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add vector class and matrix class

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This commit is contained in:
Daniel Weschke
2019-12-20 12:29:56 +01:00
parent b0db7ab3dc
commit 0df813797d
31 changed files with 4308 additions and 94 deletions
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docs/build/html/mathematics.html vendored
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@@ -34,10 +34,10 @@
<div class="section" id="module-mathematics">
<span id="mathematics-module"></span><h1>mathematics module<a class="headerlink" href="#module-mathematics" title="Permalink to this headline"></a></h1>
<p>Mathematical functions.</p>
<p>Mathematical functions and objects.</p>
<dl class="field-list simple">
<dt class="field-odd">Date</dt>
<dd class="field-odd"><p>2019-10-30</p>
<dd class="field-odd"><p>2019-12-12</p>
</dd>
</dl>
<span class="target" id="module-mathematics"></span><dl class="function">
@@ -46,6 +46,562 @@
<dd><p>Compute the lowest common multiple of a and b</p>
</dd></dl>
<dl class="class">
<dt id="mathematics.matrix">
<em class="property">class </em><code class="sig-name descname">matrix</code><a class="reference internal" href="_modules/mathematics.html#matrix"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
<p>Use/create matrix like list of lists</p>
<dl class="method">
<dt id="mathematics.matrix.rotate_x">
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_x" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the x dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx' &amp; yy' &amp; yz' &amp; t_y' \\
zx' &amp; zy' &amp; zz' &amp; t_z' \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix} =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; \cos \theta &amp; -\sin \theta &amp; 0 \\
0 &amp; \sin \theta &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}
\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx &amp; yy &amp; yz &amp; t_y \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.rotate_y">
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_y" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the y dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}
xx' &amp; xy' &amp; xz' &amp; t_x' \\
yx &amp; yy &amp; yz &amp; t_y \\
zx' &amp; zy' &amp; zz' &amp; t_z' \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix} =
\begin{bmatrix}
\cos \theta &amp; 0 &amp; \sin \theta &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
-\sin \theta &amp; 0 &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}
\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx &amp; yy &amp; yz &amp; t_y \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.rotate_z">
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rotate_z" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the z dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}
xx' &amp; xy' &amp; xz' &amp; t_x' \\
yx' &amp; yy' &amp; yz' &amp; t_y' \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix} =
\begin{bmatrix}
\cos \theta &amp; -\sin \theta &amp; 0 &amp; 0 \\
\sin \theta &amp; \cos \theta &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx &amp; yy &amp; yz &amp; t_y \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.rx">
<em class="property">static </em><code class="sig-name descname">rx</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rx"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rx" title="Permalink to this definition"></a></dt>
<dd><p>Rotation matrix about the x direction.</p>
<p>Rotates the coordinate system of vectors</p>
<div class="math notranslate nohighlight">
\[\begin{split}R_{x}(\theta) =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; \cos \theta &amp; -\sin \theta &amp; 0 \\
0 &amp; \sin \theta &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.ry">
<em class="property">static </em><code class="sig-name descname">ry</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.ry"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.ry" title="Permalink to this definition"></a></dt>
<dd><p>Rotation matrix about the y direction.</p>
<p>Rotates the coordinate system of vectors</p>
<div class="math notranslate nohighlight">
\[\begin{split}R_{y}(\theta) =
\begin{bmatrix}
\cos \theta &amp; 0 &amp; \sin \theta &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
-\sin \theta &amp; 0 &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.rz">
<em class="property">static </em><code class="sig-name descname">rz</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.rz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.rz" title="Permalink to this definition"></a></dt>
<dd><p>Rotation matrix about the z direction.</p>
<p>Rotates the coordinate system of vectors</p>
<div class="math notranslate nohighlight">
\[\begin{split}R_{z}(\theta) =
\begin{bmatrix}
\cos \theta &amp; -\sin \theta &amp; 0 &amp; 0 \\
\sin \theta &amp; \cos \theta &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}\end{split}\]</div>
<dl class="field-list simple">
<dt class="field-odd">Example</dt>
<dd class="field-odd"><p></p></dd>
</dl>
<div class="math notranslate nohighlight">
\[\begin{split}R_{z}(\theta) \begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
\begin{bmatrix}
\cos 90° &amp; -\sin 90° &amp; 0 &amp; 0 \\
