math.qbk

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

[def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]]
[def __weibull_distrib [link math_toolkit.dist.dist_ref.dists.weibull Weibull Distribution]]

[/links to policy]
[def __Policy [link math_toolkit.policy Policy]] [/ Used in distribution template specifications]
[def __policy_section [link math_toolkit.policy Policies]] [/ Used in text to refer too.]
[def __policy_class [link math_toolkit.policy.pol_ref.pol_ref_ref policies::policy<>]]
[def __math_undefined [link math_toolkit.policy.pol_ref.assert_undefined mathematically undefined function]]
[def __policy_ref [link math_toolkit.policy.pol_ref policy reference]]
[def __math_discrete [link math_toolkit.policy.pol_ref.discrete_quant_ref discrete functions]]
[def __error_policy [link math_toolkit.policy.pol_ref.error_handling_policies error handling policies]]
[def __changing_policy_defaults [link math_toolkit.policy.pol_ref.policy_defaults changing policies defaults]]
[def __user_error_handling [link math_toolkit.policy.pol_tutorial.user_def_err_pol user error handling]]

[def __usual_accessors __cdf, __pdf, __quantile, __hazard, 
   __chf, __mean, __median, __mode, __variance, __sd, __skewness, 
   __kurtosis, __kurtosis_excess, __range and __support]

[def __gsl [@http://www.gnu.org/software/gsl/ GSL-1.9]]
[def __glibc [@http://www.gnu.org/software/libc/ GNU C Lib]]
[def __hpc [@http://docs.hp.com/en/B9106-90010/index.html HP-UX C Library]]
[def __cephes [@http://www.netlib.org/cephes/ Cephes]]


[def __why_complements [link why_complements why complements?]]
[def __complements [link complements complements]]

[/ Some composite templates]
[template super[x]'''<superscript>'''[x]'''</superscript>''']
[template sub[x]'''<subscript>'''[x]'''</subscript>''']
[template floor[x]'''&#x230A;'''[x]'''&#x230B;''']
[template floorlr[x][lfloor][x][rfloor]]
[template ceil[x] '''&#x2308;'''[x]'''&#x2309;''']

[template header_file[file] [@../../../../../[file] [file]]]

[template optional_policy[] 
The final __Policy argument is optional and can be used to
control the behaviour of the function: how it handles errors, 
what level of precision to use etc.  Refer to the 
[link math_toolkit.policy policy documentation for more details].]

[template discrete_quantile_warning[NAME]
[caution
The [NAME] distribution is a discrete distribution: internally
functions like the `cdf` and `pdf` are treated "as if" they are continuous 
functions, but in reality the results returned from these functions
only have meaning if an integer value is provided for the random variate 
argument.

The quantile function will by default return an integer result that has been
/rounded outwards/.  That is to say lower quantiles (where the probability is
less than 0.5) are rounded downward, and upper quantiles (where the probability
is greater than 0.5) are rounded upwards.  This behaviour
ensures that if an X% quantile is requested, then /at least/ the requested
coverage will be present in the central region, and /no more than/
the requested coverage will be present in the tails.

This behaviour can be changed so that the quantile functions are rounded
differently, or even return a real-valued result using 
[link math_toolkit.policy.pol_overview Policies].  It is strongly
recommended that you read the tutorial 
[link math_toolkit.policy.pol_tutorial.understand_dis_quant
Understanding Quantiles of Discrete Distributions] before
using the quantile function on the [NAME] distribution.  The
[link math_toolkit.policy.pol_ref.discrete_quant_ref reference docs] 
describe how to change the rounding policy
for these distributions.
] [/ caution]
] [/ template discrete_quantile_warning]

This manual is also available in 
[@http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf 
printer friendly PDF format].

