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[CI SKIP] More cosmetic and link edits to get Inspect.exe passes except for links to [@boost: which shoudl work OK when built for the documentation. Ready to merge with develop, touch wood.

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pabristow
2019-08-12 17:53:50 +01:00
parent d922852f3b
commit 327c825dfa
38 changed files with 90 additions and 111 deletions
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2
doc/distributions/binomial_example.qbk
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@@ -208,7 +208,7 @@ Now even when the confidence level is very high, the limits are really
quite close to the experimentally calculated value of 0.2. Furthermore
the difference between the two calculation methods is now really quite small.
[endsect]
[endsect] [/section:binom_conf Calculating Confidence Limits on the Frequency of Occurrence for a Binomial Distribution]
[section:binom_size_eg Estimating Sample Sizes for a Binomial Distribution.]

6
doc/distributions/cauchy.qbk
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@@ -29,7 +29,7 @@ given by:
[equation cauchy_ref1]
The location parameter x[sub 0] is the location of the
The location parameter ['x[sub 0]] is the location of the
peak of the distribution (the mode of the distribution),
while the scale parameter [gamma] specifies half the width
of the PDF at half the maximum height. If the location is
@@ -103,7 +103,7 @@ In the following table __x0 is the location parameter of the distribution,
[table
[[Function][Implementation Notes]]
[[pdf][Using the relation: pdf = 1 / ([pi] * [gamma] * (1 + ((x - __x0) / [gamma])[super 2]) ]]
[[pdf][Using the relation: ['pdf = 1 / ([pi] * [gamma] * (1 + ((x - __x0) / [gamma])[super 2]) ]]]
[[cdf and its complement][
The cdf is normally given by:
@@ -130,7 +130,7 @@ or not, and whether /x/ is less than __x0 or not.
from the probability or its complement. First the argument /p/ is
reduced to the range \[-0.5, 0.5\], then the relation
x = __x0 [plusminus] [gamma] / tan([pi] * p)
[expression x = __x0 [plusminus] [gamma] / tan([pi] * p)]
is used to obtain the result. Whether we're adding
or subtracting from __x0 is determined by whether we're

2
doc/distributions/gamma.qbk
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@@ -47,7 +47,7 @@ probability density function:
[equation gamma_dist_ref1]
Sometimes an alternative formulation is used: given parameters
[alpha]= k and [beta]= 1 / [theta], then the
[alpha] = k and [beta] = 1 / [theta], then the
distribution can be defined by the PDF:
[equation gamma_dist_ref2]

4
doc/distributions/geometric.qbk
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@@ -63,7 +63,7 @@ The geometric distribution assumes that success_fraction /p/ is fixed for all /k
The probability that there are /k/ failures before the first success
[expression Pr(Y=/k/) = (1-/p/)[super /k/]/p/]
[expression Pr(Y=/k/) = (1-/p/)[super /k/] /p/]
For example, when throwing a 6-face dice the success probability /p/ = 1/6 = 0.1666[recur].
Throwing repeatedly until a /three/ appears,
@@ -71,7 +71,7 @@ the probability distribution of the number of times /not-a-three/ is thrown is g
Geometric distribution has the Probability Density Function PDF:
[expression (1-/p/)[super /k/]/p/]
[expression (1-/p/)[super /k/] /p/]
The following graph illustrates how the PDF and CDF vary for three examples
of the success fraction /p/,

2
doc/distributions/laplace.qbk
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@@ -32,7 +32,7 @@ It is also called the double exponential distribution.
[/ Wikipedia definition is The difference between two independent identically distributed
exponential random variables is governed by a Laplace distribution.]
For location parameter /[mu]/ and scale parameter /[sigma]/, it is defined by the
For location parameter ['[mu]] and scale parameter ['[sigma]], it is defined by the
probability density function:
[equation laplace_pdf]

2
doc/distributions/rayleigh.qbk
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@@ -31,7 +31,7 @@ is a continuous distribution with the
[expression f(x; sigma) = x * exp(-x[super 2]/2 [sigma][super 2]) / [sigma][super 2]]
For sigma parameter /[sigma]/ > 0, and /x/ > 0.
For sigma parameter ['[sigma]] > 0, and /x/ > 0.
The Rayleigh distribution is often used where two orthogonal components
have an absolute value,

