# %% ot.RandomGenerator.SetSeed(0) distribution = ot.Normal(2) distribution.setDescription(["x", "y"]) func = ot.SymbolicFunction(['x', 'y'], ['2 * x - y + 3 + 0.05 * sin(0.8*x)']) input_sample = distribution.getSample(30) epsilon = ot.Normal(0, 0.1).getSample(30) output_sample = func(input_sample) + epsilon # %% # Let us run the linear model algorithm using the `LinearModelAlgorithm` class & get its associated result : # %% algo = ot.LinearModelAlgorithm(input_sample, output_sample) result = ot.LinearModelResult(algo.getResult()) # %% # # %% # We get the result structure. As the underlying model is of type regression, it assumes a noise distribution associated to the residuals. Let us get it: # %% print(result.getNoiseDistribution()) # %% # We can get also residuals: # %% print(result.getSampleResiduals())
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())
print("trend coefficients = ", result.getCoefficients())
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 expermient ==> 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]
# ---------------------
#
# We consider a linear model with the purpose of predicting the aerial biomass as a function of the soil physicochemical properties,
# and we wish to identify the predictive variables which result in the most simple and precise linear regression model.
#
# We start by creating a linear model which takes into account all of the physicochemical variables present within the Linthrust data set.
#
# Let us consider the following linear model :math:`\tilde{Y} = a_0 + \sum_{i = 1}^{d} a_i X_i + \epsilon`. If all of the predictive variables
# are considered, the regression can be performed with the help of the `LinearModelAlgorithm` class.
# %%
input_sample = sample[:, 1:dimension + 1]
output_sample = sample[:, 0]
algo_full = ot.LinearModelAlgorithm(input_sample, output_sample)
algo_full.run()
result_full = ot.LinearModelResult(algo_full.getResult())
print('R-squared = ', result_full.getRSquared())
print('Adjusted R-squared = ', result_full.getAdjustedRSquared())
# %%
# Forward stepwise regression
# ---------------------------
#
# We now wish to perform the selection of the most important predictive variables through a stepwise algorithm.
#
# It is first necessary to define a suitable function basis for the regression. Each variable is associated to a univariate basis
# and an additional basis is used in order to represent the constant term :math:`a_0`.
# %%
functions = []
functions.append(ot.SymbolicFunction(input_description, ['1.0']))