\sin 90° &amp; \cos 90° &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
\begin{bmatrix}
0 &amp; -1 &amp; 0 &amp; 0 \\
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}1 \\ 0 \\ 0 \\ 1\end{bmatrix} =
\begin{bmatrix}0 \\ 1 \\ 0 \\ 1\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.s">
<em class="property">static </em><code class="sig-name descname">s</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.s"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.s" title="Permalink to this definition"></a></dt>
<dd><p>Scaling matrix</p>
<p>uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
centered at the origin will have their centers move. To avoid this,
either scale the object when it’s located at the origin, or
perform a translation afterwards to move the object back to where
it should be.</p>
<div class="math notranslate nohighlight">
\[\begin{split}S =
\begin{bmatrix}
s_x &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; s_y &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; s_z &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.scale">
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.scale" title="Permalink to this definition"></a></dt>
<dd><p>Scaling</p>
<p>uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
centered at the origin will have their centers move. To avoid this,
either scale the object when it’s located at the origin, or
perform a translation afterwards to move the object back to where
it should be.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}
xx' &amp; xy' &amp; xz' &amp; t_x' \\
yx' &amp; yy' &amp; yz' &amp; t_y' \\
zx' &amp; zy' &amp; zz' &amp; t_z' \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix} =
\begin{bmatrix}
s_x &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; s_y &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; s_z &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx &amp; yy &amp; yz &amp; t_y \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.t">
<em class="property">static </em><code class="sig-name descname">t</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.t"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.t" title="Permalink to this definition"></a></dt>
<dd><p>Translation matrix</p>
<div class="math notranslate nohighlight">
\[\begin{split}T =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; t_x \\
0 &amp; 1 &amp; 0 &amp; t_y \\
0 &amp; 0 &amp; 1 &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.matrix.translate">
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#matrix.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.matrix.translate" title="Permalink to this definition"></a></dt>
<dd><p>Translation</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x' \\
yx &amp; yy &amp; yz &amp; t_y' \\
zx &amp; zy &amp; zz &amp; t_z' \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix} =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; t_x \\
0 &amp; 1 &amp; 0 &amp; t_y \\
0 &amp; 0 &amp; 1 &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}
xx &amp; xy &amp; xz &amp; t_x \\
yx &amp; yy &amp; yz &amp; t_y \\
zx &amp; zy &amp; zz &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; h
\end{bmatrix}\end{split}\]</div>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="mathematics.vector">
<em class="property">class </em><code class="sig-name descname">vector</code><a class="reference internal" href="_modules/mathematics.html#vector"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></p>
<p>Use/create vector like lists</p>
<ul class="simple">
<li><p>size -&gt; len(a)</p></li>
<li><p>abs -&gt; abs(a)</p></li>
<li><p>dot -&gt; a * b</p></li>
<li><p>outer -&gt; a &#64; b</p></li>
</ul>
<p>use super constructor</p>
<p>use super __iter__</p>
<p>use super __setitem__</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[1, 2, 3, 1, 2]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">vector</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<p>use super __lt__(a, b)</p>
<p>use super __le__(a, b)</p>
<p>use super __eq__(a, b)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v2</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">==</span> <span class="n">v2</span>
<span class="go">True</span>
</pre></div>
</div>
<p>use super __ne__(a, b)</p>
<p>use super __ge__(a, b)</p>
<p>use super __gt__(a, b)</p>
<p>use super __contains__</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="mi">2</span> <span class="ow">in</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="go">True</span>
</pre></div>
</div>
<p>__isub__</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">-=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[-2, -1, 0]</span>
</pre></div>
</div>
<p>__imul__</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">18</span>
</pre></div>
</div>
<p>__imatmul__</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">*=</span> <span class="n">vector</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[[3, 3, 3], [6, 6, 6], [9, 9, 9]]</span>
</pre></div>
</div>
<dl class="method">
<dt id="mathematics.vector.abs">
<em class="property">static </em><code class="sig-name descname">abs</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.abs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.abs" title="Permalink to this definition"></a></dt>
<dd><p>Return modulus parts of a complex vector</p>
