def setUp(self):
self.A = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.A = 0.5*(self.A - self.A.T)
self.TA = tensors.Skew(self.A)
self.B = np.array([[10.2,-9.3,2.5],[0.1,3.1,2.8],[0.1,3.2,-6.1]])
self.B = 0.5*(self.B - self.B.T)
self.TB = tensors.Skew(self.B)
self.a = np.array([2.2,-1.2,2.5])
self.va = tensors.Vector(self.a)
self.s = 2.1
def setUp(self):
self.SS = np.array([
[ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981],
[ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648],
[-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579],
[ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ],
[ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655],
[-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]])
self.SS_full = common.ms2ts(self.SS)
self.TSS = tensors.SymSymR4(self.SS)
self.W = np.array([[-9.36416517, 2.95527444, 8.70983194],
[-1.54693052, 8.7905658 , -5.10895168],
[-8.52740468, -0.7741642 , 2.89544992]])
self.W = 0.5 * (self.W - self.W.T)
self.TW = tensors.Skew(self.W)
self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.S = 0.5*(self.S + self.S.T)
self.TS = tensors.Symmetric(self.S)
self.WS = np.array([
[-8.3567359 , -5.39728818, -8.00844442, -8.33365112, -0.97903364, -8.23943149],
[-6.97125417, 4.34802055, 7.06281056, -1.57511617, 7.83359933, -9.37625432],
[-6.0799489 , -6.0309543 , 3.68575895, 8.84296976, 6.55799427, -9.22029379]])
self.WS_full = common.wws2ts(self.WS)
self.TWS = tensors.SkewSymR4(self.WS)
def test_spin_rate(self):
Cfull = ms2ts(
self.emodel.C_tensor(self.T, self.Q).data.reshape((6, 6)))
Sfull = ms2ts(
self.emodel.S_tensor(self.T, self.Q).data.reshape((6, 6)))
d = usym(self.d.data)
w = uskew(self.w.data)
Ofull = uskew(self.fspin.data)
dp = usym(
self.imodel.d_p(self.S, self.Q, self.H, self.L, self.T,
self.fixed).data)
wp = uskew(
self.imodel.w_p(self.S, self.Q, self.H, self.L, self.T,
self.fixed).data)
O = wp + Ofull
stress = usym(self.S.data)
e = np.einsum('ijkl,kl', Sfull, stress)
spin1 = tensors.Skew(w - wp - np.dot(e, dp) + np.dot(dp, e))
spin2 = self.model.spin(self.S, self.d, self.w, self.Q, self.H, self.L,
self.T, self.fixed)
self.assertTrue(spin1, spin2)
def setUp(self):
self.strength = 35.0
self.H = history.History()
self.H.add_scalar("strength")
self.H.set_scalar("strength", self.strength)
self.H.add_scalar("whatever")
self.H.set_scalar("whatever", 0.5)
self.tau0 = 10.0
self.tau_sat = 50.0
self.b = 2.5
self.strengthmodel = slipharden.VoceSlipHardening(
self.tau_sat, self.b, self.tau0)
self.g0 = 1.0
self.n = 3.0
self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel,
self.g0, self.n)
self.imodel = inelasticity.AsaroInelasticity(self.slipmodel)
self.L = crystallography.CubicLattice(1.0)
self.L.add_slip_system([1, 1, 0], [1, 1, 1])
self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees")
self.S = tensors.Symmetric(
np.array([[100.0, -25.0, 10.0], [-25.0, -17.0, 15.0],
[10.0, 15.0, 35.0]]))
self.T = 300.0
