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--- 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}
 
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index fbc18ba..0eff86e 100644
--- 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/cdirectional_doc.html b/docs/cdirectional_doc.html
index 12bceb5..166aabd 100644
--- 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
index 36b7ba2..33d0af0 100644
--- 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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diff --git a/docs/chessian_doc.html b/docs/chessian_doc.html
index 93be250..1f4fc77 100644
--- a/docs/chessian_doc.html
+++ b/docs/chessian_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>chessian</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="chessian_doc.m"><style type="text/css">
+      --><title>chessian</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="chessian_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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index f551ca9..da8c11b 100644
--- a/docs/cjacobian_doc.html
+++ b/docs/cjacobian_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>cjacobian</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="cjacobian_doc.m"><style type="text/css">
+      --><title>cjacobian</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="cjacobian_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×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cjacobian_doc_eq11419607670893258163.png" alt="$2n+1$" style="width:30px;height:9px;"> evaluations of <img src="cjacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="cjacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="cjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>cjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="cjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cjacobian_doc_eq11419607670893258163.png" alt="$2n+1$" style="width:30px;height:9px;"> evaluations of <img src="cjacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="cjacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="cjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>cjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="cjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = cjacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -172,7 +172,7 @@
 %       <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>
@@ -186,11 +186,11 @@
 % </html>
 %
 %% Note
-% * This function requires $2n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $2n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |cjacobian| 
 % function, and compare the result to the true result of_
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@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>cpartial</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="cpartial_doc.m"><style type="text/css">
+      --><title>cpartial</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="cpartial_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}
 
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@@ -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>
@@ -111,7 +111,7 @@
           <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="cpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="cpartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="cpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="cpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>cpartial</tt> function, and compare the result to the true result of</i></p><p><img src="cpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="cpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="cpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="cpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="cpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>cpartial</tt> function, and compare the result to the true result of</i></p><p><img src="cpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="cpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="cpartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>cpartial</tt> function,</p><pre class="codeinput">pf = cpartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -196,7 +196,7 @@
 %       <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>
@@ -211,7 +211,6 @@
 %
 %% Note
 % * This function requires 2 evaluations of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |cpartial| function, and compare the
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index b1b4e86..cc7f4c0 100644
--- a/docs/cvechessian_doc.html
+++ b/docs/cvechessian_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>cvechessian</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="cvechessian_doc.m"><style type="text/css">
+      --><title>cvechessian</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="cvechessian_doc.m"><style type="text/css">
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 html { min-height:100%; margin-bottom:1px; }
@@ -69,7 +69,7 @@
 
   </style></head><body><div class="content"><h1><tt>cvechessian</tt></h1><!--introduction--><p>Vector Hessian of a multivariate, vector-valued function using the central difference approximation.</p><p><a href="index.html">Back to Numerical Differentiation Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Note</a></li><li><a href="#5">Example</a></li><li><a href="#8">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">H = cvechessian(f,x0)
 H = cvechessian(f,x0,h)
-</pre><h2 id="2">Description</h2><p><tt>H = cvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a default relative step size of <img src="cvechessian_doc_eq16152409469914233053.png" alt="$h=10^{-200}=\varepsilon^{1/3}$" style="width:81px;height:11px;">, where <img src="cvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = cvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a user-specified relative step size <img src="cvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
+</pre><h2 id="2">Description</h2><p><tt>H = cvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a default relative step size of <img src="cvechessian_doc_eq05291420954647382719.png" alt="$h=\varepsilon^{1/3}$" style="width:37px;height:11px;">, where <img src="cvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = cvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a user-specified relative step size <img src="cvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
   <table border=1>
       <tr>
           <td></td>
@@ -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>
@@ -158,8 +158,7 @@
 % |H = cvechessian(f,x0)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
 % using the central difference approximation with a default relative step 
-% size of $h=10^{-200}=\varepsilon^{1/3}$, where $\varepsilon$ is the 
-% machine zero.
+% size of $h=\varepsilon^{1/3}$, where $\varepsilon$ is the machine zero.
 %
 % |H = cvechessian(f,x0,h)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
@@ -191,7 +190,7 @@
 %       <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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index b3832c2..ad4ec4e 100644
--- a/docs/fderivative_doc.html
+++ b/docs/fderivative_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>fderivative</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="fderivative_doc.m"><style type="text/css">
+      --><title>fderivative</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="fderivative_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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="fderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="fderivative_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="fderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="fderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of <img src="fderivative_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="fderivative_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="fderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="fderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of <img src="fderivative_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 = fderivative(f,2)
 </pre><pre class="codeoutput">
 df =
@@ -118,7 +118,7 @@
 
