def test_chain_sharing(size, backend):
xs = [np.random.rand(2, 2) for _ in range(size)]
alphabet = ''.join(get_symbol(i) for i in range(size + 1))
names = [alphabet[i:i+2] for i in range(size)]
inputs = ','.join(names)
num_exprs_nosharing = 0
for i in range(size + 1):
with shared_intermediates() as cache:
target = alphabet[i]
eq = '{}->{}'.format(inputs, target)
expr = contract_expression(eq, *(x.shape for x in xs))
expr(*xs, backend=backend)
num_exprs_nosharing += _compute_cost(cache)
with shared_intermediates() as cache:
print(inputs)
for i in range(size + 1):
target = alphabet[i]
eq = '{}->{}'.format(inputs, target)
path_info = contract_path(eq, *xs)
print(path_info[1])
expr = contract_expression(eq, *(x.shape for x in xs))
expr(*xs, backend=backend)
num_exprs_sharing = _compute_cost(cache)
print('-' * 40)
print('Without sharing: {} expressions'.format(num_exprs_nosharing))
print('With sharing: {} expressions'.format(num_exprs_sharing))
assert num_exprs_nosharing > num_exprs_sharing
def make_hmm_example(length,
latent_dim=32,
observed_dim=4,
batch_dim=10,
query=None):
symbols = symbol_stream()
b = next(symbols)
shapes = []
inputs = []
xs = []
ys = []
for t in range(length):
xs.append(next(symbols))
ys.append(next(symbols))
# Add observation matrix.
shapes.append([batch_dim, latent_dim, observed_dim])
inputs.append(b + xs[-1] + ys[-1])
if t >= 1:
# Add transition matrix.
shapes.append([batch_dim, latent_dim, latent_dim])
inputs.append(b + xs[-2] + xs[-1])
inputs = ','.join(inputs)
output = '' if query is None else b + xs[query]
eq = inputs + '->' + output
name = 'hmm_{}_{}_{}_{}_{}'.format(length, latent_dim, observed_dim,
batch_dim,
'total' if query is None else query)
contract_expression(eq, *shapes, optimize='eager') # smoke test
save(name, eq, shapes)
def test_chain_sharing(size, backend):
xs = [np.random.rand(2, 2) for _ in range(size)]
alphabet = ''.join(get_symbol(i) for i in range(size + 1))
names = [alphabet[i:i + 2] for i in range(size)]
inputs = ','.join(names)
num_exprs_nosharing = 0
for i in range(size + 1):
with shared_intermediates() as cache:
target = alphabet[i]
eq = '{}->{}'.format(inputs, target)
expr = contract_expression(eq, *(x.shape for x in xs))
expr(*xs, backend=backend)
num_exprs_nosharing += _compute_cost(cache)
with shared_intermediates() as cache:
print(inputs)
for i in range(size + 1):
target = alphabet[i]
eq = '{}->{}'.format(inputs, target)
path_info = contract_path(eq, *xs)
print(path_info[1])
expr = contract_expression(eq, *(x.shape for x in xs))
expr(*xs, backend=backend)
num_exprs_sharing = _compute_cost(cache)
print('-' * 40)
print('Without sharing: {} expressions'.format(num_exprs_nosharing))
print('With sharing: {} expressions'.format(num_exprs_sharing))
assert num_exprs_nosharing > num_exprs_sharing
def test_sharing_with_constants(backend):
inputs = 'ij,jk,kl'
outputs = 'ijkl'
equations = ['{}->{}'.format(inputs, output) for output in outputs]
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[1])
expected = [
contract_expression(eq, *shapes)(ops[0], var, ops[2])
for eq in equations
]
with shared_intermediates():
actual = [
contract_expression(eq, *ops, constants=constants)(var)
for eq in equations
]
for dim, expected_dim, actual_dim in zip(outputs, expected, actual):
assert np.allclose(expected_dim, actual_dim), 'error at {}'.format(dim)
def method2(views):
with shared_intermediates():
y = contract_expression(eqs[2], *shapes)(*views, backend=backend)
z = contract_expression(eqs[3], *shapes)(*views, backend=backend)
refs['y'] = y
refs['z'] = z
result = contract_expression('c,d->', y.shape, z.shape)(y, z, backend=backend)
result = result + method1(views) # nest method1 in method2
del y, z
assert 'y' in refs
assert 'z' in refs
assert 'y' not in refs
assert 'z' not in refs
def method1(views):
with shared_intermediates():
w = contract_expression(eqs[0], *shapes)(*views, backend=backend)
x = contract_expression(eqs[2], *shapes)(*views, backend=backend)
result = contract_expression('a,b->', w.shape, x.shape)(w, x, backend=backend)
