def test_add_mul_mix_3(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x2 = ad.Variable(name="x2", shape=[3])
x3 = ad.Variable(name="x3", shape=[3])
z = x2 * x2 + x2 + x3 + 3
y = ad.sum(z * z + x3)
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = 2 * T.ones(3)
x3_val = 3 * T.ones(3)
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={
x2: x2_val,
x3: x3_val
})
z_val = x2_val * x2_val + x2_val + x3_val + 3
expected_yval = z_val * z_val + x3_val
expected_grad_x2_val = 2 * \
(x2_val * x2_val + x2_val + x3_val + 3) * (2 * x2_val + 1)
expected_grad_x3_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) + 1
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, T.sum(expected_yval))
assert T.array_equal(grad_x2_val, expected_grad_x2_val)
assert T.array_equal(grad_x3_val, expected_grad_x3_val)
def test_einsum_multiuse(backendopt):
"""
Test manual fuse.
A B inputs
|\ |
| \ |
| \ |
| C
| /
| /
output
Note that here we assume A is split into 2 vars by some other operations.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a1", shape=[3, 2])
a_copy = ad.Variable(name="a2", shape=[3, 2])
b = ad.Variable(name="b", shape=[2, 3])
c = ad.einsum('ik,kj->ij', a, b)
output = ad.einsum('ik,ij->kj', a_copy, c)
# New graph
out_new = fuse_einsums(output, [a, a_copy, b])
assert tree_eq(output, out_new, [a, a_copy, b])
def test_einsum_multitier(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
input_nodes1, zs1 = get_tree("set1")
input_nodes2, zs2 = get_tree("set2")
out1 = zs1 + zs2
input_nodes3, zs3 = get_tree("set3")
input_nodes4, zs4 = get_tree("set4")
out2 = zs3 + zs4
out = ad.einsum("ij, jk->ik", out1, out2)
input_nodes = input_nodes1 + input_nodes2 + input_nodes3 + input_nodes4
generated_feed_dict = gen_dict(input_nodes)
executor = ad.Executor([out])
z_val, = executor.run(feed_dict=generated_feed_dict)
with OutputInjectedModeP(find_topo_sort_p([PseudoNode(out)])):
trees = find_sub_einsumtree(PseudoNode(out))
for tree in trees:
out_node, in_nodes = tree
new_z = fuse_einsums(out_node.node, in_nodes)
replace_node(out_node, new_z)
executor = ad.Executor([out])
z_new_val, = executor.run(feed_dict=generated_feed_dict)
assert float_eq(z_val, z_new_val)
def test_tree_distribution_two_layers(dist_op, backendopt):
"""
[Distributive] ((A + B) * G) * C
will produce
AGC + BGC
Note that (A+B) * G is contracted first.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a", shape=[3, 2])
b = ad.Variable(name="b", shape=[3, 2])
g = ad.Variable(name="g", shape=[2, 2])
c = ad.Variable(name="c", shape=[2, 3])
interm = ad.einsum('ik, kk->ik', dist_op(a, b), g)
output = ad.einsum('ik,kj->ij', interm, c)
new_output = distribute_tree(output)
assert isinstance(new_output, dist_op)
assert tree_eq(output, new_output, [a, b, c, g])
def test_prune_identity(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
a1 = ad.Variable(name="a1", shape=[3, 3])
a2 = ad.Variable(name="a2", shape=[3, 3])
i1 = ad.identity(3)
i2 = ad.identity(3)
i3 = ad.identity(3)
out = ad.einsum("ab,cd,ac,be,ef->abdf", a1, a2, i1, i2, i3)
prune_identity_nodes(out)
"""
Explanation to the einsum above:
The identity node i1 means that a and c should be the same dim.
we can get rid of i1 and rewrite the expr as
ad.einsum("ab,ad,be,ef->abdf", a1, a2, i2, i3).
we can also combine i2 and i3 cuz e is useless. Therefore,
we can rewrite the expr as
ad.einsum("ab,ad,bf->abdf", a1, a2, i2).