5
doc/distributions/triangular.qbk
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@@ -45,9 +45,8 @@ The [@http://en.wikipedia.org/wiki/Triangular_distribution triangular distributi
is a distribution with the
[@http://en.wikipedia.org/wiki/Probability_density_function probability density function]:
[expression f(x) =]
[expression[:2(x-a)/(b-a) (c-a) [:for a <= x <= c]]]
[expression[:2(b-x)/(b-a) (b-c) [:for c < x <= b]]]
[expression f(x) = 2(x-a)/(b-a) (c-a) [sixemspace] for a <= x <= c]
[expression f(x) = 2(b-x)/(b-a) (b-c) [sixemspace] for c < x <= b]
Parameter ['a] (lower) can be any finite value.
Parameter ['b] (upper) can be any finite value > a (lower).

11
doc/distributions/uniform.qbk
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@@ -32,15 +32,14 @@ The [@http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 continu
is a distribution with the
[@http://en.wikipedia.org/wiki/Probability_density_function probability density function]:
[expression f(x) =]
[expression 1 / (upper - lower) for lower < x < upper]
[expression zero for x < lower or x > upper]
[expression f(x) =1 / (upper - lower) [sixemspace] for lower < x < upper]
[expression f(x) =zero [sixemspace] for x < lower or x > upper]
and in this implementation:
[expression 1 / (upper - lower) for x = lower or x = upper]
[expression 1 / (upper - lower) [sixemspace] for x = lower or x = upper]
The choice of x = lower or x = upper is made because statistical use of this distribution judged is most likely:
The choice of /x = lower/ or /x = upper/ is made because statistical use of this distribution judged is most likely:
the method of maximum likelihood uses this definition.
There is also a [@http://en.wikipedia.org/wiki/Discrete_uniform_distribution *discrete* uniform distribution].
@@ -48,7 +47,7 @@ There is also a [@http://en.wikipedia.org/wiki/Discrete_uniform_distribution *di
Parameters lower and upper can be any finite value.
The [@http://en.wikipedia.org/wiki/Random_variate random variate]
x must also be finite, and is supported lower <= x <= upper.
/x/ must also be finite, and is supported /lower <= x <= upper/.
The lower parameter is also called the
[@http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm location parameter],

1
doc/fp_utilities/float_comparison.qbk
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@@ -38,7 +38,6 @@ with small differences, and due to the way floating-point values are encoded can
edit distance. This is the method documented below: if `float_distance` is a surgeon's scalpel, then `relative_difference` is more
like a Swiss army knife: both have important but different use cases.
[h5:fp_relative Relative Comparison of Floating-point Values]

2
doc/html/index.html
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@@ -126,7 +126,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: August 12, 2019 at 14:22:55 GMT</small></p></td>
<td align="left"><p><small>Last revised: August 12, 2019 at 16:46:42 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

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@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1971716"></a>Function Index</h2></div></div></div>
<a name="id1971899"></a>Function Index</h2></div></div></div>
<p><a class="link" href="s01.html#idx_id_0">1</a> <a class="link" href="s01.html#idx_id_1">2</a> <a class="link" href="s01.html#idx_id_2">4</a> <a class="link" href="s01.html#idx_id_5">A</a> <a class="link" href="s01.html#idx_id_6">B</a> <a class="link" href="s01.html#idx_id_7">C</a> <a class="link" href="s01.html#idx_id_8">D</a> <a class="link" href="s01.html#idx_id_9">E</a> <a class="link" href="s01.html#idx_id_10">F</a> <a class="link" href="s01.html#idx_id_11">G</a> <a class="link" href="s01.html#idx_id_12">H</a> <a class="link" href="s01.html#idx_id_13">I</a> <a class="link" href="s01.html#idx_id_14">J</a> <a class="link" href="s01.html#idx_id_15">K</a> <a class="link" href="s01.html#idx_id_16">L</a> <a class="link" href="s01.html#idx_id_17">M</a> <a class="link" href="s01.html#idx_id_18">N</a> <a class="link" href="s01.html#idx_id_19">O</a> <a class="link" href="s01.html#idx_id_20">P</a> <a class="link" href="s01.html#idx_id_21">Q</a> <a class="link" href="s01.html#idx_id_22">R</a> <a class="link" href="s01.html#idx_id_23">S</a> <a class="link" href="s01.html#idx_id_24">T</a> <a class="link" href="s01.html#idx_id_25">U</a> <a class="link" href="s01.html#idx_id_26">V</a> <a class="link" href="s01.html#idx_id_27">W</a> <a class="link" href="s01.html#idx_id_28">X</a> <a class="link" href="s01.html#idx_id_29">Y</a> <a class="link" href="s01.html#idx_id_30">Z</a></p>
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@@ -24,7 +24,7 @@
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1996110"></a>Class Index</h2></div></div></div>
<a name="id1999980"></a>Class Index</h2></div></div></div>
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<div class="variablelist"><dl class="variablelist">
<dt>

