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Next: <a rel="next" accesskey="n" href="Complex-Arithmetic.html#Complex-Arithmetic">Complex Arithmetic</a>,
Up: <a rel="up" accesskey="u" href="Arithmetic.html#Arithmetic">Arithmetic</a>
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<h3 class="section">17.1 Exponents and Logarithms</h3>
<!-- exp src/mappers.cc -->
<p><a name="doc_002dexp"></a>
<div class="defun">
— Mapping Function: <b>exp</b> (<var>x</var>)<var><a name="index-exp-1775"></a></var><br>
<blockquote><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>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlog.html#doc_002dlog">log</a>.
</p></blockquote></div>
<!-- expm1 src/mappers.cc -->
<p><a name="doc_002dexpm1"></a>
<div class="defun">
— Mapping Function: <b>expm1</b> (<var>x</var>)<var><a name="index-expm1-1776"></a></var><br>
<blockquote><p>Compute
<code>exp (</code><var>x</var><code>) - 1</code>
accurately in the neighborhood of zero.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dexp.html#doc_002dexp">exp</a>.
</p></blockquote></div>
<!-- log src/mappers.cc -->
<p><a name="doc_002dlog"></a>
<div class="defun">
— Mapping Function: <b>log</b> (<var>x</var>)<var><a name="index-log-1777"></a></var><br>
<blockquote><p>Compute the natural logarithm,
<code>ln (</code><var>x</var><code>)</code>,
for each element of <var>x</var>. To compute the
matrix logarithm, see <a href="Linear-Algebra.html#Linear-Algebra">Linear Algebra</a>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dexp.html#doc_002dexp">exp</a>, <a href="doc_002dlog1p.html#doc_002dlog1p">log1p</a>, <a href="doc_002dlog2.html#doc_002dlog2">log2</a>, <a href="doc_002dlog10.html#doc_002dlog10">log10</a>, <a href="doc_002dlogspace.html#doc_002dlogspace">logspace</a>.
</p></blockquote></div>
<!-- reallog scripts/specfun/reallog.m -->
<p><a name="doc_002dreallog"></a>
<div class="defun">
— Function File: <b>reallog</b> (<var>x</var>)<var><a name="index-reallog-1778"></a></var><br>
<blockquote><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.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlog.html#doc_002dlog">log</a>, <a href="doc_002drealpow.html#doc_002drealpow">realpow</a>, <a href="doc_002drealsqrt.html#doc_002drealsqrt">realsqrt</a>.
</p></blockquote></div>
<!-- log1p src/mappers.cc -->
<p><a name="doc_002dlog1p"></a>
<div class="defun">
— Mapping Function: <b>log1p</b> (<var>x</var>)<var><a name="index-log1p-1779"></a></var><br>
<blockquote><p>Compute
<code>log (1 + </code><var>x</var><code>)</code>
accurately in the neighborhood of zero.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlog.html#doc_002dlog">log</a>, <a href="doc_002dexp.html#doc_002dexp">exp</a>, <a href="doc_002dexpm1.html#doc_002dexpm1">expm1</a>.
</p></blockquote></div>
<!-- log10 src/mappers.cc -->
<p><a name="doc_002dlog10"></a>
<div class="defun">
— Mapping Function: <b>log10</b> (<var>x</var>)<var><a name="index-log10-1780"></a></var><br>
<blockquote><p>Compute the base-10 logarithm of each element of <var>x</var>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlog.html#doc_002dlog">log</a>, <a href="doc_002dlog2.html#doc_002dlog2">log2</a>, <a href="doc_002dlogspace.html#doc_002dlogspace">logspace</a>, <a href="doc_002dexp.html#doc_002dexp">exp</a>.
</p></blockquote></div>
<!-- log2 src/data.cc -->
<p><a name="doc_002dlog2"></a>
<div class="defun">
— Mapping Function: <b>log2</b> (<var>x</var>)<var><a name="index-log2-1781"></a></var><br>
— Mapping Function: [<var>f</var>, <var>e</var>] = <b>log2</b> (<var>x</var>)<var><a name="index-log2-1782"></a></var><br>
<blockquote><p>Compute the base-2 logarithm of each element of <var>x</var>.
<p>If called with two output arguments, split <var>x</var> into
binary mantissa and exponent so that
<code>1/2 <= abs(f) < 1</code>
and <var>e</var> is an integer. If
<code>x = 0</code>, <code>f = e = 0</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpow2.html#doc_002dpow2">pow2</a>, <a href="doc_002dlog.html#doc_002dlog">log</a>, <a href="doc_002dlog10.html#doc_002dlog10">log10</a>, <a href="doc_002dexp.html#doc_002dexp">exp</a>.
