def test2D(potential, field):
potAccept2D = np.zeros((NX_2D + 1, NY_2D + 1))
fieldAccept2D = np.zeros((NX_2D + 1, NY_2D + 1, 2))
for i, j in np.ndindex(potAccept2D.shape):
potAccept2D[i, j] = potential(X0_2D + DX_2D * i, Y0_2D + DY_2D * j)
fieldAccept2D[i, j] = field(X0_2D + DX_2D * i, Y0_2D + DY_2D * j)
# Boundary conditions
V0x_2D = dirBC(potAccept2D[0, :])
VNx_2D = dirBC(potAccept2D[NX_2D, :])
V0y_2D = dirBC(potAccept2D[:, 0])
VNy_2D = dirBC(potAccept2D[:, NY_2D])
E0x_2D = neuBC(fieldAccept2D[0, :, 0])
ENx_2D = neuBC(fieldAccept2D[NX_2D, :, 0])
E0y_2D = neuBC(fieldAccept2D[:, 0, 1])
ENy_2D = neuBC(fieldAccept2D[:, NY_2D, 1])
for BC0x_2D in [V0x_2D, E0x_2D]:
for BCNx_2D in [VNx_2D, ENx_2D]:
for BC0y_2D in [V0y_2D, E0y_2D]:
for BCNy_2D in [VNy_2D]: #,ENy_2D]:
for testType in ["direct", "jacobi", "gaussSeidel"]:
for cythonType in [True, False]:
if testType == "direct":
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,cythonType)
else:
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,relTol,absTol,cythonType)
test(potCalculated2D, potAccept2D)
def test2D(potential,field):
potAccept2D = np.zeros((NX_2D+1,NY_2D+1))
fieldAccept2D = np.zeros((NX_2D+1,NY_2D+1,2))
for i,j in np.ndindex(potAccept2D.shape):
potAccept2D[i,j] = potential(X0_2D+DX_2D*i,Y0_2D+DY_2D*j)
fieldAccept2D[i,j] = field( X0_2D+DX_2D*i,Y0_2D+DY_2D*j)
# Boundary conditions
V0x_2D = dirBC(potAccept2D[0, : ])
VNx_2D = dirBC(potAccept2D[NX_2D,: ])
V0y_2D = dirBC(potAccept2D[:, 0 ])
VNy_2D = dirBC(potAccept2D[:, NY_2D])
E0x_2D = neuBC(fieldAccept2D[0, :, 0])
ENx_2D = neuBC(fieldAccept2D[NX_2D,:, 0])
E0y_2D = neuBC(fieldAccept2D[:, 0, 1])
ENy_2D = neuBC(fieldAccept2D[:, NY_2D,1])
for BC0x_2D in [V0x_2D,E0x_2D]:
for BCNx_2D in [VNx_2D,ENx_2D]:
for BC0y_2D in [V0y_2D,E0y_2D]:
for BCNy_2D in [VNy_2D]:#,ENy_2D]:
for testType in ["direct","jacobi","gaussSeidel"]:
for cythonType in [True,False]:
if testType == "direct":
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,cythonType)
else:
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,relTol,absTol,cythonType)
test(potCalculated2D,potAccept2D)
# Boundary conditions
V0x = dirBC(np.zeros((NY + 1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY + 1, )))
V0y = dirBC(np.zeros((NX + 1)))
VNy = dirBC(np.zeros((NX + 1)))
start = time.clock()
potential_NoCython = esSolve.laplace2D(NX,
DX,
V0x,
VNx,
NY,
DY,
V0y,
VNy,
"gaussSeidel",
relTol=0.0,
absTol=1.0e-3,
useCython=False)
end = time.clock()
seconds_NoCython = end - start
print("No Cython took", round(seconds_NoCython, 1), "seconds.")
start = time.clock()
potential_Cython = esSolve.laplace2D(NX,
DX,
V0x,
VNx,
NY,
amplitude = 2.0
def nonGroundedWall(Yindex):
return amplitude * np.sin(np.pi * Yindex / NY)
# Boundary conditions
V0x = dirBC(np.zeros((NY+1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY+1,)))
V0y = dirBC(np.zeros((NX+1)))
VNy = dirBC(np.zeros((NX+1)))
start = time.clock()
potential_1 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0)
potential_2 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=0.5)
potential_3 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0e-3)
end = time.clock()
print("That took",round(end-start,1),"seconds.")
def plot2Darrays(arrays):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
if len(arrays) == 1:
X = np.linspace(X0, X0 + LX, num=arrays[0].shape[0])
Y = np.linspace(Y0, Y0 + LY, num=arrays[0].shape[1])
X, Y = np.meshgrid(X, Y, indexing='ij')
# Boundary conditions
V0x = dirBC(np.zeros((NY + 1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY + 1, )))
V0y = dirBC(np.zeros((NX + 1)))
VNy = dirBC(np.zeros((NX + 1)))
start = time.clock()
potential_1 = esSolve.laplace2D(NX,
DX,
V0x,
VNx,
NY,
DY,
V0y,
VNy,
"gaussSeidel",
relTol=0.0,
absTol=1.0)
potential_2 = esSolve.laplace2D(NX,
DX,
V0x,
VNx,
NY,
DY,
V0y,
VNy,
"gaussSeidel",
relTol=0.0,
DX = LX / NX
DY = LY / NY
X0 = 1.0
Y0 = 2.0
amplitude = 2.0
def nonGroundedWall(Yindex):
return amplitude * np.sin(np.pi * Yindex / NY)
# Boundary conditions
V0x = dirBC(np.zeros((NY+1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY+1,)))
V0y = dirBC(np.zeros((NX+1)))
VNy = dirBC(np.zeros((NX+1)))
start = time.clock()
potential_NoCython = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0e-3,useCython=False)
end = time.clock()
seconds_NoCython = end - start
print("No Cython took",round(seconds_NoCython,1),"seconds.")
start = time.clock()
potential_Cython = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0e-3,useCython=True)
end = time.clock()
seconds_Cython = end - start
print("Cython took",round(seconds_Cython,1),"seconds.")
print("Cython was",round(100.0*(1.0-seconds_Cython/seconds_NoCython),1),"percent faster.")
