Subject: [Boost-commit] svn:boost r82687 - trunk/libs/math/example
From: pbristow_at_[hidden]
Date: 2013-02-06 20:24:11
Author: pbristow
Date: 2013-02-02 11:31:57 EST (Sat, 02 Feb 2013)
New Revision: 82687
URL: http://svn.boost.org/trac/boost/changeset/82687
Log:
Update to distribution construction examples to include examples of multiprecision.
Text files modified:
trunk/libs/math/example/distribution_construction.cpp | 133 +++++++++++++++++++++++++++------------
1 files changed, 93 insertions(+), 40 deletions(-)
Modified: trunk/libs/math/example/distribution_construction.cpp
==============================================================================
--- trunk/libs/math/example/distribution_construction.cpp (original)
+++ trunk/libs/math/example/distribution_construction.cpp 2013-02-02 11:31:57 EST (Sat, 02 Feb 2013)
@@ -1,6 +1,6 @@
// distribution_construction.cpp
-// Copyright Paul A. Bristow 2007, 2010.
+// Copyright Paul A. Bristow 2007, 2010, 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
@@ -10,21 +10,26 @@
// Caution: this file contains Quickbook markup as well as code
// and comments, don't change any of the special comment markups!
-//[distribution_construction1
+#ifdef _MSC_VER
+# pragma warning (disable : 4996) // disable -D_SCL_SECURE_NO_WARNINGS C++ 'Checked Iterators'
+#endif
+//[distribution_construction_1
/*`
-
The structure of distributions is rather different from some other statistical libraries,
-for example in less object-oriented language like FORTRAN and C,
-that provide a few arguments to each free function.
-This library provides each distribution as a template C++ class.
+for example, those written in less object-oriented language like FORTRAN and C:
+these provide a few arguments to each free function.
+
+Boost.Math library provides each distribution as a template C++ class.
A distribution is constructed with a few arguments, and then
member and non-member functions are used to find values of the
distribution, often a function of a random variate.
-First we need some includes to access the negative binomial distribution
-(and the binomial, beta and gamma too).
+For this demonstration, first we need some includes to access the
+negative binomial distribution (and the binomial, beta and gamma distributions too).
+To demonstrate the use with a high precision User-defined floating-point type
+`cpp_dec_float` we also need an include from Boost.Multiprecision.
*/
#include <boost/math/distributions/negative_binomial.hpp> // for negative_binomial_distribution
@@ -34,14 +39,16 @@
#include <boost/math/distributions/beta.hpp> // for beta_distribution.
#include <boost/math/distributions/gamma.hpp> // for gamma_distribution.
#include <boost/math/distributions/normal.hpp> // for normal_distribution.
+
+#include <boost/multiprecision/cpp_dec_float.hpp> // for cpp_dec_float_100
/*`
Several examples of constructing distributions follow:
*/
-//] [/distribution_construction1 end of Quickbook in C++ markup]
+//] [/distribution_construction_1 end of Quickbook in C++ markup]
int main()
{
-//[distribution_construction2
+//[distribution_construction_2
/*`
First, a negative binomial distribution with 8 successes
and a success fraction 0.25, 25% or 1 in 4, is constructed like this:
@@ -52,29 +59,29 @@
*/
using namespace boost::math;
/*`
- but this might risk ambiguity with names in std random so
- *much better is explicit `using boost::math:: ` * ... statements like
+ but this might risk ambiguity with names in `std random` so
+ [*much] better is explicit `using boost::math::` statements, for example:
*/
using boost::math::negative_binomial_distribution;
/*`
and we can still reduce typing.
- Since the vast majority of applications use will be using double precision,
- the template argument to the distribution (RealType) defaults
- to type double, so we can also write:
+ Since the vast majority of applications use will be using `double` precision,
+ the template argument to the distribution (`RealType`) defaults
+ to type `double`, so we can also write:
*/
- negative_binomial_distribution<> mydist9(8., 0.25); // Uses default RealType = double.
+ negative_binomial_distribution<> mydist9(8., 0.25); // Uses default `RealType = double`.
/*`
- But the name "negative_binomial_distribution" is still inconveniently long,
- so for most distributions, a convenience typedef is provided, for example:
+ But the name `negative_binomial_distribution` is still inconveniently long,
+ so, for most distributions, a convenience `typedef` is provided, for example:
typedef negative_binomial_distribution<double> negative_binomial; // Reserved name of type double.
[caution
- This convenience typedef is /not/ provided if a clash would occur
- with the name of a function: currently only "beta" and "gamma"
+ This convenience typedef is [*not provided] if a clash would occur
+ with the name of a function: currently only `beta` and `gamma`
fall into this category.