"""
out_expect = ad.einsum("ab,ad,bf->abdf", a1, a2, i2)
assert len(out.inputs) == 3
assert tree_eq(out, out_expect, [a1, a2])
def test_mul_jacobian_one_scalar(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[2, 2])
# test both cases of left and right multiply a scalar
for y in [x1 * x2, x2 * x1]:
jacobian_x1, jacobian_x2 = ad.jacobians(y, [x1, x2])
executor = ad.Executor([y, jacobian_x1, jacobian_x2])
x1_val = T.tensor(2.)
x2_val = T.tensor([[5., 6.], [7., 8.]])
y_val, jacobian_x1_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
I = T.identity(2)
expected_jacobian_x1_val = T.einsum("ai,bj,ij->ab", I, I, x2_val)
expected_jacobian_x2_val = x1_val * T.einsum("ai,bj->abij", I, I)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_add_jacobian_scalar(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[])
y = x1 + x2
jacobian_x2, = ad.jacobians(y, [x2])
executor = ad.Executor([y, jacobian_x2])
x1_val = T.tensor(1.)
x2_val = T.tensor(1.)
y_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
expected_jacobian_x2_val = T.tensor(1.)
assert isinstance(y, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(y_val, x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_cpd_hessian_optimize_offdiag(backendopt):
dim = 3
for datatype in backendopt:
T.set_backend(datatype)
A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank)
A, B, C = A_list
A_list, input_tensor_val = init_rand_cp(dim, size, rank)
A_val, B_val, C_val = A_list
hessian = ad.hessian(loss, [A, B, C])
hessian_offdiag = [hessian[0][1], hessian[1][0]]
for node in hessian_offdiag:
optimize(node)
assert isinstance(node, ad.AddNode)
num_operations = len(
list(
filter(lambda x: isinstance(x, ad.OpNode),
find_topo_sort([node]))))
# This is currently non-deterministic.
# assert num_operations == 14
executor = ad.Executor(hessian_offdiag)
hes_diag_vals = executor.run(feed_dict={
A: A_val,
B: B_val,
C: C_val,
input_tensor: input_tensor_val,
})
def test_cpd_shared_exec(backendopt):
dim = 3
for datatype in backendopt:
T.set_backend(datatype)
input_val = init_rand_cp(dim, size, rank)
A_list, input_tensor_val = input_val
A_val, B_val, C_val = A_list
outputs = cpd_als_shared_exec(dim, size, rank, 1, input_val)
# expected values
A_val = T.einsum(
"abc,bk,ck->ak", input_tensor_val, B_val, C_val) @ T.inv(
(T.transpose(B_val) @ B_val) * (T.transpose(C_val) @ C_val))
B_val = T.einsum(
"abc,ak,ck->bk", input_tensor_val, A_val, C_val) @ T.inv(
(T.transpose(A_val) @ A_val) * (T.transpose(C_val) @ C_val))
C_val = T.einsum(
"abc,ak,bk->ck", input_tensor_val, A_val, B_val) @ T.inv(
(T.transpose(A_val) @ A_val) * (T.transpose(B_val) @ B_val))
assert T.norm(outputs[0] - A_val) < 1e-8
assert T.norm(outputs[1] - B_val) < 1e-8
assert T.norm(outputs[2] - C_val) < 1e-8
def test_hvp2(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[3, 1])
H = ad.Variable(name="H", shape=[3, 3])
v = ad.Variable(name="v", shape=[3, 1])
y = ad.sum(
ad.einsum("ab,bc->ac", ad.einsum("ab,bc->ac", ad.transpose(x), H),
x))
grad_x, = ad.gradients(y, [x])
Hv, = ad.hvp(output_node=y, node_list=[x], vector_list=[v])
executor = ad.Executor([y, grad_x, Hv])
x_val = T.tensor([[1.], [2.], [3]]) # 3x1
v_val = T.tensor([[1.], [2.], [3]]) # 3x1
H_val = T.tensor([[2., 0., 0.], [0., 2., 0.], [0., 0., 2.]]) # 3x3
y_val, grad_x_val, Hv_val = executor.run(feed_dict={
x: x_val,
H: H_val,
v: v_val
})
expected_yval = T.sum(T.transpose(x_val) @ H_val @ x_val)
expected_grad_x_val = 2 * H_val @ x_val
expected_hv_val = T.tensor([[4.], [8.], [12.]])
