def symbol_eqtn_fx2y2(n, x2_neg=False, shape=None):
y2eq, vy = symbol_eqtn_fy2(n, x2_neg=x2_neg)[1:]
y2eq = y2eq.tolist()
for iv in range(n):
y2eq[iv] = y2eq[iv].subs([(vy["tau1"][iv], 1.0), (vy["tau2"][iv], 1.0), (vy["y2"][iv], 0.0)])
fx2, v = symbol_eqtn_fx2(n, Iext2="Iext2")[1:]
fx2 = fx2.tolist()
v.update(vy)
del vy
for iv in range(n):
fx2[iv] = fx2[iv].subs(v["y2"][iv], y2eq[iv])
fx2 = Array(fx2)
if shape is not None:
if len(shape) > 1:
fx2 = fx2.reshape(shape[0], shape[1])
else:
fx2 = fx2.reshape(shape[0], )
return lambdify([v["x2"], v["z"], v["g"], v["Iext2"], v["s"], v["tau1"]], fx2, 'numpy'), fx2, v
def symbol_calc_fx1y1_6d_diff_x1(n, shape=None):
fx1, v = symbol_eqtn_fx1(n, model="6d", x1_neg=True, slope="slope", Iext1="Iext1", shape=None)[1:]
fx1 = fx1.tolist()
fy1, vy = symbol_eqtn_fy1(n, shape=None)[1:]
fy1 = fy1.tolist()
v.update(vy)
del vy
dfx1 = []
for ix in range(n):
fy1[ix] = fy1[ix].subs(v["y1"][ix], 0.0).subs(v["tau1"][ix], 1.0)
fx1[ix] = fx1[ix].subs(v["y1"][ix], fy1[ix])
dfx1.append(fx1[ix].diff(v["x1"][ix]))
dfx1 = Array(dfx1)
if shape is not None:
if len(shape) > 1:
dfx1 = dfx1.reshape(shape[0], shape[1])
else:
dfx1 = dfx1.reshape(shape[0], )
return lambdify([v["x1"], v["yc"], v["Iext1"], v["a"], v["b"], v["d"], v["tau1"]], dfx1, "numpy"), dfx1, v
def symbol_calc_2d_taylor(n,
x_taylor="x1lin",
order=2,
x1_neg=True,
slope="slope",
Iext1="Iext1",
shape=None):
fx1ser, v = symbol_eqtn_fx1(n,
model="2d",
x1_neg=x1_neg,
slope=slope,
Iext1=Iext1)[1:]
fx1ser = fx1ser.tolist()
x_taylor = symbol_vars(n, [x_taylor])[0]
v.update({"x_taylor": x_taylor})
for ix in range(shape_to_size(v["x1"].shape)):
fx1ser[ix] = series(fx1ser[ix],
x=v["x1"][ix],
x0=x_taylor[ix],
n=order).removeO() #
fx1ser = Array(fx1ser)
if shape is not None:
if len(shape) > 1:
fx1ser = fx1ser.reshape(shape[0], shape[1])
else:
fx1ser = fx1ser.reshape(shape[0], )
return lambdify([
v["x1"], x_taylor, v["z"], v["y1"], v[Iext1], v[slope], v["a"], v["b"],
v["d"], v["tau1"]
], fx1ser, "numpy"), fx1ser, v
def symbol_calc_x0cr_r(n, zmode=array("lin"), shape=None):
# Define the z equilibrium expression...
# if epileptor_model == "2d":
zeq, vx = symbol_eqtn_fx1(n, model="2d", x1_neg=True, slope="slope", Iext1="Iext1")[1:]
zeq = zeq.tolist()
for iv in range(n):
zeq[iv] = zeq[iv].subs([(vx["z"][iv], 0.0), (vx["tau1"][iv], 1.0)])
# else:
# zeq = calc_fx1(x1eq, z=0.0, y1=y1=calc_fy1(x1eq, y11), Iext1=I1, model="6d", x1_neg=True,
# shape=Iext1.shape).tolist()
# Define the fz expression...
# fz = calc_fz(x1eq, z=zeq, x0=x0, x0cr=x0cr, r=r, zmode=zmode, z_pos=True, model="2d", shape=Iext1.shape).tolist()
fz, v = symbol_eqtn_fz(n, zmode, z_pos=True, model="2d", x0="x0", K="K")[1:]
fz = fz.tolist()
for iv in range(n):
fz[iv] = fz[iv].subs([(v['K'][iv], 0.0), (v["tau1"][iv], 1.0), (v["tau0"][iv], 1.0), (v["z"][iv], zeq[iv])])
v.update(vx)
del vx
x1_rest, x1_cr, x0_rest, x0_cr, vv = symbol_vars(len(zeq), ["x1_rest", "x1_cr", "x0_rest", "x0_cr"],
shape=v["x1"].shape)
v.update(vv)