    2.7816e-07
 
-</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="fderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="fderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of</i></p><p><img src="fderivative_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="fderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="fderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of</i></p><p><img src="fderivative_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 = fderivative(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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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
 % |fderivative| function, and compare the result to the true result of
@@ -215,7 +214,7 @@
 % _at $t=1$ using the |fderivative| 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/fdirectional_doc.html b/docs/fdirectional_doc.html
index 976416a..d275d3a 100644
--- a/docs/fdirectional_doc.html
+++ b/docs/fdirectional_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>fdirectional</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="fdirectional_doc.m"><style type="text/css">
+      --><title>fdirectional</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="fdirectional_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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="fdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="fdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="fdirectional_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="fdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="fdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="fdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>fdirectional</tt> function, and compare the result to the true result of <img src="fdirectional_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="fdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="fdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="fdirectional_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="fdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="fdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="fdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>fdirectional</tt> function, and compare the result to the true result of <img src="fdirectional_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 = fdirectional(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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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 |fdirectional| 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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index c5ce4a3..0f266b6 100644
--- a/docs/fgradient_doc.html
+++ b/docs/fgradient_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>fgradient</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="fgradient_doc.m"><style type="text/css">
+      --><title>fgradient</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="fgradient_doc.m"><style type="text/css">
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 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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
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@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
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index e312eca..d5b9518 100644
--- a/docs/fhessian_doc.html
+++ b/docs/fhessian_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>fhessian</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="fhessian_doc.m"><style type="text/css">
+      --><title>fhessian</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="fhessian_doc.m"><style type="text/css">
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@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
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@@ -168,7 +168,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
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@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>fjacobian</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="fjacobian_doc.m"><style type="text/css">
+      --><title>fjacobian</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="fjacobian_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -105,7 +105,7 @@
           <td style="text-align:center">m×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="fjacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="fjacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="fjacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="fjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>fjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="fjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="fjacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="fjacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="fjacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="fjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>fjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="fjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = fjacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -172,7 +172,7 @@
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 %           <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -186,11 +186,11 @@
 % </html>
 %
 %% Note
-% * This function requires $n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |fjacobian| 
 % function, and compare the result to the true result of_
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@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
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-      --><title>fpartial</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="fpartial_doc.m"><style type="text/css">
+      --><title>fpartial</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="fpartial_doc.m"><style type="text/css">
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@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -111,7 +111,7 @@
           <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="fpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="fpartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="fpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="fpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>fpartial</tt> function, and compare the result to the true result of</i></p><p><img src="fpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="fpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="fpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="fpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="fpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>fpartial</tt> function, and compare the result to the true result of</i></p><p><img src="fpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="fpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="fpartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>fpartial</tt> function,</p><pre class="codeinput">pf = fpartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -196,7 +196,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -211,7 +211,6 @@
 %
 %% Note
 % * This function requires 2 evaluations of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |fpartial| function, and compare the
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+++ b/docs/fvechessian_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>fvechessian</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="fvechessian_doc.m"><style type="text/css">
+      --><title>fvechessian</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="fvechessian_doc.m"><style type="text/css">
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 html { min-height:100%; margin-bottom:1px; }
@@ -69,7 +69,7 @@
 
   </style></head><body><div class="content"><h1><tt>fvechessian</tt></h1><!--introduction--><p>Vector Hessian of a multivariate, vector-valued function using the forward difference approximation.</p><p><a href="index.html">Back to Numerical Differentiation Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Note</a></li><li><a href="#5">Example</a></li><li><a href="#8">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">H = fvechessian(f,x0)
 H = fvechessian(f,x0,h)
-</pre><h2 id="2">Description</h2><p><tt>H = fvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a default relative step size of <img src="fvechessian_doc_eq16152409469914233053.png" alt="$h=10^{-200}=\varepsilon^{1/3}$" style="width:81px;height:11px;">, where <img src="fvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = fvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a user-specified relative step size <img src="fvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
+</pre><h2 id="2">Description</h2><p><tt>H = fvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a default relative step size of <img src="fvechessian_doc_eq05291420954647382719.png" alt="$h=\varepsilon^{1/3}$" style="width:37px;height:11px;">, where <img src="fvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = fvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a user-specified relative step size <img src="fvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
   <table border=1>
       <tr>
           <td></td>
@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -154,8 +154,7 @@
 % |H = fvechessian(f,x0)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
 % using the forward difference approximation with a default relative step 
-% size of $h=10^{-200}=\varepsilon^{1/3}$, where $\varepsilon$ is the 
-% machine zero.
+% size of $h=\varepsilon^{1/3}$, where $\varepsilon$ is the machine zero.
 %
 % |H = fvechessian(f,x0,h)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
@@ -187,7 +186,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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index ecfbb03..b323382 100644
--- a/docs/iabs_doc.html
+++ b/docs/iabs_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.
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+      --><title>iabs</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="iabs_doc.m"><style type="text/css">
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+++ b/docs/iatan2_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
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-      --><title>iatan2</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="iatan2_doc.m"><style type="text/css">
+      --><title>iatan2</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="iatan2_doc.m"><style type="text/css">
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+++ b/docs/iatan2d_doc.html
@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
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-      --><title>iatan2d</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="iatan2d_doc.m"><style type="text/css">
+      --><title>iatan2d</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="iatan2d_doc.m"><style type="text/css">
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index 6834a22..54fdcc7 100644
--- a/docs/iderivative_doc.html
+++ b/docs/iderivative_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>iderivative</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="iderivative_doc.m"><style type="text/css">
+      --><title>iderivative</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="iderivative_doc.m"><style type="text/css">
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@@ -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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</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 1 evaluation of <img src="iderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="iderivative_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="iderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="iderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of <img src="iderivative_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 1 evaluation of <img src="iderivative_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="iderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="iderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of <img src="iderivative_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 = iderivative(f,2)
 </pre><pre class="codeoutput">
 df =
@@ -118,7 +118,7 @@
 
