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test_serial_ncpsolve.py
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test_serial_ncpsolve.py
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import unittest
import numpy as np
from dolo.numeric.optimize.ncpsolve import ncpsolve
def josephy(x):
# Computes the function value F(x) of the NCP-example by Josephy.
n=len(x)
Fx=np.zeros(n)
Fx[0]=3*x[0]**2+2*x[0]*x[1]+2*x[1]**2+x[2]+3*x[3]-6
Fx[1]=2*x[0]**2+x[0]+x[1]**2+3*x[2]+2*x[3]-2
Fx[2]=3*x[0]**2+x[0]*x[1]+2*x[1]**2+2*x[2]+3*x[3]-1
Fx[3]=x[0]**2+3*x[1]**2+2*x[2]+3*x[3]-3;
return Fx
def Djosephy(x):
# Local Variables: x, DFx, n
# Function calls: Djosephy, zeros, length
#%
#% Computes the Jacobian DF(x) of the NCP-example by Josephy
#%
n = len(x)
DFx = np.zeros( (n, n) )
DFx[0,0] = 6.*x[0]+2.*x[1]
DFx[0,1] = 2.*x[0]+4.*x[1]
DFx[0,2] = 1.
DFx[0,3] = 3.
DFx[1,0] = 4.*x[0]+1.
DFx[1,1] = 2.*x[1]
DFx[1,2] = 3.
DFx[1,3] = 2.
DFx[2,0] = 6.*x[0]+x[1]
DFx[2,1] = x[0]+4.*x[1]
DFx[2,2] = 2.
DFx[2,3] = 3.
DFx[3,0] = 2.*x[0]
DFx[3,1] = 6.*x[1]
DFx[3,2] = 2.
DFx[3,3] = 3.
return DFx
class SerialSolve(unittest.TestCase):
#
# def test_serial_smooth(self):
#
# x0 = np.array([0.5,0.5,0.5,0.5])
#
#
# lb = np.array([0.0,0.6,0.0,0.0])
# ub = np.array([1.0,1.0,1.0,0.4])
#
# fval = np.array([ 0.5, 0.5, 0.1,0.5 ])
#
# jac = np.array([
# [1.0,0.2,0.1,0.0],
# [1.0,0.2,0.1,0.0],
# [0.0,1.0,0.2,0.0],
# [0.1,1.0,0.2,0.1]
# ])
#
# N = 10
# d = len(fval)
#
# s_x0 = np.row_stack([x0]*N)
# s_lb = np.row_stack([lb]*N)
# s_ub = np.row_stack([ub]*N)
# s_fval = np.row_stack([fval]*N)
#
#
# s_jac = np.zeros( (N,d,d) )
# for i in range(N):
# s_jac[i,:,:] = jac
#
# from dolo.numeric.ncpsolve import smooth
#
# [fnew, Jnew] = smooth(x0, lb, ub, fval, J=jac)
#
# serial_fnew_true = np.zeros( (N,d) )
# serial_Jnew_true = np.zeros( (N,d,d) )
# for n in range(N):
# serial_fnew_true[n,:] = fnew
# serial_Jnew_true[n,:,:] = Jnew
#
#
# [serial_fnew, serial_Jnew] = smooth(s_x0, s_lb, s_ub, s_fval, J=s_jac, serial=True)
#
# from numpy.testing import assert_equal
#
# assert_equal(serial_fnew, serial_fnew_true)
# assert_equal(serial_Jnew, serial_Jnew_true)
def test_serial_solve(self):
fun = lambda x: [-josephy(x), -Djosephy(x)]
x0=np.array( [1.25, 0.01, 0.01, 0.50] )
lb=np.array( [0.00, 0.00, 0.00, 0.00] )
# ub=np.array( [inf, inf, inf, inf] )
ub=np.array( [1e20, 1e20, 1e20, 1e20] )
# resp = ncpsolve(fun, lb, ub, x0, tol=1e-15)
sol = np.array( [ 1.22474487e+00, 0.00000000e+00, 3.60543164e-17, 5.00000000e-01])
# assert_almost_equal(sol, resp)
N = 10
d = len(x0)
s_x0 = np.row_stack([x0]*N)
s_lb = np.row_stack([lb]*N)
s_ub = np.row_stack([ub]*N)
def serial_fun(xvec):
resp = np.zeros( (N,d) )
dresp = np.zeros( (N,d,d) )
for n in range(N):
[v, dv] = fun(xvec[n,:])
resp[n,:] = v
dresp[n,:,:] = dv
return [resp, dresp]
res = serial_fun(s_x0)[0]
serial_sol = ncpsolve( serial_fun, s_lb, s_ub, s_x0, jactype='serial', verbose=True)
print(serial_sol)
if __name__ == '__main__':
from numpy import inf
fun = lambda x: [-josephy(x), -Djosephy(x)]
x0=np.array( [1.25, 0.01, 0.01, 0.50] )
lb=np.array( [0.00, 0.00, 0.00, 0.00] )
ub=np.array( [inf, inf, inf, inf] )
resp = ncpsolve(fun, lb, ub, x0, tol=1e-15)
sol = np.array( [ 1.22474487e+00, 0.00000000e+00, 3.60543164e-17, 5.00000000e-01])
from numpy.testing import assert_almost_equal
assert_almost_equal(sol, resp[0])
N = 2
d = len(x0)
serial_sol_check = np.zeros((d,N))
for n in range(N):
serial_sol_check[:,n] = resp[0]
s_x0 = np.column_stack([x0]*N)
s_lb = np.column_stack([lb]*N)
s_ub = np.column_stack([ub]*N)
def serial_fun(xvec):
resp = np.zeros( (d,N) )
dresp = np.zeros( (d,d,N) )
for n in range(N):
[v, dv] = fun(xvec[:,n])
resp[:,n] = v
dresp[:,:,n] = dv
return [resp, dresp]
serial_sol = ncpsolve( serial_fun, s_lb, s_ub, s_x0, serial=True)
err = abs(serial_sol[0] - serial_sol_check).max()
assert_almost_equal( serial_sol[0], serial_sol_check )