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@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2001226"></a>Typedef Index</h2></div></div></div>
<a name="id2002651"></a>Typedef Index</h2></div></div></div>
<p><a class="link" href="s03.html#idx_id_67">A</a> <a class="link" href="s03.html#idx_id_68">B</a> <a class="link" href="s03.html#idx_id_69">C</a> <a class="link" href="s03.html#idx_id_70">D</a> <a class="link" href="s03.html#idx_id_71">E</a> <a class="link" href="s03.html#idx_id_72">F</a> <a class="link" href="s03.html#idx_id_73">G</a> <a class="link" href="s03.html#idx_id_74">H</a> <a class="link" href="s03.html#idx_id_75">I</a> <a class="link" href="s03.html#idx_id_78">L</a> <a class="link" href="s03.html#idx_id_80">N</a> <a class="link" href="s03.html#idx_id_81">O</a> <a class="link" href="s03.html#idx_id_82">P</a> <a class="link" href="s03.html#idx_id_84">R</a> <a class="link" href="s03.html#idx_id_85">S</a> <a class="link" href="s03.html#idx_id_86">T</a> <a class="link" href="s03.html#idx_id_87">U</a> <a class="link" href="s03.html#idx_id_88">V</a> <a class="link" href="s03.html#idx_id_89">W</a></p>
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@@ -24,7 +24,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2004621"></a>Macro Index</h2></div></div></div>
<a name="id2005974"></a>Macro Index</h2></div></div></div>
<p><a class="link" href="s04.html#idx_id_99">B</a> <a class="link" href="s04.html#idx_id_103">F</a></p>
<div class="variablelist"><dl class="variablelist">
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@@ -23,7 +23,7 @@
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id2006057"></a>Index</h2></div></div></div>
<a name="id2007433"></a>Index</h2></div></div></div>
<p><a class="link" href="s05.html#idx_id_124">1</a> <a class="link" href="s05.html#idx_id_125">2</a> <a class="link" href="s05.html#idx_id_126">4</a> <a class="link" href="s05.html#idx_id_127">5</a> <a class="link" href="s05.html#idx_id_128">7</a> <a class="link" href="s05.html#idx_id_129">A</a> <a class="link" href="s05.html#idx_id_130">B</a> <a class="link" href="s05.html#idx_id_131">C</a> <a class="link" href="s05.html#idx_id_132">D</a> <a class="link" href="s05.html#idx_id_133">E</a> <a class="link" href="s05.html#idx_id_134">F</a> <a class="link" href="s05.html#idx_id_135">G</a> <a class="link" href="s05.html#idx_id_136">H</a> <a class="link" href="s05.html#idx_id_137">I</a> <a class="link" href="s05.html#idx_id_138">J</a> <a class="link" href="s05.html#idx_id_139">K</a> <a class="link" href="s05.html#idx_id_140">L</a> <a class="link" href="s05.html#idx_id_141">M</a> <a class="link" href="s05.html#idx_id_142">N</a> <a class="link" href="s05.html#idx_id_143">O</a> <a class="link" href="s05.html#idx_id_144">P</a> <a class="link" href="s05.html#idx_id_145">Q</a> <a class="link" href="s05.html#idx_id_146">R</a> <a class="link" href="s05.html#idx_id_147">S</a> <a class="link" href="s05.html#idx_id_148">T</a> <a class="link" href="s05.html#idx_id_149">U</a> <a class="link" href="s05.html#idx_id_150">V</a> <a class="link" href="s05.html#idx_id_151">W</a> <a class="link" href="s05.html#idx_id_152">X</a> <a class="link" href="s05.html#idx_id_153">Y</a> <a class="link" href="s05.html#idx_id_154">Z</a></p>
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2
doc/html/math_toolkit/contact.html
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@@ -27,7 +27,7 @@
<a name="math_toolkit.contact"></a><a class="link" href="contact.html" title="Contact Info and Support">Contact Info and Support</a>
</h2></div></div></div>
<p>
The main place to see and raise issues is now at <a href="%40https://github.com/boostorg/math/" target="_top">GIThub</a>.
The main place to see and raise issues is now at <a href="https://github.com/boostorg/math/" target="_top">GIThub</a>.
Currently open bug reports can be viewed <a href="https://github.com/boostorg/math/issues" target="_top">here</a>.
</p>
<p>