self.mu = 29000.0
self.E = 120000.0
self.nu = 0.3
self.emodel = elasticity.CubicLinearElasticModel(
self.E, self.nu, self.mu, "moduli")
self.dn = np.array([[4.1, 2.8, -1.2], [3.1, 7.1, 0.2], [4, 2, 3]])
self.dn = 0.5 * (self.dn + self.dn.T)
self.d = tensors.Symmetric(self.dn)
self.wn = np.array([[-9.36416517, 2.95527444, 8.70983194],
[-1.54693052, 8.7905658, -5.10895168],
[-8.52740468, -0.7741642, 2.89544992]])
self.wn = 0.5 * (self.wn - self.wn.T)
self.w = tensors.Skew(self.wn)
self.dmodel = crystaldamage.NilDamageModel()
self.model = kinematics.DamagedStandardKinematicModel(
self.emodel, self.imodel, self.dmodel)
self.fspin = self.model.spin(self.S, self.d, self.w, self.Q, self.H,
self.L, self.T, history.History())
self.fixed = self.model.decouple(self.S, self.d, self.w, self.Q,
self.H, self.L, self.T,
history.History())
def setUp(self):
self.scalar = 2.5
self.vector = tensors.Vector(np.array([1.0, 2.0, 3.0]))
self.ranktwo = tensors.RankTwo(
np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]))
self.symmetric = tensors.Symmetric(np.eye(3))
q = np.array([[1.0, 2.0, 3.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])
q = 0.5 * (q - q.T)
self.skew = tensors.Skew(q)
self.orientation = rotations.Orientation(30.0,
60.0,
80.0,
angle_type="degrees")
self.hist1 = history.History()
self.hist2 = history.History(store=False)
self.add_all(self.hist1)
self.add_all(self.hist2)
self.storage = np.zeros((self.hist2.size, ))
self.hist2.set_data(self.storage)
self.set_all(self.hist1)
self.set_all(self.hist2)
def test_W(self):
for i in range(self.lattice.ngroup):
for j in range(self.lattice.nslip(i)):
self.assertEqual(
tensors.Skew(
np.dot(self.QM,np.dot(np.outer(self.lattice.slip_directions[i][j].data,
self.lattice.slip_planes[i][j].data), self.QM.T))),
self.lattice.N(i,j,self.Q))
def setUp(self): self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]]) self.S = 0.5*(self.S + self.S.T) self.TS = tensors.Symmetric(self.S) self.G = np.array([[10.2,-9.3,2.5],[0.1,3.1,2.8],[0.1,3.2,-6.1]]) self.TG = tensors.RankTwo(self.G) self.W = np.array([[-5.0,7.1,1.0],[-0.2,0.25,1.2],[-0.4,0.4,-2]]) self.W = 0.5*(self.W - self.W.T) self.TW = tensors.Skew(self.W)
def setUp(self):
self.q = rotations.Orientation(30.0, 60.0, 80.0, angle_type = "degrees")
self.Q = self.q.to_matrix()
self.v = np.array([1.2,-2.0,3.0])
self.Tv = tensors.Vector(self.v)
self.A = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.TA = tensors.RankTwo(self.A)
self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.S = 0.5*(self.S + self.S.T)
self.TS = tensors.Symmetric(self.S)
self.W = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.W = 0.5*(self.W - self.W.T)
self.TW = tensors.Skew(self.W)
self.R1 = np.array([[[[ 7.09627147, 9.22330744, -1.36602973],
[-7.86118175, -1.6342633 , -5.75516189],
[ 2.61734248, 6.40678382, 3.37981603]],
[[ 5.65100254, -7.88797059, 7.31396665],
[-6.35471595, 5.67698069, -8.18795178],
