#! /usr/bin/env python

from __future__ import print_function
from openturns import *


dim = 10
R = CorrelationMatrix(dim)
for i in range(dim):
    for j in range(i):
        R[i, j] = (i + j + 1.0) / (2.0 * dim)
mean = NumericalPoint(dim, 2.0)
sigma = NumericalPoint(dim, 3.0)
distribution = Normal(mean, sigma, R)

size = 100
sample = distribution.getSample(size)
sampleX = NumericalSample(size, dim - 1)
sampleY = NumericalSample(size, 1)
for i in range(size):
    sampleY[i, 0] = sample[i, 0]
    for j in range(1, dim):
        sampleX[i, j - 1] = sample[i, j]

sampleZ = NumericalSample(size, 1)
for i in range(size):
    sampleZ[i, 0] = sampleY[i, 0] * sampleY[i, 0]

selection = Indices(5)
selection.fill()
print('selection = ', selection)

# PartialPearson : Independence Pearson test between 2 samples : firstSample of dimension n and secondSample of dimension 1. If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample), PartialPearson performs the Independence Pearson test simultaneously on firstSample[i] and secondSample, for i in the selection. For all i, it is supposed that the couple (firstSample[i] and secondSample) is issued from a gaussian  vector.
# Probability of the H0 reject zone : 1-0.90

print('PartialPearsonXY=', HypothesisTest.PartialPearson(
    sampleX, sampleY, selection, 0.90))

selection2 = Indices(1, 0)
sampleX0 = NumericalSample(size, 1)
for i in range(size):
    sampleX0[i, 0] = sampleX[i, 0]

# The three tests must be equal
print('PartialPearsonX0Y=', HypothesisTest.PartialPearson(
    sampleX, sampleY, selection2, 0.90))
print('PearsonX0Y=', HypothesisTest.Pearson(sampleX0, sampleY, 0.90))
print('FullPearsonX0Y=', HypothesisTest.FullPearson(
    sampleX0, sampleY, 0.90))

# FullPearson : Independence Pearson test between 2 samples : firstSample of dimension n and secondSample of dimension 1. If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample), FullPearson performs the Independence Pearson test simultaneously on firstSample[i] and secondSample. For all i, it is supposed that the couple (firstSample[i] and secondSample) is issued from a gaussian  vector.
# Probability of the H0 reject zone : 1-0.90
print('FullPearsonXY=', HypothesisTest.FullPearson(
    sampleX, sampleY, 0.90))
print('FullPearsonYY=', HypothesisTest.FullPearson(
    sampleY, sampleY, 0.90))

# PartialSpearman test between 2 samples : firstSample of dimension n and secondSample of dimension 1. If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample), PartialSpearman performs the Independence Spearman test simultaneously on firstSample[i] and secondSample, for i in the selection.
# Probability of the H0 reject zone : 1-0.90

# The three tests must be equal
print('PartialSpearmanX0Y=', HypothesisTest.PartialSpearman(
    sampleX, sampleY, selection2, 0.90))
print('SpearmanX0Y=', HypothesisTest.Spearman(sampleX0, sampleY, 0.90))
print('FullSpearmanX0Y=', HypothesisTest.FullSpearman(
    sampleX0, sampleY, 0.90))

print('PartialSpearmanXY=', HypothesisTest.PartialSpearman(
    sampleX, sampleY, selection, 0.90))

# FullSpearman : Spearman test between 2 samples : firstSample of dimension n and secondSample of dimension 1. If firstSample[i] is the numerical sample extracted from firstSample (ith coordinate of each point of the numerical sample), FullSpearman performs the Independence Spearman test simultaneously on all firstSample[i] and secondSample.
# Probability of the H0 reject zone : 1-0.90

print('FullSpearmanYZ=', HypothesisTest.FullSpearman(
    sampleY, sampleZ, 0.90))
print('FullSpearmanYY=', HypothesisTest.FullSpearman(
    sampleY, sampleY, 0.90))

# Regression test between 2 samples : firstSample of dimension n and
# secondSample of dimension 1. If firstSample[i] is the numerical sample
# extracted from firstSample (ith coordinate of each point of the
# numerical sample), PartialRegression performs the Regression test
# simultaneously on all firstSample[i] and secondSample, for i in the
# selection. The Regression test tests ifthe regression model between two
# scalar numerical samples is significant. It is based on the deviation
# analysis of the regression. The Fisher distribution is used.

# The two tests must be equal
print('PartialRegressionX0Y=', HypothesisTest.PartialRegression(
    sampleX, sampleY, selection2, 0.90))
print('FullRegressionX0Y=', HypothesisTest.FullRegression(
    sampleX0, sampleY, 0.90))

print('PartialRegressionXY=', HypothesisTest.PartialRegression(
    sampleX, sampleY, selection, 0.90))

# Regression test between 2 samples : firstSample of dimension n and
# secondSample of dimension 1. If firstSample[i] is the numerical sample
# extracted from firstSample (ith coordinate of each point of the
# numerical sample), FullRegression performs the Regression test
# simultaneously on all firstSample[i] and secondSample. The Regression
# test tests if the regression model between two scalar numerical samples
# is significant. It is based on the deviation analysis of the regression.
# The Fisher distribution is used.

print('FullRegressionXZ=', HypothesisTest.FullRegression(
    sampleX, sampleY, 0.90))
print('FullRegressionZZ=', HypothesisTest.FullRegression(
    sampleZ, sampleZ, 0.90))
