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git-subtree-dir: xo-distribution
git-subtree-mainline: 4e022df686
git-subtree-split: 036ca5d817
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Roland Conybeare 2025-05-11 15:52:36 -05:00
commit ecd019e8bb
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xo-distribution/.gitignore vendored Normal file
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# clangd working space (see emacs+lsp)
.cache
# typical cmake build directory (source-tree-nephew)
.build*
# symlink to builddir/compile_commands.json; should be set manually in dev sandbox
compile_commands.json

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xo-distribution/CMakeLists.txt Normal file
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# xo-distribution/CMakeLists.txt
cmake_minimum_required(VERSION 3.10)
project(xo_distribution VERSION 1.0)
include(GNUInstallDirs)
include(cmake/xo-bootstrap-macros.cmake)
xo_cxx_toplevel_options3()
#add_subdirectory(example)
add_subdirectory(src/distribution) # note refcnt dep -> not header-only
add_subdirectory(utest)
xo_export_cmake_config(${PROJECT_NAME} ${PROJECT_VERSION} ${PROJECT_NAME}Targets)

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xo-distribution/cmake/xo-bootstrap-macros.cmake Normal file
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# ----------------------------------------------------------------
# for example:
# $ PREFIX=/usr/local # for example
# $ cmake -DCMAKE_MODULE_PATH=prefix -DCMAKE_INSTALL_PREFIX=$PREFIX -B .build
#
# will get
# CMAKE_MODULE_PATH
# from xo-cmake-config --cmake-module-path
#
# and expect .cmake macros in
# CMAKE_MODULE_PATH/xo_macros/xo_cxx.cmake
# ----------------------------------------------------------------
find_program(XO_CMAKE_CONFIG_EXECUTABLE NAMES xo-cmake-config REQUIRED)
if ("${XO_CMAKE_CONFIG_EXECUTABLE}" STREQUAL "XO_CMAKE_CONFIG_EXECUTABLE-NOT_FOUND")
message(FATAL "could not find xo-cmake-config executable")
endif()
message(STATUS "XO_CMAKE_CONFIG_EXECUTABLE=${XO_CMAKE_CONFIG_EXECUTABLE}")
if (NOT XO_SUBMODULE_BUILD)
if (("${CMAKE_MODULE_PATH}" STREQUAL "") OR ("${CMAKE_MODULE_PATH}" STREQUAL prefix))
# default to typical install location for xo-project-macros
execute_process(COMMAND ${XO_CMAKE_CONFIG_EXECUTABLE} --cmake-module-path OUTPUT_VARIABLE CMAKE_MODULE_PATH)
message(STATUS "CMAKE_MODULE_PATH=${CMAKE_MODULE_PATH}")
endif()
endif()
# needs to have been installed somewhere on CMAKE_MODULE_PATH,
# (e.g. from xo-cmake with the same value for CMAKE_INSTALL_PREFIX)
#
include(xo_macros/xo_cxx)
xo_cxx_bootstrap_message()

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xo-distribution/cmake/xo_distributionConfig.cmake.in Normal file
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@PACKAGE_INIT@
include(CMakeFindDependencyMacro)
find_dependency(refcnt)
include("${CMAKE_CURRENT_LIST_DIR}/xo_distributionTargets.cmake")
check_required_components("@PROJECT_NAME@")

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xo-distribution/include/xo/distribution/Distribution.hpp Normal file
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/* @file Distribution.hpp */
#pragma once
#include "xo/refcnt/Refcounted.hpp"
namespace xo {
namespace distribution {
/* abstract api for a cumulative probability distribution.
* over supplied Domain
*/
template<typename Domain>
class Distribution : public ref::Refcount {
public:
virtual double cdf(Domain const & x) const = 0;
}; /*Distribution*/
} /*namespace distribution*/
} /*namespace xo*/
/* end Distribution.hpp */

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xo-distribution/include/xo/distribution/Empirical.hpp Normal file
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/* @file Empirical.hpp */
#pragma once
#include "xo/distribution/Distribution.hpp"
#include "xo/ordinaltree/RedBlackTree.hpp"
#include "xo/indentlog/scope.hpp"
#include <map>
#include <cstdint>
namespace xo {
namespace distribution {
/* representation for counter,
* recording #of samples with the same value
*/
using CounterRep = uint32_t;
/* counter; for use with StdEmpirical distribution below
*/
class Counter {
public:
Counter() = default;
Counter(CounterRep n) : count_(n) {}
CounterRep count() const { return count_; }
void incr() { ++count_; }
operator CounterRep () const { return count_; }
Counter & operator+=(CounterRep n) { count_ += n; return *this; }
private:
CounterRep count_ = 0;
}; /*Counter*/
} /*namespace disitribution*/
} /*namespace xo*/
/* end Empirical.hpp */

