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</style></head><body><divclass="content"><h1><tt>mat2vec_C</tt></h1><!--introduction--><p>Transforms the condition function for a matrix-valued IVP into the condition function for its corresponding vector-valued IVP.</p><p><ahref="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><ahref="#1">Syntax</a></li><li><ahref="#2">Description</a></li><li><ahref="#4">Input/Output Parameters</a></li><li><ahref="#5">Note</a></li><li><ahref="#6">See also</a></li></ul></div><h2id="1">Syntax</h2><preclass="language-matlab">Cv = mat2vec_C(Cm)
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Cv = mat2vec_C(Cm,p)
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</pre><h2id="2">Description</h2><p><tt>Cv = mat2vec_C(Cm)</tt> transforms the condition function <imgsrc="mat2vec_C_doc_eq00129393535309650535.png" alt="$C(t,\mathbf{M})$" style="width:37px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq03500430948250792091.png" alt="$C:\mathrm{R}\times\mathrm{R}^{p\times p}\to\mathrm{B}$" style="width:86px;height:9px;">) for a matrix-valued IVP into a condition function <imgsrc="mat2vec_C_doc_eq08442474580442073854.png" alt="$C(t,\mathbf{y})$" style="width:32px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq08809622711522139656.png" alt="$C:\mathrm{R}\times\mathrm{R}^{p^{2}}\to\mathrm{B}$" style="width:79px;height:11px;">) (where <imgsrc="mat2vec_C_doc_eq15557481901179112500.png" alt="$\mathbf{f}:\mathrm{R}\times\mathrm{R}^{p^{2}}\to\mathrm{R}^{p^{2}}$" style="width:83px;height:11px;">) for its corresponding vector-valued IVP. It is assumed that <imgsrc="mat2vec_C_doc_eq01518063970584319034.png" alt="$\mathbf{M}$" style="width:12px;height:8px;"> is a square matrix.</p><p><tt>Cv = mat2vec_C(Cm,p)</tt> transforms the condition function <imgsrc="mat2vec_C_doc_eq00129393535309650535.png" alt="$C(t,\mathbf{M})$" style="width:37px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq09727063517930851148.png" alt="$C:\mathrm{R}\times\mathrm{R}^{p\times r}\to\mathrm{B}$" style="width:86px;height:9px;">) for a matrix-valued IVP into a condition function <imgsrc="mat2vec_C_doc_eq08442474580442073854.png" alt="$C(t,\mathbf{y})$" style="width:32px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq11074000726716562484.png" alt="$C:\mathrm{R}\times\mathrm{R}^{pr}\to\mathrm{B}$" style="width:80px;height:8px;">) (where <imgsrc="mat2vec_C_doc_eq00831713686490939019.png" alt="$\mathbf{f}:\mathrm{R}\times\mathrm{R}^{pr}\to\mathrm{R}^{p^{2}}$" style="width:84px;height:11px;">) for its corresponding vector-valued IVP.</p><h2id="4">Input/Output Parameters</h2><p>
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</style></head><body><divclass="content"><h1><tt>mat2vec_C</tt></h1><!--introduction--><p>Transforms the condition function for a matrix-valued IVP into the condition function for its corresponding vector-valued IVP.</p><p><ahref="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><ahref="#1">Syntax</a></li><li><ahref="#2">Description</a></li><li><ahref="#3">Input/Output Parameters</a></li><li><ahref="#4">See also</a></li></ul></div><h2id="1">Syntax</h2><preclass="language-matlab">Cv = mat2vec_C(Cm,p)
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</pre><h2id="2">Description</h2><p><tt>Cv = mat2vec_C(Cm,p)</tt> transforms the condition function <imgsrc="mat2vec_C_doc_eq00129393535309650535.png" alt="$C(t,\mathbf{M})$" style="width:37px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq09727063517930851148.png" alt="$C:\mathrm{R}\times\mathrm{R}^{p\times r}\to\mathrm{B}$" style="width:86px;height:9px;">) for a matrix-valued IVP into a condition function <imgsrc="mat2vec_C_doc_eq08442474580442073854.png" alt="$C(t,\mathbf{y})$" style="width:32px;height:11px;"> (where <imgsrc="mat2vec_C_doc_eq11074000726716562484.png" alt="$C:\mathrm{R}\times\mathrm{R}^{pr}\to\mathrm{B}$" style="width:80px;height:8px;">) for its corresponding vector-valued IVP.</p><h2id="3">Input/Output Parameters</h2><p>
