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‎Numerical Differentiation Toolbox.mltbx‎

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‎docs/iderivative_doc.html‎

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<!--
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--><title>iderivative</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-08-27"><meta name="DC.source" content="iderivative_doc.m"><style type="text/css">
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--><title>iderivative</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-10-09"><meta name="DC.source" content="iderivative_doc.m"><style type="text/css">
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html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}
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html { min-height:100%; margin-bottom:1px; }
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<table border=1>
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<tr>
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<td></td>
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<td style="text-align:center"><b>Symbol</b></td>
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<td style="text-align:center"><b>Variable</b></td>
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<td style="text-align:center"><b>Symbol</b></td>
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<td style="text-align:center"><b>Description</b></td>
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<td style="text-align:center"><b>Format</b></td>
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</tr>
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<tr>
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<td rowspan="3" style="text-align:center"><b>Input</b></td>
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<td style="text-align:center"><TT>f</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(x)" title="" /></td>
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<td><TT>f</TT></td>
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<td>univariate, vector-valued function (<img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}:\mathbb{R}\rightarrow\mathbb{R}^{m}" title="" />)</td>
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<td style="text-align:center">1×1<BR>function_handle</td>
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</tr>
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<tr>
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<td style="text-align:center"><TT>x0</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;x_{0}" title="" /></td>
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<td><TT>x0</TT></td>
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<td>point at which to differentiate</td>
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<td style="text-align:center">1×1<BR>double</td>
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</tr>
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<tr>
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<td style="text-align:center"><TT>h</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
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<td><TT>h</TT></td>
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<td>(OPTIONAL) step size</td>
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<td style="text-align:center">1×1<BR>double</td>
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</tr>
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<tr>
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<td rowspan="1" style="text-align:center"><b>Output</b></td>
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<td style="text-align:center"><TT>df</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\dfrac{d\mathbf{f}}{dx}\bigg\rvert_{x=x_{0}}" title="" /></td>
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<td><TT>df</TT></td>
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<td>derivative of <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(x)" title="" /> evaluated at <img src="https://latex.codecogs.com/svg.latex?\inline&space;x=x_{0}" title="" /></td>
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<td style="text-align:center">m×1<BR>double</td>
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</tr>
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</pre><pre class="codeoutput">
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df =
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0.5403
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-0.8415
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0.540302305868140
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-0.841470984807897
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</pre><p>Calculating the error,</p><pre class="codeinput">error = df-[cos(1);-sin(1)]
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</pre><pre class="codeoutput">
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% <table border=1>
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% <tr>
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% <td></td>
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% <td style="text-align:center"><b>Symbol</b></td>
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% <td style="text-align:center"><b>Variable</b></td>
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% <td style="text-align:center"><b>Symbol</b></td>
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% <td style="text-align:center"><b>Description</b></td>
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% <td style="text-align:center"><b>Format</b></td>
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% </tr>
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% <td rowspan="3" style="text-align:center"><b>Input</b></td>
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% <td style="text-align:center"><TT>f</TT></td>
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% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(x)" title="" /></td>
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% <td><TT>f</TT></td>
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% <td>univariate, vector-valued function (<img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}:\mathbb{R}\rightarrow\mathbb{R}^{m}" title="" />)</td>
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% <td style="text-align:center">1×1<BR>function_handle</td>
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% </tr>
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% <tr>
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% <td style="text-align:center"><TT>x0</TT></td>
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% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;x_{0}" title="" /></td>
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% <td><TT>x0</TT></td>
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% <td>point at which to differentiate</td>
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% <td style="text-align:center">1×1<BR>double</td>
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% </tr>
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% <td style="text-align:center"><TT>h</TT></td>
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% <td><TT>h</TT></td>
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% </tr>
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% <td rowspan="1" style="text-align:center"><b>Output</b></td>
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% <td style="text-align:center"><TT>df</TT></td>
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% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\dfrac{d\mathbf{f}}{dx}\bigg\rvert_{x=x_{0}}" title="" /></td>
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% <td><TT>df</TT></td>
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% <td>derivative of <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(x)" title="" /> evaluated at <img src="https://latex.codecogs.com/svg.latex?\inline&space;x=x_{0}" title="" /></td>
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% <td style="text-align:center">m×1<BR>double</td>
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% </tr>

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‎docs/idirectional_doc.html‎

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<!--
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This HTML was auto-generated from MATLAB code.
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To make changes, update the MATLAB code and republish this document.
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--><title>idirectional</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-08-27"><meta name="DC.source" content="idirectional_doc.m"><style type="text/css">
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--><title>idirectional</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2021-10-09"><meta name="DC.source" content="idirectional_doc.m"><style type="text/css">
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html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}
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html { min-height:100%; margin-bottom:1px; }
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<table border=1>
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<td></td>
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<td style="text-align:center"><b>Variable</b></td>
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<td style="text-align:center"><b>Symbol</b></td>
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<td style="text-align:center"><b>Description</b></td>
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<td style="text-align:center"><b>Format</b></td>
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</tr>
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<tr>
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<td rowspan="4" style="text-align:center"><b>Input</b></td>
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<td style="text-align:center"><TT>f</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;f(\mathbf{x})" title="" /></td>
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<td><TT>f</TT></td>
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<td>multivariate, scalar-valued function (<img src="https://latex.codecogs.com/svg.latex?\inline&space;f:\mathbb{R}^{n}\rightarrow\mathbb{R}" title="" />)</td>
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<td style="text-align:center">1×1<BR>function_handle</td>
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</tr>
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<tr>
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<td style="text-align:center"><TT>x0</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{x}_{0}" title="" /></td>
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<td><TT>x0</TT></td>
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<td>point at which to evaluate the directional derivative</td>
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<td style="text-align:center">n×1<BR>double</td>
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</tr>
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<tr>
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<td style="text-align:center"><TT>v</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{v}" title="" /></td>
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<td><TT>v</TT></td>
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<td>vector defining direction of differentiation</td>
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<td style="text-align:center">n×1<BR>double</td>
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<td style="text-align:center"><TT>h</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
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<td style="text-align:center">1×1<BR>double</td>
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</tr>
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<tr>
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<td rowspan="1" style="text-align:center"><b>Output</b></td>
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<td style="text-align:center"><TT>Dv</TT></td>
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<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;D_{\mathbf{v}}f(\mathbf{x}_{0})" title="" /></td>
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<td><TT>Dv</TT></td>
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<td>directional derivative of <img src="https://latex.codecogs.com/svg.latex?\inline&space;f(\mathbf{x})" title="" />
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evaluated at <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{x}=\mathbf{x}_{0}" title="" />
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in the direction of <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{v}" title="" /></td>
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</pre><pre class="codeoutput">
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Dv =
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</pre><p>Calculating the error,</p><pre class="codeinput">error = Dv-(31250+60*sin(8)^2*cos(8))
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</pre><pre class="codeoutput">
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% <table border=1>
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% <tr>
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% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;f(\mathbf{x})" title="" /></td>
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% <td><TT>f</TT></td>
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% </tr>
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% <td rowspan="1" style="text-align:center"><b>Output</b></td>
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% <td style="text-align:center"><TT>Dv</TT></td>
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% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;D_{\mathbf{v}}f(\mathbf{x}_{0})" title="" /></td>
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% <td>directional derivative of <img src="https://latex.codecogs.com/svg.latex?\inline&space;f(\mathbf{x})" title="" />
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% evaluated at <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{x}=\mathbf{x}_{0}" title="" />
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% in the direction of <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{v}" title="" /></td>

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