]
@@ -138,13 +145,13 @@
We can, of course, still provide the type explicitly thus:
*/
- // Explicit double precision:
+ // Explicit double precision: both arguments are double:
negative_binomial_distribution<double> mydist1(8., 0.25);
// Explicit float precision, double arguments are truncated to float:
negative_binomial_distribution<float> mydist2(8., 0.25);
- // Explicit float precision, integer & double arguments converted to float.
+ // Explicit float precision, integer & double arguments converted to float:
negative_binomial_distribution<float> mydist3(8, 0.25);
// Explicit float precision, float arguments, so no conversion:
@@ -160,30 +167,76 @@
negative_binomial_distribution<long double> mydist7(8., 0.25);
/*`
- And if you have your own RealType called MyFPType,
- for example NTL RR (an arbitrary precision type), then we can write:
+ And you can use your own RealType,
+ for example, `boost::math::cpp_dec_float_50` (an arbitrary 50 decimal digits precision type),
+ then we can write:
+ */
+ using namespace boost::multiprecision;
- negative_binomial_distribution<MyFPType> mydist6(8, 1); // Integer arguments -> MyFPType.
+ negative_binomial_distribution<cpp_dec_float_50> mydist8(8, 0.25);
+ // `integer` arguments are promoted to your RealType exactly, but
+ // `double` argument are converted to RealType,
+ // possibly losing precision, so don't write:
- [heading Default arguments to distribution constructors.]
+ negative_binomial_distribution<cpp_dec_float_50> mydist20(8, 0.23456789012345678901234567890);
+ // to avoid truncation of second parameter to `0.2345678901234567`.
- Note that default constructor arguments are only provided for some distributions.
- So if you wrongly assume a default argument you will get an error message, for example:
+ negative_binomial_distribution<cpp_dec_float_50> mydist21(8, cpp_dec_float_50("0.23456789012345678901234567890") );
- negative_binomial_distribution<> mydist8;
+ // Ensure that all potentially significant digits are shown.
+ std::cout.precision(std::numeric_limits<cpp_dec_float_50>::digits10);
+ cpp_dec_float_50 x("1.23456789012345678901234567890");
+ std::cout << pdf(mydist8, x) << std::endl;
+/*` showing 0.00012630010495970320103876754721976419438231705359935
- [pre error C2512 no appropriate default constructor available.]
+[warning When using multiprecision, it is all too easy to get accidental truncation!]
- No default constructors are provided for the negative binomial,
- because it is difficult to chose any sensible default values for this distribution.
- For other distributions, like the normal distribution,
- it is obviously very useful to provide 'standard'
- defaults for the mean and standard deviation thus:
+For example, if you write
+*/
+ std::cout << pdf(mydist8, 1.23456789012345678901234567890) << std::endl;
+/*`
+showing 0.00012630010495970318465064569310967179576805651692929,
+which is wrong at about the 17th decimal digit!
- normal_distribution(RealType mean = 0, RealType sd = 1);
+This is because the value provided is truncated to a `double`, effectively
+ `double x = 1.23456789012345678901234567890;`
- So in this case we can write:
- */
+Then the now `double x` is passed to function `pdf`,
+and this truncated `double` value is finally promoted to `cpp_dec_float_50`.
+
+Another way of quietly getting the wrong answer is to write:
+*/
+ std::cout << pdf(mydist8, cpp_dec_float_50(1.23456789012345678901234567890)) << std::endl;
+/*`
+A correct way from a multi-digit string value is
+*/
+ std::cout << pdf(mydist8, cpp_dec_float_50("1.23456789012345678901234567890")) << std::endl;
+/*`
+
+[tip Getting about 17 decimal digits followed by many zeros is often a sign of accidental truncation.]
+*/
+
+/*`
+[h4 Default arguments to distribution constructors.]
+
+Note that default constructor arguments are only provided for some distributions.
+So if you wrongly assume a default argument, you will get an error message, for example:
+
+ negative_binomial_distribution<> mydist8;
+
+[pre error C2512 no appropriate default constructor available.]
+
+No default constructors are provided for the `negative binomial` distribution,
+because it is difficult to chose any sensible default values for this distribution.
+
+For other distributions, like the normal distribution,
+it is obviously very useful to provide 'standard'
+defaults for the mean (zero) and standard deviation (unity) thus:
+
+ normal_distribution(RealType mean = 0, RealType sd = 1);
+
+So in this case we can write:
+*/
using boost::math::normal;
normal norm1; // Standard normal distribution.
@@ -193,7 +246,7 @@
return 0;
} // int main()
-/*`There is no useful output from this program, of course. */
+/*`There is no useful output from this demonstration program, of course. */
-//] [/end of distribution_construction2]
+//] [/end of distribution_construction_2]