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Add texturemerge code.
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/*************************************************************************
ALGLIB 3.16.0 (source code generated 2019-12-19)
Copyright (c) Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _statistics_pkg_h
#define _statistics_pkg_h
#include "ap.h"
#include "alglibinternal.h"
#include "linalg.h"
#include "specialfunctions.h"
#include "alglibmisc.h"
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (DATATYPES)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)
#endif
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{
#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Calculation of the distribution moments: mean, variance, skewness, kurtosis.
INPUT PARAMETERS:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
OUTPUT PARAMETERS
Mean - mean.
Variance- variance.
Skewness- skewness (if variance<>0; zero otherwise).
Kurtosis- kurtosis (if variance<>0; zero otherwise).
NOTE: variance is calculated by dividing sum of squares by N-1, not N.
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemoments(const real_1d_array &x, const ae_int_t n, double &mean, double &variance, double &skewness, double &kurtosis, const xparams _xparams = alglib::xdefault);
void samplemoments(const real_1d_array &x, double &mean, double &variance, double &skewness, double &kurtosis, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Calculation of the mean.
INPUT PARAMETERS:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
NOTE:
This function return result which calculated by 'SampleMoments' function
and stored at 'Mean' variable.
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplemean(const real_1d_array &x, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double samplemean(const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Calculation of the variance.
INPUT PARAMETERS:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
NOTE:
This function return result which calculated by 'SampleMoments' function
and stored at 'Variance' variable.
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplevariance(const real_1d_array &x, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double samplevariance(const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Calculation of the skewness.
INPUT PARAMETERS:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
NOTE:
This function return result which calculated by 'SampleMoments' function
and stored at 'Skewness' variable.
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double sampleskewness(const real_1d_array &x, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double sampleskewness(const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Calculation of the kurtosis.
INPUT PARAMETERS:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
NOTE:
This function return result which calculated by 'SampleMoments' function
and stored at 'Kurtosis' variable.
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
double samplekurtosis(const real_1d_array &x, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double samplekurtosis(const real_1d_array &x, const xparams _xparams = alglib::xdefault);
/*************************************************************************
ADev
Input parameters:
X - sample
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
Output parameters:
ADev- ADev
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void sampleadev(const real_1d_array &x, const ae_int_t n, double &adev, const xparams _xparams = alglib::xdefault);
void sampleadev(const real_1d_array &x, double &adev, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Median calculation.
Input parameters:
X - sample (array indexes: [0..N-1])
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
Output parameters:
Median
-- ALGLIB --
Copyright 06.09.2006 by Bochkanov Sergey
*************************************************************************/
void samplemedian(const real_1d_array &x, const ae_int_t n, double &median, const xparams _xparams = alglib::xdefault);
void samplemedian(const real_1d_array &x, double &median, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Percentile calculation.