      0
 
-</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="iderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="iderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of</i></p><p><img src="iderivative_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="iderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="iderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of</i></p><p><img src="iderivative_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 = iderivative(f,1)
 </pre><pre class="codeoutput">
 df =
@@ -177,7 +177,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -192,7 +192,6 @@
 %
 %% Note
 % * This function requires 1 evaluation 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
 % |iderivative| function, and compare the result to the true result of
@@ -212,7 +211,7 @@
 % _at $t=1$ using the |iderivative| 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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index a07480c..a3f7900 100644
--- a/docs/idirectional_doc.html
+++ b/docs/idirectional_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>idirectional</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="idirectional_doc.m"><style type="text/css">
+      --><title>idirectional</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="idirectional_doc.m"><style type="text/css">
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 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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</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 1 evaluations of <img src="idirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="idirectional_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="idirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="idirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="idirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>idirectional</tt> function, and compare the result to the true result of <img src="idirectional_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 1 evaluation of <img src="idirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="idirectional_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="idirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="idirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="idirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>idirectional</tt> function, and compare the result to the true result of <img src="idirectional_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 = idirectional(f,x0,v)
@@ -181,7 +181,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -198,12 +198,12 @@
 % </html>
 %
 %% Note
-% * This function requires 1 evaluations of $f(\mathbf{x})$.
+% * This function requires 1 evaluation of $f(\mathbf{x})$.
 % * This implementation does _not_ assume that $\mathbf{v}$ is a unit
 % 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 |idirectional| 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/idot_doc.html b/docs/idot_doc.html
index 8d2d943..f40f1ed 100644
--- a/docs/idot_doc.html
+++ b/docs/idot_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>idot</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="idot_doc.m"><style type="text/css">
+      --><title>idot</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="idot_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/igradient_doc.html b/docs/igradient_doc.html
index 60d7a37..e6cf440 100644
--- a/docs/igradient_doc.html
+++ b/docs/igradient_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>igradient</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="igradient_doc.m"><style type="text/css">
+      --><title>igradient</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="igradient_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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -169,7 +169,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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diff --git a/docs/ihessian_doc.html b/docs/ihessian_doc.html
index 84b5a3a..54fe398 100644
--- a/docs/ihessian_doc.html
+++ b/docs/ihessian_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>ihessian</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="ihessian_doc.m"><style type="text/css">
+      --><title>ihessian</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="ihessian_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; }
@@ -94,13 +94,13 @@
       <tr>
           <td style="text-align:center"><TT>hi</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-          <td>(OPTIONAL) step size for complex-step approximation</td>
+          <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
           <td style="text-align:center"><TT>hc</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-          <td>(OPTIONAL) relative step size for central difference approximation</td>
+          <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -180,13 +180,13 @@
 %       <tr>
 %           <td style="text-align:center"><TT>hi</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-%           <td>(OPTIONAL) step size for complex-step approximation</td>
+%           <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
 %           <td style="text-align:center"><TT>hc</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-%           <td>(OPTIONAL) relative step size for central difference approximation</td>
+%           <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>ijacobian</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="ijacobian_doc.m"><style type="text/css">
+      --><title>ijacobian</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="ijacobian_doc.m"><style type="text/css">
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@@ -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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -105,7 +105,7 @@
           <td style="text-align:center">m×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="ijacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="ijacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="ijacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="ijacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>ijacobian</tt> function, and compare the result to the true result of</i></p><p><img src="ijacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="ijacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="ijacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="ijacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="ijacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>ijacobian</tt> function, and compare the result to the true result of</i></p><p><img src="ijacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = ijacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -169,7 +169,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -183,11 +183,11 @@
 % </html>
 %
 %% Note
-% * This function requires $n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |ijacobian| 
 % function, and compare the result to the true result of_
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+      --><title>imax</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="imax_doc.m"><style type="text/css">
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+      --><title>imin</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="imin_doc.m"><style type="text/css">
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+      --><title>imod</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="imod_doc.m"><style type="text/css">
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+      --><title>Numerical Differentiation Toolbox Documentation</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="index.m"><style type="text/css">
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+      --><title>ipartial</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="ipartial_doc.m"><style type="text/css">
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@@ -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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -111,7 +111,7 @@
           <td style="text-align:center">m×1<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires 1 evaluation of <img src="ipartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="ipartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="ipartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="ipartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>ipartial</tt> function, and compare the result to the true result of</i></p><p><img src="ipartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="ipartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 1 evaluation of <img src="ipartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="ipartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="ipartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>ipartial</tt> function, and compare the result to the true result of</i></p><p><img src="ipartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="ipartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="ipartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>ipartial</tt> function,</p><pre class="codeinput">pf = ipartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -194,7 +194,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -209,7 +209,6 @@
 %
 %% Note
 % * This function requires 1 evaluation of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |ipartial| function, and compare the
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diff --git a/docs/irem_doc.html b/docs/irem_doc.html
index 3c24e7a..a1dcaf4 100644
--- a/docs/irem_doc.html
+++ b/docs/irem_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>irem</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="irem_doc.m"><style type="text/css">
+      --><title>irem</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="irem_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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index 02d53d0..1d5ab0e 100644
--- a/docs/ivechessian_doc.html
+++ b/docs/ivechessian_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>ivechessian</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="ivechessian_doc.m"><style type="text/css">
+      --><title>ivechessian</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="ivechessian_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; }
@@ -94,13 +94,13 @@
       <tr>
           <td style="text-align:center"><TT>hi</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-          <td>(OPTIONAL) relative step size for complex-step approximation</td>
+          <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
           <td style="text-align:center"><TT>hc</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-          <td>(OPTIONAL) relative step size for central difference approximation</td>
+          <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -198,13 +198,13 @@
 %       <tr>
 %           <td style="text-align:center"><TT>hi</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-%           <td>(OPTIONAL) relative step size for complex-step approximation</td>
+%           <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
 %           <td style="text-align:center"><TT>hc</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-%           <td>(OPTIONAL) relative step size for central difference approximation</td>
+%           <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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index 9580450..c8c8b52 100644
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diff --git a/technicaldocumentation/Numerical_Differentiation.pdf b/technicaldocumentation/Numerical_Differentiation.pdf
index c18ef9b..3378f50 100644
Binary files a/technicaldocumentation/Numerical_Differentiation.pdf and b/technicaldocumentation/Numerical_Differentiation.pdf differ
diff --git a/tests/testsuites/TEST_complexified.m b/tests/testsuites/TEST_complexified.m
index d8d9f64..71df451 100644
--- a/tests/testsuites/TEST_complexified.m
+++ b/tests/testsuites/TEST_complexified.m
@@ -131,7 +131,7 @@
 
 %% idot
 
-% vector valued functions of x
+% vector-valued functions of x
 f = @(x) [x;
           x^2;
           x^3];
@@ -150,7 +150,7 @@
 % derivative of dot product of f and g
 dhdx = @(x) dfdx(x).'*g(x)+f(x).'*dgdx(x);
 
-% point at which to differentiate
+% evaluation point
 x0 = 2;
 
 % --------------------------------
@@ -287,7 +287,7 @@
 
 %% inorm
 
-% point at which to differentiate
+% evaluation point
 x0 = [1;
       2;
       3];
diff --git a/tests/testsuites/TEST_partial.m b/tests/testsuites/TEST_partial.m
index 4e85604..5eca871 100644
--- a/tests/testsuites/TEST_partial.m
+++ b/tests/testsuites/TEST_partial.m
@@ -59,7 +59,7 @@
 f = @(x) [x^4;
           x^3];
 
