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#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
from math import sin
ot.TESTPREAMBLE()
# lm build
print("Fit y ~ 3 - 2 x + 0.05 * sin(x) model using 20 points (sin(x) ~ noise)")
size = 20
oneSample = ot.Sample(size, 1)
twoSample = ot.Sample(size, 1)
for i in range(size):
oneSample[i, 0] = 7.0 * sin(-3.5 + (6.5 * i) / (size - 1.0)) + 2.0
twoSample[i, 0] = -2.0 * oneSample[i, 0] + 3.0 + 0.05 * sin(oneSample[i, 0])
test = ot.LinearModelAlgorithm(oneSample, twoSample)
result = ot.LinearModelResult(test.getResult())
analysis = ot.LinearModelAnalysis(result)
print(analysis)
# Compute confidence level (95%) for coefficients estimate
alpha = 0.95
# interval confidence bounds
interval = analysis.getCoefficientsConfidenceInterval(alpha)
print("confidence intervals with level=%1.2f : %s" % (alpha, interval))
print("")
print("")
print("")
print("Fit y ~ 1 + 0.1 x + 10 x^2 model using 100 points")
ot.RandomGenerator.SetSeed(0)
size = 100
# Define a linespace from 0 to 10 with size points
# We use a Box experiment ==> remove 0 & 1 points
experiment = ot.Box([size - 2])
X = experiment.generate()
# X is defined in [0,1]
X *= [10]
# Stack X2
X2 = ot.Sample(X)
for i in range(size):
X2[i, 0] = X[i, 0] * X2[i, 0]
X.stack(X2)
# Define y
Y = ot.Sample(size, 1)
for i in range(size):
Y[i, 0] = (
1.0 + 0.1 * X[i, 0] + 10.0 * X[i, 0] * X[i, 0] + 0.1 * ot.DistFunc.rNormal()
)
test = ot.LinearModelAlgorithm(X, Y)
result = test.getResult()
analysis = ot.LinearModelAnalysis(result)
print(analysis)
# Compute confidence level (95%) for coefficients estimate
alpha = 0.95
# interval confidence bounds
interval = analysis.getCoefficientsConfidenceInterval(alpha)
print("confidence intervals with level=%1.2f : %s" % (alpha, interval))
# https://github.com/openturns/openturns/issues/1729
ot.RandomGenerator.SetSeed(1789)
sample_size = 14605 # 14604 : OK, 14605 : Fail
a0 = 0.6
a1 = 2.0
x = ot.Normal(0.5, 0.2).getSample(sample_size)
epsilon = ot.Exponential(0.1).getSample(sample_size)
y = ot.Sample([[a0]] * sample_size) + a1 * x + epsilon
algo = ot.LinearModelAlgorithm(x, y)
result = algo.getResult()
analysis = ot.LinearModelAnalysis(result)
results = str(analysis)
# Fix #1820
ot.RandomGenerator.SetSeed(0)
distribution = ot.Normal()
sample = distribution.getSample(30)
func = ot.SymbolicFunction("x", "2 * x + 1")
firstSample = sample
secondSample = func(sample) + ot.Normal().getSample(30)
linear_model = ot.LinearModelAlgorithm(firstSample, secondSample)
linear_result = linear_model.getResult()
test_result = ot.LinearModelTest.LinearModelFisher(
firstSample, secondSample, linear_result
)
linear_model_analysis = ot.LinearModelAnalysis(linear_result)
ott.assert_almost_equal(
test_result.getStatistic(), linear_model_analysis.getFisherScore(), 1e-13, 0
)
ott.assert_almost_equal(
test_result.getPValue(), linear_model_analysis.getFisherPValue(), 0, 0
)
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