refs['w'] = w
refs['x'] = x
del w, x
assert 'w' in refs
assert 'x' in refs
assert 'w' not in refs, 'cache leakage'
assert 'x' not in refs, 'cache leakage'
return result
def method1(views):
with shared_intermediates():
w = contract_expression(eqs[0], *shapes)(*views, backend=backend)
x = contract_expression(eqs[2], *shapes)(*views, backend=backend)
result = contract_expression("a,b->", w.shape,
x.shape)(w, x, backend=backend)
refs["w"] = w
refs["x"] = x
del w, x
assert "w" in refs
assert "x" in refs
assert "w" not in refs, "cache leakage"
assert "x" not in refs, "cache leakage"
return result
def method2(views):
with shared_intermediates():
y = contract_expression(eqs[2], *shapes)(*views, backend=backend)
z = contract_expression(eqs[3], *shapes)(*views, backend=backend)
refs["y"] = y
refs["z"] = z
result = contract_expression("c,d->", y.shape,
z.shape)(y, z, backend=backend)
result = result + method1(views) # nest method1 in method2
del y, z
assert "y" in refs
assert "z" in refs
assert "y" not in refs
assert "z" not in refs
def method1(views):
with shared_intermediates():
w = contract_expression(eqs[0], *shapes)(*views, backend=backend)
x = contract_expression(eqs[2], *shapes)(*views, backend=backend)
result = contract_expression('a,b->', w.shape,
x.shape)(w, x, backend=backend)
refs['w'] = w
refs['x'] = x
del w, x
assert 'w' in refs
assert 'x' in refs
assert 'w' not in refs, 'cache leakage'
assert 'x' not in refs, 'cache leakage'
return result
def method2(views):
with shared_intermediates():
y = contract_expression(eqs[2], *shapes)(*views, backend=backend)
z = contract_expression(eqs[3], *shapes)(*views, backend=backend)
refs['y'] = y
refs['z'] = z
result = contract_expression('c,d->', y.shape,
z.shape)(y, z, backend=backend)
result = result + method1(views) # nest method1 in method2
del y, z
assert 'y' in refs
assert 'z' in refs
assert 'y' not in refs
assert 'z' not in refs
def test_tensorflow_with_constants(constants):
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
non_const, = {0, 1, 2} - constants
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[non_const])
res_exp = contract(eq,
*(ops[i] if i in constants else var for i in range(3)))
expr = contract_expression(eq, *ops, constants=constants)
# check tensorflow
with tf.Session(config=_TF_CONFIG).as_default():
res_got = expr(var, backend='tensorflow')
assert all(array is None or infer_backend(array) == 'tensorflow'
for array in expr._evaluated_constants['tensorflow'])
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check tensorflow call returns tensorflow still
res_got3 = expr(backends.to_tensorflow(var))
assert isinstance(res_got3, tf.Tensor)
def test_torch_with_constants(constants):
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
non_const, = {0, 1, 2} - constants
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[non_const])
res_exp = contract(eq,
*(ops[i] if i in constants else var for i in range(3)))
expr = contract_expression(eq, *ops, constants=constants)
# check torch
res_got = expr(var, backend='torch')
assert all(array is None or infer_backend(array) == 'torch'
for array in expr._evaluated_constants['torch'])
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check torch call returns torch still
res_got3 = expr(backends.to_torch(var))
assert isinstance(res_got3, torch.Tensor)
res_got3 = res_got3.numpy(
) if res_got3.device.type == 'cpu' else res_got3.cpu().numpy()
assert np.allclose(res_exp, res_got3)
def test_torch_with_constants():
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[1])
res_exp = contract(eq, ops[0], var, ops[2])
expr = contract_expression(eq, *ops, constants=constants)
# check torch
res_got = expr(var, backend='torch')
assert 'torch' in expr._evaluated_constants
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check torch call returns torch still
res_got3 = expr(backends.to_torch(var), backend='torch')
assert isinstance(res_got3, torch.Tensor)
res_got3 = res_got3.numpy(
) if res_got3.device.type == 'cpu' else res_got3.cpu().numpy()
