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<span id="Exponents-and-Logarithms"></span><div class="header">
<p>
Next: <a href="Complex-Arithmetic.html" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<span id="Exponents-and-Logarithms-1"></span><h3 class="section">17.1 Exponents and Logarithms</h3>
<span id="XREFexp"></span><dl>
<dt id="index-exp">: <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>.
</p>
<p>To compute the matrix exponential, see <a href="Linear-Algebra.html">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>.
</p></dd></dl>
<span id="XREFexpm1"></span><dl>
<dt id="index-expm1">: <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>
<span id="XREFlog"></span><dl>
<dt id="index-log">: <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>.
</p>
<p>To compute the matrix logarithm, see <a href="Linear-Algebra.html">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>
<span id="XREFreallog"></span><dl>
<dt id="index-reallog">: <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>.
</p>
<p>If any element results in a complex return value <code>reallog</code> aborts and
issues an error.
</p>
<p><strong>See also:</strong> <a href="#XREFlog">log</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>
<span id="XREFlog1p"></span><dl>
<dt id="index-log1p">: <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>
<span id="XREFlog10"></span><dl>
<dt id="index-log10">: <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>
<span id="XREFlog2"></span><dl>
<dt id="index-log2">: <em></em> <strong>log2</strong> <em>(<var>x</var>)</em></dt>
<dt id="index-log2-1">: <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 <= abs(f) < 1</code><!-- /@w -->
and <var>e</var> is an integer. If
<code>x = 0</code><!-- /@w -->, <code>f = e = 0</code><!-- /@w -->.
</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>
<span id="XREFpow2"></span><dl>
<dt id="index-pow2">: <em></em> <strong>pow2</strong> <em>(<var>x</var>)</em></dt>
<dt id="index-pow2-1">: <em></em> <strong>pow2</strong> <em>(<var>f</var>, <var>e</var>)</em></dt>
<dd><p>With one input argument, compute
2 .^ x
for each element of <var>x</var>.
</p>
<p>With two input arguments, return
f .* (2 .^ e).
</p>
<p><strong>See also:</strong> <a href="#XREFlog2">log2</a>, <a href="#XREFnextpow2">nextpow2</a>, <a href="Arithmetic-Ops.html#XREFpower">power</a>.
</p></dd></dl>
<span id="XREFnextpow2"></span><dl>
<dt id="index-nextpow2">: <em><var>n</var> =</em> <strong>nextpow2</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the exponent for the smallest power of two larger than the input.
</p>
<p>For each element in the input array <var>x</var>, return the first integer
<var>n</var> such that
2^n ≥ abs (x).
</p>
<p><strong>See also:</strong> <a href="#XREFpow2">pow2</a>, <a href="#XREFlog2">log2</a>.
</p></dd></dl>
<span id="XREFrealpow"></span><dl>
<dt id="index-realpow">: <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.
</p>
<p>This is equivalent to <code><var>x</var> .^ <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="Arithmetic-Ops.html#XREFpower">power</a>, <a href="#XREFreallog">reallog</a>, <a href="#XREFrealsqrt">realsqrt</a>.
</p></dd></dl>
<span id="XREFsqrt"></span><dl>
<dt id="index-sqrt">: <em></em> <strong>sqrt</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Compute the square root of each element of <var>x</var>.
</p>
<p>If <var>x</var> is negative, a complex result is returned.
</p>
<p>To compute the matrix square root, see <a href="Linear-Algebra.html">Linear Algebra</a>.
</p>
<p><strong>See also:</strong> <a href="#XREFrealsqrt">realsqrt</a>, <a href="#XREFnthroot">nthroot</a>.
</p></dd></dl>
<span id="XREFrealsqrt"></span><dl>
<dt id="index-realsqrt">: <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>.
</p>
<p>If any element results in a complex return value <code>realsqrt</code> aborts and
issues an error.
</p>
<p><strong>See also:</strong> <a href="#XREFsqrt">sqrt</a>, <a href="#XREFrealpow">realpow</a>, <a href="#XREFreallog">reallog</a>.
</p></dd></dl>
<span id="XREFcbrt"></span><dl>
<dt id="index-cbrt">: <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>.
</p>
<p>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>
<span id="XREFnthroot"></span><dl>
<dt id="index-nthroot">: <em></em> <strong>nthroot</strong> <em>(<var>x</var>, <var>n</var>)</em></dt>
<dd>
<p>Compute the real (non-complex) <var>n</var>-th root of <var>x</var>.
</p>
<p><var>x</var> must have all real entries and <var>n</var> must be a scalar.
If <var>n</var> is an even integer and <var>x</var> has negative entries then
<code>nthroot</code> aborts and issues an error.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">nthroot (-1, 3)
⇒ -1
(-1) ^ (1 / 3)
⇒ 0.50000 - 0.86603i
</pre></div>
<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" accesskey="n" rel="next">Complex Arithmetic</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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