73 | | <h1>bdm::LQG Class Reference</h1><!-- doxytag: class="bdm::LQG" --><!-- doxytag: inherits="bdm::Designer" --><hr/><a name="_details"></a><h2>Detailed Description</h2> |
74 | | <p>Linear Quadratic Gaussian designer for constant penalizations and constant target Its internals are very close to <a class="el" href="classbdm_1_1Kalman.html" title="Common abstract base for Kalman filters.">Kalman</a> estimator </p> |
75 | | |
76 | | <p><code>#include <<a class="el" href="ctrlbase_8h_source.html">ctrlbase.h</a>></code></p> |
77 | | |
78 | | <p><a href="classbdm_1_1LQG-members.html">List of all members.</a></p> |
79 | | <table border="0" cellpadding="0" cellspacing="0"> |
80 | | <tr><td colspan="2"><h2>Public Member Functions</h2></td></tr> |
81 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad70ccc26e555b7f96c778a08b0d2153e"></a><!-- doxytag: member="bdm::LQG::set_system" ref="ad70ccc26e555b7f96c778a08b0d2153e" args="(shared_ptr< StateSpace< fsqmat > > S0)" --> |
82 | | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ad70ccc26e555b7f96c778a08b0d2153e">set_system</a> (<a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>< <a class="el" href="classbdm_1_1StateSpace.html">StateSpace</a>< <a class="el" href="classbdm_1_1fsqmat.html">fsqmat</a> > > S0)</td></tr> |
83 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">set system parameters from given matrices <br/></td></tr> |
84 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abe34f68bc868096df1473487b920bae3"></a><!-- doxytag: member="bdm::LQG::set_control_parameters" ref="abe34f68bc868096df1473487b920bae3" args="(const mat &Qy0, const mat &Qu0, const vec &y_req0, int horizon0)" --> |
85 | | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#abe34f68bc868096df1473487b920bae3">set_control_parameters</a> (const mat &Qy0, const mat &Qu0, const vec &y_req0, int horizon0)</td></tr> |
86 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">set penalization matrices and control horizon <br/></td></tr> |
87 | | <tr><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#aec1a44c57a4569335a943462b35c3156">initialize</a> ()</td></tr> |
88 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">set system parameters from <a class="el" href="classbdm_1_1Kalman.html" title="Common abstract base for Kalman filters.">Kalman</a> filter <a href="#aec1a44c57a4569335a943462b35c3156"></a><br/></td></tr> |
89 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a96c8fb67798ccd783467fcb607296954"></a><!-- doxytag: member="bdm::LQG::validate" ref="a96c8fb67798ccd783467fcb607296954" args="()" --> |
| 70 | <h1>bdm::LQG Class Reference</h1><!-- doxytag: class="bdm::LQG" --><!-- doxytag: inherits="bdm::Designer" --><code>#include <<a class="el" href="ctrlbase_8h_source.html">ctrlbase.h</a>></code> |
| 71 | <p> |
| 72 | |
| 73 | <p> |
| 74 | <a href="classbdm_1_1LQG-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0"> |
| 75 | <tr><td></td></tr> |
| 76 | <tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr> |
| 77 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d70ccc26e555b7f96c778a08b0d2153e"></a><!-- doxytag: member="bdm::LQG::set_system" ref="d70ccc26e555b7f96c778a08b0d2153e" args="(shared_ptr< StateSpace< fsqmat > > S0)" --> |
| 78 | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#d70ccc26e555b7f96c778a08b0d2153e">set_system</a> (<a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>< <a class="el" href="classbdm_1_1StateSpace.html">StateSpace</a>< <a class="el" href="classbdm_1_1fsqmat.html">fsqmat</a> > > S0)</td></tr> |
| 79 | |
| 80 | <tr><td class="mdescLeft"> </td><td class="mdescRight">set system parameters from given matrices <br></td></tr> |
| 81 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="be34f68bc868096df1473487b920bae3"></a><!-- doxytag: member="bdm::LQG::set_control_parameters" ref="be34f68bc868096df1473487b920bae3" args="(const mat &Qy0, const mat &Qu0, const vec &y_req0, int horizon0)" --> |
| 82 | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#be34f68bc868096df1473487b920bae3">set_control_parameters</a> (const mat &Qy0, const mat &Qu0, const vec &y_req0, int horizon0)</td></tr> |
| 83 | |
| 84 | <tr><td class="mdescLeft"> </td><td class="mdescRight">set penalization matrices and control horizon <br></td></tr> |
| 85 | <tr><td class="memItemLeft" nowrap align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ec1a44c57a4569335a943462b35c3156">initialize</a> ()</td></tr> |
| 86 | |