del vv
# solve the fz expression for rx0 and x0cr, assuming the following two points (x1eq,x0) = [(-5/3,0.0),(-4/3,1.0)]...
# ...and WITHOUT COUPLING
x0cr = []
r = []
for iv in range(n):
fz_sol = solve([fz[iv].subs([(v["x1"][iv], x1_rest[iv]), (v["x0"][iv], x0_rest[iv]),
(zeq[iv], zeq[iv].subs(v["x1"][iv], x1_rest[iv]))]),
fz[iv].subs([(v["x1"][iv], x1_cr[iv]), (v["x0"][iv], x0_cr[iv]),
(zeq[iv], zeq[iv].subs(v["x1"][iv], x1_cr[iv]))])],
v["x0cr"][iv], v["r"][iv])
x0cr.append(fz_sol[v["x0cr"][iv]])
r.append(fz_sol[v["r"][iv]])
# Convert the solution of x0cr from expression to function that accepts numpy arrays as inputs:
x0cr = Array(x0cr)
r = Array(r)
if shape is not None:
if len(shape) > 1:
x0cr = x0cr.reshape(shape[0], shape[1])
r = r.reshape(shape[0], shape[1])
else:
x0cr = x0cr.reshape(shape[0], )
r = r.reshape(shape[0], )
return (lambdify([v["y1"], v["Iext1"], v["a"], v["b"], v["x1_rest"], v["x1_cr"], v["x0_rest"], v["x0_cr"]],
x0cr, 'numpy'),
lambdify([v["y1"], v["Iext1"], v["a"], v["b"], v["x1_rest"], v["x1_cr"], v["x0_rest"], v["x0_cr"]],
r, 'numpy')), \
(x0cr, r), v
def symbol_eqtn_fx1z(n, model="6d", zmode=array("lin"), shape=None): #x1_neg=True, z_pos=True,
# TODO: for the extreme z_pos = False case where we have terms like 0.1 * z ** 7
# TODO: for the extreme x1_neg = False case where we have to solve for x2 as well
fx1, v = symbol_eqtn_fx1(n, model, x1_neg=True, slope="slope", Iext1="Iext1")[1:]
fx1 = fx1.tolist()
fz, vz = symbol_eqtn_fz(n, zmode, True, model, x0="x0", K="K")[1:]
fz = fz.tolist()
v.update(vz)
del vz
if model != "2d":
y1eq, vy = symbol_eqtn_fy1(n)[1:]
y1eq = y1eq.tolist()
for iv in range(n):
y1eq[iv] = y1eq[iv].subs([(vy["tau1"][iv], 1.0), (vy["y1"][iv], 0.0)])
v.update(vy)
del vy
z = []
for iv in range(n):
z.append(fx1[iv].subs([(v["tau1"][iv], 1.0), (v["y1"][iv], y1eq[iv]), (v["z"][iv], 0.0)]))
else:
z = []
for iv in range(n):
z.append(fx1[iv].subs([(v["tau1"][iv], 1.0), (v["z"][iv], 0.0)]))
fx1z = []
for iv in range(n):
fx1z.append(fz[iv].subs([(v["z"][iv], z[iv])]))
# Convert the solution of x0cr from expression to function that accepts numpy arrays as inputs:
fx1z = Array(fx1z)
if shape is not None:
if len(shape) > 1:
fx1z = fx1z.reshape(shape[0], shape[1])
else:
fx1z = fx1z.reshape(shape[0], )
if model == "2d":
fx1z_lambda = lambdify([v["x1"], v["x0"], v["K"], v["w"], v["x0cr"], v["r"], v["y1"], v["Iext1"], v["a"],
v["b"], v["tau1"], v["tau0"]], fx1z, 'numpy')
else:
fx1z_lambda = lambdify([v["x1"], v["x0"], v["K"], v["w"], v["yc"], v["Iext1"], v["a"], v["b"], v["d"],
v["tau1"], v["tau0"]], fx1z, 'numpy')
return fx1z_lambda, fx1z, v
def test_array_permutedims():
sa = symbols('a0:144')
m1 = Array(sa[:6], (2, 3))
assert permutedims(m1, (1, 0)) == transpose(m1)
assert m1.tomatrix().T == permutedims(m1, (1, 0)).tomatrix()
assert m1.tomatrix().T == transpose(m1).tomatrix()