</p><h2id="5">Note</h2><div><ul><li>If <imgsrc="mat2vec_C_doc_eq03729901751903020778.png" alt="$p$" style="width:6px;height:8px;"> is not input, it is assumed that the state matrix (<imgsrc="mat2vec_C_doc_eq01518063970584319034.png" alt="$\mathbf{M}$" style="width:12px;height:8px;">) is a square matrix.</li></ul></div><h2id="6">See also</h2><p><ahref="mat2vec_ode_doc.html"><tt>mat2vec_ode</tt></a> | <ahref="mat2vec_IC_doc.html"><tt>mat2vec_IC</tt></a> | <ahref="vec2mat_sol_doc.html"><tt>vec2mat_sol</tt></a></p><pclass="footer"><br><ahref="https://www.mathworks.com/products/matlab/">Published with MATLAB® R2022a</a><br></p></div><!--
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</p><h2id="4">See also</h2><p><ahref="mat2vec_IC_doc.html"><tt>mat2vec_IC</tt></a> | <ahref="mat2vec_ode_doc.html"><tt>mat2vec_ode</tt></a> | <ahref="vec2mat_sol_doc.html"><tt>vec2mat_sol</tt></a></p><pclass="footer"><br><ahref="https://www.mathworks.com/products/matlab/">Published with MATLAB® R2022a</a><br></p></div><!--
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%% |mat2vec_C|
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% Transforms the condition function for a matrix-valued IVP into the
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% condition function for its corresponding vector-valued IVP.
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%
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% <index.html Back to IVP Solver Toolbox Contents>.
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%% Syntax
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% Cv = mat2vec_C(Cm)
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% Cv = mat2vec_C(Cm,p)
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%% Description
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% |Cv = mat2vec_C(Cm)| transforms the condition function
</style></head><body><divclass="content"><h1><tt>mat2vec_ode</tt></h1><!--introduction--><p>Transforms a matrix-valued ODE into a vector-valued ODE.</p><p><ahref="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><ahref="#1">Syntax</a></li><li><ahref="#2">Description</a></li><li><ahref="#4">Input/Output Parameters</a></li><li><ahref="#5">Note</a></li><li><ahref="#6">See also</a></li></ul></div><h2id="1">Syntax</h2><preclass="language-matlab">f = mat2vec_ode(F)
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f = mat2vec_ode(F,p)
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</pre><h2id="2">Description</h2><p><tt>f = mat2vec_ode(F)</tt> transforms the matrix-valued ODE <imgsrc="mat2vec_fun_doc_eq01774414981705130240.png" alt="$d\mathbf{M}/dt=\mathbf{F}(t,\mathbf{M})$" style="width:84px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq15903383774327063487.png" alt="$\mathbf{F}:\mathrm{R}\times\mathrm{R}^{p\times p}\to\mathrm{R}^{p\times p}$" style="width:100px;height:9px;"> into the vector-valued ODE <imgsrc="mat2vec_fun_doc_eq11546780198861005830.png" alt="$d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$" style="width:71px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq15557481901179112500.png" alt="$\mathbf{f}:\mathrm{R}\times\mathrm{R}^{p^{2}}\to\mathrm{R}^{p^{2}}$" style="width:83px;height:11px;">). It is assumed that <imgsrc="mat2vec_fun_doc_eq01518063970584319034.png" alt="$\mathbf{M}$" style="width:12px;height:8px;"> is a square matrix.