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https://github.com/asem000/kernex
Stencil computations in JAX
https://github.com/asem000/kernex
jax kernel stencil
Last synced: about 1 month ago
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Stencil computations in JAX
- Host: GitHub
- URL: https://github.com/asem000/kernex
- Owner: ASEM000
- License: mit
- Created: 2022-07-10T10:01:41.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2023-10-01T17:58:34.000Z (over 1 year ago)
- Last Synced: 2024-11-26T10:01:28.224Z (about 2 months ago)
- Topics: jax, kernel, stencil
- Language: Python
- Homepage:
- Size: 1.86 MB
- Stars: 66
- Watchers: 1
- Forks: 3
- Open Issues: 8
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
Differentiable Stencil computations in JAX
[**Installation**](#Installation)
|[**Description**](#Description)
|[**Quick example**](#QuickExample)
|[**More Examples**](#MoreExamples)
|[**Benchmarking**](#Benchmarking)
[](https://pepy.tech/project/kernex)
[](https://colab.research.google.com/drive/14UEqKzIyZsDzQ9IMeanvztXxbbbatTYV?usp=sharing)
[](https://codecov.io/gh/ASEM000/kernex)
[](https://zenodo.org/badge/latestdoi/512400616)
```python
pip install kernex
```
Kernex extends `jax.vmap`/`jax.lax.map`/`jax.pmap` with `kmap` and `jax.lax.scan` with `kscan` for general stencil computations.
kmap kscan
```python
import kernex as kex
import jax.numpy as jnp
@kex.kmap(kernel_size=(3,))
def sum_all(x):
return jnp.sum(x)
x = jnp.array([1,2,3,4,5])
print(sum_all(x))
# [ 6 9 12]
```
```python
import kernex as kex
import jax.numpy as jnp
@kex.kscan(kernel_size=(3,))
def sum_all(x):
return jnp.sum(x)
x = jnp.array([1,2,3,4,5])
print(sum_all(x))
# [ 6 13 22]
````
`jax.vmap` is used to sum each window content.
`lax.scan` is used to update the array and the window sum is calculated sequentially.
the first three rows represents the three sequential steps used to get the solution in the last row.
1️⃣ Convolution operation
```python
import jax
import jax.numpy as jnp
import kernex as kex
@jax.jit
@kex.kmap(
kernel_size= (3,3,3),
padding = ('valid','same','same'))
def kernex_conv2d(x,w):
# JAX channel first conv2d with 3x3x3 kernel_size
return jnp.sum(x*w)
```
2️⃣ Laplacian operation
```python
# see also
# https://numba.pydata.org/numba-doc/latest/user/stencil.html#basic-usage
import jax
import jax.numpy as jnp
import kernex as kex
@kex.kmap(
kernel_size=(3,3),
padding= 'valid',
relative=True) # `relative`= True enables relative indexing
def laplacian(x):
return ( 0*x[1,-1] + 1*x[1,0] + 0*x[1,1] +
1*x[0,-1] +-4*x[0,0] + 1*x[0,1] +
0*x[-1,-1] + 1*x[-1,0] + 0*x[-1,1] )
print(laplacian(jnp.ones([10,10])))
# [[0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.],
# [0., 0., 0., 0., 0., 0., 0., 0.]]
```
3️⃣ Get Patches of an array
```python
import jax
import jax.numpy as jnp
import kernex as kex
@kex.kmap(kernel_size=(3,3),relative=True)
def identity(x):
# similar to numba.stencil
# this function returns the top left cell in the padded/unpadded kernel view
# or center cell if `relative`=True
return x[0,0]
# unlike numba.stencil , vector output is allowed in kernex
# this function is similar to
# `jax.lax.conv_general_dilated_patches(x,(3,),(1,),padding='same')`
@jax.jit
@kex.kmap(kernel_size=(3,3),padding='same')
def get_3x3_patches(x):
# returns 5x5x3x3 array
return x
mat = jnp.arange(1,26).reshape(5,5)
print(mat)
# [[ 1 2 3 4 5]
# [ 6 7 8 9 10]
# [11 12 13 14 15]
# [16 17 18 19 20]
# [21 22 23 24 25]]
# get the view at array index = (0,0)
print(get_3x3_patches(mat)[0,0])
# [[0 0 0]
# [0 1 2]
# [0 6 7]]
```
4️⃣ Linear convection
Problem setup Stencil view
```python
import jax
import jax.numpy as jnp
import kernex as kex
import matplotlib.pyplot as plt
# see https://nbviewer.org/github/barbagroup/CFDPython/blob/master/lessons/01_Step_1.ipynb
tmax,xmax = 0.5,2.0
nt,nx = 151,51
dt,dx = tmax/(nt-1) , xmax/(nx-1)
u = jnp.ones([nt,nx])