assert m1.tomatrix().C == conjugate(m1).tomatrix()
assert m1.tomatrix().H == adjoint(m1).tomatrix()
assert m1.tomatrix().T == m1.transpose().tomatrix()
assert m1.tomatrix().C == m1.conjugate().tomatrix()
assert m1.tomatrix().H == m1.adjoint().tomatrix()
raises(ValueError, lambda: permutedims(m1, (0,)))
raises(ValueError, lambda: permutedims(m1, (0, 0)))
raises(ValueError, lambda: permutedims(m1, (1, 2, 0)))
# Some tests with random arrays:
dims = 6
shape = [random.randint(1,5) for i in range(dims)]
elems = [random.random() for i in range(tensorproduct(*shape))]
ra = Array(elems, shape)
perm = list(range(dims))
# Randomize the permutation:
random.shuffle(perm)
# Test inverse permutation:
assert permutedims(permutedims(ra, perm), _af_invert(perm)) == ra
# Test that permuted shape corresponds to action by `Permutation`:
assert permutedims(ra, perm).shape == tuple(Permutation(perm)(shape))
z = Array.zeros(4,5,6,7)
assert permutedims(z, (2, 3, 1, 0)).shape == (6, 7, 5, 4)
assert permutedims(z, [2, 3, 1, 0]).shape == (6, 7, 5, 4)
assert permutedims(z, Permutation([2, 3, 1, 0])).shape == (6, 7, 5, 4)
po = Array(sa, [2, 2, 3, 3, 2, 2])
raises(ValueError, lambda: permutedims(po, (1, 1)))
raises(ValueError, lambda: po.transpose())
raises(ValueError, lambda: po.adjoint())
assert permutedims(po, reversed(range(po.rank()))) == Array(
[[[[[[sa[0], sa[72]], [sa[36], sa[108]]], [[sa[12], sa[84]], [sa[48], sa[120]]], [[sa[24],
sa[96]], [sa[60], sa[132]]]],
[[[sa[4], sa[76]], [sa[40], sa[112]]], [[sa[16],
sa[88]], [sa[52], sa[124]]],
[[sa[28], sa[100]], [sa[64], sa[136]]]],
[[[sa[8],
sa[80]], [sa[44], sa[116]]], [[sa[20], sa[92]], [sa[56], sa[128]]], [[sa[32],
sa[104]], [sa[68], sa[140]]]]],
[[[[sa[2], sa[74]], [sa[38], sa[110]]], [[sa[14],
sa[86]], [sa[50], sa[122]]], [[sa[26], sa[98]], [sa[62], sa[134]]]],
[[[sa[6],
sa[78]], [sa[42], sa[114]]], [[sa[18], sa[90]], [sa[54], sa[126]]], [[sa[30],
sa[102]], [sa[66], sa[138]]]],
[[[sa[10], sa[82]], [sa[46], sa[118]]], [[sa[22],
sa[94]], [sa[58], sa[130]]],
[[sa[34], sa[106]], [sa[70], sa[142]]]]]],
[[[[[sa[1],
sa[73]], [sa[37], sa[109]]], [[sa[13], sa[85]], [sa[49], sa[121]]], [[sa[25],
sa[97]], [sa[61], sa[133]]]],
[[[sa[5], sa[77]], [sa[41], sa[113]]], [[sa[17],
sa[89]], [sa[53], sa[125]]],
[[sa[29], sa[101]], [sa[65], sa[137]]]],
[[[sa[9],
sa[81]], [sa[45], sa[117]]], [[sa[21], sa[93]], [sa[57], sa[129]]], [[sa[33],
sa[105]], [sa[69], sa[141]]]]],
[[[[sa[3], sa[75]], [sa[39], sa[111]]], [[sa[15],
sa[87]], [sa[51], sa[123]]], [[sa[27], sa[99]], [sa[63], sa[135]]]],
[[[sa[7],
sa[79]], [sa[43], sa[115]]], [[sa[19], sa[91]], [sa[55], sa[127]]], [[sa[31],
sa[103]], [sa[67], sa[139]]]],
[[[sa[11], sa[83]], [sa[47], sa[119]]], [[sa[23],
sa[95]], [sa[59], sa[131]]],
[[sa[35], sa[107]], [sa[71], sa[143]]]]]]])
assert permutedims(po, (1, 0, 2, 3, 4, 5)) == Array(