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, expected_yval)
assert T.array_equal(grad_x_val, expected_grad_x_val)
assert T.array_equal(Hv_val, expected_hv_val)
def cpd_gradient_descent(size, rank, learning_rate):
dim = 3
for datatype in BACKEND_TYPES:
T.set_backend(datatype)
A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank)
A, B, C = A_list
grad_A, grad_B, grad_C = ad.gradients(loss, [A, B, C])
executor = ad.Executor([loss, grad_A, grad_B, grad_C])
A_list, input_tensor_val = init_rand_cp(dim, size, rank)
A_val, B_val, C_val = A_list
for i in range(100):
loss_val, grad_A_val, grad_B_val, grad_C_val = executor.run(
feed_dict={
input_tensor: input_tensor_val,
A: A_val,
B: B_val,
C: C_val
})
A_val -= learning_rate * grad_A_val
B_val -= learning_rate * grad_B_val
C_val -= learning_rate * grad_C_val
print(f'At iteration {i} the loss is: {loss_val}')
def test_jtjvps(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2])
A = ad.Variable(name="A", shape=[3, 2])
v = ad.Variable(name="v", shape=[2])
y = ad.einsum('ab, b->a', A, x)
jtjvp_x, = ad.jtjvps(y, [x], [v])
executor = ad.Executor([y, jtjvp_x])
x_val = T.tensor([1., 2.])
A_val = T.tensor([[1., 2.], [3., 4.], [5, 6]])
v_val = T.tensor([3., 4.])
y_val, jtjvp_x_val = executor.run(feed_dict={
x: x_val,
A: A_val,
v: v_val
})
expected_yval = T.einsum('ab, b->a', A_val, x_val)
expected_jtjvp_x_val = T.einsum('ba, ac->bc', T.transpose(A_val),
A_val)
expected_jtjvp_x_val = T.einsum('ab, b->a', expected_jtjvp_x_val,
v_val)
assert isinstance(jtjvp_x, ad.Node)
assert T.array_equal(y_val, expected_yval)
assert T.array_equal(jtjvp_x_val, expected_jtjvp_x_val)
def test_vjps(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2])
A = ad.Variable(name="A", shape=[3, 2])
v = ad.Variable(name="v", shape=[3])
y = ad.einsum('ab, b->a', A, x)
transposed_vjp_x, = ad.transposed_vjps(y, [x], v)
executor = ad.Executor([y, transposed_vjp_x])
x_val = T.tensor([1., 2.]) # 1x3
A_val = T.tensor([[1., 2.], [3., 4.], [5, 6]])
v_val = T.tensor([1., 2., 3.])
