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<title>Chapter 23. Backgrounders</title>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<title>Chapter 4. Mathematical Constants</title>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<title>Chapter 3. Specified-width floating-point typedefs</title>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<title>Chapter 5. Statistical Distributions and Functions</title>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<dl class="toc"><dt><span class="section"><a href="math_toolkit/daubechies_filters.html">Daubechies Filters</a></span></dt></dl>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -45,8 +44,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="titlepage">
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<div><h1 class="title">
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<a name="math_toolkit"></a>Math Toolkit 4.1.0</h1></div>
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<a name="math_toolkit"></a>Math Toolkit 4.1.1</h1></div>
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<div><div class="authorgroup">
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<div class="author"><h3 class="author">
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<span class="firstname">Nikhar</span> <span class="surname">Agrawal</span>
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@@ -133,10 +134,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"><p><small>Last revised: February 23, 2023 at 18:11:17 GMT</small></p></td>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/empirical_cdf.html" title="Empirical Cumulative Distribution Function"><span class="index-entry-level-1">Empirical Cumulative Distribution Function</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/fibonacci_numbers.html" title="Fibonacci Numbers"><span class="index-entry-level-1">Fibonacci Numbers</span></a></p></li>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<p><a class="link" href="s04.html#idx_id_102">B</a> <a class="link" href="s04.html#idx_id_106">F</a></p>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
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|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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<li class="listitem" style="list-style-type: none">
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<p><span class="index-entry-level-0">Chatterjee Correlation</span></p>
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<li class="listitem" style="list-style-type: none"><p><span class="bold"><strong><a class="link" href="../math_toolkit/chatterjee_correlation.html" title="Chatterjee Correlation"><span class="index-entry-level-1">chatterjee_correlation</span></a></strong></span></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/chatterjee_correlation.html" title="Chatterjee Correlation"><span class="index-entry-level-1">constants</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/chatterjee_correlation.html" title="Chatterjee Correlation"><span class="index-entry-level-1">O</span></a></p></li>
|
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</ul></div>
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</li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/chatterjee_correlation.html" title="Chatterjee Correlation"><span class="index-entry-level-0">chatterjee_correlation</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none">
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<p><span class="index-entry-level-0">Chebyshev Polynomials</span></p>
|
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<div class="index"><ul class="index" style="list-style-type: none; ">
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/chebyshev.html" title="Chebyshev Polynomials"><span class="index-entry-level-1">accuracy</span></a></p></li>
|
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@@ -2477,6 +2487,7 @@
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation"><span class="index-entry-level-1">Cardinal Cubic B-spline interpolation</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/double_exponential/de_caveats.html" title="Caveats"><span class="index-entry-level-1">Caveats</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/internals/centered_continued_fraction.html" title="Centered Continued Fractions"><span class="index-entry-level-1">Centered Continued Fractions</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/chatterjee_correlation.html" title="Chatterjee Correlation"><span class="index-entry-level-1">Chatterjee Correlation</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/sf_poly/chebyshev.html" title="Chebyshev Polynomials"><span class="index-entry-level-1">Chebyshev Polynomials</span></a></p></li>
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||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/overview/complements.html" title="Complements are supported too - and when to use them"><span class="index-entry-level-1">Complements are supported too - and when to use them</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/real_concepts.html" title="Conceptual Requirements for Real Number Types"><span class="index-entry-level-1">Conceptual Requirements for Real Number Types</span></a></p></li>
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||||
@@ -3002,6 +3013,7 @@
|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">interpolation</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">multiprecision</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">operator</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">performance</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">prime</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">support</span></a></p></li>
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||||
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|
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|
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|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/dist_ref/dists/empirical_cdf.html" title="Empirical Cumulative Distribution Function"><span class="index-entry-level-1">Empirical Cumulative Distribution Function</span></a></p></li>
|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/number_series/fibonacci_numbers.html" title="Fibonacci Numbers"><span class="index-entry-level-1">Fibonacci Numbers</span></a></p></li>
|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/diff0.html" title="Lanczos Smoothing Derivatives"><span class="index-entry-level-1">Lanczos Smoothing Derivatives</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/powers/ct_pow.html" title="Compile Time Power of a Runtime Base"><span class="index-entry-level-1">Compile Time Power of a Runtime Base</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/cubic_hermite.html" title="Cubic Hermite interpolation"><span class="index-entry-level-1">Cubic Hermite interpolation</span></a></p></li>
