def plotGrid(dim,level):
sg = pysg.sparseGrid(dim=dim,level=level)
sg.generatePoints()
points = sg.indices
pts = len(points)
xpts = np.empty(pts)
if dim==1:
for i in xrange(pts):
pt = tuple(points[i])
xpts[i] = sg.gP[pt].pointPosition(pt)[0]
plt.plot(xpts,np.ones_like(xpts),'*')
elif dim==2:
ypts = np.empty(pts)
for i in xrange(pts):
pt = tuple(points[i])
xpts[i], ypts[i] = sg.gP[pt].pointPosition(pt)
plt.plot(xpts,ypts,'*')
else:
if dim > 3:
print "Showing first three dimensions only"
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ypts = np.empty(pts)
zpts = np.empty(pts)
for i in xrange(pts):
pt = tuple(points[i])
xpts[i], ypts[i], zpts[i] = sg.gP[pt].pointPosition(pt)[:3]
ax.scatter(xpts, ypts, zpts)
def example():
# There is an error here. the coefficient for loc [0.25,0.5] should be 0.
def f(x):
return x[0]
dim = 2
level = 3
sg = pysg.sparseGrid(dim=dim,level=level)
sg.setFunctionValues(f)
sg.nodal2Hier()
sg.setCoefficients()
total = 0
for i in xrange(len(sg.indices)):
total += sg.gP[tuple(sg.indices[i])].coeff
total /= 2**((level-1)*dim)*(dim+1)
print total
def example():
# There is an error here. the coefficient for loc [0.25,0.5] should be 0.
def f(x):
return x[0]
dim = 2
level = 3
sg = pysg.sparseGrid(dim=dim, level=level)
sg.setFunctionValues(f)
sg.nodal2Hier()
sg.setCoefficients()
total = 0
for i in xrange(len(sg.indices)):
total += sg.gP[tuple(sg.indices[i])].coeff
total /= 2**((level - 1) * dim) * (dim + 1)
print total
def testSGNoBound3D(self):
sg = pysg.sparseGrid(3,3)
sg.generatePoints()
# right number of grid points
self.assertEqual(len(sg.indices),31)
for i in range(len(sg.indices)):
sum = 1.0
pos = sg.gP[tuple(sg.indices[i])].pos
for j in range(len(pos)):
sum *= 4.*pos[j]*(1.0-pos[j])
sg.gP[tuple(sg.indices[i])].fv = sum
# convert to hierarchical values
sg.nodal2Hier()
# does the evaluation of sparse grid function in
# hierarchical values give the correct value gv
for i in range(len(sg.indices)):
self.assertEqual(sg.gP[tuple(sg.indices[i])].fv,\
sg.evalFunct(sg.gP[tuple(sg.indices[i])].pos))
def sparseGridPosList(dim, levels):
sg = pysg.sparseGrid(dim, levels)
sg.generatePoints()
n = len(sg.indices)
positions = np.zeros((dim, n))
for i in range(n):
positions[:, i] = sg.gP[tuple(sg.indices[i])].pos
return (positions)
#positions = sparseGridPosList(dim, levels)
#fig2, axs2 = plt.subplots(1, 1, figsize=(10, 10))
#axs2.plot(positions[0,:], positions[1,:], 'x')
#
#fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
#ax.scatter(positions[0,:], positions[1,:], positions[2,:])
def testSGNoBound3D(self):
sg = pysg.sparseGrid(3, 3)
sg.generatePoints()
# right number of grid points
self.assertEqual(len(sg.indices), 31)
for i in range(len(sg.indices)):
sum = 1.0
pos = sg.gP[tuple(sg.indices[i])].pos
for j in range(len(pos)):
sum *= 4. * pos[j] * (1.0 - pos[j])
sg.gP[tuple(sg.indices[i])].fv = sum
# convert to hierarchical values
sg.nodal2Hier()
# does the evaluation of sparse grid function in
# hierarchical values give the correct value gv
for i in range(len(sg.indices)):
self.assertEqual(sg.gP[tuple(sg.indices[i])].fv,\
sg.evalFunct(sg.gP[tuple(sg.indices[i])].pos))
def testSGNoBound3D(self):
#
# SG is a sparse grid of dimension 3 and level 3.
# Create sg.indices which stores level and position for each point.
#
sg = pysg.sparseGrid(3,3)
#
# Determine sg.gP with the coordinates of the points
# associated with the sparse grid index set.
#
sg.generatePoints()
#
# Print the points in the grid.
#
print ""
print "Coordinates of points in 3D sparse grid of level 3."
print ""
for i in range ( len(sg.indices) ):
sg.gP[tuple(sg.indices[i])].printPoint()
#
# Did we compute the right number of grid points?
#
self.assertEqual ( len ( sg.indices), 31 )
#
# Evaluate 4x(1-x)*4y(1-y)*4z(1-z) at each grid point.
#
for i in range ( len(sg.indices) ):
sum = 1.0
pos = sg.gP[tuple(sg.indices[i])].pos
for j in range(len(pos)):
sum *= 4.*pos[j]*(1.0-pos[j])
sg.gP[tuple(sg.indices[i])].fv = sum
#
# Convert the sparse grid from nodal to hierarchical values.
#
sg.nodal2Hier()
#
# Does the evaluation of the sparse grid function in
# hierarchical values give the correct value gv?
#
for i in range(len(sg.indices)):
self.assertEqual(sg.gP[tuple(sg.indices[i])].fv,\
sg.evalFunct(sg.gP[tuple(sg.indices[i])].pos))
def prob4():
"""Plot the grid points for a 2-D grid of level 5.
"""
grid = pysg.sparseGrid(2,5)
grid.plotGrid()
def prob4():
"""Plot the grid points for a 2-D grid of level 5.
"""
grid = pysg.sparseGrid(2, 5)
grid.plotGrid()