2
doc/html/math_toolkit/conventions.html
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@@ -27,7 +27,7 @@
<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
</h2></div></div></div>
<p>
<a class="indexterm" name="id998501"></a>
<a class="indexterm" name="id999858"></a>
</p>
<p>
This documentation aims to use of the following naming and formatting conventions.

18
doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
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@@ -59,10 +59,11 @@
</p></blockquote></div>
<p>
The location parameter x<sub>0</sub> is the location of the peak of the distribution
(the mode of the distribution), while the scale parameter &#947; specifies half
the width of the PDF at half the maximum height. If the location is zero,
and the scale 1, then the result is a standard Cauchy distribution.
The location parameter <span class="emphasis"><em>x<sub>0</sub></em></span> is the location of the peak
of the distribution (the mode of the distribution), while the scale parameter
&#947; specifies half the width of the PDF at half the maximum height. If the
location is zero, and the scale 1, then the result is a standard Cauchy
distribution.
</p>
<p>
The distribution is important in physics as it is the solution to the differential
@@ -189,7 +190,8 @@
</td>
<td>
<p>
Using the relation: pdf = 1 / (&#960; * &#947; * (1 + ((x - x<sub>0 </sub>) / &#947;)<sup>2</sup>)
Using the relation: <span class="emphasis"><em>pdf = 1 / (&#960; * &#947; * (1 + ((x - x<sub>0 </sub>)
/ &#947;)<sup>2</sup>) </em></span>
</p>
</td>
</tr>
@@ -245,9 +247,9 @@
from the probability or its complement. First the argument <span class="emphasis"><em>p</em></span>
is reduced to the range [-0.5, 0.5], then the relation
</p>
<p>
x = x<sub>0 </sub> &#177; &#947; / tan(&#960; * p)
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">x = x<sub>0 </sub> &#177; &#947; / tan(&#960; * p)</span>
</p></blockquote></div>
<p>
is used to obtain the result. Whether we're adding or subtracting
from x<sub>0 </sub> is determined by whether we're starting from the complement

4
doc/html/math_toolkit/dist_ref/dists/gamma_dist.html
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@@ -83,8 +83,8 @@
</p></blockquote></div>
<p>
Sometimes an alternative formulation is used: given parameters &#945;= k and
&#946;= 1 / &#952;, then the distribution can be defined by the PDF:
Sometimes an alternative formulation is used: given parameters &#945; = k and
&#946; = 1 / &#952;, then the distribution can be defined by the PDF:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../../equations/gamma_dist_ref2.svg"></span>

