def test_trend(self):
N = 100
M = 1000
P = 10
mean = ot.SymbolicFunction("x", "sign(x)")
cov = ot.SquaredExponential([1.0], [0.1])
mesh = ot.IntervalMesher([N]).build(ot.Interval(-2.0, 2.0))
process = ot.GaussianProcess(ot.TrendTransform(mean, mesh), cov, mesh)
sample = process.getSample(M)
algo = ot.KarhunenLoeveSVDAlgorithm(sample, 1e-6)
algo.run()
result = algo.getResult()
trend = ot.TrendTransform(
ot.P1LagrangeEvaluation(sample.computeMean()), mesh)
sample2 = process.getSample(P)
sample2.setName('reduction of sign(x) w/o trend')
reduced1 = ot.KarhunenLoeveReduction(result)(sample2)
reduced2 = ot.KarhunenLoeveReduction(result, trend)(sample2)
g = sample2.drawMarginal(0)
g.setColors(["red"])
g1 = reduced1.drawMarginal(0)
g1.setColors(["blue"])
drs = g1.getDrawables()
for i, d in enumerate(drs):
d.setLineStyle("dashed")
drs[i] = d
g1.setDrawables(drs)
g.add(g1)
g2 = reduced2.drawMarginal(0)
g2.setColors(["green"])
drs = g2.getDrawables()
for i, d in enumerate(drs):
d.setLineStyle("dotted")
drs[i] = d
g2.setDrawables(drs)
g.add(g2)
if 0:
from openturns.viewer import View
View(g).save('reduction.png')
#! /usr/bin/env python
import openturns as ot
import openturns.testing as ott
mesh = ot.RegularGrid(0.0, 1.0, 4)
values = ot.Sample([[0.5], [1.5], [1.0], [-0.5]])
field = ot.Field(mesh, values)
evaluation = ot.P1LagrangeEvaluation(field)
x = [2.3]
y = evaluation(x)
print(y)
ott.assert_almost_equal(y, [0.55])
# Learning sample on meshD
mesher = ot.IntervalMesher([7, 7])
lowerbound = [-1.0, -1.0]
upperBound = [1, 1]
interval = ot.Interval(lowerbound, upperBound)
meshD = mesher.build(interval)
sample = ot.ProcessSample(meshD, 10, 1)
field = ot.Field(meshD, 1)
for k in range(sample.getSize()):
field.setValues(ot.Normal().getSample(64))
sample[k] = field
lagrange = ot.P1LagrangeEvaluation(sample)
# New mesh
mesh = ot.Mesh(
ot.MonteCarloExperiment(ot.ComposedDistribution([ot.Uniform(-1, 1)] * 2),
200).generate())
import openturns as ot
from openturns.viewer import View
N = 100
M = 1000
P = 10
mean = ot.SymbolicFunction("x", "sign(x)")
cov = ot.SquaredExponential([1.0], [0.1])
mesh = ot.IntervalMesher([N]).build(ot.Interval(-2.0, 2.0))
process = ot.GaussianProcess(ot.TrendTransform(mean, mesh), cov, mesh)
sample = process.getSample(M)
algo = ot.KarhunenLoeveSVDAlgorithm(sample, 1e-6)
algo.run()
result = algo.getResult()
trend = ot.TrendTransform(ot.P1LagrangeEvaluation(sample.computeMean()), mesh)
sample2 = process.getSample(P)
sample2.setName('reduction of sign(x) w/o trend')
reduced1 = ot.KarhunenLoeveReduction(result)(sample2)
reduced2 = ot.KarhunenLoeveReduction(result, trend)(sample2)
g = sample2.drawMarginal(0)
g.setColors(["red"])
g1 = reduced1.drawMarginal(0)
g1.setColors(["blue"])
drs = g1.getDrawables()
for i, d in enumerate(drs):
d.setLineStyle("dashed")
drs[i] = d
g1.setDrawables(drs)
g.add(g1)
g2 = reduced2.drawMarginal(0)
g2.setColors(["green"])
dY1 = 0.5 * Y1 * (Y0 - 1.0)
return [dY0, dY1]
phi_func = ot.PythonFunction(2, 2, flow)
# Create the mesh
discretization = [N] * 2
mesh = ot.IntervalMesher(discretization).build(interval)
# Covariance model
covariance = ot.TensorizedCovarianceModel(
[ot.SquaredExponential([0.2] * 2, [0.3])] * 2)
process = ot.GaussianProcess(ot.TrendTransform(phi_func), covariance, mesh)
field = process.getRealization()
f = ot.Function(ot.P1LagrangeEvaluation(field))
ot.ResourceMap.SetAsUnsignedInteger("Field-LevelNumber", 64)
ot.ResourceMap.SetAsScalar("Field-ArrowRatio", 0.01)
ot.ResourceMap.SetAsScalar("Field-ArrowScaling", 0.03)
graph = field.draw()
print("f=", f.getInputDimension(), "->", f.getOutputDimension())
phi = ot.ValueFunction(f)
solver = ot.RungeKutta(phi)
initialState = [0.5, 1.0]
timeGrid = ot.RegularGrid(0.0, 0.1, 10000)
result = solver.solve(initialState, timeGrid)
print(result)
curve = ot.Curve(result)
curve.setColor("red")
curve.setLineWidth(2)
graph.add(curve)
import openturns as ot
from math import exp
from matplotlib import pyplot as plt
from openturns.viewer import View
mesh = ot.RegularGrid(0.0, 1.0, 4)
values = [[0.5], [1.5], [1.0], [-0.5]]
field = ot.Field(mesh, values)
func = ot.P1LagrangeEvaluation(field)
func.setDescription(['$x$', '$y$'])
graph = func.draw(-1.0, 4.0, 1024)
cloud = ot.Cloud(mesh.getVertices(), values)
cloud.setPointStyle("square")
graph.add(cloud)
graph.setColors(["blue", "red"])
fig = plt.figure(figsize=(10, 4))
plt.suptitle('P1 Lagrange interpolation')
func_axis = fig.add_subplot(111)
view = View(graph, figure=fig, axes=[func_axis], add_legend=False)