[ 9.10447016, 8.91183436, -6.65254333]],
[[ 3.20429862, 2.99308849, 4.0035241 ],
[-4.02440197, -4.39975872, -4.33542791],
[ 9.36746226, -2.91156335, 4.51572032]]],
[[[-9.23675199, 8.63546962, 6.83448027],
[ 4.35044123, 2.24508666, 9.80054664],
[ 0.30835223, -4.05208575, 5.68966326]],
[[ 6.40300092, -8.25998136, 5.63566553],
[-5.02801101, 5.64005224, -7.39586166],
[ 5.90893633, 6.02074669, 1.37112738]],
[[-2.68485216, -4.67660156, 3.52618441],
[-2.52484812, -0.08561168, 3.39072868],
[ 9.11295675, 2.63102786, -4.82285415]]],
[[[ 8.31973154, 4.76081593, 4.38377207],
[ 6.22896742, -3.83995097, 5.37501029],
[-0.16770967, 7.9453854 , -4.95548491]],
[[-5.67884611, -8.44970885, -7.42037867],
[-5.19908193, -7.87006493, 1.65949787],
[-3.25934672, 6.27340198, 5.98643056]],
[[-4.20166968, -2.38276224, 3.04551936],
[ 3.68445989, -5.84357996, 3.61183543],
[ 1.54886677, 3.3659842 , 6.43067337]]]])
self.TR1 = tensors.RankFour(self.R1)
self.SS1 = np.array([
[ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981],
[ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648],
[-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579],
[ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ],
[ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655],
[-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]])
self.SSS1 = ms2ts(self.SS1)
self.TSS1 = tensors.SymSymR4(self.SS1)
def test_w_p(self):
w = tensors.Skew(np.zeros((3, 3)))
for g in range(self.L.ngroup):
for i in range(self.L.nslip(g)):
w += self.slipmodel.slip(g, i, self.S, self.Q, self.H, self.L,
self.T, self.fixed) * self.L.N(
g, i, self.Q)
self.assertEqual(
w,
self.model.w_p(self.S, self.Q, self.H, self.L, self.T, self.fixed))
def setUp(self):
self.scalar = 2.5
self.vector = tensors.Vector(np.array([1.0, 2.0, 3.0]))
self.ranktwo = tensors.RankTwo(
np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]))
self.symmetric = tensors.Symmetric(np.eye(3))
q = np.array([[1.0, 2.0, 3.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]])
q = 0.5 * (q - q.T)
self.skew = tensors.Skew(q)
self.hist = history.History()
self.add_all(self.hist)
self.set_all(self.hist)
def test_correctly_integrates(self):
# So we are rotating about x where t is the rotation in radians
R = lambda t: np.array([[1.0,0,0],[0,np.cos(t),-np.sin(t)],[0,np.sin(t), np.cos(t)]])
q0 = rotations.Orientation(R(0.0))
spin = tensors.Skew(np.array([
[0,0,0],
[0,0,-1.0],
[0,1.0,0]]))
nsteps = 1000 # Well it's not the most accurate integration
ang = np.pi/4.0
qf = rotations.Orientation(R(ang))
q = q0
for i in range(nsteps):
q = rotations.wexp(spin * ang/nsteps) * q
self.assertTrue(np.allclose(q.quat, qf.quat))
def setUp(self):
self.tau0 = 10.0
self.tau_sat = 50.0
self.b = 2.5
self.strengthmodel = slipharden.VoceSlipHardening(
self.tau_sat, self.b, self.tau0)
self.g0 = 1.0
self.n = 3.0
self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel,
self.g0, self.n)
self.imodel = inelasticity.AsaroInelasticity(self.slipmodel)