4
doc/html/math_toolkit/dist_ref/dists/geometric_dist.html
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@@ -105,7 +105,7 @@
first success
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">Pr(Y=<span class="emphasis"><em>k</em></span>) = (1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup><span class="emphasis"><em>p</em></span></span>
<span class="serif_italic">Pr(Y=<span class="emphasis"><em>k</em></span>) = (1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup> <span class="emphasis"><em>p</em></span></span>
</p></blockquote></div>
<p>
For example, when throwing a 6-face dice the success probability <span class="emphasis"><em>p</em></span>
@@ -117,7 +117,7 @@
Geometric distribution has the Probability Density Function PDF:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">(1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup><span class="emphasis"><em>p</em></span></span>
<span class="serif_italic">(1-<span class="emphasis"><em>p</em></span>)<sup><span class="emphasis"><em>k</em></span></sup> <span class="emphasis"><em>p</em></span></span>
</p></blockquote></div>
<p>
The following graph illustrates how the PDF and CDF vary for three examples

4
doc/html/math_toolkit/dist_ref/dists/laplace_dist.html
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@@ -56,8 +56,8 @@
1972, p. 930). It is also called the double exponential distribution.
</p>
<p>
For location parameter /&#956;/ and scale parameter /&#963;/, it is defined by the
probability density function:
For location parameter <span class="emphasis"><em>&#956;</em></span> and scale parameter <span class="emphasis"><em>&#963;</em></span>,
it is defined by the probability density function:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../../equations/laplace_pdf.svg"></span>

3
doc/html/math_toolkit/dist_ref/dists/rayleigh.html
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@@ -58,7 +58,8 @@
<span class="serif_italic">f(x; sigma) = x * exp(-x<sup>2</sup>/2 &#963;<sup>2</sup>) / &#963;<sup>2</sup></span>
</p></blockquote></div>
<p>
For sigma parameter /&#963;/ &gt; 0, and <span class="emphasis"><em>x</em></span> &gt; 0.
For sigma parameter <span class="emphasis"><em>&#963;</em></span> &gt; 0, and <span class="emphasis"><em>x</em></span>
&gt; 0.
</p>
<p>
The Rayleigh distribution is often used where two orthogonal components

27
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@@ -74,31 +74,12 @@
density function</a>:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">f(x) =</span>
<span class="serif_italic">f(x) = 2(x-a)/(b-a) (c-a) &#8198; for a &lt;= x &lt;=
c</span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">
<div class="blockquote"><blockquote class="blockquote">
<p>
2(x-a)/(b-a) (c-a)
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
for a &lt;= x &lt;= c
</p></blockquote></div>
</blockquote></div>
</span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">
<div class="blockquote"><blockquote class="blockquote">
<p>
2(b-x)/(b-a) (b-c)
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
for c &lt; x &lt;= b
</p></blockquote></div>
</blockquote></div>
</span>
<span class="serif_italic">f(x) = 2(b-x)/(b-a) (b-c) &#8198; for c &lt; x &lt;=
b</span>
</p></blockquote></div>
<p>
Parameter <span class="emphasis"><em>a</em></span> (lower) can be any finite value. Parameter

20
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@@ -59,26 +59,23 @@
density function</a>:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">f(x) =</span>
<span class="serif_italic">f(x) =1 / (upper - lower) &#8198; for lower &lt;
x &lt; upper</span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">1 / (upper - lower) for lower &lt; x &lt;
upper</span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">zero for x &lt; lower or x &gt; upper</span>
<span class="serif_italic">f(x) =zero &#8198; for x &lt; lower or x &gt; upper</span>
</p></blockquote></div>
<p>
and in this implementation:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="serif_italic">1 / (upper - lower) for x = lower or x =
<span class="serif_italic">1 / (upper - lower) &#8198; for x = lower or x =
upper</span>
</p></blockquote></div>
<p>
The choice of x = lower or x = upper is made because statistical use of
this distribution judged is most likely: the method of maximum likelihood
uses this definition.
The choice of <span class="emphasis"><em>x = lower</em></span> or <span class="emphasis"><em>x = upper</em></span>
is made because statistical use of this distribution judged is most likely:
the method of maximum likelihood uses this definition.
</p>
<p>
There is also a <a href="http://en.wikipedia.org/wiki/Discrete_uniform_distribution" target="_top"><span class="bold"><strong>discrete</strong></span> uniform distribution</a>.
@@ -88,7 +85,8 @@
</p>
<p>
The <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
x must also be finite, and is supported lower &lt;= x &lt;= upper.
<span class="emphasis"><em>x</em></span> must also be finite, and is supported <span class="emphasis"><em>lower
&lt;= x &lt;= upper</em></span>.
</p>
<p>
The lower parameter is also called the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target="_top">location