Input parameters:
X - sample (array indexes: [0..N-1])
N - N>=0, sample size:
* if given, only leading N elements of X are processed
* if not given, automatically determined from size of X
P - percentile (0<=P<=1)
Output parameters:
V - percentile
-- ALGLIB --
Copyright 01.03.2008 by Bochkanov Sergey
*************************************************************************/
void samplepercentile(const real_1d_array &x, const ae_int_t n, const double p, double &v, const xparams _xparams = alglib::xdefault);
void samplepercentile(const real_1d_array &x, const double p, double &v, const xparams _xparams = alglib::xdefault);
/*************************************************************************
2-sample covariance
Input parameters:
X - sample 1 (array indexes: [0..N-1])
Y - sample 2 (array indexes: [0..N-1])
N - N>=0, sample size:
* if given, only N leading elements of X/Y are processed
* if not given, automatically determined from input sizes
Result:
covariance (zero for N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double cov2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double cov2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Pearson product-moment correlation coefficient
Input parameters:
X - sample 1 (array indexes: [0..N-1])
Y - sample 2 (array indexes: [0..N-1])
N - N>=0, sample size:
* if given, only N leading elements of X/Y are processed
* if not given, automatically determined from input sizes
Result:
Pearson product-moment correlation coefficient
(zero for N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
double pearsoncorr2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double pearsoncorr2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Spearman's rank correlation coefficient
Input parameters:
X - sample 1 (array indexes: [0..N-1])
Y - sample 2 (array indexes: [0..N-1])
N - N>=0, sample size:
* if given, only N leading elements of X/Y are processed
* if not given, automatically determined from input sizes
Result:
Spearman's rank correlation coefficient
(zero for N=0 or N=1)
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmancorr2(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams = alglib::xdefault);
double spearmancorr2(const real_1d_array &x, const real_1d_array &y, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Covariance matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X are used
* if not given, automatically determined from input size
M - M>0, number of variables:
* if given, only leading M columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M,M], covariance matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void covm(const real_2d_array &x, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Pearson product-moment correlation matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X are used
* if not given, automatically determined from input size
M - M>0, number of variables:
* if given, only leading M columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M,M], correlation matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void pearsoncorrm(const real_2d_array &x, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Spearman's rank correlation matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X are used
* if not given, automatically determined from input size
M - M>0, number of variables:
* if given, only leading M columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M,M], correlation matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm(const real_2d_array &x, const ae_int_t n, const ae_int_t m, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void spearmancorrm(const real_2d_array &x, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Cross-covariance matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M1], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
Y - array[N,M2], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X/Y are used
* if not given, automatically determined from input sizes
M1 - M1>0, number of variables in X:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
M2 - M2>0, number of variables in Y:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M1,M2], cross-covariance matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void covm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void covm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Pearson product-moment cross-correlation matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M1], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
Y - array[N,M2], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X/Y are used
* if not given, automatically determined from input sizes
M1 - M1>0, number of variables in X:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
M2 - M2>0, number of variables in Y:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void pearsoncorrm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Spearman's rank cross-correlation matrix
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - array[N,M1], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
Y - array[N,M2], sample matrix:
* J-th column corresponds to J-th variable
* I-th row corresponds to I-th observation
N - N>=0, number of observations:
* if given, only leading N rows of X/Y are used
* if not given, automatically determined from input sizes
M1 - M1>0, number of variables in X:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
M2 - M2>0, number of variables in Y:
* if given, only leading M1 columns of X are used
* if not given, automatically determined from input size
OUTPUT PARAMETERS:
C - array[M1,M2], cross-correlation matrix (zero if N=0 or N=1)
-- ALGLIB --
Copyright 28.10.2010 by Bochkanov Sergey
*************************************************************************/
void spearmancorrm2(const real_2d_array &x, const real_2d_array &y, const ae_int_t n, const ae_int_t m1, const ae_int_t m2, real_2d_array &c, const xparams _xparams = alglib::xdefault);
void spearmancorrm2(const real_2d_array &x, const real_2d_array &y, real_2d_array &c, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function replaces data in XY by their ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* ranking starts from 0, ends at NFeatures-1
* sum of within-row values is equal to (NFeatures-1)*NFeatures/2
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
XY - array[NPoints,NFeatures], dataset
NPoints - number of points
NFeatures- number of features
OUTPUT PARAMETERS:
XY - data are replaced by their within-row ranks;
ranking starts from 0, ends at NFeatures-1
-- ALGLIB --
Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdata(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nfeatures, const xparams _xparams = alglib::xdefault);
void rankdata(real_2d_array &xy, const xparams _xparams = alglib::xdefault);
/*************************************************************************
This function replaces data in XY by their CENTERED ranks:
* XY is processed row-by-row
* rows are processed separately
* tied data are correctly handled (tied ranks are calculated)
* centered ranks are just usual ranks, but centered in such way that sum
of within-row values is equal to 0.0.