assert np.allclose(res_exp, res_got3)
def test_cupy_with_constants(constants): # pragma: no cover
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
non_const, = {0, 1, 2} - constants
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[non_const])
res_exp = contract(eq,
*(ops[i] if i in constants else var for i in range(3)))
expr = contract_expression(eq, *ops, constants=constants)
# check cupy
res_got = expr(var, backend='cupy')
# check cupy versions of constants exist
assert all(array is None or infer_backend(array) == 'cupy'
for array in expr._evaluated_constants['cupy'])
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check cupy call returns cupy still
res_got3 = expr(cupy.asarray(var))
assert isinstance(res_got3, cupy.ndarray)
assert np.allclose(res_exp, res_got3.get())
def test_sparse(string):
views = helpers.build_views(string)
# sparsify views so they don't become dense during contraction
for view in views:
np.random.seed(42)
mask = np.random.choice([False, True], view.shape, True, [0.05, 0.95])
view[mask] = 0
ein = contract(string, *views, optimize=False, use_blas=False)
shps = [v.shape for v in views]
expr = contract_expression(string, *shps, optimize=True)
# test non-conversion mode
sparse_views = [sparse.COO.from_numpy(x) for x in views]
sparse_opt = expr(*sparse_views, backend='sparse')
# check type is maintained when not using numpy arrays
assert isinstance(sparse_opt, sparse.COO)
assert np.allclose(ein, sparse_opt.todense())
# try raw contract
sparse_opt = contract(string, *sparse_views, backend='sparse')
assert isinstance(sparse_opt, sparse.COO)
assert np.allclose(ein, sparse_opt.todense())
def test_tensorflow_with_constants():
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[1])
res_exp = contract(eq, ops[0], var, ops[2])
expr = contract_expression(eq, *ops, constants=constants)
# check tensorflow
sess = tf.Session(config=_TF_CONFIG)
with sess.as_default():
res_got = expr(var, backend='tensorflow')
sess.close()
assert 'tensorflow' in expr._evaluated_constants
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check tensorflow call returns tensorflow still
res_got3 = expr(backends.to_tensorflow(var), backend='tensorflow')
assert isinstance(res_got3, tf.Tensor)
def create_diagonal_mask_operation(self):
weights_index_names = self.WEIGHTS_INDEX_NAMES[:self.order]
operands = ','.join(map(lambda x: 'b' + x, weights_index_names))
expression = f"{operands}->{weights_index_names}"
shapes = [(self.DEFAULT_JET_COUNT, self.DEFAULT_JET_COUNT)
] * self.order
return contract_expression(expression, *shapes)
def test_no_sharing_separate_cache(backend):
eq = 'ab,bc,cd->'
views = helpers.build_views(eq)
expr = contract_expression(eq, *(v.shape for v in views))
print('-' * 40)
print('Without sharing:')
with shared_intermediates() as cache:
expr(*views, backend=backend)
expected = count_cached_ops(cache)
expected.update(count_cached_ops(cache)) # we expect double
print('-' * 40)
print('With sharing:')
with shared_intermediates() as cache1:
expr(*views, backend=backend)
actual = count_cached_ops(cache1)
with shared_intermediates() as cache2:
expr(*views, backend=backend)
actual.update(count_cached_ops(cache2))
print('-' * 40)
print('Without sharing: {} expressions'.format(expected))
print('With sharing: {} expressions'.format(actual))
assert actual == expected
def test_theano_with_constants(constants):
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
non_const, = {0, 1, 2} - constants
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[non_const])
res_exp = contract(eq,
*(ops[i] if i in constants else var for i in range(3)))
expr = contract_expression(eq, *ops, constants=constants)
# check theano
res_got = expr(var, backend='theano')
assert all(array is None or infer_backend(array) == 'theano'
for array in expr._evaluated_constants['theano'])
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check theano call returns theano still
res_got3 = expr(backends.to_theano(var))
assert isinstance(res_got3, theano.tensor.TensorVariable)
def test_contract_expression_interleaved_input():
