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<title>Batteries user guide : BatComplex</title>
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<h1>Module <a href="type_BatComplex.html">BatComplex</a></h1>
<pre><span class="keyword">module</span> BatComplex: <code class="code"><span class="keyword">sig</span></code> <a href="BatComplex.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info module top">
Additional and modified functions for complex numbers.<br>
</div>
<hr width="100%">
<br>
Complex numbers.
<p>
This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type <code class="code">float</code>).<br>
<pre><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> = <code class="type">Complex.t</code> = {</pre><table class="typetable">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTt.re">re</span> : <code class="type">float</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTt.im">im</span> : <code class="type">float</code>;</code></td>
</tr></table>
}
<pre><span id="VALzero"><span class="keyword">val</span> zero</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
The complex number <code class="code">0</code>.<br>
</div>
<pre><span id="VALone"><span class="keyword">val</span> one</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
The complex number <code class="code">1</code>.<br>
</div>
<pre><span id="VALi"><span class="keyword">val</span> i</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
The complex number <code class="code">i</code>.<br>
</div>
<pre><span id="VALneg"><span class="keyword">val</span> neg</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Unary negation.<br>
</div>
<pre><span id="VALconj"><span class="keyword">val</span> conj</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Conjugate: given the complex <code class="code">x + i.y</code>, returns <code class="code">x - i.y</code>.<br>
</div>
<pre><span id="VALadd"><span class="keyword">val</span> add</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Addition<br>
</div>
<pre><span id="VALsub"><span class="keyword">val</span> sub</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Subtraction<br>
</div>
<pre><span id="VALmul"><span class="keyword">val</span> mul</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Multiplication<br>
</div>
<pre><span id="VALinv"><span class="keyword">val</span> inv</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Multiplicative inverse (<code class="code">1/z</code>).<br>
</div>
<pre><span id="VALdiv"><span class="keyword">val</span> div</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Division<br>
</div>
<pre><span id="VALsqrt"><span class="keyword">val</span> sqrt</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Square root. The result <code class="code">x + i.y</code> is such that <code class="code">x > 0</code> or <code class="code">x =
0</code> and <code class="code">y >= 0</code>. This function has a discontinuity along the
negative real axis.<br>
</div>
<pre><span id="VALnorm2"><span class="keyword">val</span> norm2</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
Norm squared: given <code class="code">x + i.y</code>, returns <code class="code">x^2 + y^2</code>.<br>
</div>
<pre><span id="VALnorm"><span class="keyword">val</span> norm</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
Norm: given <code class="code">x + i.y</code>, returns <code class="code">sqrt(x^2 + y^2)</code>.<br>
</div>
<pre><span id="VALarg"><span class="keyword">val</span> arg</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from
<code class="code">-pi</code> to <code class="code">pi</code>. This function has a discontinuity along the
negative real axis.<br>
</div>
<pre><span id="VALpolar"><span class="keyword">val</span> polar</span> : <code class="type">float -> float -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">polar norm arg</code> returns the complex having norm <code class="code">norm</code>
and argument <code class="code">arg</code>.<br>
</div>
<pre><span id="VALexp"><span class="keyword">val</span> exp</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Exponentiation. <code class="code">exp z</code> returns <code class="code">e</code> to the <code class="code">z</code> power.<br>
</div>
<pre><span id="VALlog"><span class="keyword">val</span> log</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Natural logarithm (in base <code class="code">e</code>).<br>
</div>
<pre><span id="VALpow"><span class="keyword">val</span> pow</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Power function. <code class="code">pow z1 z2</code> returns <code class="code">z1</code> to the <code class="code">z2</code> power.<br>
</div>
<pre><span id="VALoperations"><span class="keyword">val</span> operations</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> <a href="BatNumber.html#TYPEnumeric">BatNumber.numeric</a></code></pre>
<pre><span id="VALinv"><span class="keyword">val</span> inv</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">inv x</code> returns the value of <code class="code">1/x</code><br>
