580 lines
21 KiB
Python
580 lines
21 KiB
Python
from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy.testing import (TestCase, assert_array_almost_equal,
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assert_array_equal, assert_)
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from scipy.sparse import csr_matrix
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from scipy.sparse.linalg import LinearOperator
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from scipy.optimize._differentiable_functions import (ScalarFunction,
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VectorFunction,
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LinearVectorFunction,
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IdentityVectorFunction)
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class ExScalarFunction:
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def __init__(self):
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self.nfev = 0
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self.ngev = 0
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self.nhev = 0
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def fun(self, x):
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self.nfev += 1
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return 2*(x[0]**2 + x[1]**2 - 1) - x[0]
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def grad(self, x):
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self.ngev += 1
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return np.array([4*x[0]-1, 4*x[1]])
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def hess(self, x):
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self.nhev += 1
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return 4*np.eye(2)
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class TestScalarFunction(TestCase):
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def test_finite_difference_grad(self):
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ex = ExScalarFunction()
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nfev = 0
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ngev = 0
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x0 = [1.0, 0.0]
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analit = ScalarFunction(ex.fun, x0, (), ex.grad,
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ex.hess, None, (-np.inf, np.inf))
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nfev += 1
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ngev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev, nfev)
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approx = ScalarFunction(ex.fun, x0, (), '2-point',
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ex.hess, None, (-np.inf, np.inf))
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(analit.f, approx.f)
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assert_array_almost_equal(analit.g, approx.g)
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x = [10, 0.3]
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f_analit = analit.fun(x)
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g_analit = analit.grad(x)
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nfev += 1
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ngev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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f_approx = approx.fun(x)
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g_approx = approx.grad(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(g_analit, g_approx)
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x = [2.0, 1.0]
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g_analit = analit.grad(x)
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ngev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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g_approx = approx.grad(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_almost_equal(g_analit, g_approx)
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x = [2.5, 0.3]
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f_analit = analit.fun(x)
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g_analit = analit.grad(x)
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nfev += 1
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ngev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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f_approx = approx.fun(x)
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g_approx = approx.grad(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(g_analit, g_approx)
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x = [2, 0.3]
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f_analit = analit.fun(x)
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g_analit = analit.grad(x)
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nfev += 1
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ngev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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f_approx = approx.fun(x)
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g_approx = approx.grad(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(g_analit, g_approx)
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def test_finite_difference_hess_linear_operator(self):
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ex = ExScalarFunction()
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nfev = 0
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ngev = 0
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nhev = 0
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x0 = [1.0, 0.0]
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analit = ScalarFunction(ex.fun, x0, (), ex.grad,
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ex.hess, None, (-np.inf, np.inf))
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nfev += 1
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ngev += 1
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev, nhev)
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approx = ScalarFunction(ex.fun, x0, (), ex.grad,
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'2-point', None, (-np.inf, np.inf))
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assert_(isinstance(approx.H, LinearOperator))
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for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
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assert_array_equal(analit.f, approx.f)
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assert_array_almost_equal(analit.g, approx.g)
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assert_array_almost_equal(analit.H.dot(v), approx.H.dot(v))
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nfev += 1
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ngev += 4
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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x = [2.0, 1.0]
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H_analit = analit.hess(x)
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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H_approx = approx.hess(x)