x, y, z = (np.random.randn(2, 2) for _ in 'xyz')
expected = np.einsum(x, [0, 1], y, [1, 2], z, [2, 3], [3, 0])
xshp, yshp, zshp = ((2, 2) for _ in 'xyz')
expr = contract_expression(xshp, [0, 1], yshp, [1, 2], zshp, [2, 3], [3, 0])
out = expr(x, y, z)
assert np.allclose(out, expected)
def test_partial_sharing(backend):
eq = 'ab,bc,de->'
x, y, z1 = helpers.build_views(eq)
z2 = 2.0 * z1 - 1.0
expr = contract_expression(eq, x.shape, y.shape, z1.shape)
print('-' * 40)
print('Without sharing:')
num_exprs_nosharing = Counter()
with shared_intermediates() as cache:
expr(x, y, z1, backend=backend)
num_exprs_nosharing.update(count_cached_ops(cache))
with shared_intermediates() as cache:
expr(x, y, z2, backend=backend)
num_exprs_nosharing.update(count_cached_ops(cache))
print('-' * 40)
print('With sharing:')
with shared_intermediates() as cache:
expr(x, y, z1, backend=backend)
expr(x, y, z2, backend=backend)
num_exprs_sharing = count_cached_ops(cache)
print('-' * 40)
print('Without sharing: {} expressions'.format(num_exprs_nosharing))
print('With sharing: {} expressions'.format(num_exprs_sharing))
assert num_exprs_nosharing['einsum'] > num_exprs_sharing['einsum']
def test_no_sharing_separate_cache(backend):
eq = 'ab,bc,cd->'
views = helpers.build_views(eq)
expr = contract_expression(eq, *(v.shape for v in views))
print('-' * 40)
print('Without sharing:')
with shared_intermediates() as cache:
expr(*views, backend=backend)
expected = count_cached_ops(cache)
expected.update(count_cached_ops(cache)) # we expect double
print('-' * 40)
print('With sharing:')
with shared_intermediates() as cache1:
expr(*views, backend=backend)
actual = count_cached_ops(cache1)
with shared_intermediates() as cache2:
expr(*views, backend=backend)
actual.update(count_cached_ops(cache2))
print('-' * 40)
print('Without sharing: {} expressions'.format(expected))
print('With sharing: {} expressions'.format(actual))
assert actual == expected
def test_partial_sharing(backend):
eq = 'ab,bc,de->'
x, y, z1 = helpers.build_views(eq)
z2 = 2.0 * z1 - 1.0
expr = contract_expression(eq, x.shape, y.shape, z1.shape)
print('-' * 40)
print('Without sharing:')
num_exprs_nosharing = Counter()
with shared_intermediates() as cache:
expr(x, y, z1, backend=backend)
num_exprs_nosharing.update(count_cached_ops(cache))
with shared_intermediates() as cache:
expr(x, y, z2, backend=backend)
num_exprs_nosharing.update(count_cached_ops(cache))
print('-' * 40)
print('With sharing:')
with shared_intermediates() as cache:
expr(x, y, z1, backend=backend)
expr(x, y, z2, backend=backend)
num_exprs_sharing = count_cached_ops(cache)
print('-' * 40)
print('Without sharing: {} expressions'.format(num_exprs_nosharing))
print('With sharing: {} expressions'.format(num_exprs_sharing))
assert num_exprs_nosharing['einsum'] > num_exprs_sharing['einsum']
def partial_trace_v1(states: tf.Tensor, subsystem: Union[int, List[int]],
n_qubits: int):
"""
Partial trace
:param states: States in vector or density matrix from to trace
:param subsystem: Subsystem to trace away
:return: Remaining states
"""
if isinstance(subsystem, int):
subsystem = [subsystem]
# Convert to density matrices
if states.shape[-1] == 1:
states = density_matrix(states)
n_qubits = intlog2(states.shape[-1])
# Construct Einstein sum-equation, inspired by:
# https://github.com/rigetti/quantumflow/blob/bf965f0ca70cd69b387f9ca8407ab38da955e925/quantumflow/qubits.py#L201
import string
# EINSTEIN_SUBSCRIPTS = string.ascii_lowercase
subscripts = list(string.ascii_lowercase)[0:n_qubits * 2]
# Make a copy of the same index n_qubits later to trace out that entry
for i in subsystem:
subscripts[n_qubits + i] = subscripts[i]
subscript_str = 'z' + ''.join(subscripts)
batch_shape = states.shape[:-2]
states_reshaped = tf.reshape(states, batch_shape + [2] * 2 * n_qubits)
expr = oe.contract_expression(subscript_str, tf.shape(states_reshaped))
result = expr(states_reshaped, backend='tensorflow')
result = tf.einsum(
subscript_str,
states_reshaped) # FIXME: einsum in tf only supports up to rank 6!