| 87 | <tr><td class="mdescLeft"> </td><td class="mdescRight">set system parameters from <a class="el" href="classbdm_1_1Kalman.html" title="Common abstract base for Kalman filters.">Kalman</a> filter <a href="#ec1a44c57a4569335a943462b35c3156"></a><br></td></tr> |
| 88 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="96c8fb67798ccd783467fcb607296954"></a><!-- doxytag: member="bdm::LQG::validate" ref="96c8fb67798ccd783467fcb607296954" args="()" --> |
91 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a5016aebbb654a0e3d653b8485e0ea86c"></a><!-- doxytag: member="bdm::LQG::update_state" ref="a5016aebbb654a0e3d653b8485e0ea86c" args="()" --> |
92 | | virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a5016aebbb654a0e3d653b8485e0ea86c">update_state</a> ()</td></tr> |
93 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">function for future use which is called at each time td; Should call <a class="el" href="classbdm_1_1LQG.html#aec1a44c57a4569335a943462b35c3156" title="set system parameters from Kalman filter">initialize()</a>! <br/></td></tr> |
94 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="addc5444b092fdb36239f83ab1ae85805"></a><!-- doxytag: member="bdm::LQG::ricatti_step" ref="addc5444b092fdb36239f83ab1ae85805" args="()" --> |
95 | | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#addc5444b092fdb36239f83ab1ae85805">ricatti_step</a> ()</td></tr> |
96 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">redesign one step of the <br/></td></tr> |
97 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae8df589bbdbdd40515f837c9c9560ed8"></a><!-- doxytag: member="bdm::LQG::redesign" ref="ae8df589bbdbdd40515f837c9c9560ed8" args="()" --> |
98 | | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ae8df589bbdbdd40515f837c9c9560ed8">redesign</a> ()</td></tr> |
99 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">Redesign control strategy. <br/></td></tr> |
100 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abd673ed2fee4289c212e03df084e8af5"></a><!-- doxytag: member="bdm::LQG::apply" ref="abd673ed2fee4289c212e03df084e8af5" args="(const vec &state, const vec &ukm)" --> |
| 90 | |
| 91 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5016aebbb654a0e3d653b8485e0ea86c"></a><!-- doxytag: member="bdm::LQG::update_state" ref="5016aebbb654a0e3d653b8485e0ea86c" args="()" --> |
| 92 | virtual void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#5016aebbb654a0e3d653b8485e0ea86c">update_state</a> ()</td></tr> |
| 93 | |
| 94 | <tr><td class="mdescLeft"> </td><td class="mdescRight">function for future use which is called at each time td; Should call <a class="el" href="classbdm_1_1LQG.html#ec1a44c57a4569335a943462b35c3156" title="set system parameters from Kalman filter">initialize()</a>! <br></td></tr> |
| 95 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ddc5444b092fdb36239f83ab1ae85805"></a><!-- doxytag: member="bdm::LQG::ricatti_step" ref="ddc5444b092fdb36239f83ab1ae85805" args="()" --> |
| 96 | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ddc5444b092fdb36239f83ab1ae85805">ricatti_step</a> ()</td></tr> |
| 97 | |
| 98 | <tr><td class="mdescLeft"> </td><td class="mdescRight">redesign one step of the <br></td></tr> |
| 99 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e8df589bbdbdd40515f837c9c9560ed8"></a><!-- doxytag: member="bdm::LQG::redesign" ref="e8df589bbdbdd40515f837c9c9560ed8" args="()" --> |
| 100 | void </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#e8df589bbdbdd40515f837c9c9560ed8">redesign</a> ()</td></tr> |
| 101 | |
| 102 | <tr><td class="mdescLeft"> </td><td class="mdescRight">Redesign control strategy. <br></td></tr> |
| 103 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bd673ed2fee4289c212e03df084e8af5"></a><!-- doxytag: member="bdm::LQG::apply" ref="bd673ed2fee4289c212e03df084e8af5" args="(const vec &state, const vec &ukm)" --> |
102 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a334668204e01d468fe107780d10d2bd8"></a><!-- doxytag: member="bdm::LQG::apply" ref="a334668204e01d468fe107780d10d2bd8" args="(const vec &cond)" --> |
103 | | virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1Designer.html#a334668204e01d468fe107780d10d2bd8">apply</a> (const vec &cond)</td></tr> |
104 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">apply control strategy to obtain control input <br/></td></tr> |
105 | | <tr><td colspan="2"><h2>Protected Attributes</h2></td></tr> |