* centering is performed by subtracting mean from each row, i.e it changes
mean value, but does NOT change higher moments
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
XY - array[NPoints,NFeatures], dataset
NPoints - number of points
NFeatures- number of features
OUTPUT PARAMETERS:
XY - data are replaced by their within-row ranks;
ranking starts from 0, ends at NFeatures-1
-- ALGLIB --
Copyright 18.04.2013 by Bochkanov Sergey
*************************************************************************/
void rankdatacentered(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nfeatures, const xparams _xparams = alglib::xdefault);
void rankdatacentered(real_2d_array &xy, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete function, we recommend to use PearsonCorr2().
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double pearsoncorrelation(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Obsolete function, we recommend to use SpearmanCorr2().
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
double spearmanrankcorrelation(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Wilcoxon signed-rank test
This test checks three hypotheses about the median of the given sample.
The following tests are performed:
* two-tailed test (null hypothesis - the median is equal to the given
value)
* left-tailed test (null hypothesis - the median is greater than or
equal to the given value)
* right-tailed test (null hypothesis - the median is less than or
equal to the given value)
Requirements:
* the scale of measurement should be ordinal, interval or ratio (i.e.
the test could not be applied to nominal variables).
* the distribution should be continuous and symmetric relative to its
median.
* number of distinct values in the X array should be greater than 4
The test is non-parametric and doesn't require distribution X to be normal
Input parameters:
X - sample. Array whose index goes from 0 to N-1.
N - size of the sample.
Median - assumed median value.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
To calculate p-values, special approximation is used. This method lets us
calculate p-values with two decimal places in interval [0.0001, 1].
"Two decimal places" does not sound very impressive, but in practice the
relative error of less than 1% is enough to make a decision.
There is no approximation outside the [0.0001, 1] interval. Therefore, if
the significance level outlies this interval, the test returns 0.0001.
-- ALGLIB --
Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void wilcoxonsignedranktest(const real_1d_array &x, const ae_int_t n, const double e, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Sign test
This test checks three hypotheses about the median of the given sample.
The following tests are performed:
* two-tailed test (null hypothesis - the median is equal to the given
value)
* left-tailed test (null hypothesis - the median is greater than or
equal to the given value)
* right-tailed test (null hypothesis - the median is less than or
equal to the given value)
Requirements:
* the scale of measurement should be ordinal, interval or ratio (i.e.
the test could not be applied to nominal variables).
The test is non-parametric and doesn't require distribution X to be normal
Input parameters:
X - sample. Array whose index goes from 0 to N-1.
N - size of the sample.
Median - assumed median value.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
While calculating p-values high-precision binomial distribution
approximation is used, so significance levels have about 15 exact digits.
-- ALGLIB --
Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplesigntest(const real_1d_array &x, const ae_int_t n, const double median, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Pearson's correlation coefficient significance test
This test checks hypotheses about whether X and Y are samples of two
continuous distributions having zero correlation or whether their
correlation is non-zero.
The following tests are performed:
* two-tailed test (null hypothesis - X and Y have zero correlation)
* left-tailed test (null hypothesis - the correlation coefficient is
greater than or equal to 0)
* right-tailed test (null hypothesis - the correlation coefficient is
less than or equal to 0).
Requirements:
* the number of elements in each sample is not less than 5
* normality of distributions of X and Y.
Input parameters:
R - Pearson's correlation coefficient for X and Y
N - number of elements in samples, N>=5.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void pearsoncorrelationsignificance(const double r, const ae_int_t n, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Spearman's rank correlation coefficient significance test
This test checks hypotheses about whether X and Y are samples of two
continuous distributions having zero correlation or whether their
correlation is non-zero.
The following tests are performed:
* two-tailed test (null hypothesis - X and Y have zero correlation)
* left-tailed test (null hypothesis - the correlation coefficient is
greater than or equal to 0)
* right-tailed test (null hypothesis - the correlation coefficient is
less than or equal to 0).
Requirements:
* the number of elements in each sample is not less than 5.
The test is non-parametric and doesn't require distributions X and Y to be
normal.