return tf.reshape(result, batch_shape + [2**n_qubits, 2**n_qubits])
def test_cupy_with_constants(): # pragma: no cover
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[1])
res_exp = contract(eq, ops[0], var, ops[2])
expr = contract_expression(eq, *ops, constants=constants)
# check cupy
res_got = expr(var, backend='cupy')
assert 'cupy' in expr._evaluated_constants
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check cupy call returns cupy still
res_got3 = expr(cupy.asarray(var), backend='cupy')
assert isinstance(res_got3, cupy.ndarray)
assert np.allclose(res_exp, res_got3.get())
def test_contract_expression_interleaved_input():
x, y, z = (np.random.randn(2, 2) for _ in 'xyz')
expected = np.einsum(x, [0, 1], y, [1, 2], z, [2, 3], [3, 0])
xshp, yshp, zshp = ((2, 2) for _ in 'xyz')
expr = contract_expression(xshp, [0, 1], yshp, [1, 2], zshp, [2, 3], [3, 0])
out = expr(x, y, z)
assert np.allclose(out, expected)
def test_theano_with_constants():
eq = 'ij,jk,kl->li'
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [
np.random.rand(*shp) if i in constants else shp
for i, shp in enumerate(shapes)
]
var = np.random.rand(*shapes[1])
res_exp = contract(eq, ops[0], var, ops[2])
expr = contract_expression(eq, *ops, constants=constants)
# check theano
res_got = expr(var, backend='theano')
assert 'theano' in expr._evaluated_constants
assert np.allclose(res_exp, res_got)
# check can call with numpy still
res_got2 = expr(var, backend='numpy')
assert np.allclose(res_exp, res_got2)
# check theano call returns theano still
res_got3 = expr(backends.to_theano(var), backend='theano')
assert isinstance(res_got3, theano.tensor.TensorVariable)
def make_dbn_example(length,
global_dim=2,
latent_dim=32,
observed_dim=4,
batch_dim=10,
query=None):
symbols = symbol_stream()
b = next(symbols)
w = next(symbols)
shapes = []
inputs = []
xs = []
ys = []
zs = []
for t in range(length):
xs.append(next(symbols))
ys.append(next(symbols))
zs.append(next(symbols))
# Add vertical dependencies.
shapes.append([batch_dim, global_dim, latent_dim])
inputs.append(b + w + xs[-1])
shapes.append([batch_dim, latent_dim, latent_dim])
inputs.append(b + xs[-1] + ys[-1])
shapes.append([batch_dim, latent_dim, latent_dim])
inputs.append(b + ys[-1] + zs[-1])
if t >= 1:
# Add horizontal dependencies.
shapes.append([batch_dim, latent_dim, latent_dim])
inputs.append(b + xs[-2] + xs[-1])
shapes.append([batch_dim, latent_dim, latent_dim])
inputs.append(b + ys[-2] + ys[-1])
inputs = ','.join(inputs)
output = '' if query is None else b + w + xs[query] + ys[query]
eq = inputs + '->' + output
name = 'dbn_{}_{}_{}_{}_{}'.format(length, latent_dim, observed_dim,
batch_dim,
'total' if query is None else query)
contract_expression(eq, *shapes, optimize='eager') # smoke test
save(name, eq, shapes)
def test_can_blas_on_healed_broadcast_dimensions():
expr = contract_expression("ab,bc,bd->acd", (5, 4), (1, 5), (4, 20))
# first contraction involves broadcasting
assert expr.contraction_list[0][2] == "bc,ab->bca"
assert expr.contraction_list[0][-1] is False
# but then is healed GEMM is usable
assert expr.contraction_list[1][2] == "bca,bd->acd"
assert expr.contraction_list[1][-1] == "GEMM"
def test_sharing_with_constants(backend):
inputs = 'ij,jk,kl'
outputs = 'ijkl'
equations = ['{}->{}'.format(inputs, output) for output in outputs]
shapes = (2, 3), (3, 4), (4, 5)
constants = {0, 2}
ops = [np.random.rand(*shp) if i in constants else shp for i, shp in enumerate(shapes)]
var = np.random.rand(*shapes[1])
expected = [contract_expression(eq, *shapes)(ops[0], var, ops[2])
for eq in equations]
with shared_intermediates():
actual = [contract_expression(eq, *ops, constants=constants)(var)
for eq in equations]
for dim, expected_dim, actual_dim in zip(outputs, expected, actual):
assert np.allclose(expected_dim, actual_dim), 'error at {}'.format(dim)
def test_can_blas_on_healed_broadcast_dimensions():
expr = contract_expression("ab,bc,bd->acd", (5, 4), (1, 5), (4, 20))
# first contraction involves broadcasting
assert expr.contraction_list[0][2] == 'bc,ab->bca'
assert expr.contraction_list[0][-1] is False
# but then is healed GEMM is usable
assert expr.contraction_list[1][2] == 'bca,bd->acd'
assert expr.contraction_list[1][-1] == 'GEMM'
def contract(self, *args: ContractArgs) -> Tensor:
contract_expression_args = tensors_to_shapes(*args)
if contract_expression_args not in self.paths:
self.paths[contract_expression_args] = oe.contract_expression(
*contract_expression_args, optimize="auto-hq"
)
return self.paths[contract_expression_args](
*(x for x in args if isinstance(x, Tensor))
)
def test_sharing_value(eq, backend):
views = helpers.build_views(eq)
shapes = [v.shape for v in views]
expr = contract_expression(eq, *shapes)
expected = expr(*views, backend=backend)
with shared_intermediates():
actual = expr(*views, backend=backend)
assert (actual == expected).all()
def test_jax(string): # pragma: no cover
views = helpers.build_views(string)
ein = contract(string, *views, optimize=False, use_blas=False)
shps = [v.shape for v in views]
expr = contract_expression(string, *shps, optimize=True)
opt = expr(*views, backend='jax')
assert np.allclose(ein, opt)
assert isinstance(opt, np.ndarray)
def test_sharing_value(eq, backend):
views = helpers.build_views(eq)
shapes = [v.shape for v in views]
expr = contract_expression(eq, *shapes)
expected = expr(*views, backend=backend)
with shared_intermediates():
actual = expr(*views, backend=backend)
assert (actual == expected).all()
def calculate_control_matrix_from_atomic(
phases: ndarray,
R_g: ndarray,
Q_liouville: ndarray,
show_progressbar: Optional[bool] = None) -> ndarray:
r"""
Calculate the control matrix from the control matrices of atomic segments.
Parameters
----------
phases: array_like, shape (n_dt, n_omega)
The phase factors for :math:`l\in\{0, 1, \dots, n-1\}`.
R_g: array_like, shape (n_dt, n_nops, d**2, n_omega)
The pulse control matrices for :math:`l\in\{1, 2, \dots, n\}`.
Q_liouville: array_like, shape (n_dt, n_nops, d**2, d**2)
The transfer matrices of the cumulative propagators for
:math:`l\in\{0, 1, \dots, n-1\}`.
show_progressbar: bool, optional
Show a progress bar for the calculation.
Returns
-------
R: ndarray, shape (n_nops, d**2, n_omega)
The control matrix :math:`\mathcal{R}(\omega)`.
Notes
-----
The control matrix is calculated by evaluating the sum
.. math::
\mathcal{R}(\omega) = \sum_{l=1}^n e^{i\omega t_{l-1}}
\mathcal{R}^{(l)}(\omega)\mathcal{Q}^{(l-1)}.