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xo-distribution/include/xo/distribution/ExplicitDist.hpp Normal file
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/* file ExplicitDist.hpp
*
* author: Roland Conybeare, Oct 2022
*/
#pragma once
#include "Distribution.hpp"
#include "Normal.hpp"
#include "xo/indentlog/scope.hpp"
#include "xo/indentlog/print/vector.hpp"
#include "xo/indentlog/print/tostr.hpp"
#include <vector>
#include <cmath>
#include <cstdint>
namespace xo {
using xo::xtag;
namespace distribution {
class ProbabilityBucket {
public:
ProbabilityBucket() = default;
double weight() const { return wt_; }
double cdf() const { return cdf_; }
/* note: when calling this, must invalidate ExplicitDist.cdf_valid_flag */
void scale_weight(double k) { this->wt_ *= k; }
void assign_weight(double w) { this->wt_ = w; }
/* implementation method: only ExplicitDist.renormalize() should call this */
void assign_cdf(double x) { this->cdf_ = x; }
void display(std::ostream & os) const {
using xo::xtag;
os << "<ProbabilityBucket"
<< xtag("wt", this->wt_)
<< xtag("cdf", this->cdf_)
<< ">";
} /*display*/
private:
/* probability assigned to this bucket.
* updated in-place by ExplicitDist.include_sample()
*/
double wt_ = 0.0;
/* cumulative probability assigned to this bucket b
* and all buckets b[i] for domain values < b
*
* invalidated by ExplicitDist.scale_bucket()
* see ExplicitDist.
*/
double cdf_ = 0.0;
}; /*ProbabilityBucket*/
inline std::ostream & operator<<(std::ostream & os, ProbabilityBucket const & x) {
x.display(os);
return os;
} /*operator<<*/
namespace detail {
/* three kinds of index here:
* 1. lo: non-negative index into ExplicitDist.lo_v_[]
* 2. hi: non-negative index into ExplicitDist.hi_v_[]
* 3. signed: if >=0: index into ExplicitDist.hi_v_[]
* if <0: index into ExplicitDist.lo_v_[]
*
* with lz=.lo_v.size(), hz=hi_v.size():
*
* .hi_v[0] .hi_v[hz-1]
* | v v
* |
* +--+--+ +--+--|--+--+ +--+
* | | | ... | | | | | ... | |
* +--+--+ +--+--|--+--+ +--+
* ^ ^
* .lo_v[lz-1] .lo_v[0]
*
* ^ ^ ^ ^
* signed -lz -1| 0 ... hz-1
*/
class ExplicitDistIndexUtil {
public:
static size_t signed2hi(int32_t signed_ix) { return signed_ix; }
static size_t signed2lo(int32_t signed_ix) { return -signed_ix - 1; }
static int32_t lo2signed(size_t lo_ix) { return -static_cast<int32_t>(lo_ix)-1; }
static int32_t hi2signed(size_t hi_ix) { return hi_ix; }
static ProbabilityBucket const * signed2bucket_c(int32_t signed_ix,
std::vector<ProbabilityBucket> const * lo_v,
std::vector<ProbabilityBucket> const * hi_v) {
if (signed_ix >= 0) {
size_t hi_ix = signed2hi(signed_ix);
if (hi_v && (hi_ix < hi_v->size()))
return &(*hi_v)[hi_ix];
} else {
size_t lo_ix = signed2lo(signed_ix);
if (lo_v && (lo_ix < lo_v->size()))
return &(*lo_v)[lo_ix];
}
return nullptr;
} /*signed2bucket_c*/
static ProbabilityBucket * signed2bucket(int32_t signed_ix,
std::vector<ProbabilityBucket> * lo_v,
std::vector<ProbabilityBucket> * hi_v) {
ProbabilityBucket const * b = signed2bucket_c(signed_ix, lo_v, hi_v);
return const_cast<ProbabilityBucket *>(b);
} /*signed2bucket*/
}; /*ExplicitDistIndexUtil*/
class ExplicitDistIterator : public ExplicitDistIndexUtil {
public:
ExplicitDistIterator() = default;
ExplicitDistIterator(int32_t signed_ix,
std::vector<ProbabilityBucket> * lo_v,
std::vector<ProbabilityBucket> * hi_v)
: signed_ix_{signed_ix}, p_lo_v_{lo_v}, p_hi_v_{hi_v} {}
ProbabilityBucket & operator*() {
ProbabilityBucket * pb = signed2bucket(this->signed_ix_,
this->p_lo_v_,
this->p_hi_v_);
if (!pb) {
throw std::runtime_error("ExplicitDistIterator: attempt to deref invalid iterator");
}
return *pb;
} /*operator**/
ExplicitDistIterator & operator++() { ++(this->signed_ix_); return *this; }
ExplicitDistIterator & operator--() { --(this->signed_ix_); return *this; }
private:
/* signed iterator */
int32_t signed_ix_ = 0;
/* will be ExplicitDist.lo_v[] */
std::vector<ProbabilityBucket> * p_lo_v_ = nullptr;
/* will be ExplicitDist.hi_v[] */
std::vector<ProbabilityBucket> * p_hi_v_ = nullptr;
}; /*ExplicitDistIterator*/
} /*namespace detail*/
/* explicit distribution with buckets.
* (if you want to avoid bucketing at the expense of memory,
* see StdEmpirical)
*
* sample-independent buckets can be faster to the extent
* {#of buckets} << {#of samples}
*
* in particular
* | StdEmpirical | PackedEmpirical
* ------------------------------+--------------+-----------------
* update existing sample/bucket | O(log(n)) | O(1)
* create new sample/bucket | O(log(n)) | O(log(n))
* cdf | O(log(n)) | O(n)
*
* PackedEmpirical offers scaling + renormalization
*
* since .cdf() is slow, .ks_stat_1sided() is supported only in StdEmpirical.
* (could generalize in future to some other implementation with fast .cdf())
*
* Require:
* Domain is something with metric, e.g. int|double.
* categorical domain not supported here.
*
* see also: statistics/Histogram. Histogram keeps more per-bucket statistics
*/
template<typename Domain>
class ExplicitDist : public Distribution<Domain>, public detail::ExplicitDistIndexUtil {
public:
using WeightVector = std::vector<ProbabilityBucket>;
using iterator = detail::ExplicitDistIterator;
public:
static rp<ExplicitDist> make(Domain bucket_dx, Domain ref_value) {
return new ExplicitDist(bucket_dx, ref_value);
}
/* create distribution with n buckets of width bucket_dx,
* covering range [ref_value, ref_value + n * bucket_dx]
*/
static rp<ExplicitDist> make_n(size_t n, Domain bucket_dx, Domain ref_value) {
return new ExplicitDist(n, bucket_dx, ref_value);
}
size_t n_bucket() const { return this->lo_v_.size() + this->hi_v_.size(); }
/* lub domain value with .cdf(lo) = 0 */
Domain lo() const {
std::size_t lz = this->lo_v_.size();
return this->ref_value_ - lz * this->bucket_dx_;
} /*lo*/
/* glb domain value with .cdf(hi) = 1 */
Domain hi() const {
std::size_t hz = this->hi_v_.size();
return this->ref_value_ + hz * this->bucket_dx_;
} /*hi*/
Domain bucket_lo(int32_t signed_ix) const {
return this->ref_value_ + signed_ix * this->bucket_dx_;
} /*bucket_lo*/
Domain bucket_mid(int32_t signed_ix) const {
return this->ref_value_ + (0.5 + signed_ix) * this->bucket_dx_;
} /*bucket_mid*/
Domain bucket_hi(int32_t signed_ix) const {
return this->bucket_lo(signed_ix + 1);
} /*bucket_hi*/
iterator begin() { return iterator(lo2signed(this->lo_v_.size() - 1),
&(this->lo_v_),
&(this->hi_v_)); }
iterator end() { return iterator(hi2signed(this->hi_v_.size()),
&(this->lo_v_),
&(this->hi_v_)); }
/* probability density at domain value x */
double density(Domain const & x) const {
/* careful! may need to renormalize */
{
ExplicitDist<Domain> * self = const_cast<ExplicitDist<Domain> *>(this);
self->check_renormalize();
}
auto v = this->lookup_bucket(x);
ProbabilityBucket const * b = v.first;
if (b) {
/* probability density is constant within each bucket */
return b->weight() / this->bucket_dx_;
} else {
return 0.0;
}
} /*density*/
/* pair {bucket glb, density} for all buckets, in increasing domain order */
std::vector<std::pair<Domain, double>> density_v() const {
/* careful! may need to renormalize */
{
ExplicitDist<Domain> * self = const_cast<ExplicitDist<Domain> *>(this);
self->check_renormalize();
}
size_t n = this->n_bucket();
std::vector<std::pair<Domain, double>> retval(n);
double w2d = 1.0 / this->bucket_dx_;
for(size_t i=0; i<n; ++i) {
Domain lo = this->bucket_lo(i);
ProbabilityBucket const * b = this->lookup_signed_bucket(i);
assert(b);
double density = b->weight() * w2d;
retval[i] = std::make_pair(lo, density);
}
return retval;
} /*density_v*/
/* return:
* .first signed bucket index ix;
* refers to .lo_v[1-ix] if ix<0;
* refers to .hi_v[+ix] if ix>=0
* .second fractional weight within bucket associated with x.
* not scaled by ProbabilityWeight.weight
*/
std::pair<int32_t, double> signed_bucket_index(Domain const & x) const {
double ix_f = ::floor((x - this->ref_value_) / this->bucket_dx_);
int32_t ix = ix_f;
/*
* ^
* |............
* | : |
* | wt : | unit area
* | : |
* +-----------+
* bucket_lo ^ bucket_lo + .bucket_dx
* x
*/
Domain bucket_lo = this->ref_value_ + (ix * this->bucket_dx_);
double wt = (x - bucket_lo) / this->bucket_dx_;
return std::make_pair(ix, wt);
} /*signed_bucket_index*/
ProbabilityBucket const * lookup_signed_bucket(int32_t signed_ix) const {
return signed2bucket_c(signed_ix, &(this->lo_v_), &(this->hi_v_));
} /*lookup_signed_bucket*/
/* non-const version with write access */
ProbabilityBucket * lookup_signed_bucket(int32_t signed_ix) {
return signed2bucket(signed_ix, &(this->lo_v_), &(this->hi_v_));
} /*lookup_signed_bucket*/
/* return null pointer if bucket that would contain x not represented
* .second is fractional weight (relative to unity) within selected bucket
*/
std::pair<ProbabilityBucket const *, double> lookup_bucket(Domain const & x) const {
/* signed index.
* ix>=0 => .lo_v[]
* ix< 0 => .hi_v[]
*/
std::pair<int32_t, double> v = this->signed_bucket_index(x);
int32_t ix = v.first;
double fraction_wt = v.second;
ProbabilityBucket const * pw = this->lookup_signed_bucket(ix);
return std::make_pair(pw, fraction_wt);
} /*lookup_bucket*/
/* non-const version */
std::pair<ProbabilityBucket *, double> lookup_bucket(Domain const & x) {
ExplicitDist<Domain> const * c_self = this;
std::pair<ProbabilityBucket const *, double> v = c_self->lookup_bucket(x);
ProbabilityBucket * b = const_cast<ProbabilityBucket *>(v.first);
double fraction_wt = v.second;
return std::make_pair(b, fraction_wt);
} /*lookup_bucket*/
/* like .lookup_bucket(), but create bucket if not already present
* .second reports fractional weight (relative to unity) within bucket
* that contains x.
*/
std::pair<ProbabilityBucket*, double> establish_bucket(Domain const & x) {
