File: Exponents-and-Logarithms.html

package info (click to toggle)
octave 3.8.2-4
links: PTS, VCS
area: main
in suites: jessie, jessie-kfreebsd
size: 84,396 kB
ctags: 45,547
sloc: cpp: 293,356; ansic: 42,041; fortran: 23,669; sh: 13,629; objc: 7,890; yacc: 7,093; lex: 3,442; java: 2,125; makefile: 1,589; perl: 1,009; awk: 974; xml: 34
file content (229 lines) | stat: -rw-r--r-- 9,903 bytes
parent folder | download | duplicates (3)
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Created by GNU Texinfo 5.2, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Octave: Exponents and Logarithms</title>

<meta name="description" content="GNU Octave: Exponents and Logarithms">
<meta name="keywords" content="GNU Octave: Exponents and Logarithms">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="Arithmetic.html#Arithmetic" rel="up" title="Arithmetic">
<link href="Complex-Arithmetic.html#Complex-Arithmetic" rel="next" title="Complex Arithmetic">
<link href="Arithmetic.html#Arithmetic" rel="prev" title="Arithmetic">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Exponents-and-Logarithms"></a>
<div class="header">
<p>
Next: <a href="Complex-Arithmetic.html#Complex-Arithmetic" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Exponents-and-Logarithms-1"></a>
<h3 class="section">17.1 Exponents and Logarithms</h3>

<a name="XREFexp"></a><dl>
<dt><a name="index-exp"></a>Mapping Function: <em></em> <strong>exp</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>e^x</code>
for each element of <var>x</var>.  To compute the matrix
exponential, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>.
</p></dd></dl>


<a name="XREFexpm1"></a><dl>
<dt><a name="index-expm1"></a>Mapping Function: <em></em> <strong>expm1</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>exp (<var>x</var>) - 1</code>
accurately in the neighborhood of zero.
</p>
<p><strong>See also:</strong> <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFlog"></a><dl>
<dt><a name="index-log"></a>Mapping Function: <em></em> <strong>log</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the natural logarithm,
<code>ln (<var>x</var>)</code>,
for each element of <var>x</var>.  To compute the
matrix logarithm, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFexp">exp</a>, <a href="#XREFlog1p">log1p</a>, <a href="#XREFlog2">log2</a>, <a href="#XREFlog10">log10</a>, <a href="Special-Utility-Matrices.html#XREFlogspace">logspace</a>.
</p></dd></dl>


<a name="XREFreallog"></a><dl>
<dt><a name="index-reallog"></a>Function File: <em></em> <strong>reallog</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return the real-valued natural logarithm of each element of <var>x</var>.  Report
an error if any element results in a complex return value.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>


<a name="XREFlog1p"></a><dl>
<dt><a name="index-log1p"></a>Mapping Function: <em></em> <strong>log1p</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute
<code>log (1 + <var>x</var>)</code>
accurately in the neighborhood of zero.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFexp">exp</a>, <a href="#XREFexpm1">expm1</a>.
</p></dd></dl>


<a name="XREFlog10"></a><dl>
<dt><a name="index-log10"></a>Mapping Function: <em></em> <strong>log10</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the base-10 logarithm of each element of <var>x</var>.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFlog2">log2</a>, <a href="Special-Utility-Matrices.html#XREFlogspace">logspace</a>, <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFlog2"></a><dl>
<dt><a name="index-log2"></a>Mapping Function: <em></em> <strong>log2</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-log2-1"></a>Mapping Function: <em>[<var>f</var>, <var>e</var>] =</em> <strong>log2</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the base-2 logarithm of each element of <var>x</var>.
</p>
<p>If called with two output arguments, split <var>x</var> into
binary mantissa and exponent so that
<code>1/2 &lt;= abs(f) &lt; 1</code>
and <var>e</var> is an integer.  If
<code>x = 0</code>, <code>f = e = 0</code>.
</p>
<p><strong>See also:</strong> <a href="#XREFpow2">pow2</a>, <a href="#XREFlog">log</a>, <a href="#XREFlog10">log10</a>, <a href="#XREFexp">exp</a>.
</p></dd></dl>