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assert_(isinstance(H_approx, LinearOperator))
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for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
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assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
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ngev += 4
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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x = [2.1, 1.2]
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H_analit = analit.hess(x)
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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H_approx = approx.hess(x)
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assert_(isinstance(H_approx, LinearOperator))
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for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
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assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
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ngev += 4
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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x = [2.5, 0.3]
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_ = analit.grad(x)
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H_analit = analit.hess(x)
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ngev += 1
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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_ = approx.grad(x)
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H_approx = approx.hess(x)
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assert_(isinstance(H_approx, LinearOperator))
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for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
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assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
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ngev += 4
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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x = [5.2, 2.3]
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_ = analit.grad(x)
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H_analit = analit.hess(x)
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ngev += 1
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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_ = approx.grad(x)
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H_approx = approx.hess(x)
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assert_(isinstance(H_approx, LinearOperator))
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for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
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assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
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ngev += 4
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.ngev, ngev)
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assert_array_equal(analit.ngev+approx.ngev, ngev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev+approx.nhev, nhev)
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class ExVectorialFunction:
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def __init__(self):
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self.nfev = 0
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self.njev = 0
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self.nhev = 0
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def fun(self, x):
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self.nfev += 1
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return np.array([2*(x[0]**2 + x[1]**2 - 1) - x[0],
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4*(x[0]**3 + x[1]**2 - 4) - 3*x[0]])
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def jac(self, x):
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self.njev += 1
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return np.array([[4*x[0]-1, 4*x[1]],
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[12*x[0]**2-3, 8*x[1]]])
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def hess(self, x, v):
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self.nhev += 1
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return v[0]*4*np.eye(2) + v[1]*np.array([[24*x[0], 0],
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[0, 8]])
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class TestVectorialFunction(TestCase):
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def test_finite_difference_jac(self):
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ex = ExVectorialFunction()
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nfev = 0
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njev = 0
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x0 = [1.0, 0.0]
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v0 = [0.0, 1.0]
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analit = VectorFunction(ex.fun, x0, ex.jac, ex.hess, None, None,
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(-np.inf, np.inf), None)
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nfev += 1
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njev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev, njev)
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approx = VectorFunction(ex.fun, x0, '2-point', ex.hess, None, None,
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(-np.inf, np.inf), None)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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assert_array_equal(analit.f, approx.f)
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assert_array_almost_equal(analit.J, approx.J)
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x = [10, 0.3]
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f_analit = analit.fun(x)
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J_analit = analit.jac(x)
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nfev += 1
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njev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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f_approx = approx.fun(x)
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J_approx = approx.jac(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(J_analit, J_approx, decimal=4)
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x = [2.0, 1.0]
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J_analit = analit.jac(x)
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njev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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J_approx = approx.jac(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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assert_array_almost_equal(J_analit, J_approx)
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x = [2.5, 0.3]
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f_analit = analit.fun(x)
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J_analit = analit.jac(x)
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nfev += 1