|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/hankel/cyl_hankel.html" title="Cyclic Hankel Functions"><span class="index-entry-level-1">Cyclic Hankel Functions</span></a></p></li>
|
||||
<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/daubechies.html" title="Daubechies Wavelets and Scaling Functions"><span class="index-entry-level-1">Daubechies Wavelets and Scaling Functions</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/directories.html" title="Directory and File Structure"><span class="index-entry-level-1">Directory and File Structure</span></a></p></li>
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/stat_tut/dist_params.html" title="Discrete Probability Distributions"><span class="index-entry-level-1">Discrete Probability Distributions</span></a></p></li>
|
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<li class="listitem" style="list-style-type: none"><p><a class="link" href="../math_toolkit/tradoffs.html#math_toolkit.tradoffs.table_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_1_20191008_on_linux" title="Table 22.2. Distribution performance comparison for different performance options with GNU C++ version 9.2.1 20191008 on linux"><span class="index-entry-level-1">Distribution performance comparison for different performance options with GNU C++ version 9.2.1 20191008 on linux</span></a></p></li>
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</li></ul></div></dd>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -10306,8 +10318,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<title>Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools</title>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -66,8 +65,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<title>Chapter 12. Interpolation</title>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -60,8 +59,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</p>
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@@ -4,10 +4,11 @@
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<title>Chapter 15. Complex Number Functions</title>
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Report on C++ Library Extensions</a>.
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -56,8 +55,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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@@ -33,9 +34,7 @@
|
||||
section. Thank you to all who contributed to the discution about this library.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -43,8 +42,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -33,9 +34,7 @@
|
||||
section. Thank you to all who contributed to the discussion about this library.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -43,8 +42,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
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@@ -4,10 +4,11 @@
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<title>acos</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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@@ -47,9 +48,7 @@
|
||||
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/acos.png"></span>
|
||||
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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@@ -4,10 +4,11 @@
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<link rel="stylesheet" href="../math.css" type="text/css">
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<table cellpadding="2" width="100%"><tr>
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@@ -47,9 +48,7 @@
|
||||
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/acosh.png"></span>
|
||||
</p>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -34,9 +35,7 @@
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<dt><span class="section"><a href="airy/airy_root.html">Finding Zeros of Airy Functions</a></span></dt>
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</dl></div>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -44,8 +43,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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</p></blockquote></div>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -125,8 +124,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<title>Airy Ai' Function</title>
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</p></blockquote></div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -117,8 +116,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -460,9 +461,7 @@ airy_ai_zeros:
|
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Alpha</a>.
|
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -470,8 +469,7 @@ airy_ai_zeros:
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -116,8 +115,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</p></blockquote></div>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -117,8 +116,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -190,9 +191,7 @@
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of the Anderson-Darling test statistic agrees with Mathematica.
|
||||
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -200,8 +199,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -177,9 +178,7 @@
|
||||
implemented in there too.)
|
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</p>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -187,8 +186,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<title>asin</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
@@ -47,9 +48,7 @@
|
||||
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/asin.png"></span>
|
||||
</p>
|
||||
</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
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</div></td>
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@@ -4,10 +4,11 @@
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<title>asinh</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<table cellpadding="2" width="100%"><tr>
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||||
@@ -47,9 +48,7 @@
|
||||
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/asinh.png"></span>
|
||||
</p>
|
||||
</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<title>atan</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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@@ -47,9 +48,7 @@
|
||||
<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/atan.png"></span>
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<title>atanh</title>
|
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<link rel="stylesheet" href="../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<table cellpadding="2" width="100%"><tr>
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@@ -47,9 +48,7 @@
|
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<span class="bold"><strong>Formula: </strong></span> <span class="inlinemediaobject"><img src="../../images/atanh.png"></span>
|
||||
</p>
|
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -57,8 +56,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -399,9 +400,7 @@ put gamma = 0.00199852
|
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manual</a>.