<a name="XREFpow2"></a><dl>
<dt><a name="index-pow2"></a>Mapping Function: <em></em> <strong>pow2</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-pow2-1"></a>Mapping Function: <em></em> <strong>pow2</strong> <em>(<var>f</var>, <var>e</var>)</em></dt>
<dd><p>With one argument, computes
2 .^ x
for each element of <var>x</var>.
</p>
<p>With two arguments, returns
f .* (2 .^ e).
</p>
<p><strong>See also:</strong> <a href="#XREFlog2">log2</a>, <a href="#XREFnextpow2">nextpow2</a>.
</p></dd></dl>


<a name="XREFnextpow2"></a><dl>
<dt><a name="index-nextpow2"></a>Function File: <em></em> <strong>nextpow2</strong> <em>(<var>x</var>)</em></dt>
<dd><p>If <var>x</var> is a scalar, return the first integer <var>n</var> such that
2^n &ge; abs (x).
</p>
<p>If <var>x</var> is a vector, return <code>nextpow2 (length (<var>x</var>))</code>.
</p>
<p><strong>See also:</strong> <a href="#XREFpow2">pow2</a>, <a href="#XREFlog2">log2</a>.
</p></dd></dl>


<a name="XREFrealpow"></a><dl>
<dt><a name="index-realpow"></a>Function File: <em></em> <strong>realpow</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd><p>Compute the real-valued, element-by-element power operator.  This is
equivalent to <code><var>x</var>&nbsp;.^&nbsp;<var>y</var></code><!-- /@w -->, except that <code>realpow</code>
reports an error if any return value is complex.
</p>
<p><strong>See also:</strong> <a href="#XREFreallog">reallog</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>


<a name="XREFsqrt"></a><dl>
<dt><a name="index-sqrt"></a>Mapping Function: <em></em> <strong>sqrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the square root of each element of <var>x</var>.  If <var>x</var> is negative,
a complex result is returned.  To compute the matrix square root, see
<a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFrealsqrt">realsqrt</a>, <a href="#XREFnthroot">nthroot</a>.
</p></dd></dl>


<a name="XREFrealsqrt"></a><dl>
<dt><a name="index-realsqrt"></a>Function File: <em></em> <strong>realsqrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Return the real-valued square root of each element of <var>x</var>.  Report an
error if any element results in a complex return value.
</p>
<p><strong>See also:</strong> <a href="#XREFsqrt">sqrt</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFreallog">reallog</a>.
</p></dd></dl>


<a name="XREFcbrt"></a><dl>
<dt><a name="index-cbrt"></a>Mapping Function: <em></em> <strong>cbrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the real cube root of each element of <var>x</var>.
Unlike <code><var>x</var>^(1/3)</code>, the result will be negative if <var>x</var> is
negative.
</p>
<p><strong>See also:</strong> <a href="#XREFnthroot">nthroot</a>.
</p></dd></dl>


<a name="XREFnthroot"></a><dl>
<dt><a name="index-nthroot"></a>Function File: <em></em> <strong>nthroot</strong> <em>(<var>x</var>, <var>n</var>)</em></dt>
<dd>
<p>Compute the n-th root of <var>x</var>, returning real results for real
components of <var>x</var>.  For example:
</p>
<div class="example">
<pre class="example">nthroot (-1, 3)
&rArr; -1
(-1) ^ (1 / 3)
&rArr; 0.50000 - 0.86603i
</pre></div>

<p><var>x</var> must have all real entries.  <var>n</var> must be a scalar.
If <var>n</var> is an even integer and <var>X</var> has negative entries, an
error is produced.
</p>
<p><strong>See also:</strong> <a href="#XREFrealsqrt">realsqrt</a>, <a href="#XREFsqrt">sqrt</a>, <a href="#XREFcbrt">cbrt</a>.
</p></dd></dl>


<hr>
<div class="header">
<p>
Next: <a href="Complex-Arithmetic.html#Complex-Arithmetic" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html#Arithmetic" accesskey="u" rel="up">Arithmetic</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
</div>



</body>
</html>