def test_Derivative__new__():
raises(TypeError, lambda: f(x).diff((x, 2), 0))
assert f(x, y).diff([(x, y), 0]) == f(x, y)
assert f(x, y).diff([(x, y), 1]) == NDimArray([
Derivative(f(x, y), x), Derivative(f(x, y), y)])
assert f(x,y).diff(y, (x, z), y, x) == Derivative(
f(x, y), (x, z + 1), (y, 2))
assert Matrix([x]).diff(x, 2) == Matrix([0]) # is_zero exit
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 = NDimArray.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]
]]]])
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 = NDimArray.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]]]]])
