def test_minSize(self):
parameters = self.parameters.copy()
shape = parameters["problemShape"] = (1024,)
parameters["gridLevels"] = 24
parameters["minSize"] = 23
u_actual = np.random.random(shape).ravel()
A_in = operators.poisson(shape)
b = tools.flexibleMmult(A_in, u_actual)
soln, info_dict = mgSolve(A_in, b, parameters)
if self.verbose:
print "R shapes:", [r.shape for r in info_dict['R']]
print "c.v. minSize = ", parameters['minSize']
assert min(info_dict['R'][-1].shape) > parameters["minSize"]
def test_1d_noise_mg(self, parameters=None):
'''Solve a 2D Poisson equation, with the solution being 2D white noise,
i.e., np.random.random((NX,NY)). Useful as a sanity check.
'''
if parameters is None:
parameters = self.parameters
N = NX = parameters['problemShape'][0]
u_actual = np.random.random((NX,)).reshape((N, 1))
A_in = operators.poisson((NX,))
b = tools.flexibleMmult(A_in, u_actual)
u_mg, info_dict = mgSolve(A_in, b, parameters)
if self.verbose:
print 'test_1d_noise_mg: final norm is ', info_dict['norm']
def test_threshStop(self):
size = 36
u_actual = np.sin(np.array(range(int(size))) * 3.0 / size).T
A = operators.poisson((size,))
b = tools.flexibleMmult(A, u_actual)
parameters = {
'problemShape': (size,),
'gridLevels': 2,
'threshold': 8e-3,
'giveInfo': True,
}
u_mmg, info_dict = mgSolve(A, b, parameters)
residual_norm = np.linalg.norm(tools.flexibleMmult(A, u_mmg) - b)
assert parameters['threshold'] > residual_norm
def test_2d_mpl_demo(self):
'''
Plot a pretty 2D surface, and the result of solving a 2D Poisson equation
with that surface as the solution.
'''
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
sizemultiplier = 2
NX = 8 * sizemultiplier
cycles = 3
actualtraces = 8
mgtraces = 16
NY = NX
N = NX * NY
(X, Y, u_actual) = mpl_test_data(delta=1 / float(sizemultiplier))
A_in = operators.poisson((NX, NY))
b = tools.flexibleMmult(A_in, u_actual.ravel())
u_mg = mgSolve(A_in, b, {
'problemShape': (NX, NY),
'gridLevels': 2,
'iterations': 1,
'verbose': False,
'cycles': 300,
'dense': True
}
)
fig = plt.figure()
ax = Axes3D(fig)
fig.suptitle('blue is actual; red is %i v-cycles; %i unknowns' % (cycles, N))
# ax = fig.add_subplot(111,projection='3d') #not in matplotlib version 0.99, only version 1.x
ax.plot_wireframe(X, Y, u_actual,
rstride=NX / actualtraces,
cstride=NY / actualtraces,
color=((0, 0, 1.0),)
)
# ax.scatter(X,Y,u_mg[0],c=((1.,0,0),),s=40)
ax.plot_wireframe(X, Y, u_mg.reshape((NX, NY)),
rstride=NX / mgtraces,
cstride=NY / mgtraces,
color=((1.0, 0, 0),)
)
filename = 'output/test_2d_mpl_demo-%i_vycles-%i_N.png' % (cycles, N)
if self.saveFig: fig.savefig(filename)
# plt.show()
if self.verbose:
print 'norm is', (np.linalg.norm(openmg.tools.getresidual(b, A_in, u_mg[0], N)))
def test_3d_noise_mg(self):
'''Solve a 3D Poisson equation, with the solution being 2D white noise,
i.e., np.random.random((NX, NY, NZ)). Useful as a sanity check.
'''
NX = NY = NZ = 8
N = NX * NY * NZ
shape = NX, NY, NZ
u_actual = np.random.random(shape).reshape((N, 1))
A_in = operators.poisson(shape)
b = tools.flexibleMmult(A_in, u_actual)
u_mg, info_dict = mgSolve(A_in, b, {
'problemShape': shape,
'gridLevels': 3,
'iterations': 1,
'verbose': False,
'threshold': 4,
'giveInfo': True,
}
)
if self.verbose:
print 'test_1d_noise_mg: final norm is ', info_dict['norm']
def test_a(self):
'''
Poisson equation on a sine curve. In 3D?
It wasn't originally, but the restriciton algorithm was having
trouble with 1D. This might bear investigation.
'''
problemscale = 12
size = problemscale ** 3
gridLevels = 4
u_zeros = np.zeros((size,))
u_actual = np.sin(np.array(range(int(size))) * 3.0 / size).T
A = operators.poisson((size,))
b = tools.flexibleMmult(A, u_actual)
uSmoothed = smooth(A, b, u_zeros, iterations=1)
parameters = {'coarsestLevel': gridLevels - 1,
'problemShape': (problemscale, problemscale, problemscale),
'gridLevels': gridLevels,
'threshold': 8e-3,
}
u_mmg = mgSolve(A, b, parameters)
if self.verbose:
print 'norm is', (np.linalg.norm(tools.getresidual(b, A, uSmoothed.reshape((size, 1)), size)))
residual_norm = np.linalg.norm(tools.flexibleMmult(A, u_mmg) - b)
assert parameters['threshold'] > residual_norm