fixed mistakes and typos in documentation

tamaskis · Nov 29, 2022 · b0cdbd9 · b0cdbd9
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diff --git a/INSTALL/Numerical Differentiation Toolbox.mltbx b/INSTALL/Numerical Differentiation Toolbox.mltbx
diff --git a/docs/Differentiator_doc.html b/docs/Differentiator_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>Differentiator</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-12"><meta name="DC.source" content="Differentiator_doc.m"><style type="text/css">
+      --><title>Differentiator</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-28"><meta name="DC.source" content="Differentiator_doc.m"><style type="text/css">
 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}
 
 html { min-height:100%; margin-bottom:1px; }

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diff --git a/docs/cderivative_doc.html b/docs/cderivative_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>cderivative</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-12"><meta name="DC.source" content="cderivative_doc.m"><style type="text/css">
+      --><title>cderivative</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-28"><meta name="DC.source" content="cderivative_doc.m"><style type="text/css">
 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}
 
 html { min-height:100%; margin-bottom:1px; }
@@ -94,7 +94,7 @@
       <tr>
           <td style="text-align:center"><TT>h</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-          <td>(OPTIONAL) relative step size</td>
+          <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -105,7 +105,7 @@
           <td style="text-align:center">m×1<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="cderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="cderivative_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Derivative of a scalar-valued function.</h2><p><i>Approximate the derivative of <img src="cderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="cderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>cderivative</tt> function, and compare the result to the true result of <img src="cderivative_doc_eq13447770136917483844.png" alt="$f'(2)=12$" style="width:48px;height:12px;"></i>.</p><p>Approximating the derivative,</p><pre class="codeinput">f = @(x) x^3;
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="cderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Derivative of a scalar-valued function.</h2><p><i>Approximate the derivative of <img src="cderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="cderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>cderivative</tt> function, and compare the result to the true result of <img src="cderivative_doc_eq13447770136917483844.png" alt="$f'(2)=12$" style="width:48px;height:12px;"></i>.</p><p>Approximating the derivative,</p><pre class="codeinput">f = @(x) x^3;
 df = cderivative(f,2)
 </pre><pre class="codeoutput">
 df =
@@ -118,7 +118,7 @@
 
    3.3153e-10
 
-</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="cderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="cderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>cderivative</tt> function, and compare the result to the true result of</i></p><p><img src="cderivative_doc_eq07637929496866620270.png" alt="$$\left.\frac{d\mathbf{f}}{dx}\right|_{t=1}=\pmatrix{\cos{(1)}\cr-\sin{(1)}}$$" style="width:103px;height:28px;"></p><p>Approximating the derivative,</p><pre class="codeinput">f = @(t) [sin(t);cos(t)];
+</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="cderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="cderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>cderivative</tt> function, and compare the result to the true result of</i></p><p><img src="cderivative_doc_eq07766495636705099736.png" alt="$$\left.\frac{d\mathbf{f}}{dt}\right|_{t=1}=\pmatrix{\cos{(1)}\cr-\sin{(1)}}$$" style="width:102px;height:28px;"></p><p>Approximating the derivative,</p><pre class="codeinput">f = @(t) [sin(t);cos(t)];
 df = cderivative(f,1)
 </pre><pre class="codeoutput">
 df =
@@ -180,7 +180,7 @@
 %       <tr>
 %           <td style="text-align:center"><TT>h</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-%           <td>(OPTIONAL) relative step size</td>
+%           <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -195,7 +195,6 @@
 %
 %% Note
 % * This function requires 2 evaluations of $\mathbf{f}(x)$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Derivative of a scalar-valued function.
 % _Approximate the derivative of $f(x)=x^{3}$ at $x=2$ using the
 % |cderivative| function, and compare the result to the true result of
@@ -215,7 +214,7 @@
 % _at $t=1$ using the |cderivative| function, and compare the result to the
 % true result of_
 %
-% $$\left.\frac{d\mathbf{f}}{dx}\right|_{t=1}=\pmatrix{\cos{(1)}\cr-\sin{(1)}}$$
+% $$\left.\frac{d\mathbf{f}}{dt}\right|_{t=1}=\pmatrix{\cos{(1)}\cr-\sin{(1)}}$$
 %
 % Approximating the derivative,
 f = @(t) [sin(t);cos(t)];