2
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@@ -99,7 +99,7 @@
<span class="phrase"><a name="math_toolkit.factorials.sf_binomial.testing"></a></span><a class="link" href="sf_binomial.html#math_toolkit.factorials.sf_binomial.testing">Testing</a>
</h5>
<p>
The spot tests for the binomial coefficients use data generated by functions.wolfram.com.
The spot tests for the binomial coefficients use data generated by <a href="http://www.wolframalpha.com/" target="_top">Wolfram Alpha</a>.
</p>
<h5>
<a name="math_toolkit.factorials.sf_binomial.h2"></a>

3
doc/html/math_toolkit/factorials/sf_double_factorial.html
View File

@@ -119,7 +119,8 @@
<span class="phrase"><a name="math_toolkit.factorials.sf_double_factorial.testing"></a></span><a class="link" href="sf_double_factorial.html#math_toolkit.factorials.sf_double_factorial.testing">Testing</a>
</h5>
<p>
The spot tests for the double factorial use data generated by functions.wolfram.com.
The spot tests for the double factorial use data generated by <a href="http://www.wolframalpha.com/" target="_top">Wolfram
Alpha</a>.
</p>
<h5>
<a name="math_toolkit.factorials.sf_double_factorial.h2"></a>

2
doc/html/math_toolkit/factorials/sf_falling_factorial.html
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@@ -78,7 +78,7 @@
<span class="phrase"><a name="math_toolkit.factorials.sf_falling_factorial.testing"></a></span><a class="link" href="sf_falling_factorial.html#math_toolkit.factorials.sf_falling_factorial.testing">Testing</a>
</h5>
<p>
The spot tests for the falling factorials use data generated by <a href="../../functions.wolfram.com" target="_top">functions.wolfram.com</a>.
The spot tests for the falling factorials use data generated by <a href="https://functions.wolfram.com" target="_top">functions.wolfram.com</a>.
</p>
<h5>
<a name="math_toolkit.factorials.sf_falling_factorial.h2"></a>

2
doc/html/math_toolkit/factorials/sf_rising_factorial.html
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@@ -83,7 +83,7 @@
<span class="phrase"><a name="math_toolkit.factorials.sf_rising_factorial.testing"></a></span><a class="link" href="sf_rising_factorial.html#math_toolkit.factorials.sf_rising_factorial.testing">Testing</a>
</h5>
<p>
The spot tests for the rising factorials use data generated by <a href="../../functions.wolfram.com" target="_top">functions.wolfram.com</a>.
The spot tests for the rising factorials use data generated by <a href="https://functions.wolfram.com" target="_top">functions.wolfram.com</a>.
</p>
<h5>
<a name="math_toolkit.factorials.sf_rising_factorial.h2"></a>

2
doc/html/math_toolkit/hints.html
View File

@@ -66,7 +66,7 @@
</li>
<li class="listitem">
If you do not find satisfaction for your idea/feature/complaint, please
reach the author(s) preferably through the <a href="../boost%40lists.boost.org" target="_top">Boost
reach the author(s) preferably through the <a href="../../../../../lists.boost.org" target="_top">Boost
development list</a>, or raise a new <a href="https://github.com/boostorg/math/issues" target="_top">Boost.Math
issue</a>, or email the author(s) direct.
</li>