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||||
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||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -409,8 +408,7 @@ put gamma = 0.00199852
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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when using derivatives.
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -767,8 +766,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -108,9 +109,7 @@
|
||||
and for <span class="emphasis"><em>z<sub>0</sub> > 0</em></span> the steps are actually divergent.
|
||||
</p>
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</div>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -118,8 +117,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -268,9 +269,7 @@ Abscissa value that yields a potential of 3 = 0.604728
|
||||
Root was found in 10 iterations.
|
||||
</pre>
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</div>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -278,8 +277,7 @@ Root was found in 10 iterations.
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -40,9 +41,7 @@
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the Bessel Functions</a></span></dt>
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -50,8 +49,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -1367,9 +1368,7 @@ are also computed by recursions (involving gamma functions), but
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recurrence.
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -1377,8 +1376,7 @@ are also computed by recursions (involving gamma functions), but
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -215,9 +216,7 @@ is also known as the spherical
|
||||
and <a class="link" href="sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_neumann</a>.
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -225,8 +224,7 @@ is also known as the spherical
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Alpha</a>.
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|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -765,8 +764,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -1180,9 +1181,7 @@ are also computed by recursions (involving gamma functions), but
|
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two values and f<sub>ν</sub>, the Wronskian yields I<sub>ν</sub>(x) directly.
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -1190,8 +1189,7 @@ are also computed by recursions (involving gamma functions), but
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -272,9 +273,7 @@ for small <span class="emphasis"><em>x</em></span>:
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main definition as x → 0.
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -282,8 +281,7 @@ for small <span class="emphasis"><em>x</em></span>:
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -243,8 +242,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<title>Bilinear Uniform Interpolation</title>
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@@ -124,9 +125,7 @@
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<span class="identifier">Bilinear</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">13.2</span> <span class="identifier">ns</span>
|
||||
</pre>
|
||||
</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -134,8 +133,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
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@@ -4,10 +4,11 @@
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<title>Bivariate Statistics</title>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -147,8 +146,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
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@@ -4,10 +4,11 @@
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<title>Locating Function Minima using Brent's algorithm</title>
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</li>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -659,8 +658,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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|
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@@ -4,10 +4,11 @@
|
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<title>If and How to Build a Boost.Math Library, and its Examples and Tests</title>
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@@ -145,9 +146,7 @@
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the sources. Boost.Build will do this automatically when appropriate.
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -155,8 +154,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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ISO Standard</a>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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differentiable, but not three or four times differentiable.
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of data by spline functions.</em></span> Diss. City, University of London, 1975.
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<span class="special">}</span> <span class="comment">// Namespaces</span>
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<a name="math_toolkit.chatterjee_correlation"></a><a class="link" href="chatterjee_correlation.html" title="Chatterjee Correlation">Chatterjee Correlation</a>
|
||||
</h2></div></div></div>
|
||||
<h4>
|
||||
<a name="math_toolkit.chatterjee_correlation.h0"></a>
|
||||
<span class="phrase"><a name="math_toolkit.chatterjee_correlation.synopsis"></a></span><a class="link" href="chatterjee_correlation.html#math_toolkit.chatterjee_correlation.synopsis">Synopsis</a>
|
||||
</h4>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">chatterjee_correlation</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span> <span class="special">{</span>
|
||||
|
||||
<span class="identifier">C</span><span class="special">++</span><span class="number">17</span><span class="special">:</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ExecutionPolicy</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Container</span><span class="special">></span>
|
||||
<span class="keyword">auto</span> <span class="identifier">chatterjee_correlation</span><span class="special">(</span><span class="identifier">ExecutionPolicy</span><span class="special">&&</span> <span class="identifier">exec</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Container</span><span class="special">&</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Container</span><span class="special">&</span> <span class="identifier">v</span><span class="special">);</span>
|
||||
|
||||
<span class="identifier">C</span><span class="special">++</span><span class="number">11</span><span class="special">:</span>
|
||||
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Container</span><span class="special">></span>
|
||||
<span class="keyword">auto</span> <span class="identifier">chatterjee_correlation</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Container</span><span class="special">&</span> <span class="identifier">u</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Container</span><span class="special">&</span> <span class="identifier">v</span><span class="special">);</span>
|
||||
<span class="special">}</span>
|
||||
</pre>
|
||||
<h4>
|
||||
<a name="math_toolkit.chatterjee_correlation.h1"></a>
|
||||
<span class="phrase"><a name="math_toolkit.chatterjee_correlation.description"></a></span><a class="link" href="chatterjee_correlation.html#math_toolkit.chatterjee_correlation.description">Description</a>
|
||||
</h4>
|
||||
<p>
|
||||
The classical correlation coefficients like the Pearson's correlation are useful
|
||||
primarily for distinguishing when one dataset depends linearly on another.