y_val, transposed_vjp_x_val = executor.run(feed_dict={
x: x_val,
A: A_val,
v: v_val
})
expected_yval = T.einsum('ab, b->a', A_val, x_val)
expected_transposed_vjp_x_val = T.einsum('b, ba->a', v_val, A_val)
assert isinstance(transposed_vjp_x, ad.Node)
assert T.array_equal(y_val, expected_yval)
assert T.array_equal(transposed_vjp_x_val,
expected_transposed_vjp_x_val)
def test_einsum(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x2 = ad.Variable(name="x2", shape=[3, 2])
x3 = ad.Variable(name="x3", shape=[2, 3])
matmul = ad.einsum('ik,kj->ij', x2, x3)
y = ad.sum(matmul)
grad_x2, grad_x3 = ad.gradients(y, [x2, x3])
executor = ad.Executor([y, grad_x2, grad_x3])
x2_val = T.tensor([[1, 2], [3, 4], [5, 6]]) # 3x2
x3_val = T.tensor([[7, 8, 9], [10, 11, 12]]) # 2x3
y_val, grad_x2_val, grad_x3_val = executor.run(feed_dict={
x2: x2_val,
x3: x3_val
})
expected_grad_sum = T.ones_like(T.dot(x2_val, x3_val))
expected_yval = T.sum(T.dot(x2_val, x3_val))
expected_grad_x2_val = T.dot(expected_grad_sum, T.transpose(x3_val))
expected_grad_x3_val = T.dot(T.transpose(x2_val), expected_grad_sum)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, expected_yval)
assert T.array_equal(grad_x2_val, expected_grad_x2_val)
assert T.array_equal(grad_x3_val, expected_grad_x3_val)
def test_three_mul_jacobian(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
x3 = ad.Variable(name="x3", shape=[2, 2])
y = x1 * x2 * x3
jacobian_x1, = ad.jacobians(y, [x1])
executor = ad.Executor([y, jacobian_x1])
x1_val = T.tensor([[1., 2.], [3., 4.]])
x2_val = T.tensor([[5., 6.], [7., 8.]])
x3_val = T.tensor([[9., 10.], [11., 12.]])
y_val, jacobian_x1_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
I = T.identity(2)
expected_jacobian_x1_val = T.einsum("ai,bj,ij,ij->abij", I, I, x2_val,
x3_val)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val * x3_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
def test_s2s_hvp(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[3])
H = ad.Variable(name="H", shape=[3, 3])
v = ad.Variable(name="v", shape=[3])
y = ad.einsum("a,ab,b->", x, H, x)
grad_x, = ad.gradients(y, [x])
Hv, = ad.hvp(output_node=y, node_list=[x], vector_list=[v])
x_val = T.tensor([1., 2., 3.]) # 3
v_val = T.tensor([1., 2., 3.]) # 3
H_val = T.tensor([[2., 0., 0.], [0., 2., 0.], [0., 0., 2.]]) # 3x3
expected_yval = T.einsum("a,ab,b->", x_val, H_val, x_val)
expected_grad_x_val = 2 * T.einsum("ab,b->a", H_val, x_val)
expected_hv_val = T.tensor([4., 8., 12.])
StS = SourceToSource()
forward_str = StS.forward([y], backend=datatype)
m = import_code(forward_str)
y_val_s2s, = m.forward([x_val, H_val])
grad_str = StS.gradients(y, [x], backend=datatype)
m = import_code(grad_str)
grad_x_val_s2s, = m.gradients([x_val, H_val])
hvp_str = StS.hvp(y, [x], [v], backend=datatype)
m = import_code(hvp_str)
Hv_val_s2s, = m.hvp([x_val, H_val, v_val])
assert isinstance(y, ad.Node)
assert T.array_equal(y_val_s2s, expected_yval)
assert T.array_equal(grad_x_val_s2s, expected_grad_x_val)
assert T.array_equal(Hv_val_s2s, expected_hv_val)
def test_three_mul_jacobian_scalars(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[])
x2 = ad.Variable(name="x2", shape=[])
x3 = ad.Variable(name="x3", shape=[])
y = x1 * x2 * x3
jacobian_x1, = ad.jacobians(y, [x1])
executor = ad.Executor([y, jacobian_x1])
x1_val = T.tensor(1.)
x2_val = T.tensor(2.)
x3_val = T.tensor(3.)
y_val, jacobian_x1_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
expected_jacobian_x1_val = x2_val * x3_val
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, x1_val * x2_val * x3_val)
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
def test_s2s_jtjvp(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x = ad.Variable(name="x", shape=[2])
A = ad.Variable(name="A", shape=[3, 2])
v = ad.Variable(name="v", shape=[2])
y = ad.einsum("ab,b->a", A, x)
jtjvp_x, = ad.jtjvps(y, [x], [v])
x_val = T.tensor([1., 2.])