<dl class="field-list simple">
</dl>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.ang">
<em class="property">static </em><code class="sig-name descname">ang</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ang"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ang" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="mathematics.vector.arg">
<em class="property">static </em><code class="sig-name descname">arg</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.arg"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.arg" title="Permalink to this definition"></a></dt>
<dd><p>Return phase parts of a complex vector</p>
<dl class="field-list simple">
</dl>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.ch_cs">
<code class="sig-name descname">ch_cs</code><span class="sig-paren">(</span><em class="sig-param">cs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ch_cs"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ch_cs" title="Permalink to this definition"></a></dt>
<dd><p>Transform this vector from its defined coordinate system to a
new coordinate system, defined by the given coordinate system (u,
v and w direction vectors).</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
u_x &amp; u_y &amp; u_z &amp; 0 \\
v_x &amp; v_y &amp; v_z &amp; 0 \\
w_x &amp; w_y &amp; w_z &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.conjugate">
<em class="property">static </em><code class="sig-name descname">conjugate</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.conjugate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.conjugate" title="Permalink to this definition"></a></dt>
<dd><p>New vector object</p>
<dl class="field-list simple">
</dl>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.cross">
<em class="property">static </em><code class="sig-name descname">cross</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.cross"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.cross" title="Permalink to this definition"></a></dt>
<dd><p>Cross product</p>
<dl class="field-list simple">
</dl>
<p>c is orthogonal to both a and b.
The direction of c can be found with the right-hand rule.</p>
<div class="math notranslate nohighlight">
\[\vec{c} = \vec{a} \times \vec{b}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.full">
<em class="property">static </em><code class="sig-name descname">full</code><span class="sig-paren">(</span><em class="sig-param">length</em>, <em class="sig-param">fill_value</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.full"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.full" title="Permalink to this definition"></a></dt>
<dd><p>Returns a vector of length m or matrix of size m rows, n
columns filled with v.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>length</strong> (<em>int</em>) – length of the vector, e. g. 3</p></li>
<li><p><strong>fill_value</strong> – Fill value</p></li>
</ul>
</dd>
<dt class="field-even">Type fill_value</dt>
<dd class="field-even"><p>scalar</p>
</dd>
<dt class="field-odd">Example</dt>
<dd class="field-odd"><p></p></dd>
</dl>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">vector</span><span class="o">.</span><span class="n">full</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[7, 7, 7]</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.im">
<em class="property">static </em><code class="sig-name descname">im</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.im"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.im" title="Permalink to this definition"></a></dt>
<dd><p>Return the imaginary parts of a complex vector</p>
<dl class="field-list simple">
</dl>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.normalize">
<em class="property">static </em><code class="sig-name descname">normalize</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.normalize"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.normalize" title="Permalink to this definition"></a></dt>
<dd><p>Normalize a vector (i. e. the vector has a length of 1)</p>
<dl class="field-list simple">
</dl>
<div class="math notranslate nohighlight">
\[\vec{e}_a = \frac{\vec{a}}{|\vec{a}|}\]</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><code class="xref py py-meth docutils literal notranslate"><span class="pre">norm()</span></code> for a norm (magnitude) of a vector</p>
</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.ones">
<em class="property">static </em><code class="sig-name descname">ones</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.ones"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.ones" title="Permalink to this definition"></a></dt>
<dd><p>Returns a vector of length m or matrix of size rows, n
columns filled with ones.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>length</strong> (<em>int</em>) – lhape of the vector, e. g. 3</p>
</dd>
<dt class="field-even">Example</dt>
<dd class="field-even"><p></p></dd>
</dl>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[1.0, 1.0, 1.0]</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.random">
<em class="property">static </em><code class="sig-name descname">random</code><span class="sig-paren">(</span><em class="sig-param">shape</em>, <em class="sig-param">lmin=0.0</em>, <em class="sig-param">lmax=1.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.random"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.random" title="Permalink to this definition"></a></dt>