/* signed index.
* ix>=0 => .lo_v[]
* ix< 0 => .hi_v[]
*/
std::pair<int32_t, double> v = this->signed_bucket_index(x);
int32_t ix = v.first;
double fraction_wt = v.second;
ProbabilityBucket * pw = nullptr;
if (ix >= 0) {
size_t hi_ix = signed2hi(ix);
if (hi_ix >= this->hi_v_.size()) {
/* need to expand .hi_v[] */
this->hi_v_.resize(hi_ix+1);
}
pw = &(this->hi_v_[hi_ix]);
} else {
size_t lo_ix = signed2lo(ix);
if (lo_ix >= this->lo_v_.size()) {
/* need to expand .lo_v[] */
this->lo_v_.resize(lo_ix+1);
}
pw = &(this->lo_v_[lo_ix]);
}
return std::make_pair(pw, fraction_wt);
} /*establish_bucket*/
void scale_bucket_by_signed_index(int32_t signed_ix, double k) {
ProbabilityBucket * b = this->lookup_signed_bucket(signed_ix);
if (b) {
b->scale_weight(k);
this->cdf_valid_flag_ = false;
} else {
/* if bucket isn't represented, then corresponding weight is zero,
* both before and after scaling. In this special case
* representation didn't change -> don't invalidate cdf
*/
}
} /*scale_bucket_by_signed_index*/
/* scale probability assigned to bucket for domain value x, by factor k */
void scale_bucket(Domain const & x, double k) {
assert(k >= 0.0);
std::pair<int32_t, double> v = this->signed_bucket_index(x);
this->scale_bucket_by_signed_index(v.first, k);
} /*scale_bucket*/
/* scale probability weight for buckets in [lo, hi] by fn(p)
* for a point p in each bucket, however:
* under no circumstances try to evaluate fn() outside [lo, hi]
* (relevant if either lo/hi fall inside a bucket)
*/
template<typename Function>
void scale_interval(Domain const & lo,
Domain const & hi,
Function && fn)
{
XO_SCOPE_DISABLED(lscope);
/* note: using inclusive upper index bounds here;
* variying from idiomatic c++ style for symmetry
*/
int32_t min_bucket_ix = lo2signed(this->lo_v_.size() - 1);
int32_t max_bucket_ix = hi2signed(this->hi_v_.size() - 1);
int32_t lo_ix = this->signed_bucket_index(lo).first;
int32_t hi_ix = this->signed_bucket_index(hi).first;
/* start_ix: lowest explicit bucket associating with [lo, hi) */
int32_t start_ix = std::max(min_bucket_ix, lo_ix + 1);
/* end_ix: highest explicit bucket associating with [lo, hi) */
int32_t end_ix = std::min(max_bucket_ix, hi_ix);
if (lscope.enabled()) {
lscope.log(xtag("min_bucket_ix", min_bucket_ix),
xtag("max_bucket_ix", max_bucket_ix),
xtag("lo_ix", lo_ix),
xtag("hi_ix", hi_ix),
xtag("start_ix", start_ix),
xtag("end_ix", end_ix));
}
/* for endpoints: avoid evaluating fn() outside [lo, hi] */
if (min_bucket_ix <= lo_ix) {
double lo_k = fn(lo);
if (lscope.enabled())
lscope.log("A", xtag("lo_ix", lo_ix), xtag("lo_k", lo_k));
this->scale_bucket_by_signed_index(lo_ix, lo_k);
}
for(int32_t ix = start_ix; ix <= end_ix; ++ix) {
double k = fn(this->bucket_mid(ix));
if (lscope.enabled())
lscope.log("B", xtag("ix", ix), xtag("k", k));
this->scale_bucket_by_signed_index(ix, k);
}
/* for endpoints: avoid evaluating fn() outside [lo, hi] */
if (hi_ix <= max_bucket_ix) {
double hi_k = fn(hi);
if (lscope.enabled())
lscope.log("C", xtag("hi_ix", hi_ix), xtag("hi_k", hi_k));
this->scale_bucket_by_signed_index(hi_ix, hi_k);
}
} /*scale_interval*/
template<typename Function>
void scale_all(Function && fn)
{
this->scale_interval(this->lo(), this->hi(), fn);
} /*scale_all*/
/* convenience: scale by scaled normal cdf.
*
* support use case where:
* 1. explicit dist represents distribution of asset value;
* 2. assume one party A to trade/order has noisy signal,
* with normally-distributed error around (unknown) true value s,
* with variance o^2;
* 3. observe a trade/order at some price p,
* giving us one-sided information about A's knowledge in two scenarios:
* i. A trades
* ii. A does not trade
*
* We will be applying Bayes' rule to update prior.
* If buy(p) = {A buys},
* N(x) is cumulative normal distribution:
* N(x) -> 0 as x -> -oo;
* N(x) -> 1 as x -> +oo;
*
* -1/2 2
* (d/dx)N(x) = (2.pi) . exp(-x /2)
* then:
* P{s=s'}
* P{s=s'|buy(p)} = ---------.P{buy(p)|s=s'}
* P{buy(p)}
*
* P{s=s'}
* = ---------.N[(1/o)(s'-p)],
* P{buy(p)}
*
* In this scenario, P{s=s'} is our prior, represented by distribution *this.
* The unconditional probability P{buy(p)} is not a function of s', so:
*
* /
* |
* P{buy(p)} = | P{s=s'} . N[(1/o)(s'-p)] . ds'
* |
* /
*
* in other words can scale explicit prior *this by N[(1/o)(s'-p)] then renormalize
* so total probability weight is 1.
*
* Conversely, if event is {A sells}, similar argument leads to scaling
* by N[(1/o)(p-s')]
*
* sign. scale by N[(1/sigma).sign.(x-mean)]
*/
void scale_by_normal_cdf(int sign, Domain const & mean, Domain const & sigma) {
auto fn([sign, mean, sigma](Domain const & s) {
return Normal::cdf_impl(sign * (s - mean) / sigma);
});
this->scale_all(fn);
} /*scale_by_normal_cdf*/
// ----- inherited from Distribution<Domain> -----
/* note: marked const; actually "logically const" */
virtual double cdf(Domain const & x) const override {
/* .cdf() is slow here, because partial sums aren't stored
* --> have to sum over O(n) buckets
*/
{
ExplicitDist<Domain> * self = const_cast<ExplicitDist<Domain> *>(this);
self->check_renormalize();
}
std::pair<ProbabilityBucket const *, double> v = this->lookup_bucket(x);
ProbabilityBucket const * b = v.first;
double fraction_wt = v.second;
if (b) {
/* for bucket that x belongs to, treat as uniformly distributed
* fraction_wt = 1.0 -> 100% of b -> b.cdf()
* fraction_wt = 0.0 -> 0% of b -> b.cdf() - b.weight()
*/
return b->cdf() + (fraction_wt - 1.0) * b->weight();
} else {
if (x >= this->ref_value_) {
/* x falls above farthest .hi_v[] */
return 1.0;
} else {
/* x falls below farthest .lo_v[] */
return 0.0;
}
}
} /*cdf*/
/* O(n). restores .cdf_valid_flag */
void renormalize() {
/* [1] compute sum of probability weights
* [2] rescale all buckets so sum is 1.
* [3] restore .cdf_valid_flag
*/
/* [1] */
double lo_sum_prob = 0.0;
for (ProbabilityBucket & b : this->lo_v_) {
assert(lo_sum_prob >= 0.0);
lo_sum_prob += b.weight();
}
double hi_sum_prob = 0.0;
for (ProbabilityBucket & b : this->hi_v_) {
assert(hi_sum_prob >= 0.0);
hi_sum_prob += b.weight();
}
assert(lo_sum_prob + hi_sum_prob > 0.0);
/* [2] */
double renorm_factor = 1.0 / (lo_sum_prob + hi_sum_prob);
{
double lo_tail = lo_sum_prob;
/* iterate over buckets < .ref_value, in /descending/ domain order */
for (ProbabilityBucket & b : this->lo_v_) {
b.scale_weight(renorm_factor);
b.assign_cdf(lo_tail);
/* reduce tail after assign cdf to b, since
* lo_tail includes b's probability weight
*/
lo_tail -= b.weight();
/* numerical roundoff can cause this */
if (lo_tail < 0.0)
lo_tail = 0.0;
}
}
{
double cum_prob = lo_sum_prob;
/* iterate over buckets >= .refvalue, in /ascending/ domain order */
for (ProbabilityBucket & b : this->hi_v_) {
b.scale_weight(renorm_factor);
/* increase cum_prob before assign cdf to b,
* since b.cdf should include b's probability weight
*/
cum_prob += b.weight();
/* numerical roundoff can cause this */
if (cum_prob >= 1.0)
cum_prob = 1.0;
b.assign_cdf(cum_prob);
}
}
/* [3] */
this->cdf_valid_flag_ = true;
} /*renormalize*/
void check_renormalize() {
if (!this->cdf_valid_flag_) {
this->renormalize();
}
} /*check_renormalize*/
void display(std::ostream & os) const {
os << "<ExplicitDist";
os << xtag("cdf_valid_flag", this->cdf_valid_flag_);
os << xtag("bucket_dx", this->bucket_dx_);
os << xtag("ref_value", this->ref_value_);
os << xtag("lz", this->lo_v_.size());
os << xtag("hz", this->hi_v_.size());
os << xtag("lo_v", this->lo_v_);
os << xtag("hi_v", this->hi_v_);
os << ">";
} /*display*/
std::string display_string() const { return xo::tostr(*this); }
private:
ExplicitDist(Domain bucket_dx, Domain ref_value)
: cdf_valid_flag_{true},
bucket_dx_{bucket_dx},
ref_value_{ref_value},
lo_v_{},
hi_v_{1}
{
assert(bucket_dx_ > 0.0);
/* must have at least one bucket, since need total probability weight = 1 */
this->hi_v_[0].assign_weight(1.0);
this->hi_v_[0].assign_cdf(1.0);
}
ExplicitDist(size_t n, Domain bucket_dx, Domain ref_value)
: cdf_valid_flag_{true},
bucket_dx_{bucket_dx},
ref_value_{ref_value},
lo_v_{},
hi_v_{n}
{
assert(bucket_dx > 0.0);
/* must have at least one bucket, since need total probability weight = 1 */
assert(n > 0);
double w = 1.0 / n;
for(size_t i = 0; i<n; ++i) {
this->hi_v_[i].assign_weight(w);
this->hi_v_[i].assign_cdf((i+1)*w);
}
} /*ctor*/
private:
/* with lz=.lo_v.size(), hz=hi_v.size():
*
* .ref_value - .bucket_dx * lz
* | .ref_value
* | | .hi_v[0] .hi_v[hz-1]
* v v v v
* |
* +--+--+ +--+--|--+--+ +--+
* | | | ... | | | | | ... | |
* +--+--+ +--+--|--+--+ +--+
* |
* ^ ^ ^
* .lo_v[lz-1] .lo_v[0] .ref_value + .bucket_dx * hz
*
*/
/* .cdf_valid_flag:
* -> false whenever .scale_bucket() runs.
* -> true whenever .renormalize() runs.
*
* if false, then *this is 'not a probability distribution':
* Sum b[i].weight != 1.0 (summing over probability buckets .lo_v[], .hi_v[])
* i
*/
bool cdf_valid_flag_ = true;
/* width of each bucket */
Domain bucket_dx_;
/* natural value here would be 0.
* use .pos_v[] for values >= .ref_value
* use .neg_v[] for values < .ref_value
*/
Domain ref_value_;
/* buckets for domain values < .ref_value
*
* with dx = .bucket_dx
* .lo_v[i] represents weights in range
* [.ref_value - (i+1) * dx, .ref_value - i * dx)
*/
WeightVector lo_v_;
/* buckets for domain values > .ref_value
*
* with dx = .bucket_dx
* .hi_v[i] represents weights in range
* [.ref_value + i * dx, .ref_value + (i+1) * dx))
*/
WeightVector hi_v_;
}; /*ExplicitDist*/
template<typename Domain>
inline std::ostream &
operator<<(std::ostream & os, ExplicitDist<Domain> const & x) {
x.display(os);
return os;
} /*operator<<*/
} /*namespace distribution*/
} /*namespace xo*/
/* end ExplicitDist.hpp */