-% true partial derivative with respect to x
+% true partial derivative
 pf_true = @(x) [4*x^3;
                 3*x^2];
 
diff --git a/tests/testsuites/TEST_vechessian.m b/tests/testsuites/TEST_vechessian.m
index a94a913..03d23d3 100644
--- a/tests/testsuites/TEST_vechessian.m
+++ b/tests/testsuites/TEST_vechessian.m
@@ -107,7 +107,7 @@
 f = @(x) [x(1)^5*x(2)+x(1)*sin(x(2))^3;
           x(1)^3+x(2)^4-3*x(1)^2*x(2)^2];
 
-% true vector Hessians
+% true vector Hessian
 H1 = @(x) [20*x(1)^3*x(2),5*x(1)^4+3*sin(x(2))^2*cos(x(2));
            5*x(1)^4+3*sin(x(2))^2*cos(x(2)),...
            6*x(1)*sin(x(2))*cos(x(2))^2-3*x(1)*sin(x(2))^3];
diff --git a/toolbox/doc/Numerical_Differentiation.pdf b/toolbox/doc/Numerical_Differentiation.pdf
index c18ef9b..3378f50 100644
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@@ -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}
 
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+++ b/toolbox/doc/html_NDT/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/toolbox/doc/html_NDT/cdirectional_doc.html b/toolbox/doc/html_NDT/cdirectional_doc.html
index 12bceb5..166aabd 100644
--- a/toolbox/doc/html_NDT/cdirectional_doc.html
+++ b/toolbox/doc/html_NDT/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;
diff --git a/toolbox/doc/html_NDT/cdirectional_doc_eq01316382371180660608.png b/toolbox/doc/html_NDT/cdirectional_doc_eq01316382371180660608.png
index 7cbbe03..0686e65 100644
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diff --git a/toolbox/doc/html_NDT/cgradient_doc.html b/toolbox/doc/html_NDT/cgradient_doc.html
index 36b7ba2..33d0af0 100644
--- a/toolbox/doc/html_NDT/cgradient_doc.html
+++ b/toolbox/doc/html_NDT/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>
diff --git a/toolbox/doc/html_NDT/cgradient_doc_eq01316382371180660608.png b/toolbox/doc/html_NDT/cgradient_doc_eq01316382371180660608.png
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diff --git a/toolbox/doc/html_NDT/chessian_doc.html b/toolbox/doc/html_NDT/chessian_doc.html
index 93be250..1f4fc77 100644
--- a/toolbox/doc/html_NDT/chessian_doc.html
+++ b/toolbox/doc/html_NDT/chessian_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>chessian</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="chessian_doc.m"><style type="text/css">
+      --><title>chessian</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="chessian_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>
diff --git a/toolbox/doc/html_NDT/chessian_doc_eq01316382371180660608.png b/toolbox/doc/html_NDT/chessian_doc_eq01316382371180660608.png
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index ad38f02..a30d194 100644
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index cdeaeed..039b70b 100644
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diff --git a/toolbox/doc/html_NDT/cjacobian_doc.html b/toolbox/doc/html_NDT/cjacobian_doc.html
index f551ca9..da8c11b 100644
--- a/toolbox/doc/html_NDT/cjacobian_doc.html
+++ b/toolbox/doc/html_NDT/cjacobian_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>cjacobian</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="cjacobian_doc.m"><style type="text/css">
+      --><title>cjacobian</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="cjacobian_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×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cjacobian_doc_eq11419607670893258163.png" alt="$2n+1$" style="width:30px;height:9px;"> evaluations of <img src="cjacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="cjacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="cjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>cjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="cjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="cjacobian_doc_eq11419607670893258163.png" alt="$2n+1$" style="width:30px;height:9px;"> evaluations of <img src="cjacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="cjacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="cjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>cjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="cjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = cjacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -172,7 +172,7 @@
 %       <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>
@@ -186,11 +186,11 @@
 % </html>
 %
 %% Note
-% * This function requires $2n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $2n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |cjacobian| 
 % function, and compare the result to the true result of_
diff --git a/toolbox/doc/html_NDT/cjacobian_doc_eq01917383932827545039.png b/toolbox/doc/html_NDT/cjacobian_doc_eq01917383932827545039.png
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diff --git a/toolbox/doc/html_NDT/cpartial_doc.html b/toolbox/doc/html_NDT/cpartial_doc.html
index fcd952d..c5b293b 100644
--- a/toolbox/doc/html_NDT/cpartial_doc.html
+++ b/toolbox/doc/html_NDT/cpartial_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>cpartial</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="cpartial_doc.m"><style type="text/css">
+      --><title>cpartial</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="cpartial_doc.m"><style type="text/css">
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 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>
@@ -111,7 +111,7 @@
           <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="cpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="cpartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="cpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="cpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>cpartial</tt> function, and compare the result to the true result of</i></p><p><img src="cpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="cpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="cpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="cpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="cpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>cpartial</tt> function, and compare the result to the true result of</i></p><p><img src="cpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="cpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="cpartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="cpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>cpartial</tt> function,</p><pre class="codeinput">pf = cpartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -196,7 +196,7 @@
 %       <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>
@@ -211,7 +211,6 @@
 %
 %% Note
 % * This function requires 2 evaluations of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |cpartial| function, and compare the
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index b1b4e86..cc7f4c0 100644
--- a/toolbox/doc/html_NDT/cvechessian_doc.html
+++ b/toolbox/doc/html_NDT/cvechessian_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>cvechessian</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="cvechessian_doc.m"><style type="text/css">
+      --><title>cvechessian</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="cvechessian_doc.m"><style type="text/css">
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@@ -69,7 +69,7 @@
 