Input parameters:
R - Spearman's rank correlation coefficient for X and Y
N - number of elements in samples, N>=5.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void spearmanrankcorrelationsignificance(const double r, const ae_int_t n, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
One-sample t-test
This test checks three hypotheses about the mean of the given sample. The
following tests are performed:
* two-tailed test (null hypothesis - the mean is equal to the given
value)
* left-tailed test (null hypothesis - the mean is greater than or
equal to the given value)
* right-tailed test (null hypothesis - the mean is less than or equal
to the given value).
The test is based on the assumption that a given sample has a normal
distribution and an unknown dispersion. If the distribution sharply
differs from normal, the test will work incorrectly.
INPUT PARAMETERS:
X - sample. Array whose index goes from 0 to N-1.
N - size of sample, N>=0
Mean - assumed value of the mean.
OUTPUT PARAMETERS:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
NOTE: this function correctly handles degenerate cases:
* when N=0, all p-values are set to 1.0
* when variance of X[] is exactly zero, p-values are set
to 1.0 or 0.0, depending on difference between sample mean and
value of mean being tested.
-- ALGLIB --
Copyright 08.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest1(const real_1d_array &x, const ae_int_t n, const double mean, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Two-sample pooled test
This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
* two-tailed test (null hypothesis - the means are equal)
* left-tailed test (null hypothesis - the mean of the first sample is
greater than or equal to the mean of the second sample)
* right-tailed test (null hypothesis - the mean of the first sample is
less than or equal to the mean of the second sample).
Test is based on the following assumptions:
* given samples have normal distributions
* dispersions are equal
* samples are independent.
Input parameters:
X - sample 1. Array whose index goes from 0 to N-1.
N - size of sample.
Y - sample 2. Array whose index goes from 0 to M-1.
M - size of sample.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
NOTE: this function correctly handles degenerate cases:
* when N=0 or M=0, all p-values are set to 1.0
* when both samples has exactly zero variance, p-values are set
to 1.0 or 0.0, depending on difference between means.
-- ALGLIB --
Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void studentttest2(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
/*************************************************************************
Two-sample unpooled test
This test checks three hypotheses about the mean of the given samples. The
following tests are performed:
* two-tailed test (null hypothesis - the means are equal)
* left-tailed test (null hypothesis - the mean of the first sample is
greater than or equal to the mean of the second sample)
* right-tailed test (null hypothesis - the mean of the first sample is
less than or equal to the mean of the second sample).
Test is based on the following assumptions:
* given samples have normal distributions
* samples are independent.
Equality of variances is NOT required.
Input parameters:
X - sample 1. Array whose index goes from 0 to N-1.
N - size of the sample.
Y - sample 2. Array whose index goes from 0 to M-1.
M - size of the sample.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
NOTE: this function correctly handles degenerate cases:
* when N=0 or M=0, all p-values are set to 1.0
* when both samples has zero variance, p-values are set
to 1.0 or 0.0, depending on difference between means.
* when only one sample has zero variance, test reduces to 1-sample
version.
-- ALGLIB --
Copyright 18.09.2006 by Bochkanov Sergey
*************************************************************************/
void unequalvariancettest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Mann-Whitney U-test
This test checks hypotheses about whether X and Y are samples of two
continuous distributions of the same shape and same median or whether
their medians are different.
The following tests are performed:
* two-tailed test (null hypothesis - the medians are equal)
* left-tailed test (null hypothesis - the median of the first sample
is greater than or equal to the median of the second sample)
* right-tailed test (null hypothesis - the median of the first sample
is less than or equal to the median of the second sample).
Requirements:
* the samples are independent
* X and Y are continuous distributions (or discrete distributions well-
approximating continuous distributions)
* distributions of X and Y have the same shape. The only possible
difference is their position (i.e. the value of the median)
* the number of elements in each sample is not less than 5
* the scale of measurement should be ordinal, interval or ratio (i.e.
the test could not be applied to nominal variables).
The test is non-parametric and doesn't require distributions to be normal.
Input parameters:
X - sample 1. Array whose index goes from 0 to N-1.