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/* @file Exponential.hpp */
#pragma once
#include "xo/distribution/Distribution.hpp"
#include <limits>
#include <cmath>
namespace xo {
namespace distribution {
/* Exponential probability distribution */
class Exponential : public Distribution<double> {
public:
explicit Exponential(double lm) : lambda_(lm) {}
/* exponential probability density:
*
* -lm.x
* p(x) = { lm . e , x > 0
* { 0 , x <= 0
*
*/
static double density_impl(double lambda, double x) {
if(x <= 0.0)
return 0.0;
return lambda * ::exp(-lambda * x);
} /*density_impl*/
/* exponential distribution:
*
* -lm.x
* F(x) = 1 - e , x > 0
* F(x) = 0 , x <= 0
*/
static double distr_impl(double lambda, double x) {
if(x <= 0.0)
return 0.0;
return 1.0 - ::exp(-lambda * x);
} /*distr_impl*/
/* compute x: F(x)=y, where F(x)
* is the cumulative exponential probability distributio.
*
* -lm.x
* F(x) = 1 - e , x>0
*
* -lm.x
* e = 1 - F(x)
*
* -lm.x = ln(1 - F(x))
*
* x = -ln(1 - F(x)) / lm, 0 < F(x) < 1
*/
static double distr_inverse_impl(double lambda, double Fx) {
if(Fx < 0.0)
return -1.0 * std::numeric_limits<double>::infinity();
if(Fx >= 1.0)
return +1.0 * std::numeric_limits<double>::infinity();
return (-1.0 / lambda) * ::log(1.0 - Fx);
} /*distr_inverse_impl*/
double lambda() const { return lambda_; }
double density(double x) const {
return density_impl(this->lambda_, x);
} /*density*/
double distribution(double x) const {
return distr_impl(this->lambda_, x);
} /*distribution*/
double distribution_inverse(double y) const {
return distr_inverse_impl(this->lambda_, y);
} /*distribution_inverse*/
// ----- inherited from Distribution<double> -----
virtual double cdf(double const & x) const override {
return distribution(x);
} /*cdf*/
private:
/* intensity parameter.
* require: lambda > 0
*/
double lambda_ = 1.0;
}; /*Exponential*/
} /*namespace distribution*/
} /*namespace xo*/
/* end Exponential.cpp */