   </style></head><body><div class="content"><h1><tt>cvechessian</tt></h1><!--introduction--><p>Vector Hessian of a multivariate, vector-valued function using the central difference approximation.</p><p><a href="index.html">Back to Numerical Differentiation Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Note</a></li><li><a href="#5">Example</a></li><li><a href="#8">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">H = cvechessian(f,x0)
 H = cvechessian(f,x0,h)
-</pre><h2 id="2">Description</h2><p><tt>H = cvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a default relative step size of <img src="cvechessian_doc_eq16152409469914233053.png" alt="$h=10^{-200}=\varepsilon^{1/3}$" style="width:81px;height:11px;">, where <img src="cvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = cvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a user-specified relative step size <img src="cvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
+</pre><h2 id="2">Description</h2><p><tt>H = cvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a default relative step size of <img src="cvechessian_doc_eq05291420954647382719.png" alt="$h=\varepsilon^{1/3}$" style="width:37px;height:11px;">, where <img src="cvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = cvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="cvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="cvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="cvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the central difference approximation with a user-specified relative step size <img src="cvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
   <table border=1>
       <tr>
           <td></td>
@@ -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>
@@ -158,8 +158,7 @@
 % |H = cvechessian(f,x0)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
 % using the central difference approximation with a default relative step 
-% size of $h=10^{-200}=\varepsilon^{1/3}$, where $\varepsilon$ is the 
-% machine zero.
+% size of $h=\varepsilon^{1/3}$, where $\varepsilon$ is the machine zero.
 %
 % |H = cvechessian(f,x0,h)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
@@ -191,7 +190,7 @@
 %       <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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diff --git a/toolbox/doc/html_NDT/fderivative_doc.html b/toolbox/doc/html_NDT/fderivative_doc.html
index b3832c2..ad4ec4e 100644
--- a/toolbox/doc/html_NDT/fderivative_doc.html
+++ b/toolbox/doc/html_NDT/fderivative_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>fderivative</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="fderivative_doc.m"><style type="text/css">
+      --><title>fderivative</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="fderivative_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}
 
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@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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="fderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="fderivative_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="fderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="fderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of <img src="fderivative_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="fderivative_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="fderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="fderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of <img src="fderivative_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 = fderivative(f,2)
 </pre><pre class="codeoutput">
 df =
@@ -118,7 +118,7 @@
 
    2.7816e-07
 
-</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="fderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="fderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of</i></p><p><img src="fderivative_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="fderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="fderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>fderivative</tt> function, and compare the result to the true result of</i></p><p><img src="fderivative_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 = fderivative(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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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
 % |fderivative| function, and compare the result to the true result of
@@ -215,7 +214,7 @@
 % _at $t=1$ using the |fderivative| 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/toolbox/doc/html_NDT/fdirectional_doc.html b/toolbox/doc/html_NDT/fdirectional_doc.html
index 976416a..d275d3a 100644
--- a/toolbox/doc/html_NDT/fdirectional_doc.html
+++ b/toolbox/doc/html_NDT/fdirectional_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>fdirectional</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="fdirectional_doc.m"><style type="text/css">
+      --><title>fdirectional</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="fdirectional_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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="fdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="fdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="fdirectional_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="fdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="fdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="fdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>fdirectional</tt> function, and compare the result to the true result of <img src="fdirectional_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="fdirectional_doc_eq10041624201793903543.png" alt="$2$" style="width:5px;height:8px;"> evaluations of <img src="fdirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="fdirectional_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="fdirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="fdirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="fdirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>fdirectional</tt> function, and compare the result to the true result of <img src="fdirectional_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 = fdirectional(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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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 |fdirectional| 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;
diff --git a/toolbox/doc/html_NDT/fdirectional_doc_eq01316382371180660608.png b/toolbox/doc/html_NDT/fdirectional_doc_eq01316382371180660608.png
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diff --git a/toolbox/doc/html_NDT/fgradient_doc.html b/toolbox/doc/html_NDT/fgradient_doc.html
index c5ce4a3..0f266b6 100644
--- a/toolbox/doc/html_NDT/fgradient_doc.html
+++ b/toolbox/doc/html_NDT/fgradient_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>fgradient</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="fgradient_doc.m"><style type="text/css">
+      --><title>fgradient</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="fgradient_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
diff --git a/toolbox/doc/html_NDT/fgradient_doc_eq01316382371180660608.png b/toolbox/doc/html_NDT/fgradient_doc_eq01316382371180660608.png
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diff --git a/toolbox/doc/html_NDT/fhessian_doc.html b/toolbox/doc/html_NDT/fhessian_doc.html
index e312eca..d5b9518 100644
--- a/toolbox/doc/html_NDT/fhessian_doc.html
+++ b/toolbox/doc/html_NDT/fhessian_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>fhessian</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="fhessian_doc.m"><style type="text/css">
+      --><title>fhessian</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="fhessian_doc.m"><style type="text/css">
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 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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -168,7 +168,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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diff --git a/toolbox/doc/html_NDT/fjacobian_doc.html b/toolbox/doc/html_NDT/fjacobian_doc.html
index 26fab80..a06a48b 100644
--- a/toolbox/doc/html_NDT/fjacobian_doc.html
+++ b/toolbox/doc/html_NDT/fjacobian_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>fjacobian</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="fjacobian_doc.m"><style type="text/css">
+      --><title>fjacobian</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="fjacobian_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -105,7 +105,7 @@
           <td style="text-align:center">m×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="fjacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="fjacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="fjacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="fjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>fjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="fjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="fjacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="fjacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="fjacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="fjacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>fjacobian</tt> function, and compare the result to the true result of</i></p><p><img src="fjacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = fjacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -172,7 +172,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -186,11 +186,11 @@
 % </html>
 %
 %% Note
-% * This function requires $n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |fjacobian| 
 % function, and compare the result to the true result of_
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diff --git a/toolbox/doc/html_NDT/fpartial_doc.html b/toolbox/doc/html_NDT/fpartial_doc.html
index 861ef85..2cec734 100644
--- a/toolbox/doc/html_NDT/fpartial_doc.html
+++ b/toolbox/doc/html_NDT/fpartial_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>fpartial</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="fpartial_doc.m"><style type="text/css">
+      --><title>fpartial</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="fpartial_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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -111,7 +111,7 @@
           <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="fpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="fpartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="fpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="fpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>fpartial</tt> function, and compare the result to the true result of</i></p><p><img src="fpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="fpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 2 evaluations of <img src="fpartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="fpartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="fpartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>fpartial</tt> function, and compare the result to the true result of</i></p><p><img src="fpartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="fpartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="fpartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="fpartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>fpartial</tt> function,</p><pre class="codeinput">pf = fpartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -196,7 +196,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\sqrt{\varepsilon}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -211,7 +211,6 @@
 %
 %% Note
 % * This function requires 2 evaluations of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |fpartial| function, and compare the
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@@ -6,7 +6,7 @@
    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>fvechessian</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="fvechessian_doc.m"><style type="text/css">
+      --><title>fvechessian</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="fvechessian_doc.m"><style type="text/css">
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@@ -69,7 +69,7 @@
 