self.L = crystallography.CubicLattice(1.0)
self.L.add_slip_system([1, 1, 0], [1, 1, 1])
self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees")
self.mu = 29000.0
self.E = 120000.0
self.nu = 0.3
self.emodel = elasticity.CubicLinearElasticModel(
self.E, self.nu, self.mu, "moduli")
self.kmodel = kinematics.StandardKinematicModel(
self.emodel, self.imodel)
self.model = singlecrystal.SingleCrystalModel(self.kmodel,
self.L,
initial_rotation=self.Q)
self.model_no_rot = singlecrystal.SingleCrystalModel(
self.kmodel,
self.L,
initial_rotation=self.Q,
update_rotation=False,
verbose=False)
self.T = 300.0
self.stress_n = np.array([120.0, -60.0, 170.0, 35.0, 80.0, -90.0])
self.stress_np1 = np.array([15.0, -40.0, 120.0, 70.0, -10.0, -50.0])
self.d = np.array([0.1, -0.2, 0.25, 0.11, -0.05, 0.075])
self.w = np.array([0.1, 0.2, -0.2])
self.strength_n = 25.0
self.strength_np1 = 30.0
self.S_np1 = tensors.Symmetric(common.usym(self.stress_np1))
self.S_n = tensors.Symmetric(common.usym(self.stress_n))
self.D = tensors.Symmetric(common.usym(self.d))
self.W = tensors.Skew(common.uskew(self.w))
self.strength_n = 25.0
self.strength_np1 = 30.0
self.H_n = history.History()
self.H_n.add_scalar("strength")
self.H_n.set_scalar("strength", self.strength_n)
self.H_np1 = history.History()
self.H_np1.add_scalar("strength")
self.H_np1.set_scalar("strength", self.strength_np1)
self.dt = 2.0
self.fixed = self.kmodel.decouple(self.S_n, self.D, self.W, self.Q,
self.H_n, self.L, self.T,
history.History())
self.ts = singlecrystal.SCTrialState(self.D, self.W, self.S_n,
self.H_n, self.Q, self.L, self.T,
self.dt, self.fixed)
self.x = np.zeros((self.model.nparams, ))
self.x[:6] = self.stress_np1
self.x[6] = self.strength_np1
self.Ddir = np.array([0.01, -0.005, -0.003, 0.01, 0.02, -0.003]) * 2
self.Wdir = np.array([0.02, -0.03, 0.01]) * 2
self.nsteps = 10
def setUp(self):
self.q = rotations.Orientation(30.0, 60.0, 80.0, angle_type = "degrees")
self.W = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.W = 0.5*(self.W - self.W.T)
self.TW = tensors.Skew(self.W)
def test_apply_skew(self):
self.assertEqual(self.q.apply(self.TW),
tensors.Skew(np.dot(self.Q, np.dot(self.W, self.Q.T))))
def setUp(self):
self.L = crystallography.CubicLattice(1.0)
self.L.add_slip_system([1, 1, 0], [1, 1, 1])
self.nslip = self.L.ntotal
self.strength = 35.0
self.c = 10.0
self.beta = 2.0
self.H = history.History()
for i in range(12):
self.H.add_scalar("strength" + str(i))
self.H.set_scalar("strength" + str(i), self.strength)
for j in range(4):
self.H.add_scalar("slip_damage_" + str(j))
self.H.set_scalar("slip_damage_" + str(j), self.c * 0.4)
self.static = 20.0
self.s0 = [self.static] * self.nslip
self.k = 1000.0
self.sat = 40.0
self.m = 1.5
self.strengthmodel = slipharden.VocePerSystemHardening(
self.s0, [self.k] * self.nslip, [self.sat] * self.nslip,
[self.m] * self.nslip)
self.g0 = 1.0
self.n = 3.0