12
doc/html/math_toolkit/internals/minimax.html
View File

@@ -28,12 +28,12 @@
and the Remez Algorithm</a>
</h3></div></div></div>
<p>
The directory libs/math/minimax contains a command-line driven program for
the generation of minimax approximations using the Remez algorithm. Both
polynomial and rational approximations are supported, although the latter
are tricky to converge: it is not uncommon for convergence of rational forms
to fail. No such limitations are present for polynomial approximations which
should always converge smoothly.
The directory <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">minimax</span></code>
contains an interactive command-line driven program for the generation of
minimax approximations using the Remez algorithm. Both polynomial and rational
approximations are supported, although the latter are tricky to converge:
it is not uncommon for convergence of rational forms to fail. No such limitations
are present for polynomial approximations which should always converge smoothly.
</p>
<p>
It's worth stressing that developing rational approximations to functions

2
doc/html/math_toolkit/navigation.html
View File

@@ -27,7 +27,7 @@
<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
</h2></div></div></div>
<p>
<a class="indexterm" name="id998395"></a>
<a class="indexterm" name="id999704"></a>
</p>
<p>
Boost.Math documentation is provided in both HTML and PDF formats.

5
doc/html/math_toolkit/stat_tut/weg/binom_eg/binomial_coinflip_example.html
View File

@@ -191,11 +191,6 @@
<span class="identifier">probability</span> <span class="special">=</span> <span class="number">0.6</span><span class="special">;</span>
<span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">flip</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Quantile (flip, "</span> <span class="special">&lt;&lt;</span> <span class="identifier">probability</span> <span class="special">&lt;&lt;</span> <span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">q</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Quantile (flip, 0.6) = 5</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span>
<span class="special">{</span>

2
doc/internals/minimax.qbk
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@@ -1,6 +1,6 @@
[section:minimax Minimax Approximations and the Remez Algorithm]
The directory libs/math/minimax contains a command-line driven
The directory `libs/math/minimax` contains an interactive command-line driven
program for the generation of minimax approximations using the Remez
algorithm. Both polynomial and rational approximations are supported,
although the latter are tricky to converge: it is not uncommon for

23
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@@ -33,17 +33,19 @@
All of the tools in this header require a description of the recurrence relation: this takes the form of
a functor that returns a tuple containing the 3 coefficients, specifically, given a recurrence relation:
[/\Large $$ a_nF_{n-1} + b_nF_n + c_nF_{n+1} = 0 $$] [equation three_term_recurrence.svg]
[/\Large $$ a_nF_{n-1} + b_nF_n + c_nF_{n+1} = 0 $$]
[equation three_term_recurrence]
And a functor F then the expression:
And a functor `F` then the expression:
F(n);
[expression F(n);]
Returns a tuple containing [role serif_italic { a[sub n], b[sub n], c[sub n] }].
For example, the recurrence relation for the Bessel J and Y functions when written in this form is:
[/\Large $$ J_{v-1}(x) - \frac{2v}{x}J_v(x) + J_{v+1}(x)= 0 $$][$../equations/three_term_recurrence_bessel_jy.svg]
[/\Large $$ J_{v-1}(x) - \frac{2v}{x}J_v(x) + J_{v+1}(x)= 0 $$]
[$../equations/three_term_recurrence_bessel_jy.svg]
Therefore, given local variables /x/ and /v/ of type `double` the recurrence relation for Bessel J and Y can be encoded
in a lambda expression like this:
@@ -52,7 +54,8 @@ in a lambda expression like this:
Similarly, the Bessel I and K recurrence relation differs just by the sign of the final term:
[/\Large $$ I_{v-1}(x) - \frac{2v}{x}I_v(x) - I_{v+1}(x)= 0 $$][$../equations/three_term_recurrence_bessel_ik.svg]
[/\Large $$ I_{v-1}(x) - \frac{2v}{x}I_v(x) - I_{v+1}(x)= 0 $$]
[$../equations/three_term_recurrence_bessel_ik.svg]
And this could be encoded as:
@@ -63,9 +66,10 @@ The tools are then as follows:
template <class Recurrence, class T>
T function_ratio_from_backwards_recurrence(const Recurrence& r, const T& factor, boost::uintmax_t& max_iter);
Given a functor r which encodes the recurrence relation for function F at some location /n/, then returns the ratio:
Given a functor `r` which encodes the recurrence relation for function `F` at some location /n/, then returns the ratio:
[/\Large $$ F_n / F_{n-1} $$][$../equations/three_term_recurrence_backwards_ratio.svg]
[/\Large $$ F_n / F_{n-1} $$]
[$../equations/three_term_recurrence_backwards_ratio.svg]
This calculation is stable only if recurrence is stable in the backwards direction. Further the ratio calculated
is for the dominant solution (in the backwards direction) of the recurrence relation, if there are multiple solutions,
@@ -78,9 +82,10 @@ the maximum number of permitted iterations in the associated continued fraction.
template <class Recurrence, class T>
T function_ratio_from_forwards_recurrence(const Recurrence& r, const T& factor, boost::uintmax_t& max_iter);
Given a functor r which encodes the recurrence relation for function F at some location /n/, then returns the ratio:
Given a functor `r` which encodes the recurrence relation for function F at some location /n/, then returns the ratio:
[/\Large $$ F_n / F_{n+1} $$][$../equations/three_term_recurrence_forwards_ratio.svg]
[/\Large $$ F_n / F_{n+1} $$]
[$../equations/three_term_recurrence_forwards_ratio.svg]
This calculation is stable only if recurrence is stable in the forwards direction. Further the ratio calculated
is for the dominant solution (in the forwards direction) of the recurrence relation, if there are multiple solutions,