[[[[[[sa[0], sa[1]], [sa[2], sa[3]]], [[sa[4], sa[5]], [sa[6], sa[7]]], [[sa[8], sa[9]], [sa[10],
sa[11]]]],
[[[sa[12], sa[13]], [sa[14], sa[15]]], [[sa[16], sa[17]], [sa[18],
sa[19]]], [[sa[20], sa[21]], [sa[22], sa[23]]]],
[[[sa[24], sa[25]], [sa[26],
sa[27]]], [[sa[28], sa[29]], [sa[30], sa[31]]], [[sa[32], sa[33]], [sa[34],
sa[35]]]]],
[[[[sa[72], sa[73]], [sa[74], sa[75]]], [[sa[76], sa[77]], [sa[78],
sa[79]]], [[sa[80], sa[81]], [sa[82], sa[83]]]],
[[[sa[84], sa[85]], [sa[86],
sa[87]]], [[sa[88], sa[89]], [sa[90], sa[91]]], [[sa[92], sa[93]], [sa[94],
sa[95]]]],
[[[sa[96], sa[97]], [sa[98], sa[99]]], [[sa[100], sa[101]], [sa[102],
sa[103]]],
[[sa[104], sa[105]], [sa[106], sa[107]]]]]], [[[[[sa[36], sa[37]], [sa[38],
sa[39]]],
[[sa[40], sa[41]], [sa[42], sa[43]]],
[[sa[44], sa[45]], [sa[46],
sa[47]]]],
[[[sa[48], sa[49]], [sa[50], sa[51]]],
[[sa[52], sa[53]], [sa[54],
sa[55]]],
[[sa[56], sa[57]], [sa[58], sa[59]]]],
[[[sa[60], sa[61]], [sa[62],
sa[63]]],
[[sa[64], sa[65]], [sa[66], sa[67]]],
[[sa[68], sa[69]], [sa[70],
sa[71]]]]], [
[[[sa[108], sa[109]], [sa[110], sa[111]]],
[[sa[112], sa[113]], [sa[114],
sa[115]]],
[[sa[116], sa[117]], [sa[118], sa[119]]]],
[[[sa[120], sa[121]], [sa[122],
sa[123]]],
[[sa[124], sa[125]], [sa[126], sa[127]]],
[[sa[128], sa[129]], [sa[130],
sa[131]]]],
[[[sa[132], sa[133]], [sa[134], sa[135]]],
[[sa[136], sa[137]], [sa[138],
sa[139]]],
[[sa[140], sa[141]], [sa[142], sa[143]]]]]]])
assert permutedims(po, (0, 2, 1, 4, 3, 5)) == Array(
[[[[[[sa[0], sa[1]], [sa[4], sa[5]], [sa[8], sa[9]]], [[sa[2], sa[3]], [sa[6], sa[7]], [sa[10],
sa[11]]]],
[[[sa[36], sa[37]], [sa[40], sa[41]], [sa[44], sa[45]]], [[sa[38],
sa[39]], [sa[42], sa[43]], [sa[46], sa[47]]]]],
[[[[sa[12], sa[13]], [sa[16],
sa[17]], [sa[20], sa[21]]], [[sa[14], sa[15]], [sa[18], sa[19]], [sa[22],
sa[23]]]],
[[[sa[48], sa[49]], [sa[52], sa[53]], [sa[56], sa[57]]], [[sa[50],
sa[51]], [sa[54], sa[55]], [sa[58], sa[59]]]]],
[[[[sa[24], sa[25]], [sa[28],
sa[29]], [sa[32], sa[33]]], [[sa[26], sa[27]], [sa[30], sa[31]], [sa[34],
sa[35]]]],
[[[sa[60], sa[61]], [sa[64], sa[65]], [sa[68], sa[69]]], [[sa[62],
sa[63]], [sa[66], sa[67]], [sa[70], sa[71]]]]]],
[[[[[sa[72], sa[73]], [sa[76],
sa[77]], [sa[80], sa[81]]], [[sa[74], sa[75]], [sa[78], sa[79]], [sa[82],
sa[83]]]],
[[[sa[108], sa[109]], [sa[112], sa[113]], [sa[116], sa[117]]], [[sa[110],
sa[111]], [sa[114], sa[115]],
[sa[118], sa[119]]]]],
[[[[sa[84], sa[85]], [sa[88],
sa[89]], [sa[92], sa[93]]], [[sa[86], sa[87]], [sa[90], sa[91]], [sa[94],
sa[95]]]],
[[[sa[120], sa[121]], [sa[124], sa[125]], [sa[128], sa[129]]], [[sa[122],
sa[123]], [sa[126], sa[127]],
[sa[130], sa[131]]]]],
[[[[sa[96], sa[97]], [sa[100],
sa[101]], [sa[104], sa[105]]], [[sa[98], sa[99]], [sa[102], sa[103]], [sa[106],
sa[107]]]],