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/* @file KolmogorovSmirnov.hpp */
#pragma once
#include "Distribution.hpp"
#include "xo/indentlog/scope.hpp"
#include <cmath>
#include <cstdint>
namespace xo {
/* Kolmogorov-Smirnov probability distribution */
namespace distribution {
class KolmogorovSmirnov : public Distribution<double> {
public:
KolmogorovSmirnov() = default;
/* kolmogorov-smirnov (KS) cumulative distribution
*
* cdf is defined by the series:
*
* +oo / j 2 2 \
* P1(x) = 1 + 2 Sum | (-1) .exp(-2.j .x ) |
* j=1 \ /
*
* this converges rapidly for x > 1. expanding the first few terms:
*
* / 2 2 2 2 2 2 2 \
* P1(x) ~= 1 + 2.| -exp(-2.x ) + exp(-2.2 .x ) - exp(-2.3 .x ) + exp(-2.4 .x ) |
* \ /
*
* / 2 2 4 2 9 2 16 \
* = 1 + 2.| -exp(-2.x ) + exp(-2.x ) - exp(2.x ) + exp(-2.x ) |
* \ /
*
* / 4 9 16 \
* = 1 + 2.| T(x) + T(x) + T(x) + T(x) |
* \ /
*
* with T(x) = .term_aux(1, x)
*
* with x=1:
* term1_aux(1, 1): -0.135335
* term1_aux(2, 1): 3.35463e-4
* term1_aux(3, 1): -1.52300e-8
* term1_aux(4, 1): 1.26642e-14
* term1_aux(5, 1): -1.92875e-22
*
* with x=1.18:
* term1_aux(1, 1): -0.0617414
* term1_aux(2, 1): 1.45314e-5
* term1_aux(3, 1): -1.30374e-11
* term1_aux(4, 1): 4.45890e-20
* term1_aux(5, 1): -5.83124e-31
*
* ----------------------------------------------------------------
*
* There's an alternative series for the KS distribution,
* that converges rapidly for small x (x < ~1.18)
*
* / 2 2 \
* sqrt(2.pi) +oo / | (2j - 1) .pi | \
* P2(x) = ---------- . Sum | exp | - ------------ | |
* x j=1 \ | 2 | /
* \ 8.x /
*
* / 2 \
* | pi |
* witu U(x) = exp | - ---- |
* | 2 |
* \ 8.x /
* we have
* / 2 \
* sqrt(2.pi) +oo | (2j - 1) |
* P2(x) = ---------- . Sum | U(x) |
* x j=1 | |
* \ /
*
* / \
* sqrt(2.pi) | 9 25 49 |
* = ---------- . | U(x) + U(x) + U(x) + U(x) + .. |
* x | |
* \ /
*
* with x=1.0:
* term2_aux(1, 1): 0.291213
* term2_aux(2, 1): 1.50625e-5
* term2_aux(3, 1): 4.02964e-14
* term2_aux(4, 1): 5.57599e-27
*
* with x=1.18:
* term2_aux(1, 1.18): 0.412292
* term2_aux(2, 1.18): 3.44223e-4
* term2_aux(3, 1.18): 2.39945e-10
* term2_aux(4, 1.18): 1.39652e-19
*/
static double term1_aux(uint32_t j, double x) {
double f = ::exp(-2.0 * x * x);
/* sgn:
* +1 for j in {2, 4, 6, ..}
* -1 for j in {1, 3, 5, ..}
*/
int32_t sgn = (((j & 0x1) == 0) ? +1 : -1);
if(j == 1) {
return sgn * f;
} else {
return sgn * ::pow(f, j*j);
}
} /*term1_aux*/
/* implements P1(x) above; truncating at 4 terms.
* use .distr1() for x > ~1.18
*/
static double distr1_impl(double x) {
double f = term1_aux(1.0, x);
double f2 = f*f; /*f^2*/
double f4 = f2*f2; /*f^4*/
double f8 = f4*f4; /*f^8*/
double f9 = f8*f; /*f^9*/
double f16 = f8*f8; /*f^16*/
double r = ((f16 + f9) + f4) + f;
return 1.0 + 2.0*r;
} /*distr1_impl*/
/* pi: 3.141592... */
static constexpr double c_pi = M_PI;
/* pi^2 / 8 */
static constexpr double c_pi2_8 = 0.125 * c_pi * c_pi;
/* computes
*
* (2j-1)^2
* U(x)
*
* require:
* - j >= 1
*/
static double term2_aux(uint32_t j, double x) {
double u = ::exp(-c_pi2_8 / (x * x));
if(j == 1) {
return u;
} else {
uint32_t j2m1 = 2*j - 1;
return ::pow(u, j2m1 * j2m1);
}
} /*term2_aux*/
/* implements P2(x) above; truncating at 4 terms */
static double distr2_impl(double x) {
static double c_sqrt_2pi
= ::sqrt(2.0 * c_pi);
double scale = c_sqrt_2pi / x;
double u = term2_aux(1, x);
double u2 = u*u; /*u^2*/
double u4 = u2*u2; /*u^4*/
double u8 = u4*u4; /*u^8*/
double u16 = u8*u8; /*u^16*/
double u32 = u16*u16; /*u^32*/
double u9 = u8*u; /*u^9*/
double u25 = u16*u8*u; /*u^25*/
double u49 = u32*u16*u; /*u^49*/
double r = ((u49 + u25) + u9) + u;
return scale * r;
} /*distr2_impl*/
static double distr_impl(double x) {
using xo::tostr;
constexpr char const * c_self = "KolmogorovSmirnov::distr_impl";
if(x < 0.0)
throw std::runtime_error(tostr(c_self, "KS(x) cdf defined for x>=0"));
if(x == 0.0)
return 0;
if(x < 1.18) {
/* P2(x) converges fastest */
return distr2_impl(x);
} else {
/* P1(x) converges fastest */
return distr1_impl(x);
}
} /*distr_impl*/
/* p-value for significance of a particular value of the KS-statistic
* obtain this statistic for a sample distribution using
* Empirical.ks_stat_1sided(dexp)
* for some target distribution dexp
*
* ne.
* for 1-sided test: #of points in sample, i.e. Empirical.n_sample()
* for 2-sided test: (n1 . n2) / (n1 + n2)
* D.
* max difference between observed and expected cumulative distributions.
* see Empirical.ks_stat_1sided()
*/
static double ks_pvalue(uint32_t ne, double D)
{
using xo::scope;
using xo::xtag;
constexpr bool logging_enabled_flag = false;
scope log(XO_DEBUG(logging_enabled_flag));
double ne_sqrt = ::sqrt(ne);
/* argument to KS-distribution.
* x in [0, +oo)
*
* A large value for x -> small value for 1 - KSdist(x),
* i.e. represents probability that a sample of size ne with a
* KS-statistic of magnitude D or larger, could be drawn from
* distribution dexp.
*/
double x = ne_sqrt + 0.12 + (0.11 / ne_sqrt);
double xD = x * D;
double pvalue = 1.0 - distr_impl(xD);
log && log(xtag("ne", ne),
xtag("D", D),
xtag("ne_sqrt", ne_sqrt),
xtag("x", x),
xtag("xD", xD),
xtag("pvalue", pvalue));
return pvalue;
} /*ks_pvalue*/
/* cumulative distribution function */
double distribution(double x) const {
return distr_impl(x);
} /*distribution*/
// ----- inherited from Distribution<double> -----
virtual double cdf(double const & x) const {
return this->distribution(x);
} /*cdf*/
}; /*KolmogorovSmirnov*/
} /*namespace distribution*/
} /*namespace xo*/
/* end KolmogorovSmirnov.hpp */