1
doc/math.qbk
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@@ -446,6 +446,7 @@ and use the function's name as the link text.]
[def __Mathematica [@http://www.wolfram.com/products/mathematica/index.html Wolfram Mathematica]]
[def __Maple [@https://www.maplesoft.com Maple]]
[def __WolframAlpha [@http://www.wolframalpha.com/ Wolfram Alpha]]
[def __Wolfram_functions [@https://functions.wolfram.com functions.wolfram.com]]
[def __TOMS748 [@http://portal.acm.org/citation.cfm?id=210111 TOMS Algorithm 748: enclosing zeros of continuous functions]]
[def __TOMS910 [@http://portal.acm.org/citation.cfm?id=1916469 TOMS Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations]]
[def __why_complements [link why_complements why complements?]]

2
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@@ -1,6 +1,6 @@
[section:contact Contact Info and Support]
The main place to see and raise issues is now at [@ @https://github.com/boostorg/math/ GIThub].
The main place to see and raise issues is now at [@https://github.com/boostorg/math/ GIThub].
Currently open bug reports can be viewed [@https://github.com/boostorg/math/issues here].
All old bug reports, including closed ones, can be viewed on Trac (now read-only)

2
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@@ -70,7 +70,7 @@ Entries may indicate that updates or corrections that solve your problem are in
you are most welcome to submit [@https://github.com/boostorg/math/pulls pull requests].
* If you do not understand why things work the way they do, see the ['rationale] section.
* If you do not find satisfaction for your idea/feature/complaint,
please reach the author(s) preferably through the [@boost@lists.boost.org Boost development list],
please reach the author(s) preferably through the [@boost:lists.boost.org Boost development list],
or raise a new [@https://github.com/boostorg/math/issues Boost.Math issue],
or email the author(s) direct.

10
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@@ -175,8 +175,7 @@ of epsilon higher.
[h4 Testing]
The spot tests for the double factorial use data
generated by functions.wolfram.com.
The spot tests for the double factorial use data generated by __WolframAlpha.
[h4 Implementation]
@@ -235,7 +234,7 @@ the __tgamma_delta_ratio function.
[h4 Testing]
The spot tests for the rising factorials use data generated by [@functions.wolfram.com functions.wolfram.com].
The spot tests for the rising factorials use data generated by __Wolfram_functions.
[h4 Implementation]
@@ -284,7 +283,7 @@ the __tgamma_delta_ratio function.
[h4 Testing]
The spot tests for the falling factorials use data generated by [@functions.wolfram.com].
The spot tests for the falling factorials use data generated by __Wolfram_functions.
[h4 Implementation]
@@ -342,8 +341,7 @@ and the __beta function for larger arguments.
[h4 Testing]
The spot tests for the binomial coefficients use data
generated by functions.wolfram.com.
The spot tests for the binomial coefficients use data generated by __WolframAlpha.
[h4 Implementation]