#! /usr/bin/env python

import openturns as ot

ot.TESTPREAMBLE()
ot.RandomGenerator.SetSeed(0)

size = 100
dim = 10
R = ot.CorrelationMatrix(dim)
for i in range(dim):
    for j in range(i):
        R[i, j] = (i + j + 1.0) / (2.0 * dim)

mean = [2.0] * dim
sigma = [3.0] * dim
distribution = ot.Normal(mean, sigma, R)

sample = distribution.getSample(size)
sampleX = sample.getMarginal(range(1, dim))
sampleY = sample.getMarginal(0)

sampleZ = ot.Sample(size, 1)
for i in range(size):
    sampleZ[i, 0] = sampleY[i, 0] ** 2
print(
    "LinearModelFisher pvalue=%1.2g"
    % ot.LinearModelTest.LinearModelFisher(sampleY, sampleZ).getPValue()
)
print(
    "LinearModelResidualMean pvalue=%1.2g"
    % ot.LinearModelTest.LinearModelResidualMean(sampleY, sampleZ).getPValue()
)

# Durbin Watson
ot.RandomGenerator.SetSeed(5415)
eps = ot.Normal(0, 20)
f = ot.SymbolicFunction("x", "5+2*x+x^2-0.1*x^3")
N = 15
x = ot.Sample(
    [
        [0],
        [1.42857],
        [2.85714],
        [4.28571],
        [5.71429],
        [7.14286],
        [8.57143],
        [10],
        [11.4286],
        [12.8571],
        [14.2857],
        [15.7143],
        [17.1429],
        [18.5714],
        [20],
    ]
)
y = f(x) + eps.getSample(N)
linmodel = ot.LinearModelAlgorithm(x, y).getResult().getCoefficients()
dwTest = ot.LinearModelTest.LinearModelDurbinWatson(x, y)
print("Durbin Watson = ", dwTest)


selection = ot.Indices(5)
selection.fill()

selection2 = ot.Indices(1, 0)
sampleX0 = sampleX.getMarginal(0)

# 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 t-test is used.

# The two tests must be equal
print(
    "PartialRegressionX0Y=",
    ot.LinearModelTest.PartialRegression(sampleX, sampleY, selection2, 0.10),
)
print("FullRegressionX0Y=", ot.LinearModelTest.FullRegression(sampleX0, sampleY, 0.10))

print(
    "PartialRegressionXY=",
    ot.LinearModelTest.PartialRegression(sampleX, sampleY, selection, 0.10),
)

# 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 t-test is used.

print("FullRegressionXZ=", ot.LinearModelTest.FullRegression(sampleX, sampleY, 0.10))
# print('FullRegressionZZ=', ot.LinearModelTest.FullRegression(
# sampleZ, sampleZ, 0.10))