, const <a class="el" href="classitpp_1_1Mat.html#6fbac4b7184807da188e5b85d42f038b">cmat</a> &amp;B)</td></tr>
193
194<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">A general linear equation system solver.  <a href="group__linearequations.html#g3d33801c6488e98ad4b9e0842909644f"></a><br></td></tr>
195<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;L, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
196
197<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Forward substitution of square matrix.  <a href="group__linearequations.html#g06f1de8cabe1784c5a6d8e0704762421"></a><br></td></tr>
198<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</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> &amp;L, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
199
200<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Forward substitution of square matrix.  <a href="group__linearequations.html#gc7c3161dea713d70d5d599a835b0638f"></a><br></td></tr>
201<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;L, int p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
202
203<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Forward substitution of band matrices.  <a href="group__linearequations.html#g118cc3706a66f4627206d889bfa8db82"></a><br></td></tr>
204<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</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> &amp;L, int p, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
205
206<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Forward substitution of band matrices.  <a href="group__linearequations.html#g8c7d440ecb34fd3d1c6f015fe4877ff7"></a><br></td></tr>
207<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;U, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
208
209<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Backward substitution of square matrix.  <a href="group__linearequations.html#g4fe9c0b4ef9b22132956d99ccedd804d"></a><br></td></tr>
210<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</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> &amp;U, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
211
212<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Backward substitution of square matrix.  <a href="group__linearequations.html#gcd34872e3a3b23f4cd20647a348bbe22"></a><br></td></tr>
213<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a>&nbsp;</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> &amp;U, int q, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b)</td></tr>
214
215<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Backward substitution of band matrix.  <a href="group__linearequations.html#g4d266602981eb46a9f733c55dc1fd7a2"></a><br></td></tr>
216<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</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> &amp;U, int q, const <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;b, <a class="el" href="classitpp_1_1Vec.html#02e1bb55f60f3c2eb7a020eb1c2cfcf4">vec</a> &amp;x)</td></tr>
217
218<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Backward substitution of band matrix.  <a href="group__linearequations.html#g4dc8a32c721296c2480fd991b8a570d1"></a><br></td></tr>
219</table>
220<hr><a name="_details"></a><h2>Detailed Description</h2>
221Implementation of functions for solving linear equation systems.
222<p>
223<dl class="author" compact><dt><b>Author:</b></dt><dd>Tony Ottosson</dd></dl>
224-------------------------------------------------------------------------<p>
225Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)<p>
226This file is part of IT++ - a C++ library of mathematical, signal processing, speech processing, and communications classes and functions.<p>
227IT++ is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.<p>
228IT++ is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.<p>
229You should have received a copy of the GNU General Public License along with IT++. If not, see &lt;<a href="http://www.gnu.org/licenses/">http://www.gnu.org/licenses/</a>&gt;.<p>
230------------------------------------------------------------------------- </div>
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