|
||||
However, Pearson's correlation coefficient has a known weakness in that when
|
||||
the dependent variable has an obvious functional relationship with the independent
|
||||
variable, the value of the correlation coefficient can take on any value. As
|
||||
Chatterjee says:
|
||||
</p>
|
||||
<p>
|
||||
> Ideally, one would like a coefficient that approaches its maximum value
|
||||
if and only if one variable looks more and more like a noiseless function of
|
||||
the other, just as Pearson correlation is close to its maximum value if and
|
||||
only if one variable is close to being a noiseless linear function of the other.
|
||||
</p>
|
||||
<p>
|
||||
This is the problem Chatterjee's coefficient solves. Let X and Y be random
|
||||
variables, where Y is not constant, and let (X_i, Y_i) be samples from this
|
||||
distribution. Rearrange these samples so that X_(0) < X_{(1)} < ... X_{(n-1)}
|
||||
and create (R(X_{(i)}), R(Y_{(i)})). The Chatterjee correlation is then given
|
||||
by
|
||||
</p>
|
||||
<p>
|
||||
<span class="inlinemediaobject"><object type="image/svg+xml" data="../../equations/chatterjee_correlation.svg"></object></span>
|
||||
</p>
|
||||
<p>
|
||||
In the limit of an infinite amount of i.i.d data, the statistic lies in [0,
|
||||
1]. However, if the data is not infinite, the statistic may be negative. If
|
||||
X and Y are independent, the value is zero, and if Y is a measurable function
|
||||
of X, then the statistic is unity. The complexity is O(n log n).
|
||||
</p>
|
||||
<p>
|
||||
An example is given below:
|
||||
</p>
|
||||
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">X</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">};</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">Y</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">};</span>
|
||||
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span><span class="special">::</span><span class="identifier">chatterjee_correlation</span><span class="special">;</span>
|
||||
<span class="keyword">double</span> <span class="identifier">coeff</span> <span class="special">=</span> <span class="identifier">chatterjee_correlation</span><span class="special">(</span><span class="identifier">X</span><span class="special">,</span> <span class="identifier">Y</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
The implementation follows <a href="https://arxiv.org/pdf/1909.10140.pdf" target="_top">Chatterjee's
|
||||
paper</a>.
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>Nota bene:</em></span> If the input is an integer type the output
|
||||
will be a double precision type.
|
||||
</p>
|
||||
<h4>
|
||||
<a name="math_toolkit.chatterjee_correlation.h2"></a>
|
||||
<span class="phrase"><a name="math_toolkit.chatterjee_correlation.invariants"></a></span><a class="link" href="chatterjee_correlation.html#math_toolkit.chatterjee_correlation.invariants">Invariants</a>
|
||||
</h4>
|
||||
<p>
|
||||
The function expects at least two samples, a non-constant vector Y, and the
|
||||
same number of X's as Y's. If Y is constant, the result is a quiet NaN. The
|
||||
data set must be sorted by X values. If there are ties in the values of X,
|
||||
then the statistic is random due to the random breaking of ties. Of course,
|
||||
random numbers are not used internally, but the result is not guaranteed to
|
||||
be identical on different systems.
|
||||
</p>
|
||||
<h4>
|
||||
<a name="math_toolkit.chatterjee_correlation.h3"></a>
|
||||
<span class="phrase"><a name="math_toolkit.chatterjee_correlation.references"></a></span><a class="link" href="chatterjee_correlation.html#math_toolkit.chatterjee_correlation.references">References</a>
|
||||
</h4>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
|
||||
Chatterjee, Sourav. "A new coefficient of correlation." Journal
|
||||
of the American Statistical Association 116.536 (2021): 2009-2022.
|
||||
</li></ul></div>
|
||||
</div>
|
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
Walker and Xiaogang Zhang<p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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acceptable or not.