See Also
--------
calculate_control_matrix_from_scratch: Control matrix from scratch.
liouville_representation: Liouville representation for a given basis.
"""
n = len(R_g)
# Allocate memory
R = np.zeros(R_g.shape[1:], dtype=complex)
# Set up a reusable contraction expression. In some cases it is faster to
# also contract the time dimension in the same expression instead of
# looping over it, but we don't distinguish here for readability.
R_expr = oe.contract_expression('ijo,jk->iko', R_g.shape[1:],
Q_liouville.shape[1:])
for g in util.progressbar_range(n,
show_progressbar=show_progressbar,
desc='Calculating control matrix'):
R += R_expr(phases[g] * R_g[g], Q_liouville[g])
return R
def make_contraction(self):
input_index_names = np.array(list(self.INPUT_INDEX_NAMES))
operations = map(lambda x: f"{x}bi", input_index_names)
operations = ','.join(islice(operations, self.order))
result = f"->b{''.join(input_index_names[:self.order])}"
expression = operations + result
shapes = [(self.batch_size, self.DEFAULT_JET_COUNT, self.features)
] * self.order
return contract_expression(expression, *shapes, optimize='optimal')
def partial_trace_last(states: tf.Tensor, n_qubits2trace: int, n_qubits: int):
# Convert to density matrices
if states.shape[-1] == 1:
states = density_matrix(states)
subscripts = 'xyaza'
# Reshape to the form of subscripts
n_static = n_qubits - n_qubits2trace
states = tf.reshape(
states,
[-1, 2**n_static, 2**n_qubits2trace, 2**n_static, 2**n_qubits2trace])
expr = oe.contract_expression(subscripts, tf.shape(states))
return expr(states, backend='tensorflow')
def __init__(
self,
width=160,
height=120,
fps=100,
freq_min=12,
freq_max=15,
num_base_functions=4,
):
self.width = width
self.height = height
self.fps = np.float32(fps)
self.frequencies = np.linspace(freq_min,
freq_max + 1,
num=num_base_functions)
self.wavelets = [self._get_wavelet(f) for f in self.frequencies]
self.max_wavelet_length = max([w.shape[0] for w in self.wavelets])
self.wavelets = np.stack([
np.pad(w, (self.max_wavelet_length - w.shape[0], 0))
for w in self.wavelets
])
self.buffer_size = int(2.5 * self.max_wavelet_length)
self.buffer_time = (1 / fps) * self.buffer_size
self.activity_long = np.zeros((height, width), dtype=np.float32)
self.activity = np.zeros((height, width), dtype=np.float32)
self.buffer = np.zeros((self.buffer_size, height, width),
dtype=np.float32)
self.buffer_idx = 0
self.frame_response = np.zeros(shape=(height, width), dtype=np.float32)