N - size of the sample. N>=5
Y - sample 2. Array whose index goes from 0 to M-1.
M - size of the sample. M>=5
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
To calculate p-values, special approximation is used. This method lets us
calculate p-values with satisfactory accuracy in interval [0.0001, 1].
There is no approximation outside the [0.0001, 1] interval. Therefore, if
the significance level outlies this interval, the test returns 0.0001.
Relative precision of approximation of p-value:
N M Max.err. Rms.err.
5..10 N..10 1.4e-02 6.0e-04
5..10 N..100 2.2e-02 5.3e-06
10..15 N..15 1.0e-02 3.2e-04
10..15 N..100 1.0e-02 2.2e-05
15..100 N..100 6.1e-03 2.7e-06
For N,M>100 accuracy checks weren't put into practice, but taking into
account characteristics of asymptotic approximation used, precision should
not be sharply different from the values for interval [5, 100].
NOTE: P-value approximation was optimized for 0.0001<=p<=0.2500. Thus,
P's outside of this interval are enforced to these bounds. Say, you
may quite often get P equal to exactly 0.25 or 0.0001.
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void mannwhitneyutest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Jarque-Bera test
This test checks hypotheses about the fact that a given sample X is a
sample of normal random variable.
Requirements:
* the number of elements in the sample is not less than 5.
Input parameters:
X - sample. Array whose index goes from 0 to N-1.
N - size of the sample. N>=5
Output parameters:
P - p-value for the test
Accuracy of the approximation used (5<=N<=1951):
p-value relative error (5<=N<=1951)
[1, 0.1] < 1%
[0.1, 0.01] < 2%
[0.01, 0.001] < 6%
[0.001, 0] wasn't measured
For N>1951 accuracy wasn't measured but it shouldn't be sharply different
from table values.
-- ALGLIB --
Copyright 09.04.2007 by Bochkanov Sergey
*************************************************************************/
void jarqueberatest(const real_1d_array &x, const ae_int_t n, double &p, const xparams _xparams = alglib::xdefault);
#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Two-sample F-test
This test checks three hypotheses about dispersions of the given samples.
The following tests are performed:
* two-tailed test (null hypothesis - the dispersions are equal)
* left-tailed test (null hypothesis - the dispersion of the first
sample is greater than or equal to the dispersion of the second
sample).
* right-tailed test (null hypothesis - the dispersion of the first
sample is less than or equal to the dispersion of the second sample)
The test is based on the following assumptions:
* the given samples have normal distributions
* the samples are independent.
Input parameters:
X - sample 1. Array whose index goes from 0 to N-1.
N - sample size.
Y - sample 2. Array whose index goes from 0 to M-1.
M - sample size.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
-- ALGLIB --
Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void ftest(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
/*************************************************************************
One-sample chi-square test
This test checks three hypotheses about the dispersion of the given sample
The following tests are performed:
* two-tailed test (null hypothesis - the dispersion equals the given
number)
* left-tailed test (null hypothesis - the dispersion is greater than
or equal to the given number)
* right-tailed test (null hypothesis - dispersion is less than or
equal to the given number).
Test is based on the following assumptions:
* the given sample has a normal distribution.
Input parameters:
X - sample 1. Array whose index goes from 0 to N-1.
N - size of the sample.
Variance - dispersion value to compare with.
Output parameters:
BothTails - p-value for two-tailed test.
If BothTails is less than the given significance level
the null hypothesis is rejected.
LeftTail - p-value for left-tailed test.
If LeftTail is less than the given significance level,
the null hypothesis is rejected.
RightTail - p-value for right-tailed test.
If RightTail is less than the given significance level
the null hypothesis is rejected.