self.slipmodel = sliprules.PowerLawSlipRule(self.strengthmodel,
self.g0, self.n)
self.imodel = inelasticity.AsaroInelasticity(self.slipmodel)
self.Q = rotations.Orientation(35.0, 17.0, 14.0, angle_type="degrees")
self.S = tensors.Symmetric(
np.array([[100.0, -25.0, 10.0], [-25.0, -17.0, 15.0],
[10.0, 15.0, 35.0]]))
self.T = 300.0
self.mu = 29000.0
self.E = 120000.0
self.nu = 0.3
self.emodel = elasticity.CubicLinearElasticModel(
self.E, self.nu, self.mu, "moduli")
self.dn = np.array([[4.1, 2.8, -1.2], [3.1, 7.1, 0.2], [4, 2, 3]])
self.dn = 0.5 * (self.dn + self.dn.T)
self.d = tensors.Symmetric(self.dn)
self.wn = np.array([[-9.36416517, 2.95527444, 8.70983194],
[-1.54693052, 8.7905658, -5.10895168],
[-8.52740468, -0.7741642, 2.89544992]])
self.wn = 0.5 * (self.wn - self.wn.T)
self.w = tensors.Skew(self.wn)
self.dmodel = crystaldamage.WorkPlaneDamage()
self.nfunc = crystaldamage.SigmoidTransformation(self.c, self.beta)
self.sfunc = crystaldamage.SigmoidTransformation(self.c, self.beta)
self.dmodel = crystaldamage.PlanarDamageModel(self.dmodel, self.nfunc,
self.sfunc, self.L)
self.model = kinematics.DamagedStandardKinematicModel(
self.emodel, self.imodel, self.dmodel)
self.fspin = self.model.spin(self.S, self.d, self.w, self.Q, self.H,
self.L, self.T, history.History())
self.fixed = self.model.decouple(self.S, self.d, self.w, self.Q,
self.H, self.L, self.T,
history.History())
def test_add(self): self.assertEqual(tensors.Skew(self.A + self.B), self.TA + self.TB) self.assertEqual(tensors.Skew(self.A - self.B), self.TA - self.TB)
def diff_history_skew(fn, w0):
dfn = lambda w: np.array(fn(tensors.Skew(uskew(w))))
return differentiate(dfn, w0.data)
def diff_symmetric_skew(fn, w0):
dfn = lambda w: fn(tensors.Skew(uskew(w))).data
return tensors.SymSkewR4(differentiate(dfn, w0.data))
def test_transpose(self): self.assertEqual(tensors.Skew(self.A.T), self.TA.transpose())
def test_matrix_matrix(self): self.assertEqual(tensors.Skew(np.dot(self.A, self.B)), self.TA*self.TB)
def test_w_p(self):
self.assertEqual(
tensors.Skew(np.zeros((3, 3))),
self.model.w_p(self.S, self.Q, self.H, self.L, self.T, self.fixed))
def setUp(self):
self.WS1 = np.array([
[-8.3567359 , -5.39728818, -8.00844442, -8.33365112, -0.97903364, -8.23943149],
[-6.97125417, 4.34802055, 7.06281056, -1.57511617, 7.83359933, -9.37625432],
[-6.0799489 , -6.0309543 , 3.68575895, 8.84296976, 6.55799427, -9.22029379]])
self.WS1_full = common.wws2ts(self.WS1)
self.TWS1 = tensors.SkewSymR4(self.WS1)
self.WS2 = np.array([
[-8.80662663, 0.46179936, -5.49454144, 7.91618428, 5.34053953, -6.68997405],
[ 4.15874971, -4.59781751, 7.43746813, 8.99981425, -0.97692573, 2.5075246 ],
[ 9.53201007, -8.03524224, 0.94329443, -6.44415877, -9.92911741, 3.51742689]])
self.WS2_full = common.wws2ts(self.WS2)
self.TWS2 = tensors.SkewSymR4(self.WS2)
self.SW = np.array([
[ 5.43434005, -6.55983214, 0.29737664],
[-4.77472172, -8.51287287, -3.19380185],
[ 4.43407952, -6.02555614, 5.87786914],