[section:main_overview Overview]

[include overview.qbk]
[include structure.qbk] [/getting about]

[include result_type_calc.qbk]
[include error_handling.qbk]

[section:compilers_overview Compilers]
[compilers_overview]
[endsect]
[section:pol_overview Configuration and Policies]
[policy_overview]
[endsect]

[include thread_safety.qbk]

[section:perf_over Performance]
[performance_overview]
[endsect]
[section:history1 History and What's New]
[history]
[endsect]
[section:tr1 C99 and TR1 C Functions]
[tr1_overview]
[endsect]
[include contact_info.qbk]

[endsect] [/section:main_overview Overview]

[section:dist Statistical Distributions and Functions]
[include dist_tutorial.qbk]
[include dist_reference.qbk]
[endsect] [/section:dist Statistical Distributions and Functions]

[section:special Special Functions]

[section:sf_gamma Gamma Functions]
[include tgamma.qbk]
[include lgamma.qbk]
[include digamma.qbk]
[include gamma_ratios.qbk]
[include igamma.qbk]
[include igamma_inv.qbk]
[include gamma_derivatives.qbk]
[endsect] [/section:sf_gamma Gamma Functions]

[include factorials.qbk]

[section:sf_beta Beta Functions]
[include beta.qbk]
[include ibeta.qbk]
[include ibeta_inv.qbk]
[include beta_derivative.qbk]
[endsect] [/section:sf_beta Beta Functions]

[section:sf_erf Error Functions]
[include erf.qbk]
[include erf_inv.qbk]
[endsect] [/section:sf_erf Error Functions]

[section:sf_poly Polynomials]
[include legendre.qbk]
[include laguerre.qbk]
[include hermite.qbk]
[include spherical_harmonic.qbk]
[endsect] [/section:sf_poly Polynomials]

[section:bessel Bessel Functions]
[include bessel_introduction.qbk]
[include bessel_jy.qbk]
[include bessel_ik.qbk]
[include bessel_spherical.qbk]
[endsect] [/section:bessel Bessel Functions]

[section:ellint Elliptic Integrals]
[include ellint_introduction.qbk]
[include ellint_carlson.qbk]
[include ellint_legendre.qbk]
[endsect] [/section:ellint Elliptic Integrals]

[section:zetas Zeta Functions]
[include zeta.qbk]
[endsect]

[include expint.qbk]

[include powers.qbk]
[include sinc.qbk]
[include inv_hyper.qbk]
[include rounding_func.qbk]
[include fpclassify.qbk]
[include float_next.qbk]

[section:extern_c TR1 and C99 external "C" Functions]
[section:tr1 C99 and TR1 C Functions Overview]
[tr1_overview]
[endsect]
[include c99_ref.qbk]
[include tr1_ref.qbk]
[endsect]

[endsect] [/section:special Special Functions]

[section:toolkit Internal Details and Tools (Experimental)]

[include internals_overview.qbk]

[section:internals1 Reused Utilities]
[include constants.qbk]
[include series.qbk]
[include fraction.qbk]
[include rational.qbk]
[include roots.qbk]
[include roots_without_derivatives.qbk]
[include minima.qbk]
[endsect] [/section:internals1 Reused Utilities]

[section:internals2 Testing and Development]
[include polynomial.qbk]
[include minimax.qbk]
[include relative_error.qbk]
[include test_data.qbk]
[endsect] [/section:internals2 Testing and Development]

[endsect] [/section:toolkit Toolkit]

[section:using_udt Use with User-Defined Floating-Point Types]
[include concepts.qbk]
[endsect] [/section:using_udt Use with User Defined Floating-Point Types]

[include policy.qbk]

[include performance.qbk]

[section:backgrounders Backgrounders]
[include implementation.qbk]
[include error.qbk] [/relative error NOT handling]
[include lanczos.qbk]
[include remez.qbk]
[include references.qbk]
[endsect] [/section:backgrounds Backgrounders]

[section:status Library Status]
[section:history1 History and What's New]
[history]
[endsect]
[section:compilers Compilers]
[compilers_overview]
[endsect]
[include issues.qbk]
[include credits.qbk]
[/include test_HTML4_symbols.qbk]
[/include test_Latin1_symbols.qbk]

[endsect] [/section:status Status and Roadmap] 

[/ math.qbk
  Copyright 2008 John Maddock and Paul A. Bristow.
  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]