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -674,8 +673,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -45,8 +44,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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paper for more information on the implementation methodology.
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Some physical constants may be available in Boost.Units.
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -130,8 +129,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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at - hetp.u-net.com.
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -64,8 +63,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
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This documentation aims to use of the following naming and formatting conventions.
|
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@@ -68,9 +69,7 @@
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||||
</li>
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|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -78,8 +77,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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<title>Quaternion Creation Functions</title>
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test file</a>).
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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@@ -112,8 +111,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -189,9 +190,7 @@
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||||
in Boost.Math.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -199,8 +198,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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@@ -4,10 +4,11 @@
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<title>Cubic Hermite interpolation</title>
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@@ -244,9 +245,7 @@
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||||
the problem size gets larger.
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -254,8 +253,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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@@ -4,10 +4,11 @@
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@@ -140,9 +141,7 @@ The residual is -1.56586e-14, and the expected residual is 4.64155e-14. This is
|
||||
estimate.
|
||||
</p>
|
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</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -150,8 +149,7 @@ The residual is -1.56586e-14, and the expected residual is 4.64155e-14. This is
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
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||||
@@ -4,10 +4,11 @@
|
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<title>Daubechies Wavelets and Scaling Functions</title>
|
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<link rel="stylesheet" href="../math.css" type="text/css">
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@@ -183,6 +184,54 @@
|
||||
<span class="inlinemediaobject"><object type="image/svg+xml" data="../../graphs/daubechies_8_scaling.svg"></object></span> The 8 vanishing
|
||||
moment scaling function.
|
||||
</p>
|
||||
<p>
|
||||
Boost.Math also provides numerical evaluation of the Fourier transform of these
|
||||
functions. This is useful in sparse recovery problems where the measurements
|
||||
are taken in the Fourier basis. The usage is exhibited below:
|
||||
</p>
|
||||
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">fourier_transform_daubechies_scaling</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
||||
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">fourier_transform_daubechies_scaling</span><span class="special">;</span>
|
||||
<span class="comment">// Evaluate the Fourier transform of the 4-vanishing moment Daubechies scaling function at ω=1.8:</span>
|
||||
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">hat_phi</span> <span class="special">=</span> <span class="identifier">fourier_transform_daubechies_scaling</span><span class="special"><</span><span class="keyword">float</span><span class="special">,</span> <span class="number">4</span><span class="special">>(</span><span class="number">1.8f</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
The Fourier transform convention is unitary with the sign of the imaginary
|
||||
unit being given in Daubechies Ten Lectures. In particular, this means that
|
||||
<code class="computeroutput"><span class="identifier">fourier_transform_daubechies_scaling</span><span class="special"><</span><span class="keyword">float</span><span class="special">,</span>
|
||||
<span class="identifier">p</span><span class="special">>(</span><span class="number">0.0</span><span class="special">)</span></code> returns
|
||||
1/sqrt(2π).
|
||||
</p>
|
||||
<p>
|
||||
The implementation computes an infinite product of trigonometric polynomials
|
||||
as can be found from recursive application of the identity 𝓕[φ](ω) = m(ω/2)𝓕[φ](ω/2).
|
||||
This is neither particularly fast nor accurate, but there appears to be no
|
||||
literature on this extremely useful topic, and hence the naive method must
|
||||
suffice.