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/* @file Normal.hpp */
#pragma once
#include "Distribution.hpp"
#include <cmath>
namespace xo {
namespace distribution {
/* the guassian distribution, with mean 0 and variance 1
*/
class Normal : public Distribution<double> {
public:
Normal() = default;
/* N(0,1): mean 0, sdev 1 */
static rp<Normal> unit() { return new Normal(); }
/* normal probability density:
*
* x^2
* -(1/2) 1/2
* p(x) = e / (2.pi)
*/
static double density(double x) {
static double c_sqrt_2pi = ::sqrt(2 * M_PI);
return ::exp(-0.5 * x * x) / c_sqrt_2pi;
} /*density*/
/* cumulative distribution function for N(0,1):
*
* / x
* |
* | p(x).dx
* |
* / -oo
*
* where p(x) is the normal density function p(x) = e^[-x^2/2]
*/
static double cdf_impl(double x) {
return 0.5 * std::erfc(-M_SQRT1_2 * x);
} /*cdf_impl*/
// ----- inherited from Distribution<double> -----
virtual double cdf(double const & x) const override {
return cdf_impl(x);
} /*cdf*/
}; /*Normal*/
} /*namespace distribution*/
} /*namespace xo*/
/* end Normal.hpp */

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/* @file StdEmpirical.hpp */
#pragma once
#include "Empirical.hpp"
#include "xo/ordinaltree/RedBlackTree.hpp"
#include "xo/indentlog/scope.hpp"
#include <map>
#include <cstdint>
namespace xo {
namespace distribution {
/* an empirical distribution over a given domain
* (e.g. double as proxy for IR),
* obtained by sorting equally-weighted samples
*/
template<typename Domain>
class StdEmpirical : public Distribution<Domain> {
public:
using SampleMap = xo::tree::RedBlackTree<Domain,
Counter,
xo::tree::SumReduce<uint32_t>>;
using const_iterator = typename SampleMap::const_iterator;
public:
StdEmpirical() = default;
uint32_t n_sample() const { return n_sample_; }
const_iterator begin() const { return sample_map_.begin(); }
const_iterator end() const { return sample_map_.end(); }
/* compute kolmogorov-smirnov statistic with a non-sampled distribution.
* if d2 is sampled, should use .ks_stat_2sided() instead
*/
std::pair<double, double> ks_stat_1sided(Distribution<Domain> const & d2) const {
using xo::scope;
using xo::xtag;
constexpr char const * c_self = "Empirical::ks_stat_1sided";
constexpr bool c_logging_enabled = false;
scope lscope(c_self, c_logging_enabled);
double ks_stat = 0.0;
/* for i'th loop iteration below:
* xj_sum = sum of all x[j] with j<=i
*/
uint32_t xj_sum = 0;
/* #of sample in this distribution, as double */
double nr = 1.0 / this->n_sample();
/* loop over elements x[i] of this (sampled) distribution,
* compare cdf(x[i]) with d2.cdf(x[i])
*
* KS stat is the maximum observed difference.
*/
for(auto const & point : this->sample_map_) {
Domain const & xi = point.first;
uint32_t xi_count = point.second;
xj_sum += xi_count;
/* p1 = xi_sum / n1, where n1 = .n_sample() */
double p1 = xj_sum * nr;
double p2 = d2.cdf(xi);
double dp = std::abs(p1 - p2);
if(c_logging_enabled)
lscope.log(c_self,
xtag("xi", xi),
xtag("xi_count", xi_count),
xtag("xj_sum", xj_sum),
xtag("p1", p1),
xtag("p2", p2),
xtag("dp", dp));
ks_stat = std::max(ks_stat, dp);
}
return std::pair<double, double>(this->n_sample(), ks_stat);
} /*ks_stat_1sided*/
/* compute kolmogorov-smirnov statistic with a sampled distribution;
* assess likelihood that both samples come from the same population.
*/
std::pair<double, double> ks_stat_2sided(StdEmpirical<Domain> const & d2) {
/* loop once over both sample distributions;
* algorithm is O(n1 + n2) for two empirical
* distributions with n1,n2 points respectively
*/
/* return value observed here */
double ks_stat = 0.0;
auto ix1 = this->sample_map_.begin();
auto end_ix1 = this->sample_map_.end();
auto ix2 = d2.sample_map_.begin();
auto end_ix2 = this->sample_map_.end();
uint32_t xj1_sum = 0;
uint32_t xj2_sum = 0;
uint32_t n1 = this->n_sample();
uint32_t n2 = d2.n_sample();
double nr1 = 1.0 / n1;
double nr2 = 1.0 / n2;
/* ^
* 1| **.
* | ...*..
* | . *
* | **********
* | * .
* | .........
* | . *
* | ********
* | ..*.....
* +----------------------->
* ^ ^
* ix1 ix2
*/
while ((ix1 != end_ix1) || (ix2 != end_ix2)) {
/* on each iteration, compare sample distributions
* at smallest of (ix1->first, ix2->first)
*/
bool advance_ix1_flag = false;
bool advance_ix2_flag = false;
if (ix1 == end_ix1) {
/* only ix2 dereferenceable */
advance_ix2_flag = true;
} else if (ix2 == end_ix2) {
/* only ix1 dereferenceable */
advance_ix1_flag = true;
} else {
/* ix1,ix2 both dereferenceable */
advance_ix1_flag = (ix1->first <= ix2->first);
advance_ix2_flag = (ix2->first <= ix1->first);
}
if (advance_ix1_flag) {
xj1_sum += ix1->first;
++ix1;
}
if (advance_ix2_flag) {
xj2_sum += ix2->first;
++ix2;
}
double p1 = xj1_sum * nr1;
double p2 = xj2_sum * nr2;
double dp = std::abs(p1 - p2);
ks_stat = std::max(ks_stat, dp);
}
/* ne = effective #of points to use when comparing 2 sample dist/s */
double ne = (n1 * n2) / static_cast<double>(n1 + n2);
return std::pair<double, double>(ne, ks_stat);
#ifdef OBSOLETE
/* NOTE: this will cost O(n.log(n))
* (for empirical distributions with n points)
* if we loop over both sets of points in parallel,
* can get O(n) solution
*
*/
/* loop over points in *this */
double ks1 = this->ks_stat_1sided(d2);
/* loop over points in d2 */
double ks2 = d2.ks_stat_1sided(*this);
return std::max(ks1, ks2);
#endif
} /*ks_stat_2sided*/
// ----- inherited from Empirical<Domain> -----
/* introduce one new sample into this distribution */
virtual void include_sample(Domain const & x) {
++(this->n_sample_);
/* note: xo::tree::RedBlackTree doesn't provide the usual reference result
* from operator[]; it needs to intervene after assignment to update
* order statistics
*/
auto lhs = this->sample_map_[x];
lhs += 1;
} /*include_sample*/
// ----- inherited from Distribution<Domain> -----
virtual double cdf(Domain const & x) const override {
/* computes #of samples with values <= x */
uint32_t nx = this->sample_map_.reduce_lub(x, true /*is_closed*/);
size_t n = this->n_sample();
return static_cast<double>(nx) / n;
} /*cdf*/
private:
/* count #of calls to .include_sample() */
CounterRep n_sample_ = 0;
/* .sample_map_[x] counts the #of times
* .include_sample(x) has been called.
*/
SampleMap sample_map_;
}; /*StdEmpirical*/
} /*namespace distribution*/
} /*namespace xo*/
/* end StdEmpirical.hpp */

