In [9]:
data = math.random_uniform(spatial(x=8, y=6))
vis.plot(data) # or vis.show(data)
Out[9]:
<Figure size 1200x500 with 2 Axes>
This notebook lists useful code snippets.
from phi.flow import *
from phi.tf.flow import *
from phi.jax.stax.flow import *
from phi.torch.flow import *
2023-08-29 12:50:30.780713: I tensorflow/tsl/cuda/cudart_stub.cc:28] Could not find cuda drivers on your machine, GPU will not be used. 2023-08-29 12:50:30.830099: I tensorflow/tsl/cuda/cudart_stub.cc:28] Could not find cuda drivers on your machine, GPU will not be used. 2023-08-29 12:50:30.831296: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations. To enable the following instructions: AVX2 AVX512F FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags. 2023-08-29 12:50:31.675608: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)
backend.default_backend().list_devices('GPU')
[]
backend.default_backend().list_devices('CPU')
[torch device 'CPU' (CPU 'cpu') | 6932 MB | 2 processors | ]
assert backend.default_backend().set_default_device('CPU')
math.set_global_precision(32) # single precision is the default
x32 = math.random_normal(batch(b=4))
with math.precision(64): ## operations within this context will use 32 bit floats
x64 = math.to_float(x32)
data = math.random_normal(batch(examples=10)) * .1 # batch of scalar values
data = math.random_uniform(batch(examples=10), channel(vector='x,y')) # batch of vectors
data
(examplesᵇ=10, vectorᶜ=x,y) 0.480 ± 0.305 (2e-02...1e+00)
data.examples[0]
(x=0.191, y=0.595)
Tensor¶print(data)
print(f"{data:full:shape:dtype:color:.1f}")
(examplesᵇ=10, vectorᶜ=x,y) 0.480 ± 0.305 (2e-02...1e+00) (examplesᵇ=10, vectorᶜ=x,y) [[0.2, 0.6], [0.1, 0.7], [1.0, 0.4], [0.3, 0.3], [0.1, 0.3], [0.2, 0.7], [0.9, 0.9], [0.6, 0.6], [0.5, 0.0], [1.0, 0.3]]
Tensor¶data = math.random_uniform(spatial(x=8, y=6))
vis.plot(data) # or vis.show(data)
<Figure size 1200x500 with 2 Axes>
Tensor to NumPy¶data.numpy(order='x,y')
array([[0.45785683, 0.08527088, 0.5096399 , 0.7802357 , 0.06318313,
0.21213293],
[0.64608747, 0.63206434, 0.91747266, 0.8138582 , 0.00503629,
0.26304227],
[0.8486472 , 0.9666401 , 0.17502236, 0.1325391 , 0.5373124 ,
0.20725596],
[0.2963305 , 0.05790192, 0.23139203, 0.08626831, 0.6218854 ,
0.77004516],
[0.5287756 , 0.8242924 , 0.69254345, 0.54871184, 0.5790198 ,
0.91739386],
[0.74913627, 0.49778354, 0.48441988, 0.45968515, 0.08384019,
0.687513 ],
[0.30472183, 0.66141444, 0.26227504, 0.86061823, 0.28071064,
0.64048195],
[0.72425216, 0.7381197 , 0.2096594 , 0.65706366, 0.44790828,
0.80129623]], dtype=float32)
math.reshaped_native(data, ['extra', data.shape], to_numpy=True)
array([[0.45785683, 0.08527088, 0.5096399 , 0.7802357 , 0.06318313,
0.21213293, 0.64608747, 0.63206434, 0.91747266, 0.8138582 ,
0.00503629, 0.26304227, 0.8486472 , 0.9666401 , 0.17502236,
0.1325391 , 0.5373124 , 0.20725596, 0.2963305 , 0.05790192,
0.23139203, 0.08626831, 0.6218854 , 0.77004516, 0.5287756 ,
0.8242924 , 0.69254345, 0.54871184, 0.5790198 , 0.91739386,
0.74913627, 0.49778354, 0.48441988, 0.45968515, 0.08384019,
