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from numpy.testing import assert_array_almost_equal, TestCase, run_module_suite
import numpy as np
from scipy.optimize import fmin_slsqp
class TestSLSQP(TestCase):
"""Test fmin_slsqp using Example 14.4 from Numerical Methods for
Engineers by Steven Chapra and Raymond Canale. This example
maximizes the function f(x) = 2*x*y + 2*x - x**2 - 2*y**2, which
has a maximum at x=2,y=1.
"""
def _testfunc(self,d,*args):
"""
Arguments:
d - A list of two elements, where d[0] represents x and d[1] represents y
in the following equation.
sign - A multiplier for f. Since we want to optimize it, and the scipy
optimizers can only minimize functions, we need to multiply it by
-1 to achieve the desired solution
Returns:
2*x*y + 2*x - x**2 - 2*y**2
"""
try:
sign = args[0]
except:
sign = 1.0
x = d[0]
y = d[1]
return sign*(2*x*y + 2*x - x**2 - 2*y**2)
def _testfunc_deriv(self,d,*args):
"""
This is the derivative of testfunc, returning a numpy array
representing df/dx and df/dy.
"""
try:
sign = args[0]
except:
sign = 1.0
x = d[0]
y = d[1]
dfdx = sign*(-2*x + 2*y + 2)
dfdy = sign*(2*x - 4*y)
return np.array([ dfdx, dfdy ],float)
def test_unbounded_approximated(self):
res = fmin_slsqp(self._testfunc, [-1.0,1.0], args = (-1.0,),
iprint = 0, full_output = 1)
x,fx,its,imode,smode = res
assert_array_almost_equal(x,[2,1])
def test_unbounded_given(self):
res = fmin_slsqp(self._testfunc,[-1.0,1.0], args = (-1.0,),
iprint = 0, full_output = 1)
x,fx,its,imode,smode = res
assert_array_almost_equal(x,[2,1])
def test_bound_approximated(self):
res = fmin_slsqp(self._testfunc,[-1.0,1.0], args = (-1.0,),
eqcons = [lambda x, y: x[0]-x[1] ],
iprint = 0, full_output = 1)
x,fx,its,imode,smode = res
assert_array_almost_equal(x,[1,1])
def test_bound_equality_given(self):
res = fmin_slsqp(self._testfunc,[-1.0,1.0],
fprime = self._testfunc_deriv,
args = (-1.0,), eqcons = [lambda x, y: x[0]-x[1] ],
iprint = 0, full_output = 1)
x,fx,its,imode,smode = res
assert_array_almost_equal(x,[1,1])
def test_bound_equality_inequality_given(self):
res = fmin_slsqp(self._testfunc,[-1.0,1.0],
fprime = self._testfunc_deriv,
args = (-1.0,),
ieqcons = [lambda x, y: x[0]-x[1]-1.0],
iprint=0, full_output=1)
x,fx,its,imode,smode = res
assert_array_almost_equal(x,[2,1],decimal=3)
if __name__ == "__main__":
run_module_suite()
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