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<title>Exponents and Logarithms - Untitled</title>
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<a name="Exponents-and-Logarithms"></a>
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>
<!-- mappers.cc -->
<p><a name="doc_002dexp"></a>
<div class="defun">
— Mapping Function: <b>exp</b> (<var>x</var>)<var><a name="index-exp-1361"></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>
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<p><a name="doc_002dexpm1"></a>
<div class="defun">
— Mapping Function: <b>expm1</b> (<var>x</var>)<var><a name="index-expm1-1362"></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>
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<p><a name="doc_002dlog"></a>
<div class="defun">
— Mapping Function: <b>log</b> (<var>x</var>)<var><a name="index-log-1363"></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>
<!-- mappers.cc -->
<p><a name="doc_002dlog1p"></a>
<div class="defun">
— Mapping Function: <b>log1p</b> (<var>x</var>)<var><a name="index-log1p-1364"></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>
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<p><a name="doc_002dlog10"></a>
<div class="defun">
— Mapping Function: <b>log10</b> (<var>x</var>)<var><a name="index-log10-1365"></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>
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<p><a name="doc_002dlog2"></a>
<div class="defun">
— Mapping Function: <b>log2</b> (<var>x</var>)<var><a name="index-log2-1366"></a></var><br>
— Mapping Function: [<var>f</var>, <var>e</var>] = <b>log2</b> (<var>x</var>)<var><a name="index-log2-1367"></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>
<!-- ./general/nextpow2.m -->
<p><a name="doc_002dnextpow2"></a>
<div class="defun">
— Function File: <b>nextpow2</b> (<var>x</var>)<var><a name="index-nextpow2-1368"></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>
<!-- ./general/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-1369"></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>
</blockquote></div>
<!-- ./specfun/pow2.m -->
<p><a name="doc_002dpow2"></a>
<div class="defun">
— Mapping Function: <b>pow2</b> (<var>x</var>)<var><a name="index-pow2-1370"></a></var><br>
— Mapping Function: <b>pow2</b> (<var>f, e</var>)<var><a name="index-pow2-1371"></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>
<!-- ./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-1372"></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>
<!-- ./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-1373"></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>
<!-- ./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-1374"></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>
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<p><a name="doc_002dsqrt"></a>
<div class="defun">
— Mapping Function: <b>sqrt</b> (<var>x</var>)<var><a name="index-sqrt-1375"></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>.
</p></blockquote></div>
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