106 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9575232a3b04933e6b4c4299bf1bfe15"></a><!-- doxytag: member="bdm::LQG::S" ref="a9575232a3b04933e6b4c4299bf1bfe15" args="" --> |
107 | | <a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>< <a class="el" href="classbdm_1_1StateSpace.html">StateSpace</a>< <a class="el" href="classbdm_1_1fsqmat.html">fsqmat</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a9575232a3b04933e6b4c4299bf1bfe15">S</a></td></tr> |
108 | | <tr><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="classbdm_1_1StateSpace.html" title="Basic elements of linear state-space model.">StateSpace</a> model from which we read data. <br/></td></tr> |
109 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aad002e3dc31c59db7f286b00a8e2fc65"></a><!-- doxytag: member="bdm::LQG::y_req" ref="aad002e3dc31c59db7f286b00a8e2fc65" args="" --> |
110 | | vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#aad002e3dc31c59db7f286b00a8e2fc65">y_req</a></td></tr> |
111 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">required value of the output y at time t (assumed constant) <br/></td></tr> |
112 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a8dc7e6ca7949ded1d94ccd78cb8bb2da"></a><!-- doxytag: member="bdm::LQG::u_req" ref="a8dc7e6ca7949ded1d94ccd78cb8bb2da" args="" --> |
113 | | vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a8dc7e6ca7949ded1d94ccd78cb8bb2da">u_req</a></td></tr> |
114 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">required value of the output y at time t (assumed constant) <br/></td></tr> |
115 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae770d283502cf4da978d1d8523309869"></a><!-- doxytag: member="bdm::LQG::horizon" ref="ae770d283502cf4da978d1d8523309869" args="" --> |
116 | | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ae770d283502cf4da978d1d8523309869">horizon</a></td></tr> |
117 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">Control horizon, set to maxint for infinite horizons. <br/></td></tr> |
118 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a484963959d51059d73d9c6174782cc2f"></a><!-- doxytag: member="bdm::LQG::Qy" ref="a484963959d51059d73d9c6174782cc2f" args="" --> |
119 | | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a484963959d51059d73d9c6174782cc2f">Qy</a></td></tr> |
120 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">penalization matrix Qy <br/></td></tr> |
121 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a13f14aea28c7f7b074779ece7df5e748"></a><!-- doxytag: member="bdm::LQG::Qu" ref="a13f14aea28c7f7b074779ece7df5e748" args="" --> |
122 | | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a13f14aea28c7f7b074779ece7df5e748">Qu</a></td></tr> |
123 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">penalization matrix Qu <br/></td></tr> |
124 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a6c9fa6d9bb0be47ac5ed9183eb38562e"></a><!-- doxytag: member="bdm::LQG::td" ref="a6c9fa6d9bb0be47ac5ed9183eb38562e" args="" --> |
125 | | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a6c9fa6d9bb0be47ac5ed9183eb38562e">td</a></td></tr> |
126 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">time of the design step - from horizon->0 <br/></td></tr> |
127 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad78bb29a213eef033a9657ec2f592e80"></a><!-- doxytag: member="bdm::LQG::L" ref="ad78bb29a213eef033a9657ec2f592e80" args="" --> |
128 | | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ad78bb29a213eef033a9657ec2f592e80">L</a></td></tr> |
129 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">controller parameters <br/></td></tr> |
| 105 | |
| 106 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="334668204e01d468fe107780d10d2bd8"></a><!-- doxytag: member="bdm::LQG::apply" ref="334668204e01d468fe107780d10d2bd8" args="(const vec &cond)" --> |
| 107 | virtual vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1Designer.html#334668204e01d468fe107780d10d2bd8">apply</a> (const vec &cond)</td></tr> |
| 108 | |
| 109 | <tr><td class="mdescLeft"> </td><td class="mdescRight">apply control strategy to obtain control input <br></td></tr> |
| 110 | <tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr> |
| 111 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9575232a3b04933e6b4c4299bf1bfe15"></a><!-- doxytag: member="bdm::LQG::S" ref="9575232a3b04933e6b4c4299bf1bfe15" args="" --> |