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njev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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f_approx = approx.fun(x)
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J_approx = approx.jac(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(J_analit, J_approx)
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x = [2, 0.3]
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f_analit = analit.fun(x)
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J_analit = analit.jac(x)
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nfev += 1
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njev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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f_approx = approx.fun(x)
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J_approx = approx.jac(x)
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nfev += 3
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev+approx.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev+approx.njev, njev)
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assert_array_almost_equal(f_analit, f_approx)
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assert_array_almost_equal(J_analit, J_approx)
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def test_finite_difference_hess_linear_operator(self):
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ex = ExVectorialFunction()
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nfev = 0
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njev = 0
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nhev = 0
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x0 = [1.0, 0.0]
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v0 = [1.0, 2.0]
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analit = VectorFunction(ex.fun, x0, ex.jac, ex.hess, None, None,
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(-np.inf, np.inf), None)
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nfev += 1
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njev += 1
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nhev += 1
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assert_array_equal(ex.nfev, nfev)
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assert_array_equal(analit.nfev, nfev)
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assert_array_equal(ex.njev, njev)
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assert_array_equal(analit.njev, njev)
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assert_array_equal(ex.nhev, nhev)
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assert_array_equal(analit.nhev, nhev)
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approx = VectorFunction(ex.fun, x0, ex.jac, '2-point', None, None,
|
|
(-np.inf, np.inf), None)
|
|
assert_(isinstance(approx.H, LinearOperator))
|
|
for p in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
|
|
assert_array_equal(analit.f, approx.f)
|
|
assert_array_almost_equal(analit.J, approx.J)
|
|
assert_array_almost_equal(analit.H.dot(p), approx.H.dot(p))
|
|
nfev += 1
|
|
njev += 4
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
|
|
x = [2.0, 1.0]
|
|
H_analit = analit.hess(x, v0)
|
|
nhev += 1
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
H_approx = approx.hess(x, v0)
|
|
assert_(isinstance(H_approx, LinearOperator))
|
|
for p in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
|
|
assert_array_almost_equal(H_analit.dot(p), H_approx.dot(p),
|
|
decimal=5)
|
|
njev += 4
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
|
|
x = [2.1, 1.2]
|
|
v = [1.0, 1.0]
|
|
H_analit = analit.hess(x, v)
|
|
nhev += 1
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
H_approx = approx.hess(x, v)
|
|
assert_(isinstance(H_approx, LinearOperator))
|
|
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
|
|
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
|
|
njev += 4
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
|
|
x = [2.5, 0.3]
|
|
_ = analit.jac(x)
|
|
H_analit = analit.hess(x, v0)
|
|
njev += 1
|
|
nhev += 1
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
_ = approx.jac(x)
|
|
H_approx = approx.hess(x, v0)
|
|
assert_(isinstance(H_approx, LinearOperator))
|
|
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
|
|
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v), decimal=4)
|
|
njev += 4
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
|
|
x = [5.2, 2.3]
|
|
v = [2.3, 5.2]
|
|
_ = analit.jac(x)
|
|
H_analit = analit.hess(x, v)
|
|
njev += 1
|
|
nhev += 1
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
_ = approx.jac(x)
|
|
H_approx = approx.hess(x, v)
|
|
assert_(isinstance(H_approx, LinearOperator))
|
|
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
|
|
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v), decimal=4)
|
|
njev += 4
|
|
assert_array_equal(ex.nfev, nfev)
|
|
assert_array_equal(analit.nfev+approx.nfev, nfev)
|
|
assert_array_equal(ex.njev, njev)
|
|
assert_array_equal(analit.njev+approx.njev, njev)
|
|
assert_array_equal(ex.nhev, nhev)
|
|
assert_array_equal(analit.nhev+approx.nhev, nhev)
|
|
|
|
|
|
def test_LinearVectorFunction():
|
|
A_dense = np.array([
|
|
[-1, 2, 0],
|
|
[0, 4, 2]
|
|
])
|
|
x0 = np.zeros(3)
|
|
A_sparse = csr_matrix(A_dense)
|
|
x = np.array([1, -1, 0])
|
|
v = np.array([-1, 1])
|
|
Ax = np.array([-3, -4])
|
|
|
|
f1 = LinearVectorFunction(A_dense, x0, None)
|
|
assert_(not f1.sparse_jacobian)
|
|
|
|
f2 = LinearVectorFunction(A_dense, x0, True)
|
|
assert_(f2.sparse_jacobian)
|
|
|
|
f3 = LinearVectorFunction(A_dense, x0, False)
|
|
assert_(not f3.sparse_jacobian)
|
|
|
|
f4 = LinearVectorFunction(A_sparse, x0, None)
|
|
assert_(f4.sparse_jacobian)
|
|
|
|
f5 = LinearVectorFunction(A_sparse, x0, True)
|
|
assert_(f5.sparse_jacobian)
|
|
|
|
f6 = LinearVectorFunction(A_sparse, x0, False)
|
|
assert_(not f6.sparse_jacobian)
|
|
|
|
assert_array_equal(f1.fun(x), Ax)
|
|
assert_array_equal(f2.fun(x), Ax)
|
|
assert_array_equal(f1.jac(x), A_dense)
|
|
assert_array_equal(f2.jac(x).toarray(), A_sparse.toarray())
|
|
assert_array_equal(f1.hess(x, v).toarray(), np.zeros((3, 3)))
|
|
|
|
|
|
def test_LinearVectorFunction_memoization():
|
|
A = np.array([[-1, 2, 0], [0, 4, 2]])
|
|
x0 = np.array([1, 2, -1])
|
|
fun = LinearVectorFunction(A, x0, False)
|
|
|
|
assert_array_equal(x0, fun.x)
|
|
assert_array_equal(A.dot(x0), fun.f)
|
|
|
|
x1 = np.array([-1, 3, 10])
|
|
assert_array_equal(A, fun.jac(x1))
|
|
assert_array_equal(x1, fun.x)
|
|
assert_array_equal(A.dot(x0), fun.f)
|
|
assert_array_equal(A.dot(x1), fun.fun(x1))
|
|
assert_array_equal(A.dot(x1), fun.f)
|
|
|
|
|
|
def test_IdentityVectorFunction():
|
|
x0 = np.zeros(3)
|
|
|
|
f1 = IdentityVectorFunction(x0, None)
|
|
f2 = IdentityVectorFunction(x0, False)
|
|
f3 = IdentityVectorFunction(x0, True)
|
|
|
|
assert_(f1.sparse_jacobian)
|
|
assert_(not f2.sparse_jacobian)
|
|
assert_(f3.sparse_jacobian)
|
|
|
|
x = np.array([-1, 2, 1])
|
|
v = np.array([-2, 3, 0])
|
|
|
|
assert_array_equal(f1.fun(x), x)
|
|
assert_array_equal(f2.fun(x), x)
|
|
|
|
assert_array_equal(f1.jac(x).toarray(), np.eye(3))
|
|
assert_array_equal(f2.jac(x), np.eye(3))
|
|
|
|
assert_array_equal(f1.hess(x, v).toarray(), np.zeros((3, 3)))
|