A_val = T.tensor([[1., 2.], [3., 4.], [5, 6]])
v_val = T.tensor([3, 4])
expected_jtjvp_x_val = T.einsum("ba,bc,c->a", A_val, A_val, v_val)
StS = SourceToSource()
forward_str = StS.forward([jtjvp_x],
function_name='jtjvp',
backend=datatype)
m = import_code(forward_str)
jtjvp_x_val_s2s, = m.jtjvp([A_val, v_val])
assert isinstance(jtjvp_x, ad.Node)
assert T.array_equal(jtjvp_x_val_s2s, expected_jtjvp_x_val)
def test_jacobian_einsum(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[3, 3, 3])
x2 = ad.Variable(name="x2", shape=[3, 3, 3])
y = ad.einsum("ikl,jkl->ijk", x1, x2)
jacobian_x1, jacobian_x2 = ad.jacobians(y, [x1, x2])
executor = ad.Executor([y, jacobian_x1, jacobian_x2])
x1_val = T.random((3, 3, 3))
x2_val = T.random((3, 3, 3))
y_val, jacobian_x1_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
})
I = T.identity(3)
expected_jacobian_x1_val = T.einsum("im,kn,jno->ijkmno", I, I, x2_val)
expected_jacobian_x2_val = T.einsum("jm,kn,ino->ijkmno", I, I, x1_val)
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, T.einsum("ikl,jkl->ijk", x1_val, x2_val))
assert T.array_equal(jacobian_x1_val, expected_jacobian_x1_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_dmrg_shared_exec_iterative_solve_one_sweep():
max_mps_rank = 5
num = 7
mpo_rank = 5
size = 5
num_iter = 10
T.set_backend("numpy")
h = qtn.MPO_rand_herm(num, mpo_rank, size)
dmrg_quimb = qtn.DMRG2(h, bond_dims=[max_mps_rank])
h_tensors = load_quimb_tensors(h)
mps_tensors = load_quimb_tensors(dmrg_quimb.state)
# dmrg based on ad
mps_tensors, energy = dmrg_shared_exec_iterative_solve(
h_tensors, mps_tensors, num_iter=num_iter, max_mps_rank=max_mps_rank)
# dmrg based on quimb
opts = {'max_bond': max_mps_rank}
for _ in range(num_iter):
quimb_energy = dmrg_quimb.sweep_right(canonize=True,
verbosity=0,
**opts)
# We only test on energy (lowest eigenvalue of h), rather than the output
# mps (eigenvector), because the eigenvectors can vary a lot while keeping the
# eigenvalue unchanged.
assert (abs(energy - quimb_energy) < 1e-5)
def test_tree_distribution_w_add_output(dist_op, backendopt):
"""
Test C * (A + B) + F * (D + E)
= (C * A + C * B) + (F * D + F * E)
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a", shape=[3, 3])
b = ad.Variable(name="b", shape=[3, 3])
c = ad.Variable(name="c", shape=[3, 3])
d = ad.Variable(name="d", shape=[3, 3])
e = ad.Variable(name="e", shape=[3, 3])
f = ad.Variable(name="f", shape=[3, 3])
out1 = ad.einsum('ik,kj->ij', c, dist_op(a, b))
out2 = ad.einsum('ik,kj->ij', d, dist_op(e, f))
output = dist_op(out1, out2)
new_output = distribute_tree(output)
assert isinstance(new_output, dist_op)
for input_node in new_output.inputs:
assert isinstance(input_node, dist_op)
assert tree_eq(output, new_output, [a, b, c, d, e, f])
def test_executor_dependent(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
A = ad.Variable(name="A", shape=[3, 3])
B = ad.Variable(name="B", shape=[3, 3])
AA = ad.einsum('ab,ab->', A, A)
BB = ad.einsum('ab,ab->', B, B)
AB = ad.einsum('ab,ab->', A, B)
out_A = AA + AB
out_B = AB + AA
executor = ad.Executor({out_A, out_B})
data = gen_dict([A, B])
A_val, = executor.run(feed_dict=data,
reset_graph=False,
out_nodes=[out_A])
data2 = gen_dict([A])
data2.update({B: data[B]})
B_val, = executor.run(feed_dict=data2, out_nodes=[out_B])