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/* @file Uniform.hpp */
#pragma once
#include "Distribution.hpp"
namespace xo {
namespace distribution {
/* uniform distribution on an interval */
class Uniform : public Distribution<double> {
public:
Uniform(double lo, double hi) : lo_(lo), hi_(hi) {}
static rp<Uniform> unit() { return new Uniform(0.0, 1.0); }
static double density_impl(double lo, double hi, double x) {
if (x <= lo)
return 0.0;
if (x >= hi)
return 0.0;
return 1.0 / (hi - lo);
} /*density_impl*/
static double distr_impl(double lo, double hi, double x) {
if (x <= lo)
return 0.0;
if (x >= hi)
return 1.0;
return (x - lo) / (hi - lo);
} /*distr_impl*/
double lo() const { return lo_; }
double hi() const { return hi_; }
double density(double x) const {
return density_impl(this->lo_, this->hi_, x);
} /*density*/
double distribution(double x) const {
return distr_impl(this->lo_, this->hi_, x);
} /*distribution*/
// ----- inherited from Distribution<double> -----
virtual double cdf(double const & x) const override {
return this->distribution(x);
} /*cdf*/
private:
/* Invariant: .lo < .hi */
double lo_ = 0.0;
double hi_ = 1.0;
}; /*Uniform*/
} /*namespace distribution*/
} /*namespace xo*/