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diff --git a/docs/cderivative_doc_eq16410644637423230129.png b/docs/cderivative_doc_eq16410644637423230129.png
diff --git a/docs/cdirectional_doc.html b/docs/cdirectional_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>cdirectional</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-12"><meta name="DC.source" content="cdirectional_doc.m"><style type="text/css">
+      --><title>cdirectional</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-28"><meta name="DC.source" content="cdirectional_doc.m"><style type="text/css">
 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}
 
 html { min-height:100%; margin-bottom:1px; }
@@ -100,7 +100,7 @@
       <tr>
           <td style="text-align:center"><TT>h</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-          <td>(OPTIONAL) relative step size</td>
+          <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -114,7 +114,7 @@
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="cdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="cdirectional_doc_eq18424963133433540026.png" alt="$\mathbf{v}$" style="width:7px;height:6px;"> is a unit vector.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the directional derivative of <img src="cdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="cdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="cdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>cdirectional</tt> function, and compare the result to the true result of <img src="cdirectional_doc_eq01523243179362375954.png" alt="$D_{\mathbf{v}}f(\mathbf{x}_{0})=31250+60\sin^{2}{(8)}\cos{(8)}$" style="width:175px;height:13px;"></i>.</p><p>Approximating the directional derivative,</p><pre class="codeinput">f = @(x) x(1)^5+sin(x(2))^3;
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="cdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="cdirectional_doc_eq18424963133433540026.png" alt="$\mathbf{v}$" style="width:7px;height:6px;"> is a unit vector.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the directional derivative of <img src="cdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="cdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="cdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>cdirectional</tt> function, and compare the result to the true result of <img src="cdirectional_doc_eq16691412183709307600.png" alt="$\nabla_{\mathbf{v}}f(\mathbf{x}_{0})=31250+60\sin^{2}{(8)}\cos{(8)}$" style="width:174px;height:13px;"></i>.</p><p>Approximating the directional derivative,</p><pre class="codeinput">f = @(x) x(1)^5+sin(x(2))^3;
 x0 = [5;8];
 v = [10;20];
 Dv = cdirectional(f,x0,v)
@@ -183,7 +183,7 @@
 %       <tr>
 %           <td style="text-align:center"><TT>h</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-%           <td>(OPTIONAL) relative step size</td>
+%           <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -205,7 +205,7 @@
 % vector.
 %% Example
 % _Approximate the directional derivative of $f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$ at $\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$ in the direction of $\mathbf{v}=(10,20)^{T}$ using the |cdirectional| function, and compare the result to the true 
-% result of $D_{\mathbf{v}}f(\mathbf{x}_{0})=31250+60\sin^{2}{(8)}\cos{(8)}$_.
+% result of $\nabla_{\mathbf{v}}f(\mathbf{x}_{0})=31250+60\sin^{2}{(8)}\cos{(8)}$_.
 %
 % Approximating the directional derivative,
 f = @(x) x(1)^5+sin(x(2))^3;

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diff --git a/docs/cgradient_doc.html b/docs/cgradient_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>cgradient</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-12"><meta name="DC.source" content="cgradient_doc.m"><style type="text/css">
+      --><title>cgradient</title><meta name="generator" content="MATLAB 9.12"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-11-28"><meta name="DC.source" content="cgradient_doc.m"><style type="text/css">
 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}
 
 html { min-height:100%; margin-bottom:1px; }
@@ -94,7 +94,7 @@
       <tr>
           <td style="text-align:center"><TT>h</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-          <td>(OPTIONAL) relative step size</td>
+          <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -170,7 +170,7 @@
 %       <tr>
 %           <td style="text-align:center"><TT>h</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="" /></td>
-%           <td>(OPTIONAL) relative step size</td>
+%           <td>(OPTIONAL) relative step size (defaults to $h=\varepsilon^{1/3}$)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>

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@@ -94,7 +94,7 @@
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