0.687513 , 0.30472183, 0.66141444, 0.26227504, 0.86061823,
0.28071064, 0.64048195, 0.72425216, 0.7381197 , 0.2096594 ,
0.65706366, 0.44790828, 0.80129623]], dtype=float32)
points = math.tensor([(0, 0), (0, 1), (1, 0)], instance('points'), channel('vector'))
distances = points - math.rename_dims(points, 'points', 'others')
math.print(math.vec_length(distances))
[[0. , 1. , 1. ], [1. , 0. , 1.4142135], [1. , 1.4142135, 0. ]]
CenteredGrid¶zero_grid = CenteredGrid(0, 0, x=32, y=32, bounds=Box(x=1, y=1))
y_grid = CenteredGrid((0, 1), extrapolation.BOUNDARY, x=32, y=32)
noise_grid = CenteredGrid(Noise(), extrapolation.PERIODIC, x=32, y=32)
sin_curve = CenteredGrid(lambda x: math.sin(x), extrapolation.PERIODIC, x=100, bounds=Box(x=2 * PI))
vis.plot(zero_grid, y_grid, noise_grid, sin_curve, size=(12, 3))
<Figure size 1200x300 with 6 Axes>
StaggeredGrid¶zero_grid = StaggeredGrid(0, 0, x=32, y=32, bounds=Box(x=1, y=1))
y_grid = StaggeredGrid((0, 1), extrapolation.BOUNDARY, x=32, y=32)
noise_grid = StaggeredGrid(Noise(), extrapolation.PERIODIC, x=32, y=32)
sin_curve = StaggeredGrid(lambda x: math.sin(x), extrapolation.PERIODIC, x=100, bounds=Box(x=2 * PI))
vis.plot(zero_grid, y_grid, noise_grid, sin_curve, size=(12, 3))
<Figure size 1200x300 with 4 Axes>
StaggeredGrid from NumPy Arrays¶Given matching arrays vx and vy, we can construct a StaggeredGrid.
Note that the shapes of the arrays must match the extrapolation!
vx = math.tensor(np.zeros([33, 32]), spatial('x,y'))
vy = math.tensor(np.zeros([32, 33]), spatial('x,y'))
StaggeredGrid(math.stack([vx, vy], channel('vector')), extrapolation.BOUNDARY)
vx = math.tensor(np.zeros([32, 32]), spatial('x,y'))
vy = math.tensor(np.zeros([32, 32]), spatial('x,y'))
StaggeredGrid(math.stack([vx, vy], channel('vector')), extrapolation.PERIODIC)
vx = math.tensor(np.zeros([31, 32]), spatial('x,y'))
vy = math.tensor(np.zeros([32, 31]), spatial('x,y'))
StaggeredGrid(math.stack([vx, vy], channel('vector')), 0)
StaggeredGrid[(xˢ=32, yˢ=32, vectorᶜ=2), size=(x=32, y=32) int64, extrapolation=0]
def loss_function(x):
return math.l2_loss(math.cos(x))
initial_guess = math.tensor([1, -1], math.batch('batch'))
math.minimize(loss_function, Solve('L-BFGS-B', 0, 1e-3, x0=initial_guess))
(1.574, -1.574) along batchᵇ
def f(x):
return 2 * x
math.solve_linear(f, 84, Solve('CG', 1e-5, x0=0))
--------------------------------------------------------------------------- AssertionError Traceback (most recent call last) Cell In[17], line 4 1 def f(x): 2 return 2 * x ----> 4 math.solve_linear(f, 84, Solve('CG', 1e-5, x0=0)) File /opt/hostedtoolcache/Python/3.8.17/x64/lib/python3.8/site-packages/phiml/math/_optimize.py:538, in solve_linear(f, y, solve, grad_for_f, f_kwargs, *f_args, **f_kwargs_) 536 rank = y_tensors[0].rank 537 assert x0_tensors[0].rank == rank, f"y and x0 must have the same rank but got {y_tensors[0].shape.sizes} for y and {x0_tensors[0].shape.sizes} for x0" --> 538 y = wrap(y, *[batch(f'batch{i}') for i in range(rank - 1)], channel('vector')) 539 x0 = wrap(solve.x0, *[batch(f'batch{i}') for i in range(rank - 1)], channel('vector')) 540 solve = copy_with(solve, x0=x0) File /opt/hostedtoolcache/Python/3.8.17/x64/lib/python3.8/site-packages/phiml/math/_tensors.py:1631, in wrap(data, *shape) 1628 def wrap(data, 1629 *shape: Shape) -> Tensor: 1630 """ Short for `phiml.math.tensor()` with `convert=False`. """ -> 1631 return tensor(data, *shape, convert=False) File /opt/hostedtoolcache/Python/3.8.17/x64/lib/python3.8/site-packages/phiml/math/_tensors.py:1584, in tensor(data, convert, default_list_dim, *shape) 1582 return layout(data) 1583 elif isinstance(data, (numbers.Number, bool)): -> 1584 assert not shape, f"Trying to create a zero-dimensional Tensor from value '{data}' but shape={shape}" 1585 if convert: 1586 data = default_backend().as_tensor(data, convert_external=True) AssertionError: Trying to create a zero-dimensional Tensor from value '84' but shape=(vectorᶜ=None)
from functools import partial
periodic_laplace = partial(math.laplace, padding=extrapolation.PERIODIC)
example_input = math.ones(spatial(x=3))
matrix, bias = math.matrix_from_function(periodic_laplace, example_input)
math.print(matrix)
x=0 -2. 1. 1. along ~x x=1 1. -2. 1. along ~x x=2 1. 1. -2. along ~x
def f(x):
return math.l2_loss(math.sin(x))
f_grid = CenteredGrid(f, x=100, y=100, bounds=Box(x=2*PI, y=2*PI))
vis.plot(f_grid)
<Figure size 1200x500 with 2 Axes>
def minimize(x0):
with math.SolveTape(record_trajectories=True) as solves:
math.minimize(f, Solve('BFGS', 0, 1e-5, x0=x0))
return solves[0].x # shape (trajectory, x, y, vector)
trajectories = CenteredGrid(minimize, x=8, y=8, bounds=Box(x=2*PI, y=2*PI)).values
segments = []
for start, end in zip(trajectories.trajectory[:-1].trajectory, trajectories.trajectory[1:].trajectory):
segments.append(PointCloud(start, end - start, bounds=Box(x=2*PI, y=2*PI)))
anim_segments = field.stack(segments, batch('time'))
vis.plot(f_grid, anim_segments, overlay='args', animate='time', color='#FFFFFF', frame_time=500)
/opt/hostedtoolcache/Python/3.8.17/x64/lib/python3.8/site-packages/phiml/math/_ops.py:446: RuntimeWarning: pack_dims() default implementation is slow on large dimensions ((_cᶜ=4096)). Please implement __unpack_dim__() for Layout as defined in phiml.math.magic
return unpack_dim(stack(result, channel('_c')) if isinstance(result, Shapable) else wrap(result, channel('_c')), '_c', shape)
net = dense_net(1, 1, layers=[8, 8], activation='ReLU') # Implemented for PyTorch, TensorFlow, Jax-Stax
optimizer = adam(net, 1e-3)
BATCH = batch(batch=100)
def loss_function(data: Tensor):
prediction = math.native_call(net, data)
label = math.sin(data)
return math.l2_loss(prediction - label), data, label
print(f"Initial loss: {loss_function(math.random_normal(BATCH))[0]}")
for i in range(100):
loss, _data, _label = update_weights(net, optimizer, loss_function, data=math.random_normal(BATCH))
print(f"Final loss: {loss}")
Initial loss: (batchᵇ=100) 0.195 ± 0.172 (2e-05...6e-01) Final loss: (batchᵇ=100) 0.093 ± 0.120 (5e-07...4e-01)
parameter_count(net)
97