# This is checking A's val is not reused in B_val computationA.
assert A_val != B_val
def test_tree_distribution_ppE(dist_op, backendopt):
"""
[Distributive] ((A + B) + C) * G
will produce
AG + BG + CG
Note that (A+B) has parent (A + B) + C.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a", shape=[3, 2])
b = ad.Variable(name="b", shape=[3, 2])
c = ad.Variable(name="c", shape=[3, 2])
g = ad.Variable(name="g", shape=[2, 2])
output = ad.einsum('ik,kk->ik', dist_op(dist_op(a, b), c), g)
new_output = distribute_tree(output)
assert isinstance(new_output, dist_op)
assert tree_eq(output, new_output, [a, b, c, g])
def test_tucker_als_shared_exec(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
input_val = init_rand_tucker(dim, size, rank)
A_val_list, _, X_val = input_val
A_val_list_ad, core_val_ad, _ = tucker_als_shared_exec(
dim, size, rank, 1, input_val)
A1_val, A2_val, A3_val = A_val_list
# expected values
# ttmc: tensor times matrix chain
ttmc = T.einsum("abc,bk,cl->akl", X_val, A2_val, A3_val)
ttmc_inner = T.einsum("akl,bkl->ab", ttmc, ttmc)
mat, _, _ = T.svd(ttmc_inner)
A1_val = mat[:, :rank]
ttmc = T.einsum("abc,ak,cl->kbl", X_val, A1_val, A3_val)
ttmc_inner = T.einsum("kbl,kcl->bc", ttmc, ttmc)
mat, _, _ = T.svd(ttmc_inner)
A2_val = mat[:, :rank]
ttmc = T.einsum("abc,ak,bl->klc", X_val, A1_val, A2_val)
ttmc_inner = T.einsum("klc,kld->cd", ttmc, ttmc)
mat, _, _ = T.svd(ttmc_inner)
A3_val = mat[:, :rank]
core_val = T.einsum("abc,ak,bl,cm->klm", X_val, A1_val, A2_val, A3_val)
assert T.norm(A_val_list_ad[0] - A1_val) < 1e-8
assert T.norm(A_val_list_ad[1] - A2_val) < 1e-8
assert T.norm(A_val_list_ad[2] - A3_val) < 1e-8
assert T.norm(core_val_ad - core_val) < 1e-8
def test_einsum_fuse_w_identity(backendopt):
"""
[Fuse einsum with multiple identities]
We want to fuse
A identity identity
| \ /
| \ /
| \ /
| es
| /
| /
| /
| /
es
Here es is einsum.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a", shape=[3, 3])
es_identity = ad.einsum('ik,kj->ij', ad.identity(3), ad.identity(3))
out = ad.einsum('ai,ij->aj', a, es_identity)
tree, = find_sub_einsumtree(PseudoNode(out))
out, ins = tree
new_out = fuse_einsums(out.node, ins)
assert tree_eq(out.node, new_out, [a])
def test_add_jacobian(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
y = x1 + x2
jacobian_x2, = ad.jacobians(y, [x2])
executor = ad.Executor([y, jacobian_x2])
x1_val = T.tensor([[1, 1], [1, 1]])
x2_val = T.tensor([[1, 1], [1, 1]])
y_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val
})
I = T.identity(2)
expected_jacobian_x2_val = T.einsum("ac,bd->abcd", I, I)
assert isinstance(y, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(y_val, x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_einsum_multiuse_auto_copy(backendopt):
"""
Test autolinearization and auto fuse.
