# %% # Evaluate the hessian of the function at a particular point hessianMatrix = f.hessian(x) hessianMatrix # %% # Change the gradient method to a non centered finite difference method step = [1e-7] * f.getInputDimension() gradient = ot.NonCenteredFiniteDifferenceGradient(step, f.getEvaluation()) f.setGradient(gradient) gradient # %% # Change the hessian method to a centered finite difference method step = [1e-7] * f.getInputDimension() hessian = ot.CenteredFiniteDifferenceHessian(step, f.getEvaluation()) f.setHessian(hessian) hessian # %% # Get the number of times the function has been evaluated f.getEvaluationCallsNumber() # %% # Get the number of times the gradient has been evaluated f.getGradientCallsNumber() # %% # Get the number of times the hessian has been evaluated f.getHessianCallsNumber()
x1, x2, x3, x4 = X
return [np.cos(x2 * x2 + x4) / (x1 * x1 + 1. + x3**4)]
myFunc = ot.PythonFunction(4, 1, myPythonFunction)
# %%
# For instance, a user-defined constant step value can be considered
gradEpsilon = [1e-8] * 4
hessianEpsilon = [1e-7] * 4
gradStep = ot.ConstantStep(gradEpsilon) # Costant gradient step
hessianStep = ot.ConstantStep(hessianEpsilon) # Constant Hessian step
myFunc.setGradient(
ot.CenteredFiniteDifferenceGradient(gradStep, myFunc.getEvaluation()))
myFunc.setHessian(
ot.CenteredFiniteDifferenceHessian(hessianStep, myFunc.getEvaluation()))
# %%
# Alternatively, we can consider a finite difference step value which
# depends on the location in the input space by relying on the BlendedStep class:
gradEpsilon = [1e-8] * 4
hessianEpsilon = [1e-7] * 4
gradStep = ot.BlendedStep(gradEpsilon) # Costant gradient step
hessianStep = ot.BlendedStep(hessianEpsilon) # Constant Hessian step
myFunc.setGradient(
ot.CenteredFiniteDifferenceGradient(gradStep, myFunc.getEvaluation()))
myFunc.setHessian(
ot.CenteredFiniteDifferenceHessian(hessianStep, myFunc.getEvaluation()))
# %%
# We can then proceed in the same way as before
print('df(', x[0], ')=%.4e' % df, 'df (FD)=%.4e' % df2)
if abs(df) > 1e-5:
err_g = abs(df2 / df - 1.)
else:
err_g = abs(df - df2)
if err_g > 1e-5:
print('GRADIENT ERROR! check ' + func +
' gradient, err=%.12g' % err_g)
try:
d2f = f.hessian(x)[0, 0, 0]
except:
pass
else:
f.setHessian(
ot.CenteredFiniteDifferenceHessian(
ot.ResourceMap.GetAsScalar(
'CenteredFiniteDifferenceHessian-DefaultEpsilon'),
f.getEvaluation()))
d2f2 = f.hessian(x)[0, 0, 0]
print('d2f(', x[0], ')=%.4e' % d2f, 'd2f (FD)=%.4e' % d2f2)
if abs(d2f) > 1e-5:
err_h = abs(d2f2 / d2f - 1.)
else:
err_h = abs(d2f - d2f2)
if err_h > 1e-4:
print('HESSIAN ERROR! check ' + func +
' hessian, err=%.12g' % err_h)
nmf = ot.SymbolicFunction(['x0', 'x1'], ['x0+x1', 'x0-x1'])
marginal0 = nmf.getMarginal(0)
marginal1 = nmf.getMarginal(1)
print('marginal 0=', marginal0)
#! /usr/bin/env python
from __future__ import print_function
import openturns as ot
eps = 1e-2
# Instance creation
myFunc = ot.NumericalMathFunction(['x1', 'x2'], ['f1', 'f2', 'f3'], [
'x1*sin(x2)', 'cos(x1+x2)', '(x2+1)*exp(x1-2*x2)'])
epsilon = ot.NumericalPoint(myFunc.getInputDimension(), eps)
inPoint = ot.NumericalPoint(epsilon.getDimension(), 1.0)
myHessian = ot.CenteredFiniteDifferenceHessian(
epsilon, myFunc.getEvaluation())
print("myHessian=", repr(myHessian))
print("myFunc.hessian(", repr(inPoint), ")=",
repr(myFunc.hessian(inPoint)))
print("myHessian.hessian(", repr(inPoint), ")=",
repr(myHessian.hessian(inPoint)))
# Substitute the hessian
myFunc.setHessian(ot.CenteredFiniteDifferenceHessian(myHessian))
print("myFunc.hessian(", repr(inPoint), ")=", repr(
myFunc.hessian(inPoint)), " (after substitution)")