def getError(self):
call = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2])
ex = lambda x, y, z: x**2 + y * z
ey = lambda x, y, z: (z**2) * x + y * z
ez = lambda x, y, z: y**2 + x * z
sigma1 = lambda x, y, z: x * y + 1
sigma2 = lambda x, y, z: x * z + 2
sigma3 = lambda x, y, z: 3 + z * y
sigma4 = lambda x, y, z: 0.1 * x * y * z
sigma5 = lambda x, y, z: 0.2 * x * y
sigma6 = lambda x, y, z: 0.1 * z
Gc = self.M.gridCC
if self.sigmaTest == 1:
sigma = np.c_[call(sigma1, Gc)]
analytic = 647. / 360 # Found using sympy.
elif self.sigmaTest == 3:
sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
analytic = 37. / 12 # Found using sympy.
elif self.sigmaTest == 6:
sigma = np.c_[call(sigma1, Gc),
call(sigma2, Gc),
call(sigma3, Gc),
call(sigma4, Gc),
call(sigma5, Gc),
call(sigma6, Gc)]
analytic = 69881. / 21600 # Found using sympy.
if self.location == 'edges':
cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
Ec = np.vstack((cart(self.M.gridEx), cart(self.M.gridEy),
cart(self.M.gridEz)))
E = self.M.projectEdgeVector(Ec)
if self.invProp:
A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(
self.M, sigma),
invProp=True)
else:
A = self.M.getEdgeInnerProduct(sigma)
numeric = E.T.dot(A.dot(E))
elif self.location == 'faces':
cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
Fc = np.vstack((cart(self.M.gridFx), cart(self.M.gridFy),
cart(self.M.gridFz)))
F = self.M.projectFaceVector(Fc)
if self.invProp:
A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(
self.M, sigma),
invProp=True)
else:
A = self.M.getFaceInnerProduct(sigma)
numeric = F.T.dot(A.dot(F))
err = np.abs(numeric - analytic)
return err
def getError(self):
call = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2])
ex = lambda x, y, z: x**2+y*z
ey = lambda x, y, z: (z**2)*x+y*z
ez = lambda x, y, z: y**2+x*z
sigma1 = lambda x, y, z: x*y+1
sigma2 = lambda x, y, z: x*z+2
sigma3 = lambda x, y, z: 3+z*y
sigma4 = lambda x, y, z: 0.1*x*y*z
sigma5 = lambda x, y, z: 0.2*x*y
sigma6 = lambda x, y, z: 0.1*z
Gc = self.M.gridCC
if self.sigmaTest == 1:
sigma = np.c_[call(sigma1, Gc)]
analytic = 647./360 # Found using sympy.
elif self.sigmaTest == 3:
sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
analytic = 37./12 # Found using sympy.
elif self.sigmaTest == 6:
sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc),
call(sigma4, Gc), call(sigma5, Gc), call(sigma6, Gc)]
analytic = 69881./21600 # Found using sympy.
if self.location == 'edges':
cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
Ec = np.vstack((cart(self.M.gridEx),
cart(self.M.gridEy),
cart(self.M.gridEz)))
E = self.M.projectEdgeVector(Ec)
if self.invProp:
A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
else:
A = self.M.getEdgeInnerProduct(sigma)
numeric = E.T.dot(A.dot(E))
elif self.location == 'faces':
cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
Fc = np.vstack((cart(self.M.gridFx),
cart(self.M.gridFy),
cart(self.M.gridFz)))
F = self.M.projectFaceVector(Fc)
if self.invProp:
A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
else:
A = self.M.getFaceInnerProduct(sigma)
numeric = F.T.dot(A.dot(F))
err = np.abs(numeric - analytic)
return err
def getError(self):
z = 5 # Because 5 is just such a great number.
call = lambda fun, xy: fun(xy[:, 0], xy[:, 1])
ex = lambda x, y: x**2 + y * z
ey = lambda x, y: (z**2) * x + y * z
sigma1 = lambda x, y: x * y + 1
sigma2 = lambda x, y: x * z + 2
sigma3 = lambda x, y: 3 + z * y
Gc = self.M.gridCC
if self.sigmaTest == 1:
sigma = np.c_[call(sigma1, Gc)]
analytic = 144877. / 360 # Found using sympy. z=5
elif self.sigmaTest == 2:
sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc)]
analytic = 189959. / 120 # Found using sympy. z=5
elif self.sigmaTest == 3:
sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
analytic = 781427. / 360 # Found using sympy. z=5
if self.location == 'edges':
cart = lambda g: np.c_[call(ex, g), call(ey, g)]
Ec = np.vstack((cart(self.M.gridEx), cart(self.M.gridEy)))
E = self.M.projectEdgeVector(Ec)
if self.invProp:
A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(
self.M, sigma),
invProp=True)
else:
A = self.M.getEdgeInnerProduct(sigma)
numeric = E.T.dot(A.dot(E))
elif self.location == 'faces':
cart = lambda g: np.c_[call(ex, g), call(ey, g)]
Fc = np.vstack((cart(self.M.gridFx), cart(self.M.gridFy)))
F = self.M.projectFaceVector(Fc)
if self.invProp:
A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(
self.M, sigma),
invProp=True)
else:
A = self.M.getFaceInnerProduct(sigma)
numeric = F.T.dot(A.dot(F))
err = np.abs(numeric - analytic)
return err
def getError(self):
z = 5 # Because 5 is just such a great number.
call = lambda fun, xy: fun(xy[:, 0], xy[:, 1])
ex = lambda x, y: x**2+y*z
ey = lambda x, y: (z**2)*x+y*z
sigma1 = lambda x, y: x*y+1
sigma2 = lambda x, y: x*z+2
sigma3 = lambda x, y: 3+z*y
Gc = self.M.gridCC
if self.sigmaTest == 1:
sigma = np.c_[call(sigma1, Gc)]
analytic = 144877./360 # Found using sympy. z=5
elif self.sigmaTest == 2:
sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc)]
analytic = 189959./120 # Found using sympy. z=5
elif self.sigmaTest == 3:
sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
analytic = 781427./360 # Found using sympy. z=5
if self.location == 'edges':
cart = lambda g: np.c_[call(ex, g), call(ey, g)]
Ec = np.vstack((cart(self.M.gridEx),
cart(self.M.gridEy)))
E = self.M.projectEdgeVector(Ec)
if self.invProp:
A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
else:
A = self.M.getEdgeInnerProduct(sigma)
numeric = E.T.dot(A.dot(E))
elif self.location == 'faces':
cart = lambda g: np.c_[call(ex, g), call(ey, g)]
Fc = np.vstack((cart(self.M.gridFx),
cart(self.M.gridFy)))
F = self.M.projectFaceVector(Fc)
if self.invProp:
A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
else:
A = self.M.getFaceInnerProduct(sigma)
numeric = F.T.dot(A.dot(F))
err = np.abs(numeric - analytic)
return err