</div>
<pre><span id="VALsucc"><span class="keyword">val</span> succ</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Add <a href="BatComplex.html#VALone"><code class="code"><span class="constructor">BatComplex</span>.one</code></a> to this number.<br>
</div>
<pre><span id="VALpred"><span class="keyword">val</span> pred</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
Remove <a href="BatComplex.html#VALone"><code class="code"><span class="constructor">BatComplex</span>.one</code></a> from this number.<br>
</div>
<pre><span id="VALabs"><span class="keyword">val</span> abs</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">abs c</code> returns the module of this complex number,
i.e. <code class="code">abs c = <span class="constructor">Float</span>.sqrt((re c) *. (re c) +. (im c) *. (im c) )</code><br>
</div>
<pre><span id="VALmodulo"><span class="keyword">val</span> modulo</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VALpow"><span class="keyword">val</span> pow</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VALcompare"><span class="keyword">val</span> compare</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> int</code></pre>
<pre><span id="VALord"><span class="keyword">val</span> ord</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatOrd.html#TYPEorder">BatOrd.order</a></code></pre>
<pre><span id="VALequal"><span class="keyword">val</span> equal</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> bool</code></pre>
<pre><span id="VALof_int"><span class="keyword">val</span> of_int</span> : <code class="type">int -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VALto_int"><span class="keyword">val</span> to_int</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> int</code></pre><div class="info ">
<code class="code">to_int c</code> is the integer part of the real part of <code class="code">c</code><br>
</div>
<pre><span id="VALof_string"><span class="keyword">val</span> of_string</span> : <code class="type">string -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code">of_string s</code> accepts strings with the following formats:
<p>
(<int>|<float>) (+|-) i ( * | . | ) (<int>|<float>)
<p>
where (a|b|c) is either a or b or c.
<p>
In addition the following degenerate formats are also accepted:
<p>
(+|-) i ( * | . | ) (<int>|<float>)
<p>
(<int>|<float>) (+|-) i
<p>
(<int>|<float>)<br>
</div>
<pre><span id="VALto_string"><span class="keyword">val</span> to_string</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> string</code></pre>
<pre><span id="VAL(+)"><span class="keyword">val</span> (+)</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VAL(-)"><span class="keyword">val</span> (-)</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VAL( * )"><span class="keyword">val</span> ( * )</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VAL(/)"><span class="keyword">val</span> (/)</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VAL( ** )"><span class="keyword">val</span> ( ** )</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a></code></pre>
<pre><span id="VAL(--)"><span class="keyword">val</span> (--)</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> <a href="BatEnum.html#TYPEt">BatEnum.t</a></code></pre>
<pre><span id="VAL(---)"><span class="keyword">val</span> (---)</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> -> <a href="BatComplex.html#TYPEt">t</a> <a href="BatEnum.html#TYPEt">BatEnum.t</a></code></pre>
<pre><span id="VALof_float"><span class="keyword">val</span> of_float</span> : <code class="type">float -> <a href="BatComplex.html#TYPEt">t</a></code></pre><div class="info ">
<code class="code"><span class="constructor">Complex</span>.of_float x</code> returns the complex number <code class="code">x+0i</code><br>
</div>
<pre><span id="VALto_float"><span class="keyword">val</span> to_float</span> : <code class="type"><a href="BatComplex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
<code class="code"><span class="constructor">Complex</span>.to_float (a+bi)</code> returns the float <code class="code">a</code><br>
</div>
<br>
<h6 id="6_Submodulesgroupingallinfixoperators">Submodules grouping all infix operators</h6><br>
<pre><span class="keyword">module</span> <a href="BatComplex.Infix.html">Infix</a>: <code class="type"><a href="BatNumber.Infix.html">BatNumber.Infix</a></code><code class="type"> with type bat__infix_t = t</code></pre>
<pre><span class="keyword">module</span> <a href="BatComplex.Compare.html">Compare</a>: <code class="type"><a href="BatNumber.Compare.html">BatNumber.Compare</a></code><code class="type"> with type bat__compare_t = t</code></pre><br>
<h6 id="6_Boilerplatecode">Boilerplate code</h6><br>
<pre><span id="VALprint"><span class="keyword">val</span> print</span> : <code class="type">'a <a href="BatInnerIO.html#TYPEoutput">BatInnerIO.output</a> -> <a href="BatComplex.html#TYPEt">t</a> -> unit</code></pre><div class="info ">
<div class="h7" id="7_Printing">Printing</div><br>
</div>
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