|
||||
</p>
|
||||
<p>
|
||||
<span class="inlinemediaobject"><img src="../../graphs/fourier_transform_daubechies.png"></span>
|
||||
</p>
|
||||
<p>
|
||||
A benchmark can be found in <code class="computeroutput"><span class="identifier">reporting</span><span class="special">/</span><span class="identifier">performance</span><span class="special">/</span><span class="identifier">fourier_transform_daubechies_performance</span><span class="special">.</span><span class="identifier">cpp</span></code>; the
|
||||
results on a ~2021 M1 Macbook pro are presented below:
|
||||
</p>
|
||||
<p>
|
||||
Run on (10 X 24.1212 MHz CPU s) CPU Caches: L1 Data 64 KiB (x10) L1 Instruction
|
||||
128 KiB (x10) L2 Unified 4096 KiB (x5) Load Average: 1.33, 1.52, 1.62 -----------------------------------------------------------
|
||||
Benchmark Time -----------------------------------------------------------
|
||||
FourierTransformDaubechiesScaling<double, 1> 70.3 ns FourierTransformDaubechiesScaling<double,
|
||||
2> 330 ns FourierTransformDaubechiesScaling<double, 3> 335 ns FourierTransformDaubechiesScaling<double,
|
||||
4> 364 ns FourierTransformDaubechiesScaling<double, 5> 386 ns FourierTransformDaubechiesScaling<double,
|
||||
6> 436 ns FourierTransformDaubechiesScaling<double, 7> 447 ns FourierTransformDaubechiesScaling<double,
|
||||
8> 473 ns FourierTransformDaubechiesScaling<double, 9> 503 ns FourierTransformDaubechiesScaling<double,
|
||||
10> 554 ns
|
||||
</p>
|
||||
<p>
|
||||
Due to the low accuracy of this method, <code class="computeroutput"><span class="keyword">float</span></code>
|
||||
precision is arg-promoted to <code class="computeroutput"><span class="keyword">double</span></code>,
|
||||
and hence takes just as long as <code class="computeroutput"><span class="keyword">double</span></code>
|
||||
precision to execute.
|
||||
</p>
|
||||
<h4>
|
||||
<a name="math_toolkit.daubechies.h1"></a>
|
||||
<span class="phrase"><a name="math_toolkit.daubechies.references"></a></span><a class="link" href="daubechies.html#math_toolkit.daubechies.references">References</a>
|
||||
@@ -202,9 +251,7 @@
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
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<td align="left"></td>
|
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -212,8 +259,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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|
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|
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|
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@@ -4,10 +4,11 @@
|
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|
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@@ -179,9 +180,7 @@
|
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|
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|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -189,8 +188,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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|
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|
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|
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|
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@@ -4,10 +4,11 @@
|
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<title>Numerical Differentiation</title>
|
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@@ -346,9 +347,7 @@
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</li>
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</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -356,8 +355,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
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|
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@@ -4,10 +4,11 @@
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<title>Lanczos Smoothing Derivatives</title>
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -119,8 +118,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -388,8 +387,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -104,8 +103,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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of normally distributed weights to meet a specification.
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<dt><span class="section"><a href="dists/weibull_dist.html">Weibull Distribution</a></span></dt>
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -638,8 +637,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
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@@ -358,8 +357,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
@@ -601,9 +602,7 @@ from presumed-known mean and variance.
|
||||
MathWorld</a>
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -611,8 +610,7 @@ from presumed-known mean and variance.
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
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|
||||
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|
||||
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|
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||||
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||||
@@ -4,10 +4,11 @@
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<title>Binomial Distribution</title>
|
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<table cellpadding="2" width="100%"><tr>
|
||||
@@ -696,7 +697,7 @@
|
||||
<p>
|
||||
Using the relation:
|
||||
</p>
|
||||
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">](</span><span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span>
|
||||
<pre class="table-programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">](</span><span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span>
|
||||
<span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="identifier">p</span><span class="special">](</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">)</span>
|
||||
<span class="special">=</span> <a class="link" href="../../sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a><span class="special">(</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span></pre>
|
||||
<p>
|
||||
@@ -885,9 +886,7 @@
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -895,8 +894,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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|
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@@ -4,10 +4,11 @@
|
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<title>Cauchy-Lorentz Distribution</title>
|
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<link rel="stylesheet" href="../../../math.css" type="text/css">
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|
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@@ -291,9 +292,7 @@
|
||||
</li>
|
||||
</ul></div>
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</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -301,8 +300,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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@@ -4,10 +4,11 @@
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@@ -394,9 +395,7 @@ independent, normally distributed random
|
||||
</li>
|
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</ul></div>
|
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</div>
|
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -404,8 +403,7 @@ independent, normally distributed random
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
|
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@@ -4,10 +4,11 @@
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<title>Empirical Cumulative Distribution Function</title>
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<table cellpadding="2" width="100%"><tr>
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@@ -185,9 +186,7 @@
|
||||
is itself a fairly expensive operation.