A B inputs
|\ |
| \ |
| \ |
| C
| /
| /
output
Next: we would need to autoprune.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a1", shape=[3, 2])
b = ad.Variable(name="b", shape=[2, 3])
c = ad.einsum('ik,kj->ij', a, b)
output = ad.einsum('ik,ij->kj', a, c)
linearize(output)
all_nodes = find_topo_sort([output])
cloned_nodes = [
tmp for tmp in all_nodes if isinstance(tmp, ad.CloneNode)
]
out_new = fuse_einsums(output, [*cloned_nodes, b])
# Test that every inputs is now fused.
assert all([not isinstance(x, ad.EinsumNode) for x in out_new.inputs])
assert tree_eq(output, out_new, [*cloned_nodes, b])
def test_sub_jacobian_w_chain(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[2, 2])
x2 = ad.Variable(name="x2", shape=[2, 2])
x3 = ad.Variable(name="x3", shape=[2, 2])
y = x1 - x2
z = x3 - y
jacobian_x2, = ad.jacobians(z, [x2])
executor = ad.Executor([z, jacobian_x2])
x1_val = T.tensor([[1, 1], [1, 1]])
x2_val = T.tensor([[1, 1], [1, 1]])
x3_val = T.tensor([[1, 1], [1, 1]])
z_val, jacobian_x2_val = executor.run(feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val
})
I = T.identity(2)
expected_jacobian_x2_val = T.einsum("ac,bd->abcd", I, I)
assert isinstance(z, ad.Node)
assert isinstance(jacobian_x2, ad.Node)
assert T.array_equal(z_val, x3_val - x1_val + x2_val)
assert T.array_equal(jacobian_x2_val, expected_jacobian_x2_val)
def test_einsum_fuse_graph(backendopt):
"""
[Fuse einsum used twice]
This case is rather subtle.
We want to auto fuse
A B C
| \ /
| es
| /|
| / |
es |
\ |
es
Here es is einsum.
"""
for datatype in backendopt:
T.set_backend(datatype)
a = ad.Variable(name="a", shape=[3, 3])
b = ad.Variable(name="b", shape=[3, 2])
c = ad.Variable(name="c", shape=[2, 3])
BC = ad.einsum('ik, kj->ij', b, c) # 3x3
ABC = ad.einsum('ik, kj->ij', a, BC) # 3x3
out = ad.einsum('jk, ki->ji', ABC, BC) # 3x3
linearize(out)
tree, = find_sub_einsumtree(PseudoNode(out))
out, ins = tree
new_z = fuse_einsums(out.node, ins)
assert tree_eq(out.node, new_z, [a, b, c])
def test_add_mul_mix_2(backendopt):
for datatype in backendopt:
T.set_backend(datatype)
x1 = ad.Variable(name="x1", shape=[3])
x2 = ad.Variable(name="x2", shape=[3])
x3 = ad.Variable(name="x3", shape=[3])
x4 = ad.Variable(name="x4", shape=[3])
y = ad.sum(x1 + x2 * x3 * x4)
grad_x1, grad_x2, grad_x3, grad_x4 = ad.gradients(y, [x1, x2, x3, x4])
executor = ad.Executor([y, grad_x1, grad_x2, grad_x3, grad_x4])
x1_val = 1 * T.ones(3)
x2_val = 2 * T.ones(3)
x3_val = 3 * T.ones(3)
x4_val = 4 * T.ones(3)
y_val, grad_x1_val, grad_x2_val, grad_x3_val, grad_x4_val = executor.run(
feed_dict={
x1: x1_val,
x2: x2_val,
x3: x3_val,
x4: x4_val
})
assert isinstance(y, ad.Node)
assert T.array_equal(y_val, T.sum(x1_val + x2_val * x3_val * x4_val))
assert T.array_equal(grad_x1_val, T.ones_like(x1_val))
assert T.array_equal(grad_x2_val, x3_val * x4_val)
assert T.array_equal(grad_x3_val, x2_val * x4_val)
assert T.array_equal(grad_x4_val, x2_val * x3_val)