# Decay background activity slower than 'current' activity.
# The activity of 1 s ago will still contribute 5% to the 'current' activity.
self.activity_decay = np.exp(np.log(0.05) / self.fps)
self.activity_long_decay = np.exp(np.log(0.1) / self.fps)
self.einsum_expression = opt_einsum.contract_expression(
"ij,jkl->ikl", self.wavelets.shape,
(self.wavelets.shape[1], height, width))
self.warmup_period_over = False
self.rolling_mean = np.zeros(shape=(height, width), dtype=np.float32)
self.temp_full_buffer = np.zeros(shape=(self.wavelets.shape[1], height,
width),
dtype=np.float32)
self.temp_one_frame_buffer = np.zeros(shape=(height, width),
dtype=np.float32)
def test_chain_2(size, backend):
xs = [np.random.rand(2, 2) for _ in range(size)]
shapes = [x.shape for x in xs]
alphabet = ''.join(get_symbol(i) for i in range(size + 1))
names = [alphabet[i:i+2] for i in range(size)]
inputs = ','.join(names)
with shared_intermediates():
print(inputs)
for i in range(size):
target = alphabet[i:i+2]
eq = '{}->{}'.format(inputs, target)
path_info = contract_path(eq, *xs)
print(path_info[1])
expr = contract_expression(eq, *shapes)
expr(*xs, backend=backend)
print('-' * 40)
def test_contract_expressions(string, optimize, use_blas, out_spec):
views = helpers.build_views(string)
shapes = [view.shape for view in views]
expected = contract(string, *views, optimize=False, use_blas=False)
expr = contract_expression(string, *shapes, optimize=optimize, use_blas=use_blas)
if out_spec and ("->" in string) and (string[-2:] != "->"):
out, = helpers.build_views(string.split('->')[1])
expr(*views, out=out)
else:
out = expr(*views)
assert np.allclose(out, expected)
# check representations
assert string in expr.__repr__()
assert string in expr.__str__()
def test_contract_expression_with_constants(string, constants):
views = helpers.build_views(string)
expected = contract(string, *views, optimize=False, use_blas=False)
shapes = [view.shape for view in views]
expr_args = []
ctrc_args = []
for i, (shape, view) in enumerate(zip(shapes, views)):
if i in constants:
expr_args.append(view)
else:
expr_args.append(shape)
ctrc_args.append(view)
expr = contract_expression(string, *expr_args, constants=constants)
print(expr)
out = expr(*ctrc_args)
assert np.allclose(expected, out)
def test_chain_2_growth(backend):
sizes = list(range(1, 21))
costs = []
for size in sizes:
xs = [np.random.rand(2, 2) for _ in range(size)]
alphabet = ''.join(get_symbol(i) for i in range(size + 1))
names = [alphabet[i:i+2] for i in range(size)]
inputs = ','.join(names)
with shared_intermediates() as cache:
for i in range(size):
target = alphabet[i:i+2]
eq = '{}->{}'.format(inputs, target)
expr = contract_expression(eq, *(x.shape for x in xs))
expr(*xs, backend=backend)
costs.append(_compute_cost(cache))
print('sizes = {}'.format(repr(sizes)))
print('costs = {}'.format(repr(costs)))
for size, cost in zip(sizes, costs):
print('{}\t{}'.format(size, cost))
def test_contract_expression_checks():
# check optimize needed
with pytest.raises(ValueError):
contract_expression("ab,bc->ac", (2, 3), (3, 4), optimize=False)
# check sizes are still checked
with pytest.raises(ValueError):
contract_expression("ab,bc->ac", (2, 3), (3, 4), (42, 42))
# check if out given
out = np.empty((2, 4))
with pytest.raises(ValueError):
contract_expression("ab,bc->ac", (2, 3), (3, 4), out=out)
# check still get errors when wrong ranks supplied to expression
expr = contract_expression("ab,bc->ac", (2, 3), (3, 4))
# too few arguments
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 3))
assert "`ContractExpression` takes exactly 2" in str(err)
# too many arguments
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 3), np.random.rand(2, 3), np.random.rand(2, 3))
assert "`ContractExpression` takes exactly 2" in str(err)
# wrong shapes
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 3, 4), np.random.rand(3, 4))
assert "Internal error while evaluating `ContractExpression`" in str(err)
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 4), np.random.rand(3, 4, 5))
assert "Internal error while evaluating `ContractExpression`" in str(err)
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 3), np.random.rand(3, 4), out=np.random.rand(2, 4, 6))
assert "Internal error while evaluating `ContractExpression`" in str(err)
# should only be able to specify out
with pytest.raises(ValueError) as err:
expr(np.random.rand(2, 3), np.random.rand(3, 4), order='F')
assert "only valid keyword arguments to a `ContractExpression`" in str(err)
def test_complete_sharing(backend):
eq = 'ab,bc,cd->'
views = helpers.build_views(eq)
expr = contract_expression(eq, *(v.shape for v in views))
print('-' * 40)
print('Without sharing:')
with shared_intermediates() as cache:
expr(*views, backend=backend)
expected = count_cached_ops(cache)
print('-' * 40)
print('With sharing:')
with shared_intermediates() as cache:
expr(*views, backend=backend)
expr(*views, backend=backend)
actual = count_cached_ops(cache)
print('-' * 40)
print('Without sharing: {} expressions'.format(expected))
print('With sharing: {} expressions'.format(actual))
assert actual == expected