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -195,8 +194,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<title>Exponential Distribution</title>
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<table cellpadding="2" width="100%"><tr>
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@@ -305,15 +306,13 @@
|
||||
Distributions</a>.)
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
|
||||
<a href="https://www.google.com/books/edition/Extreme_Value_Distributions/GwBqDQAAQBAJ?hl=en&gbpv=0" target="_top">Extreme
|
||||
<a href="https://www.google.com/books/edition/Extreme_Value_Distributions/GwBqDQAAQBAJ?hl=en&gbpv=0" target="_top">Extreme
|
||||
Value Distributions, Theory and Applications Samuel Kotz & Saralees
|
||||
Nadarajah</a> discuss the relationship of the types of extreme
|
||||
value distributions.
|
||||
</li></ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -321,8 +320,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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|
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@@ -4,10 +4,11 @@
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<title>Extreme Value Distribution</title>
|
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@@ -65,7 +66,7 @@
|
||||
</p>
|
||||
<p>
|
||||
The relationship of the types of extreme value distributions, of which
|
||||
this is but one, is discussed by <a href="https://www.google.com/books/edition/Extreme_Value_Distributions/GwBqDQAAQBAJ?hl=en&gbpv=0" target="_top">Extreme
|
||||
this is but one, is discussed by <a href="https://www.google.com/books/edition/Extreme_Value_Distributions/GwBqDQAAQBAJ?hl=en&gbpv=0" target="_top">Extreme
|
||||
Value Distributions, Theory and Applications Samuel Kotz & Saralees
|
||||
Nadarajah</a>.
|
||||
</p>
|
||||
@@ -314,9 +315,7 @@
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -324,8 +323,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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</p>
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@@ -4,10 +4,11 @@
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<td align="left"></td>
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|
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -428,8 +427,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
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|
||||
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||||
@@ -4,10 +4,11 @@
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -359,8 +358,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
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|
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|
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||||
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||||
@@ -4,10 +4,11 @@
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<title>Geometric Distribution</title>
|
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<link rel="stylesheet" href="../../../math.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -836,8 +835,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@@ -4,10 +4,11 @@
|
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<title>Hyperexponential Distribution</title>
|
||||
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<table cellpadding="2" width="100%"><tr>
|
||||
@@ -1452,9 +1453,7 @@
|
||||
</li>
|
||||
</ul></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -1462,8 +1461,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</div></td>
|
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</tr></table>
|
||||
</div>
|
||||
<hr>
|
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<a accesskey="p" href="geometric_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
|
||||
@@ -4,10 +4,11 @@
|
||||
<title>Hypergeometric Distribution</title>
|
||||
<link rel="stylesheet" href="../../../math.css" type="text/css">
|
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
@@ -41,11 +42,11 @@
|
||||
<span class="keyword">typedef</span> <span class="identifier">RealType</span> <span class="identifier">value_type</span><span class="special">;</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">Policy</span> <span class="identifier">policy_type</span><span class="special">;</span>
|
||||
<span class="comment">// Construct:</span>
|
||||
<span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span> <span class="comment">// r=defective/failures/success, n=trials/draws, N=total population.</span>
|
||||
<span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="identifier">uint64_t</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">uint64_t</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">uint64_t</span> <span class="identifier">N</span><span class="special">);</span> <span class="comment">// r=defective/failures/success, n=trials/draws, N=total population.</span>
|
||||
<span class="comment">// Accessors:</span>
|
||||
<span class="keyword">unsigned</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">unsigned</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="keyword">unsigned</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">uint64_t</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">uint64_t</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="identifier">uint64_t</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="keyword">typedef</span> <span class="identifier">hypergeometric_distribution</span><span class="special"><></span> <span class="identifier">hypergeometric</span><span class="special">;</span>
|
||||
@@ -104,25 +105,25 @@
|
||||
<span class="phrase"><a name="math_toolkit.dist_ref.dists.hypergeometric_dist.member_functions"></a></span><a class="link" href="hypergeometric_dist.html#math_toolkit.dist_ref.dists.hypergeometric_dist.member_functions">Member
|
||||
Functions</a>
|
||||
</h5>
|
||||
<pre class="programlisting"><span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">r</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">);</span>
|
||||
<pre class="programlisting"><span class="identifier">hypergeometric_distribution</span><span class="special">(</span><span class="identifier">uint64_t</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">uint64_t</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">uint64_t</span> <span class="identifier">N</span><span class="special">);</span>
|
||||
</pre>
|
||||
<p>
|
||||
Constructs a hypergeometric distribution with a population of <span class="emphasis"><em>N</em></span>
|
||||
objects, of which <span class="emphasis"><em>r</em></span> are defective, and from which
|
||||
<span class="emphasis"><em>n</em></span> are sampled.