[ 1.89488869, -5.65383917, 8.83717547],
[-7.18030867, 1.56100537, -9.83238641],
[-4.52369317, -3.07284914, -7.54966999]])
self.SW_full = common.ws2ts(self.SW)
self.TSW = tensors.SymSkewR4(self.SW)
self.SS = np.array([
[ 5.99159801, -2.24342348, 0.26667281, -0.95466199, 3.98931478, -0.10846981],
[ 1.86468226, -4.32391908, -7.82738638, -7.45008989, 5.89874777, 0.45820648],
[-5.92565398, 2.4862829 , -6.02112389, 6.75455965, 4.65183463, 9.96900579],
[ 0.60378883, -3.72189328, -7.63388446, -5.76559403, -0.3119789 , -1.1527258 ],
[ 4.56813135, -6.06783828, -6.18341368, 8.06169686, -9.56928844, 9.08114655],
[-8.25516614, 6.30663846, 7.2084381 , -7.38280703, -5.96279902, 8.9935982 ]])
self.SS_full = common.ms2ts(self.SS)
self.TSS = tensors.SymSymR4(self.SS)
self.R = np.array([[[[-8.03675620e+00, 2.58575052e+00, 2.44069661e+00],
[ 4.75021663e+00, 1.24463394e+00, -8.69751301e-01],
[-1.46310894e+00, -1.15053235e+00, -3.75342982e+00]],
[[-7.64033956e+00, 4.19956720e+00, -4.87644982e+00],
[ 1.06577507e+00, 8.94272637e+00, 6.57264250e-01],
[-4.22613258e+00, -5.08830314e+00, 1.57718186e+00]],
[[-4.02243082e+00, -4.75463781e+00, -8.88662152e+00],
[-1.30383950e+00, -1.98063574e+00, -3.18963544e+00],
[-7.52071674e+00, 1.08931933e+00, 2.86988431e+00]]],
[[[ 5.28621060e+00, -6.83799668e+00, 8.98005935e+00],
[-7.92741122e+00, 5.75699425e-01, 1.66782544e+00],
[ 2.60041984e+00, -1.04476986e-02, -6.12424787e+00]],
[[-3.73727368e+00, 6.59764771e+00, -1.18045587e+00],
[ 4.08567441e+00, 2.66148943e+00, -6.82495588e-01],
[-1.64417262e+00, 5.33119298e+00, 8.11045988e-03]],
[[-5.90193883e+00, -2.63316107e+00, 5.61381825e+00],
[-6.08591194e+00, 8.77285539e+00, -7.15230533e+00],
[ 3.15093096e+00, 1.41350149e+00, 1.11702016e+00]]],
[[[-9.61472764e-01, -1.91492497e+00, 9.48275324e+00],
[ 6.68841134e+00, 3.23412041e+00, -3.41944541e+00],
[-9.80203467e+00, 6.58425335e+00, -2.16548636e+00]],
[[ 6.63950740e+00, 3.91551441e+00, -8.98229111e+00],
[ 9.84606756e+00, -8.16145090e+00, 8.41929062e-01],
[-1.93839620e+00, 7.44485127e+00, -2.70832414e+00]],
[[ 9.79265531e+00, -1.18212395e+00, -5.39433704e+00],
[ 4.87152614e+00, 9.47287450e+00, 5.53838514e+00],
[ 9.30443367e+00, 1.27090319e+00, 1.60409739e+00]]]])
self.TR = tensors.RankFour(self.R)
self.S = np.array([[4.1,2.8,-1.2],[3.1,7.1,0.2],[4,2,3]])
self.S = 0.5*(self.S + self.S.T)
self.TS = tensors.Symmetric(self.S)
self.scalar = 5.2
self.G = np.array([[ 9.50640677, 1.79084726, -2.8877036 ],
[-1.63159958, 2.52866904, -8.71585042],
[ 5.01859685, -8.7324075 , -0.42919134]])
self.TG = tensors.RankTwo(self.G)
self.W = np.array([[-9.36416517, 2.95527444, 8.70983194],
[-1.54693052, 8.7905658 , -5.10895168],
[-8.52740468, -0.7741642 , 2.89544992]])
self.W = 0.5 * (self.W - self.W.T)
self.TW = tensors.Skew(self.W)
def test_scalar_mult(self): self.assertEqual(tensors.Skew(self.s*self.A), self.s * self.TA) self.assertEqual(tensors.Skew(self.A / self.s), self.TA / self.s)