   </style></head><body><div class="content"><h1><tt>fvechessian</tt></h1><!--introduction--><p>Vector Hessian of a multivariate, vector-valued function using the forward difference approximation.</p><p><a href="index.html">Back to Numerical Differentiation Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">Note</a></li><li><a href="#5">Example</a></li><li><a href="#8">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">H = fvechessian(f,x0)
 H = fvechessian(f,x0,h)
-</pre><h2 id="2">Description</h2><p><tt>H = fvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a default relative step size of <img src="fvechessian_doc_eq16152409469914233053.png" alt="$h=10^{-200}=\varepsilon^{1/3}$" style="width:81px;height:11px;">, where <img src="fvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = fvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a user-specified relative step size <img src="fvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
+</pre><h2 id="2">Description</h2><p><tt>H = fvechessian(f,x0)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a default relative step size of <img src="fvechessian_doc_eq05291420954647382719.png" alt="$h=\varepsilon^{1/3}$" style="width:37px;height:11px;">, where <img src="fvechessian_doc_eq13794615980392037191.png" alt="$\varepsilon$" style="width:5px;height:6px;"> is the machine zero.</p><p><tt>H = fvechessian(f,x0,h)</tt> numerically evaluates the vector Hessian of <img src="fvechessian_doc_eq15898890414513100043.png" alt="$\mathbf{f}$" style="width:5px;height:8px;"> with respect to <img src="fvechessian_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> at <img src="fvechessian_doc_eq13769496404156091705.png" alt="$\mathbf{x}=\mathbf{x}_{0}$" style="width:32px;height:7px;"> using the forward difference approximation with a user-specified relative step size <img src="fvechessian_doc_eq16410644637423230129.png" alt="$h$" style="width:6px;height:8px;">.</p><h2 id="3">Input/Output Parameters</h2><p>
   <table border=1>
       <tr>
           <td></td>
@@ -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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -154,8 +154,7 @@
 % |H = fvechessian(f,x0)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
 % using the forward difference approximation with a default relative step 
-% size of $h=10^{-200}=\varepsilon^{1/3}$, where $\varepsilon$ is the 
-% machine zero.
+% size of $h=\varepsilon^{1/3}$, where $\varepsilon$ is the machine zero.
 %
 % |H = fvechessian(f,x0,h)| numerically evaluates the vector Hessian of 
 % $\mathbf{f}$ with respect to $\mathbf{x}$ at $\mathbf{x}=\mathbf{x}_{0}$ 
@@ -187,7 +186,7 @@
 %       <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 <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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diff --git a/toolbox/doc/html_NDT/iatan2d_doc.html b/toolbox/doc/html_NDT/iatan2d_doc.html
index 21168cb..e73e56a 100644
--- a/toolbox/doc/html_NDT/iatan2d_doc.html
+++ b/toolbox/doc/html_NDT/iatan2d_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>iatan2d</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="iatan2d_doc.m"><style type="text/css">
+      --><title>iatan2d</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="iatan2d_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; }
diff --git a/toolbox/doc/html_NDT/iatan2d_doc_eq18006487826433731914.png b/toolbox/doc/html_NDT/iatan2d_doc_eq18006487826433731914.png
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diff --git a/toolbox/doc/html_NDT/iderivative_doc.html b/toolbox/doc/html_NDT/iderivative_doc.html
index 6834a22..54fdcc7 100644
--- a/toolbox/doc/html_NDT/iderivative_doc.html
+++ b/toolbox/doc/html_NDT/iderivative_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>iderivative</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="iderivative_doc.m"><style type="text/css">
+      --><title>iderivative</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="iderivative_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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</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 1 evaluation of <img src="iderivative_doc_eq15621115338434299399.png" alt="$\mathbf{f}(x)$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="iderivative_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="iderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="iderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of <img src="iderivative_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 1 evaluation of <img src="iderivative_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="iderivative_doc_eq07863013981449083213.png" alt="$f(x)=x^{3}$" style="width:46px;height:12px;"> at <img src="iderivative_doc_eq04851200360885152548.png" alt="$x=2$" style="width:26px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of <img src="iderivative_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 = iderivative(f,2)
 </pre><pre class="codeoutput">
 df =
@@ -118,7 +118,7 @@
 