[[[sa[132], sa[133]], [sa[136], sa[137]], [sa[140], sa[141]]], [[sa[134],
sa[135]], [sa[138], sa[139]],
[sa[142], sa[143]]]]]]])
po2 = po.reshape(4, 9, 2, 2)
assert po2 == Array([[[[sa[0], sa[1]], [sa[2], sa[3]]], [[sa[4], sa[5]], [sa[6], sa[7]]], [[sa[8], sa[9]], [sa[10], sa[11]]], [[sa[12], sa[13]], [sa[14], sa[15]]], [[sa[16], sa[17]], [sa[18], sa[19]]], [[sa[20], sa[21]], [sa[22], sa[23]]], [[sa[24], sa[25]], [sa[26], sa[27]]], [[sa[28], sa[29]], [sa[30], sa[31]]], [[sa[32], sa[33]], [sa[34], sa[35]]]], [[[sa[36], sa[37]], [sa[38], sa[39]]], [[sa[40], sa[41]], [sa[42], sa[43]]], [[sa[44], sa[45]], [sa[46], sa[47]]], [[sa[48], sa[49]], [sa[50], sa[51]]], [[sa[52], sa[53]], [sa[54], sa[55]]], [[sa[56], sa[57]], [sa[58], sa[59]]], [[sa[60], sa[61]], [sa[62], sa[63]]], [[sa[64], sa[65]], [sa[66], sa[67]]], [[sa[68], sa[69]], [sa[70], sa[71]]]], [[[sa[72], sa[73]], [sa[74], sa[75]]], [[sa[76], sa[77]], [sa[78], sa[79]]], [[sa[80], sa[81]], [sa[82], sa[83]]], [[sa[84], sa[85]], [sa[86], sa[87]]], [[sa[88], sa[89]], [sa[90], sa[91]]], [[sa[92], sa[93]], [sa[94], sa[95]]], [[sa[96], sa[97]], [sa[98], sa[99]]], [[sa[100], sa[101]], [sa[102], sa[103]]], [[sa[104], sa[105]], [sa[106], sa[107]]]], [[[sa[108], sa[109]], [sa[110], sa[111]]], [[sa[112], sa[113]], [sa[114], sa[115]]], [[sa[116], sa[117]], [sa[118], sa[119]]], [[sa[120], sa[121]], [sa[122], sa[123]]], [[sa[124], sa[125]], [sa[126], sa[127]]], [[sa[128], sa[129]], [sa[130], sa[131]]], [[sa[132], sa[133]], [sa[134], sa[135]]], [[sa[136], sa[137]], [sa[138], sa[139]]], [[sa[140], sa[141]], [sa[142], sa[143]]]]])
assert permutedims(po2, (3, 2, 0, 1)) == Array([[[[sa[0], sa[4], sa[8], sa[12], sa[16], sa[20], sa[24], sa[28], sa[32]], [sa[36], sa[40], sa[44], sa[48], sa[52], sa[56], sa[60], sa[64], sa[68]], [sa[72], sa[76], sa[80], sa[84], sa[88], sa[92], sa[96], sa[100], sa[104]], [sa[108], sa[112], sa[116], sa[120], sa[124], sa[128], sa[132], sa[136], sa[140]]], [[sa[2], sa[6], sa[10], sa[14], sa[18], sa[22], sa[26], sa[30], sa[34]], [sa[38], sa[42], sa[46], sa[50], sa[54], sa[58], sa[62], sa[66], sa[70]], [sa[74], sa[78], sa[82], sa[86], sa[90], sa[94], sa[98], sa[102], sa[106]], [sa[110], sa[114], sa[118], sa[122], sa[126], sa[130], sa[134], sa[138], sa[142]]]], [[[sa[1], sa[5], sa[9], sa[13], sa[17], sa[21], sa[25], sa[29], sa[33]], [sa[37], sa[41], sa[45], sa[49], sa[53], sa[57], sa[61], sa[65], sa[69]], [sa[73], sa[77], sa[81], sa[85], sa[89], sa[93], sa[97], sa[101], sa[105]], [sa[109], sa[113], sa[117], sa[121], sa[125], sa[129], sa[133], sa[137], sa[141]]], [[sa[3], sa[7], sa[11], sa[15], sa[19], sa[23], sa[27], sa[31], sa[35]], [sa[39], sa[43], sa[47], sa[51], sa[55], sa[59], sa[63], sa[67], sa[71]], [sa[75], sa[79], sa[83], sa[87], sa[91], sa[95], sa[99], sa[103], sa[107]], [sa[111], sa[115], sa[119], sa[123], sa[127], sa[131], sa[135], sa[139], sa[143]]]]])