<dd><p>Returns a random vector of length n or matrix of size m rows, n
columns filled with random numbers.</p>
<dl class="field-list simple">
<dt class="field-odd">Example</dt>
<dd class="field-odd"><p></p></dd>
</dl>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">random</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[0.9172905912930438, 0.8908124278322492, 0.5256002790725927]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">random</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[1.2563665665080803, 1.9270454509964547, 1.2381672401270487]</span>
</pre></div>
</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.re">
<em class="property">static </em><code class="sig-name descname">re</code><span class="sig-paren">(</span><em class="sig-param">a</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.re"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.re" title="Permalink to this definition"></a></dt>
<dd><p>Return the real parts of a complex vector</p>
<dl class="field-list simple">
</dl>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.rotate_x">
<code class="sig-name descname">rotate_x</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_x"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_x" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the x dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; \cos \theta &amp; -\sin \theta &amp; 0 \\
0 &amp; \sin \theta &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.rotate_y">
<code class="sig-name descname">rotate_y</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_y"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_y" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the y dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
\cos \theta &amp; 0 &amp; \sin \theta &amp; 0 \\
0 &amp; 1 &amp; 0 &amp; 0 \\
-\sin \theta &amp; 0 &amp; \cos \theta &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.rotate_z">
<code class="sig-name descname">rotate_z</code><span class="sig-paren">(</span><em class="sig-param">theta</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.rotate_z"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.rotate_z" title="Permalink to this definition"></a></dt>
<dd><p>Rotation about the z dirction.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
\cos \theta &amp; -\sin \theta &amp; 0 &amp; 0 \\
\sin \theta &amp; \cos \theta &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.scale">
<code class="sig-name descname">scale</code><span class="sig-paren">(</span><em class="sig-param">sx</em>, <em class="sig-param">sy=None</em>, <em class="sig-param">sz=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.scale" title="Permalink to this definition"></a></dt>
<dd><p>Scaling</p>
<p>uniform scaling if sx=sy=sz=s.
Note that scaling happens around the origin, so objects not
centered at the origin will have their centers move. To avoid this,
either scale the object when it’s located at the origin, or
perform a translation afterwards to move the object back to where
it should be.</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
s_x &amp; 0 &amp; 0 &amp; 0 \\
0 &amp; s_y &amp; 0 &amp; 0 \\
0 &amp; 0 &amp; s_z &amp; 0 \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.translate">
<code class="sig-name descname">translate</code><span class="sig-paren">(</span><em class="sig-param">tx</em>, <em class="sig-param">ty</em>, <em class="sig-param">tz</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.translate"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.translate" title="Permalink to this definition"></a></dt>
<dd><p>Translation</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{bmatrix}x' \\ y' \\ z' \\ h'\end{bmatrix} =
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; t_x \\
0 &amp; 1 &amp; 0 &amp; t_y \\
0 &amp; 0 &amp; 1 &amp; t_z \\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\begin{bmatrix}x \\ y \\ z \\ h\end{bmatrix}\end{split}\]</div>
</dd></dl>
<dl class="method">
<dt id="mathematics.vector.xyz">
<code class="sig-name descname">xyz</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.xyz"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.xyz" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="mathematics.vector.zeros">
<em class="property">static </em><code class="sig-name descname">zeros</code><span class="sig-paren">(</span><em class="sig-param">length</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mathematics.html#vector.zeros"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#mathematics.vector.zeros" title="Permalink to this definition"></a></dt>
<dd><p>Returns a zero vector of length m or matrix of size rows, n
columns filled with zeros.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>length</strong> (<em>int</em>) – length of the vector, e. g. 3</p>
</dd>
<dt class="field-even">Example</dt>
<dd class="field-even"><p></p></dd>
</dl>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">v</span> <span class="o">=</span> <span class="n">zeros</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
<span class="go">[0.0, 0.0, 0.0]</span>
</pre></div>
</div>
</dd></dl>
</dd></dl>
</div>