      0
 
-</pre><h2 id="7">Example #2: Derivative of a vector-valued function.</h2><p><i>Approximate the derivative of</i></p><p><img src="iderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="iderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of</i></p><p><img src="iderivative_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="iderivative_doc_eq05437446654055475759.png" alt="$$\mathbf{f}(t)=\pmatrix{\sin{t}\cr\cos{t}}$$" style="width:71px;height:27px;"></p><p><i>at <img src="iderivative_doc_eq06658196661290597197.png" alt="$t=1$" style="width:23px;height:8px;"> using the <tt>iderivative</tt> function, and compare the result to the true result of</i></p><p><img src="iderivative_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 = iderivative(f,1)
 </pre><pre class="codeoutput">
 df =
@@ -177,7 +177,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -192,7 +192,6 @@
 %
 %% Note
 % * This function requires 1 evaluation 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
 % |iderivative| function, and compare the result to the true result of
@@ -212,7 +211,7 @@
 % _at $t=1$ using the |iderivative| 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)];
diff --git a/toolbox/doc/html_NDT/iderivative_doc_eq04851200360885152548.png b/toolbox/doc/html_NDT/iderivative_doc_eq04851200360885152548.png
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diff --git a/toolbox/doc/html_NDT/idirectional_doc.html b/toolbox/doc/html_NDT/idirectional_doc.html
index a07480c..a3f7900 100644
--- a/toolbox/doc/html_NDT/idirectional_doc.html
+++ b/toolbox/doc/html_NDT/idirectional_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>idirectional</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="idirectional_doc.m"><style type="text/css">
+      --><title>idirectional</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="idirectional_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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</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 1 evaluations of <img src="idirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="idirectional_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="idirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="idirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="idirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>idirectional</tt> function, and compare the result to the true result of <img src="idirectional_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 1 evaluation of <img src="idirectional_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li><li>This implementation does <i>not</i> assume that <img src="idirectional_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="idirectional_doc_eq01884748342197511736.png" alt="$f(\mathbf{x})=x_{1}^{5}+\sin^{3}{x_{2}}$" style="width:90px;height:13px;"> at <img src="idirectional_doc_eq12407751216247896965.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,8)^{T}$" style="width:77px;height:13px;"> in the direction of <img src="idirectional_doc_eq09462939248311057343.png" alt="$\mathbf{v}=(10,20)^{T}$" style="width:63px;height:13px;"> using the <tt>idirectional</tt> function, and compare the result to the true result of <img src="idirectional_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 = idirectional(f,x0,v)
@@ -181,7 +181,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -198,12 +198,12 @@
 % </html>
 %
 %% Note
-% * This function requires 1 evaluations of $f(\mathbf{x})$.
+% * This function requires 1 evaluation of $f(\mathbf{x})$.
 % * This implementation does _not_ assume that $\mathbf{v}$ is a unit
 % 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 |idirectional| 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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-%           <td>(OPTIONAL) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
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-          <td>(OPTIONAL) relative step size for central difference approximation</td>
+          <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
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-%           <td>(OPTIONAL) relative step size for central difference approximation</td>
+%           <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
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+      --><title>ijacobian</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="ijacobian_doc.m"><style type="text/css">
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       <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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -105,7 +105,7 @@
           <td style="text-align:center">m×n<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="ijacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="ijacobian_doc_eq01316382371180660608.png" alt="$f(\mathbf{x})$" style="width:21px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="ijacobian_doc_eq04102358847639648958.png" alt="$$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:102px;height:48px;"></p><p><i>at <img src="ijacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>ijacobian</tt> function, and compare the result to the true result of</i></p><p><img src="ijacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
+</p><h2 id="4">Note</h2><div><ul><li>This function requires <img src="ijacobian_doc_eq06671788856257458288.png" alt="$n+1$" style="width:25px;height:9px;"> evaluations of <img src="ijacobian_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example</h2><p><i>Approximate the Jacobian of</i></p><p><img src="ijacobian_doc_eq01917383932827545039.png" alt="$$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$" style="width:101px;height:48px;"></p><p><i>at <img src="ijacobian_doc_eq14200116697587921679.png" alt="$\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$" style="width:88px;height:13px;"> using the <tt>ijacobian</tt> function, and compare the result to the true result of</i></p><p><img src="ijacobian_doc_eq02119102318186630099.png" alt="$$\mathbf{J}(\mathbf{x}_{0})=\pmatrix{1 &amp; 0 &amp; 0 \cr 0 &amp; 0 &amp; 5 \cr 0 &amp; 48&#xA;&amp; -2 \cr 7\cos{(5)} &amp; 0 &amp; \sin{(5)}}$$" style="width:161px;height:50px;"></p><p>Approximating the Jacobian,</p><pre class="codeinput">f = @(x) [x(1);5*x(3);4*x(2)^2-2*x(3);x(3)*sin(x(1))];
 x0 = [5;6;7];
 J = ijacobian(f,x0)
 </pre><pre class="codeoutput">
@@ -169,7 +169,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -183,11 +183,11 @@
 % </html>
 %
 %% Note
-% * This function requires $n+1$ evaluations of $f(\mathbf{x})$.
+% * This function requires $n+1$ evaluations of $\mathbf{f}(\mathbf{x})$.
 %% Example
 % _Approximate the Jacobian of_
 %
-% $$f(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
+% $$\mathbf{f}(\mathbf{x})=\pmatrix{x_{1} \cr 5x_{3} \cr 4x_{2}^{2}-2x_{3} \cr x_{3}\sin{x_{1}}}$$
 %
 % _at $\mathbf{x}=\mathbf{x}_{0}=(5,6,7)^{T}$ using the |ijacobian| 
 % function, and compare the result to the true result of_
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diff --git a/toolbox/doc/html_NDT/imax_doc.html b/toolbox/doc/html_NDT/imax_doc.html
index f0384df..255d4a7 100644
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+++ b/toolbox/doc/html_NDT/imax_doc.html
@@ -6,7 +6,7 @@
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 This HTML was auto-generated from MATLAB code.
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+      --><title>imax</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="imax_doc.m"><style type="text/css">
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diff --git a/toolbox/doc/html_NDT/imin_doc.html b/toolbox/doc/html_NDT/imin_doc.html
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--- a/toolbox/doc/html_NDT/imin_doc.html
+++ b/toolbox/doc/html_NDT/imin_doc.html
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    <!--