</p></blockquote></div>
<!-- pow2 scripts/specfun/pow2.m -->
<p><a name="doc_002dpow2"></a>
<div class="defun">
— Mapping Function: <b>pow2</b> (<var>x</var>)<var><a name="index-pow2-1783"></a></var><br>
— Mapping Function: <b>pow2</b> (<var>f, e</var>)<var><a name="index-pow2-1784"></a></var><br>
<blockquote><p>With one argument, computes
2 .^ x
for each element of <var>x</var>.
<p>With two arguments, returns
f .* (2 .^ e).
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dlog2.html#doc_002dlog2">log2</a>, <a href="doc_002dnextpow2.html#doc_002dnextpow2">nextpow2</a>.
</p></blockquote></div>
<!-- nextpow2 scripts/general/nextpow2.m -->
<p><a name="doc_002dnextpow2"></a>
<div class="defun">
— Function File: <b>nextpow2</b> (<var>x</var>)<var><a name="index-nextpow2-1785"></a></var><br>
<blockquote><p>If <var>x</var> is a scalar, return the first integer <var>n</var> such that
2^n ≥ abs (x).
<p>If <var>x</var> is a vector, return <code>nextpow2 (length (</code><var>x</var><code>))</code>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dpow2.html#doc_002dpow2">pow2</a>, <a href="doc_002dlog2.html#doc_002dlog2">log2</a>.
</p></blockquote></div>
<!-- realpow scripts/specfun/realpow.m -->
<p><a name="doc_002drealpow"></a>
<div class="defun">
— Function File: <b>realpow</b> (<var>x, y</var>)<var><a name="index-realpow-1786"></a></var><br>
<blockquote><p>Compute the real-valued, element-by-element power operator. This is
equivalent to <var>x</var><code> .^ </code><var>y</var><!-- /@w -->, except that <code>realpow</code>
reports an error if any return value is complex.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dreallog.html#doc_002dreallog">reallog</a>, <a href="doc_002drealsqrt.html#doc_002drealsqrt">realsqrt</a>.
</p></blockquote></div>
<!-- sqrt src/mappers.cc -->
<p><a name="doc_002dsqrt"></a>
<div class="defun">
— Mapping Function: <b>sqrt</b> (<var>x</var>)<var><a name="index-sqrt-1787"></a></var><br>
<blockquote><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>.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drealsqrt.html#doc_002drealsqrt">realsqrt</a>, <a href="doc_002dnthroot.html#doc_002dnthroot">nthroot</a>.
</p></blockquote></div>
<!-- realsqrt scripts/specfun/realsqrt.m -->
<p><a name="doc_002drealsqrt"></a>
<div class="defun">
— Function File: <b>realsqrt</b> (<var>x</var>)<var><a name="index-realsqrt-1788"></a></var><br>
<blockquote><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.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dsqrt.html#doc_002dsqrt">sqrt</a>, <a href="doc_002drealpow.html#doc_002drealpow">realpow</a>, <a href="doc_002dreallog.html#doc_002dreallog">reallog</a>.
</p></blockquote></div>
<!-- cbrt src/mappers.cc -->
<p><a name="doc_002dcbrt"></a>
<div class="defun">
— Mapping Function: <b>cbrt</b> (<var>x</var>)<var><a name="index-cbrt-1789"></a></var><br>
<blockquote><p>Compute the real cube root of each element of <var>x</var>.
Unlike <var>x</var><code>^(1/3)</code>, the result will be negative if <var>x</var> is
negative.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002dnthroot.html#doc_002dnthroot">nthroot</a>.
</p></blockquote></div>
<!-- nthroot scripts/specfun/nthroot.m -->
<p><a name="doc_002dnthroot"></a>
<div class="defun">
— Function File: <b>nthroot</b> (<var>x, n</var>)<var><a name="index-nthroot-1790"></a></var><br>
<blockquote>
<p>Compute the n-th root of <var>x</var>, returning real results for real
components of <var>x</var>. For example:
<pre class="example"> nthroot (-1, 3)
⇒ -1
(-1) ^ (1 / 3)
⇒ 0.50000 - 0.86603i
</pre>
<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.
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<p class="noindent"><strong>See also:</strong> <a href="doc_002drealsqrt.html#doc_002drealsqrt">realsqrt</a>, <a href="doc_002dsqrt.html#doc_002dsqrt">sqrt</a>, <a href="doc_002dcbrt.html#doc_002dcbrt">cbrt</a>.
</p></blockquote></div>
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