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<pre class="programlisting"><span class="identifier">uint64_t</span> <span class="identifier">total</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Returns the total number of objects <span class="emphasis"><em>N</em></span>.
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<pre class="programlisting"><span class="identifier">uint64_t</span> <span class="identifier">defective</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Returns the number of objects <span class="emphasis"><em>r</em></span> in population <span class="emphasis"><em>N</em></span>
|
||||
which are defective.
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
<pre class="programlisting"><span class="identifier">uint64_t</span> <span class="identifier">sample_count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
||||
</pre>
|
||||
<p>
|
||||
Returns the number of objects <span class="emphasis"><em>n</em></span> which are sampled
|
||||
@@ -158,8 +159,8 @@
|
||||
<a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.range">range</a> and <a class="link" href="../nmp.html#math_toolkit.dist_ref.nmp.support">support</a>.
|
||||
</p>
|
||||
<p>
|
||||
The domain of the random variable is the unsigned integers in the range
|
||||
[max(0, n + r - N), min(n, r)]. A <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
|
||||
The domain of the random variable are the 64-bit unsigned integers in the
|
||||
range [max(0, n + r - N), min(n, r)]. A <a class="link" href="../../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
|
||||
is raised if the random variable is outside this range, or is not an integral
|
||||
value.
|
||||
</p>
|
||||
@@ -343,9 +344,7 @@
|
||||
|
||||
</p></blockquote></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||||
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -353,8 +352,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</div></td>
|
||||
</tr></table>
|
||||
</div>
|
||||
<hr>
|
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<div class="spirit-nav">
|
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<a accesskey="p" href="hyperexponential_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_chi_squared_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
|
||||
@@ -4,10 +4,11 @@
|
||||
<title>Inverse Chi Squared Distribution</title>
|
||||
<link rel="stylesheet" href="../../../math.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
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<link rel="home" href="../../../index.html" title="Math Toolkit 4.1.0">
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|
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<link rel="up" href="../dists.html" title="Distributions">
|
||||
<link rel="prev" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
|
||||
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|
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
@@ -456,9 +457,7 @@
|
||||
</li>
|
||||
</ol></div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
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<td align="left"></td>
|
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -466,8 +465,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
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</div></td>
|
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</tr></table>
|
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</div>
|
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<hr>
|
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<div class="spirit-nav">
|
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<a accesskey="p" href="hypergeometric_dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="inverse_gamma_dist.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
|
||||
@@ -4,10 +4,11 @@
|
||||
<title>Inverse Gamma Distribution</title>
|
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<link rel="stylesheet" href="../../../math.css" type="text/css">
|
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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@@ -350,9 +351,7 @@
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
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Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
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@@ -360,8 +359,7 @@
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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@@ -4,10 +4,11 @@
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@@ -429,9 +430,7 @@
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -439,8 +438,7 @@
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
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@@ -4,10 +4,11 @@
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@@ -333,9 +334,7 @@
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</p></div>
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|
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
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|
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Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
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Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||||
@@ -343,8 +342,7 @@
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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