 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
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+      --><title>imin</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="imin_doc.m"><style type="text/css">
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diff --git a/toolbox/doc/html_NDT/imod_doc.html b/toolbox/doc/html_NDT/imod_doc.html
index ae073b7..d1a7e66 100644
--- a/toolbox/doc/html_NDT/imod_doc.html
+++ b/toolbox/doc/html_NDT/imod_doc.html
@@ -6,7 +6,7 @@
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 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>imod</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="imod_doc.m"><style type="text/css">
+      --><title>imod</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="imod_doc.m"><style type="text/css">
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index 6c1f5fb..778974c 100644
--- a/toolbox/doc/html_NDT/index.html
+++ b/toolbox/doc/html_NDT/index.html
@@ -6,7 +6,7 @@
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 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
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+      --><title>Numerical Differentiation Toolbox Documentation</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="index.m"><style type="text/css">
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diff --git a/toolbox/doc/html_NDT/inorm_doc.html b/toolbox/doc/html_NDT/inorm_doc.html
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--- a/toolbox/doc/html_NDT/inorm_doc.html
+++ b/toolbox/doc/html_NDT/inorm_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.
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+      --><title>inorm</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="inorm_doc.m"><style type="text/css">
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diff --git a/toolbox/doc/html_NDT/ipartial_doc.html b/toolbox/doc/html_NDT/ipartial_doc.html
index f3205d8..9fc66c5 100644
--- a/toolbox/doc/html_NDT/ipartial_doc.html
+++ b/toolbox/doc/html_NDT/ipartial_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>ipartial</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="ipartial_doc.m"><style type="text/css">
+      --><title>ipartial</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="ipartial_doc.m"><style type="text/css">
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 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) step size</td>
+          <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -111,7 +111,7 @@
           <td style="text-align:center">m×1<BR>double</td>
       </tr>
   </table>
-</p><h2 id="4">Note</h2><div><ul><li>This function requires 1 evaluation of <img src="ipartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li><li>If the function is scalar-valued, then <img src="ipartial_doc_eq14613861381496079316.png" alt="$m=1$" style="width:29px;height:8px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="ipartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="ipartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>ipartial</tt> function, and compare the result to the true result of</i></p><p><img src="ipartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="ipartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
+</p><h2 id="4">Note</h2><div><ul><li>This function requires 1 evaluation of <img src="ipartial_doc_eq03403988016607310992.png" alt="$\mathbf{f}(\mathbf{x})$" style="width:19px;height:11px;">.</li></ul></div><h2 id="5">Example #1: Partial derivative of a scalar-valued function.</h2><p><i>Approximate the partial derivative of <img src="ipartial_doc_eq06064307167709903380.png" alt="$f(x,y)=x^{3}\sin{y}$" style="width:80px;height:12px;"> with respect to <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;"> at at <img src="ipartial_doc_eq06799230972799164765.png" alt="$(x,y)=(5,1)$" style="width:63px;height:11px;"> using the <tt>ipartial</tt> function, and compare the result to the true result of</i></p><p><img src="ipartial_doc_eq09129385801709187487.png" alt="$$\left.\frac{\partial f}{\partial y}\right|_{(x,y)=(5,1)}=5^{3}\cos{(1)}$$" style="width:113px;height:29px;"></p><p>First, we rewrite this function as <img src="ipartial_doc_eq00554480612770079530.png" alt="$f(\mathbf{x})=x_{1}^{3}\sin{x_{2}}$" style="width:74px;height:12px;">.</p><pre class="codeinput">f = @(x) x(1)^3*sin(x(2));
 </pre><p>Since the second component of <img src="ipartial_doc_eq17274866754917724950.png" alt="$\mathbf{x}$" style="width:7px;height:5px;"> represents <img src="ipartial_doc_eq14521328786523663806.png" alt="$y$" style="width:6px;height:8px;">, to approximate the derivative, we use</p><pre class="codeinput">k = 2;
 </pre><p>Approximating the partial derivative using the <tt>ipartial</tt> function,</p><pre class="codeinput">pf = ipartial(f,[5;1],k)
 </pre><pre class="codeoutput">
@@ -194,7 +194,7 @@
 %       <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) step size</td>
+%           <td>(OPTIONAL) step size (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
@@ -209,7 +209,6 @@
 %
 %% Note
 % * This function requires 1 evaluation of $\mathbf{f}(\mathbf{x})$.
-% * If the function is scalar-valued, then $m=1$.
 %% Example #1: Partial derivative of a scalar-valued function.
 % _Approximate the partial derivative of $f(x,y)=x^{3}\sin{y}$ with respect
 % to $y$ at at $(x,y)=(5,1)$ using the |ipartial| function, and compare the
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+++ b/toolbox/doc/html_NDT/irem_doc.html
@@ -6,7 +6,7 @@
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 This HTML was auto-generated from MATLAB code.
 To make changes, update the MATLAB code and republish this document.
-      --><title>irem</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="irem_doc.m"><style type="text/css">
+      --><title>irem</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="irem_doc.m"><style type="text/css">
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--- a/toolbox/doc/html_NDT/ivechessian_doc.html
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+      --><title>ivechessian</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="ivechessian_doc.m"><style type="text/css">
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@@ -94,13 +94,13 @@
       <tr>
           <td style="text-align:center"><TT>hi</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-          <td>(OPTIONAL) relative step size for complex-step approximation</td>
+          <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
           <td style="text-align:center"><TT>hc</TT></td>
           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-          <td>(OPTIONAL) relative step size for central difference approximation</td>
+          <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
           <td style="text-align:center">1×1<BR>double</td>
       </tr>
       <tr>
@@ -198,13 +198,13 @@
 %       <tr>
 %           <td style="text-align:center"><TT>hi</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}" title="" /></td>
-%           <td>(OPTIONAL) relative step size for complex-step approximation</td>
+%           <td>(OPTIONAL) step size for complex-step approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{i}=10^{-200}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
 %           <td style="text-align:center"><TT>hc</TT></td>
 %           <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}" title="" /></td>
-%           <td>(OPTIONAL) relative step size for central difference approximation</td>
+%           <td>(OPTIONAL) relative step size for central difference approximation (defaults to <img src="https://latex.codecogs.com/svg.latex?\inline&space;h_{c}=\varepsilon^{1/3}" title="" />)</td>
 %           <td style="text-align:center">1×1<BR>double</td>
 %       </tr>
 %       <tr>
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