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set(SELF_LIB xo_distribution)
set(SELF_SRCS Normal.cpp)
xo_add_shared_library4(${SELF_LIB} ${PROJECT_NAME}Targets ${PROJECT_VERSION} 1 ${SELF_SRCS})
xo_dependency(${SELF_LIB} refcnt)

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/* @file Normal.cpp */
#include "Normal.hpp"
namespace xo {
} /*namespace xo*/
/* end Normal.cpp */

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# build unittest distribution/utest
set(SELF_EXE utest.distribution)
set(SELF_SRCS
distribution_utest_main.cpp
Normal.test.cpp
Uniform.test.cpp)
xo_add_utest_executable(${SELF_EXE} ${SELF_SRCS})
xo_self_dependency(${SELF_EXE} xo_distribution)
xo_external_target_dependency(${SELF_EXE} Catch2 Catch2::Catch2)
# end CMakeLists.txt

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/* @file Normal.test.cpp */
#include "xo/distribution/Normal.hpp"
#include <catch2/catch.hpp>
namespace xo {
using xo::distribution::Normal;
namespace ut {
TEST_CASE("normal", "[distribution]") {
auto n01 = Normal::unit();
CHECK(n01->cdf(-3.0) == Approx(0.001349898).margin(1e-9));
CHECK(n01->cdf(-2.0) == Approx(0.0227501319).margin(1e-9));
CHECK(n01->cdf(-1.0) == Approx(0.1586552539).margin(1e-9));
CHECK(n01->cdf(0.0) == 0.5);
CHECK(n01->cdf(1.0) == 1.0 - n01->cdf(-1.0));
CHECK(n01->cdf(2.0) == 1.0 - n01->cdf(-2.0));
CHECK(n01->cdf(3.0) == 1.0 - n01->cdf(-3.0));
} /*TEST_CASE(normal)*/
} /*namespace ut*/
} /*namespace xo*/
/* end Normal.test.cpp */

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xo-distribution/utest/Uniform.test.cpp Normal file
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/* @file Uniform.test.cpp */
#include "xo/distribution/Uniform.hpp"
#include <catch2/catch.hpp>
namespace xo {
using xo::distribution::Uniform;
namespace ut {
TEST_CASE("uniform", "[distribution]") {
auto u = Uniform::unit();
CHECK(u->cdf(-3.0) == 0.0);
CHECK(u->cdf(-2.0) == 0.0);
CHECK(u->cdf(-1.0) == 0.0);
CHECK(u->cdf(0.0) == 0.0);
CHECK(u->cdf(0.05) == 0.05);
CHECK(u->cdf(0.5) == 0.5);
CHECK(u->cdf(0.95) == 0.95);
CHECK(u->cdf(1.0) == 1.0);
CHECK(u->cdf(2.0) == 1.0);
CHECK(u->cdf(3.0) == 1.0);
} /*TEST_CASE(uniform)*/
} /*namespace ut*/
} /*namespace xo*/
/* end Uniform.test.cpp */

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xo-distribution/utest/distribution_utest_main.cpp Normal file
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/* file distribution_utest_main.cpp */
#define CATCH_CONFIG_MAIN
#include "catch2/catch.hpp"
/* end distribution_utest_main.cpp */