-- ALGLIB --
Copyright 19.09.2006 by Bochkanov Sergey
*************************************************************************/
void onesamplevariancetest(const real_1d_array &x, const ae_int_t n, const double variance, double &bothtails, double &lefttail, double &righttail, const xparams _xparams = alglib::xdefault);
#endif
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS)
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_BASESTAT) || !defined(AE_PARTIAL_BUILD)
void samplemoments(/* Real */ ae_vector* x,
ae_int_t n,
double* mean,
double* variance,
double* skewness,
double* kurtosis,
ae_state *_state);
double samplemean(/* Real */ ae_vector* x,
ae_int_t n,
ae_state *_state);
double samplevariance(/* Real */ ae_vector* x,
ae_int_t n,
ae_state *_state);
double sampleskewness(/* Real */ ae_vector* x,
ae_int_t n,
ae_state *_state);
double samplekurtosis(/* Real */ ae_vector* x,
ae_int_t n,
ae_state *_state);
void sampleadev(/* Real */ ae_vector* x,
ae_int_t n,
double* adev,
ae_state *_state);
void samplemedian(/* Real */ ae_vector* x,
ae_int_t n,
double* median,
ae_state *_state);
void samplepercentile(/* Real */ ae_vector* x,
ae_int_t n,
double p,
double* v,
ae_state *_state);
double cov2(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
double pearsoncorr2(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
double spearmancorr2(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
void covm(/* Real */ ae_matrix* x,
ae_int_t n,
ae_int_t m,
/* Real */ ae_matrix* c,
ae_state *_state);
void pearsoncorrm(/* Real */ ae_matrix* x,
ae_int_t n,
ae_int_t m,
/* Real */ ae_matrix* c,
ae_state *_state);
void spearmancorrm(/* Real */ ae_matrix* x,
ae_int_t n,
ae_int_t m,
/* Real */ ae_matrix* c,
ae_state *_state);
void covm2(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t m1,
ae_int_t m2,
/* Real */ ae_matrix* c,
ae_state *_state);
void pearsoncorrm2(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t m1,
ae_int_t m2,
/* Real */ ae_matrix* c,
ae_state *_state);
void spearmancorrm2(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t m1,
ae_int_t m2,
/* Real */ ae_matrix* c,
ae_state *_state);
void rankdata(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nfeatures,
ae_state *_state);
ae_bool _trypexec_rankdata(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nfeatures, ae_state *_state);
void rankdatacentered(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nfeatures,
ae_state *_state);
ae_bool _trypexec_rankdatacentered(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nfeatures, ae_state *_state);
double pearsoncorrelation(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
double spearmanrankcorrelation(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
#endif
#if defined(AE_COMPILE_WSR) || !defined(AE_PARTIAL_BUILD)
void wilcoxonsignedranktest(/* Real */ ae_vector* x,
ae_int_t n,
double e,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
#if defined(AE_COMPILE_STEST) || !defined(AE_PARTIAL_BUILD)
void onesamplesigntest(/* Real */ ae_vector* x,
ae_int_t n,
double median,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
#if defined(AE_COMPILE_CORRELATIONTESTS) || !defined(AE_PARTIAL_BUILD)
void pearsoncorrelationsignificance(double r,
ae_int_t n,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
void spearmanrankcorrelationsignificance(double r,
ae_int_t n,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
#if defined(AE_COMPILE_STUDENTTTESTS) || !defined(AE_PARTIAL_BUILD)
void studentttest1(/* Real */ ae_vector* x,
ae_int_t n,
double mean,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
void studentttest2(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
void unequalvariancettest(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
#if defined(AE_COMPILE_MANNWHITNEYU) || !defined(AE_PARTIAL_BUILD)
void mannwhitneyutest(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
#if defined(AE_COMPILE_JARQUEBERA) || !defined(AE_PARTIAL_BUILD)
void jarqueberatest(/* Real */ ae_vector* x,
ae_int_t n,
double* p,
ae_state *_state);
#endif
#if defined(AE_COMPILE_VARIANCETESTS) || !defined(AE_PARTIAL_BUILD)
void ftest(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
void onesamplevariancetest(/* Real */ ae_vector* x,
ae_int_t n,
double variance,
double* bothtails,
double* lefttail,
double* righttail,
ae_state *_state);
#endif
}
#endif