</p><p><tt>f = mat2vec_ode(F,p)</tt> transforms the matrix-valued ODE <imgsrc="mat2vec_fun_doc_eq01774414981705130240.png" alt="$d\mathbf{M}/dt=\mathbf{F}(t,\mathbf{M})$" style="width:84px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq14844018579718567230.png" alt="$\mathbf{F}:\mathrm{R}\times\mathrm{R}^{p\times r}\to\mathrm{R}^{p\times r}$" style="width:99px;height:9px;">) into the vector-valued ODE <imgsrc="mat2vec_fun_doc_eq11546780198861005830.png" alt="$d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$" style="width:71px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq16176746348441022933.png" alt="$\mathbf{f}:\mathrm{R}\times\mathrm{R}^{pr}\to\mathrm{R}^{pr}$" style="width:85px;height:8px;">). <tt>p</tt> specifies the number of rows of <tt>M</tt>.</p><h2id="4">Input/Output Parameters</h2><p>
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</style></head><body><divclass="content"><h1><tt>mat2vec_ode</tt></h1><!--introduction--><p>Transforms a matrix-valued ODE into a vector-valued ODE.</p><p><ahref="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><ahref="#1">Syntax</a></li><li><ahref="#2">Description</a></li><li><ahref="#3">Input/Output Parameters</a></li><li><ahref="#4">See also</a></li></ul></div><h2id="1">Syntax</h2><preclass="language-matlab">f = mat2vec_ode(F,p)
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</pre><h2id="2">Description</h2><p><tt>f = mat2vec_ode(F,p)</tt> transforms the matrix-valued ODE <imgsrc="mat2vec_fun_doc_eq01774414981705130240.png" alt="$d\mathbf{M}/dt=\mathbf{F}(t,\mathbf{M})$" style="width:84px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq14844018579718567230.png" alt="$\mathbf{F}:\mathrm{R}\times\mathrm{R}^{p\times r}\to\mathrm{R}^{p\times r}$" style="width:99px;height:9px;">) into the vector-valued ODE <imgsrc="mat2vec_fun_doc_eq11546780198861005830.png" alt="$d\mathbf{y}/dt=\mathbf{f}(t,\mathbf{y})$" style="width:71px;height:11px;"> (where <imgsrc="mat2vec_fun_doc_eq16176746348441022933.png" alt="$\mathbf{f}:\mathrm{R}\times\mathrm{R}^{pr}\to\mathrm{R}^{pr}$" style="width:85px;height:8px;">). <tt>p</tt> specifies the number of rows of <tt>M</tt>.</p><h2id="3">Input/Output Parameters</h2><p>
</p><h2id="5">Note</h2><div><ul><li>If <imgsrc="mat2vec_fun_doc_eq03729901751903020778.png" alt="$p$" style="width:6px;height:8px;"> is not input, it is assumed that the state matrix (<imgsrc="mat2vec_fun_doc_eq01518063970584319034.png" alt="$\mathbf{M}$" style="width:12px;height:8px;">) is a square matrix.</li></ul></div><h2id="6">See also</h2><p><ahref="mat2vec_IC_doc.html"><tt>mat2vec_IC</tt></a> | <ahref="mat2vec_C_doc.html"><tt>mat2vec_C</tt></a> | <ahref="vec2mat_sol_doc.html"><tt>vec2mat_sol</tt></a></p><pclass="footer"><br><ahref="https://www.mathworks.com/products/matlab/">Published with MATLAB® R2022a</a><br></p></div><!--
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</p><h2id="4">See also</h2><p><ahref="mat2vec_IC_doc.html"><tt>mat2vec_IC</tt></a> | <ahref="mat2vec_C_doc.html"><tt>mat2vec_C</tt></a> | <ahref="vec2mat_sol_doc.html"><tt>vec2mat_sol</tt></a></p><pclass="footer"><br><ahref="https://www.mathworks.com/products/matlab/">Published with MATLAB® R2022a</a><br></p></div><!--
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%% |mat2vec_ode|
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% Transforms a matrix-valued ODE into a vector-valued ODE.
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%
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% <index.html Back to IVP Solver Toolbox Contents>.
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%% Syntax
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% f = mat2vec_ode(F)
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% f = mat2vec_ode(F,p)
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%% Description
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% |f = mat2vec_ode(F)| transforms the matrix-valued ODE
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