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 *
2022-09-13 13:21:59.556844: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 AVX512F FMA To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags. 2022-09-13 13:21:59.708110: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudart.so.11.0'; dlerror: libcudart.so.11.0: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /opt/hostedtoolcache/Python/3.8.13/x64/lib 2022-09-13 13:21:59.708138: I tensorflow/stream_executor/cuda/cudart_stub.cc:29] Ignore above cudart dlerror if you do not have a GPU set up on your machine. 2022-09-13 13:21:59.741688: E tensorflow/stream_executor/cuda/cuda_blas.cc:2981] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered 2022-09-13 13:22:00.438957: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /opt/hostedtoolcache/Python/3.8.13/x64/lib 2022-09-13 13:22:00.439056: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /opt/hostedtoolcache/Python/3.8.13/x64/lib 2022-09-13 13:22:00.439065: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly. 2022-09-13 13:22:01.583094: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: AVX2 AVX512F FMA To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags. 2022-09-13 13:22:01.583582: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /opt/hostedtoolcache/Python/3.8.13/x64/lib 2022-09-13 13:22:01.583603: W tensorflow/stream_executor/cuda/cuda_driver.cc:263] failed call to cuInit: UNKNOWN ERROR (303) 2022-09-13 13:22:01.583623: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (fv-az456-114): /proc/driver/nvidia/version does not exist WARNING:absl: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')
[PyTorch device 'CPU' (CPU 'cpu') | 6944 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) 0.608 ± 0.282 (5e-02...1e+00)
data.examples[0]
(x=0.871, y=0.789)
Tensor¶print(data)
print(f"{data:full:shape:dtype:color:.1f}")
(examplesᵇ=10, vectorᶜ=x,y) 0.608 ± 0.282 (5e-02...1e+00) (examplesᵇ=10, vectorᶜ=x,y) [[0.9, 0.8], [0.5, 0.6], [0.8, 0.3], [1.0, 0.5], [0.2, 0.8], [0.3, 0.0], [0.9, 0.9], [0.7, 0.5], [0.2, 0.9], [0.9, 0.4]]
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([[0.17616528, 0.6013631 , 0.36094433, 0.20472902, 0.16400862,
0.25677615],
[0.32719547, 0.15396899, 0.05899274, 0.9278435 , 0.5518921 ,
0.1579479 ],
[0.45076597, 0.09556979, 0.9008163 , 0.13820606, 0.81804067,
0.6819951 ],
[0.4794073 , 0.82579744, 0.24724197, 0.7119945 , 0.37868965,
0.64616275],
[0.7137551 , 0.8280042 , 0.31106597, 0.6682521 , 0.12629735,
0.566531 ],
[0.7600771 , 0.9057115 , 0.9751028 , 0.46944147, 0.67437017,
0.7993089 ],
[0.66953206, 0.46907622, 0.43060178, 0.2922321 , 0.07208836,
0.5162261 ],
[0.55641645, 0.1779018 , 0.5964567 , 0.23663741, 0.9713944 ,
0.7174101 ]], dtype=float32)
math.reshaped_native(data, ['extra', data.shape], to_numpy=True)
array([[0.17616528, 0.6013631 , 0.36094433, 0.20472902, 0.16400862,
0.25677615, 0.32719547, 0.15396899, 0.05899274, 0.9278435 ,
0.5518921 , 0.1579479 , 0.45076597, 0.09556979, 0.9008163 ,
0.13820606, 0.81804067, 0.6819951 , 0.4794073 , 0.82579744,
0.24724197, 0.7119945 , 0.37868965, 0.64616275, 0.7137551 ,
0.8280042 , 0.31106597, 0.6682521 , 0.12629735, 0.566531 ,
0.7600771 , 0.9057115 , 0.9751028 , 0.46944147, 0.67437017,
0.7993089 , 0.66953206, 0.46907622, 0.43060178, 0.2922321 ,
0.07208836, 0.5162261 , 0.55641645, 0.1779018 , 0.5964567 ,
0.23663741, 0.9713944 , 0.7174101 ]], 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 5 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, 0, x0=0))
tensor(42.)
from functools import partial
periodic_laplace = partial(math.laplace, padding=extrapolation.PERIODIC)
matrix = math.jit_compile_linear(periodic_laplace).sparse_matrix(math.zeros(spatial(x=5)), format='coo') # csr, csc, coo
math.print(matrix.values)
1., 1., -2., 1., 1., -2., 1., 1., -2., 1., 1., -2., 1., 1., -2.
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')).with_color('#FFFFFF')
vis.plot(vis.overlay(f_grid, *segments, anim_segments), animate='time', frame_time=500)
<Figure size 640x480 with 0 Axes>
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) 0.197 ± 0.218 (9e-06...7e-01) Final loss: (batchᵇ=100) 0.180 ± 0.188 (5e-06...6e-01)
parameter_count(net)
97