| 112 | <a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>< <a class="el" href="classbdm_1_1StateSpace.html">StateSpace</a>< <a class="el" href="classbdm_1_1fsqmat.html">fsqmat</a> > > </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#9575232a3b04933e6b4c4299bf1bfe15">S</a></td></tr> |
| 113 | |
| 114 | <tr><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="classbdm_1_1StateSpace.html" title="Basic elements of linear state-space model.">StateSpace</a> model from which we read data. <br></td></tr> |
| 115 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ad002e3dc31c59db7f286b00a8e2fc65"></a><!-- doxytag: member="bdm::LQG::y_req" ref="ad002e3dc31c59db7f286b00a8e2fc65" args="" --> |
| 116 | vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ad002e3dc31c59db7f286b00a8e2fc65">y_req</a></td></tr> |
| 117 | |
| 118 | <tr><td class="mdescLeft"> </td><td class="mdescRight">required value of the output y at time t (assumed constant) <br></td></tr> |
| 119 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8dc7e6ca7949ded1d94ccd78cb8bb2da"></a><!-- doxytag: member="bdm::LQG::u_req" ref="8dc7e6ca7949ded1d94ccd78cb8bb2da" args="" --> |
| 120 | vec </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#8dc7e6ca7949ded1d94ccd78cb8bb2da">u_req</a></td></tr> |
| 121 | |
| 122 | <tr><td class="mdescLeft"> </td><td class="mdescRight">required value of the output y at time t (assumed constant) <br></td></tr> |
| 123 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e770d283502cf4da978d1d8523309869"></a><!-- doxytag: member="bdm::LQG::horizon" ref="e770d283502cf4da978d1d8523309869" args="" --> |
| 124 | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#e770d283502cf4da978d1d8523309869">horizon</a></td></tr> |
| 125 | |
| 126 | <tr><td class="mdescLeft"> </td><td class="mdescRight">Control horizon, set to maxint for infinite horizons. <br></td></tr> |
| 127 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="484963959d51059d73d9c6174782cc2f"></a><!-- doxytag: member="bdm::LQG::Qy" ref="484963959d51059d73d9c6174782cc2f" args="" --> |
| 128 | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#484963959d51059d73d9c6174782cc2f">Qy</a></td></tr> |
| 129 | |
| 130 | <tr><td class="mdescLeft"> </td><td class="mdescRight">penalization matrix Qy <br></td></tr> |
| 131 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="13f14aea28c7f7b074779ece7df5e748"></a><!-- doxytag: member="bdm::LQG::Qu" ref="13f14aea28c7f7b074779ece7df5e748" args="" --> |
| 132 | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#13f14aea28c7f7b074779ece7df5e748">Qu</a></td></tr> |
| 133 | |
| 134 | <tr><td class="mdescLeft"> </td><td class="mdescRight">penalization matrix Qu <br></td></tr> |
| 135 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6c9fa6d9bb0be47ac5ed9183eb38562e"></a><!-- doxytag: member="bdm::LQG::td" ref="6c9fa6d9bb0be47ac5ed9183eb38562e" args="" --> |
| 136 | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#6c9fa6d9bb0be47ac5ed9183eb38562e">td</a></td></tr> |
| 137 | |
| 138 | <tr><td class="mdescLeft"> </td><td class="mdescRight">time of the design step - from horizon->0 <br></td></tr> |
| 139 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d78bb29a213eef033a9657ec2f592e80"></a><!-- doxytag: member="bdm::LQG::L" ref="d78bb29a213eef033a9657ec2f592e80" args="" --> |
| 140 | mat </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#d78bb29a213eef033a9657ec2f592e80">L</a></td></tr> |
| 141 | |
| 142 | <tr><td class="mdescLeft"> </td><td class="mdescRight">controller parameters <br></td></tr> |
135 | | <tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a753e909ac3694cde54b4fc718e24fa09"></a><!-- doxytag: member="bdm::LQG::dimy" ref="a753e909ac3694cde54b4fc718e24fa09" args="" --> |
136 | | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#a753e909ac3694cde54b4fc718e24fa09">dimy</a></td></tr> |
137 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">convenience parameters <br/></td></tr> |
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| 147 | |
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| 149 | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#753e909ac3694cde54b4fc718e24fa09">dimy</a></td></tr> |
| 150 | |
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| 153 | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1LQG.html#ff701d81aa4f32e0a07a5910f06c8969">dimu</a></td></tr> |
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| 187 | <tr><td class="mdescLeft"> </td><td class="mdescRight">post qr matrix <br></td></tr> |