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_symskewsym_skewsymsym(self):
A1 = tensors.SymSkewR4Sym_SkewSymR4SymR4(self.TWS, self.TS)
A2_ten = np.einsum('km,mlst', self.S, self.WS_full) - np.einsum('kmst,ml',
self.WS_full, self.S)
A2 = tensors.SymSymR4(common.ts2ms(A2_ten))
self.assertEqual(A1, A2)
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_tensor_S(self): ST = self.model.S_tensor(self.T) S = self.model.S(self.T) self.assertEqual(ST, tensors.SymSymR4(S))
def test_tensor_C(self): CT = self.model.C_tensor(self.T) C = self.model.C(self.T) self.assertEqual(CT, tensors.SymSymR4(C))
def test_id_dev(self): ot = np.zeros((6,6)) ot[:3,:3] = 1.0/3.0 id_t = tensors.SymSymR4(np.eye(6) - ot) self.assertEqual(id_t, tensors.SymSymR4.id_dev())
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_douter(self):
self.assertEqual(tensors.SymSymR4(common.ts2ms(np.einsum('ij,kl', self.S, self.S2))), tensors.douter(self.TS, self.TS2))
def test_id(self): id_t = tensors.SymSymR4(np.eye(6)) self.assertEqual(id_t, tensors.SymSymR4.id())
def test_product_sym_sym(self): self.assertEqual(tensors.SymSymR4(np.dot(self.SS1, self.SS2)), self.TSS1 * self.TSS2)
def test_scalar_mult(self): self.assertEqual(tensors.SymSymR4(self.scalar * self.SS1), self.scalar * self.TSS1) self.assertEqual(tensors.SymSymR4(self.scalar * self.SS2), self.TSS2 * self.scalar) self.assertEqual(tensors.SymSymR4(self.SS1 / self.scalar), self.TSS1 / self.scalar)
def test_negate(self): self.assertEqual(tensors.SymSymR4(-self.SS1), -self.TSS1)
def test_add(self): self.assertEqual(tensors.SymSymR4(self.SS1 + self.SS2), self.TSS2 + self.TSS1) self.assertEqual(tensors.SymSymR4(self.SS1 - self.SS2), self.TSS1 - self.TSS2)
def diff_symmetric_symmetric(fn, s0):
dfn = lambda s: fn(tensors.Symmetric(usym(s))).data
return tensors.SymSymR4(differentiate(dfn, s0.data))