c = 0.5
# kscan moves sequentially in row-major order and updates in-place using lax.scan.
F = kernex.kscan(
kernel_size = (3,3),
padding = ((1,1),(1,1)),
# n for time axis , i for spatial axis (optional naming)
named_axis={0:'n',1:'i'},
relative=True
)
# boundary condtion as a function
def bc(u):
return 1
# initial condtion as a function
def ic1(u):
return 1
def ic2(u):
return 2
def linear_convection(u):
return ( u['i','n-1'] - (c*dt/dx) * (u['i','n-1'] - u['i-1','n-1']) )
F[:,0] = F[:,-1] = bc # assign 1 for left and right boundary for all t
# square wave initial condition
F[:,:int((nx-1)/4)+1] = F[:,int((nx-1)/2):] = ic1
F[0:1, int((nx-1)/4)+1 : int((nx-1)/2)] = ic2
# assign linear convection function for
# interior spatial location [1:-1]
# and start from t>0 [1:]
F[1:,1:-1] = linear_convection
kx_solution = F(jnp.array(u))
plt.figure(figsize=(20,7))
for line in kx_solution[::20]:
plt.plot(jnp.linspace(0,xmax,nx),line)
```
5️⃣ Gaussian blur
```python
import jax
import jax.numpy as jnp
import kernex as kex
def gaussian_blur(image, sigma, kernel_size):
x = jnp.linspace(-(kernel_size - 1) / 2.0, (kernel_size- 1) / 2.0, kernel_size)
w = jnp.exp(-0.5 * jnp.square(x) * jax.lax.rsqrt(sigma))
w = jnp.outer(w, w)
w = w / w.sum()
@kex.kmap(kernel_size=(kernel_size, kernel_size), padding="same")
def conv(x):
return jnp.sum(x * w)
return conv(image)
```
6️⃣ Depthwise convolution
```python
import jax
import jax.numpy as jnp
import kernex as kex
@jax.jit
@jax.vmap
@kex.kmap(
kernel_size= (3,3),
padding = ('same','same'))
def kernex_depthwise_conv2d(x,w):
return jnp.sum(x*w)
h,w,c = 5,5,2
k=3
x = jnp.arange(1,h*w*c+1).reshape(c,h,w)
w = jnp.arange(1,k*k*c+1).reshape(c,k,k)
print(kernex_depthwise_conv2d(x,w))
````
7️⃣ Average pooling 2D
```python
@jax.vmap # vectorize over the channel dimension
@kex.kmap(kernel_size=(3,3), strides=(2,2))
def avgpool_2d(x):
# define the kernel for the Average pool operation over the spatial dimensions
return jnp.mean(x)
````
8️⃣ Runge-Kutta integration
```python
# lets solve dydt = y, where y0 = 1 and y(t)=e^t
# using Runge-Kutta 4th order method
# f(t,y) = y
import jax.numpy as jnp
import matplotlib.pyplot as plt
import kernex as kex
t = jnp.linspace(0, 1, 5)
y = jnp.zeros(5)
x = jnp.stack([y, t], axis=0)
dt = t[1] - t[0] # 0.1
f = lambda tn, yn: yn
def ic(x):
""" initial condition y0 = 1 """
return 1.
def rk4(x):
""" runge kutta 4th order integration step """
# ┌────┬────┬────┐ ┌──────┬──────┬──────┐
# │ y0 │*y1*│ y2 │ │[0,-1]│[0, 0]│[0, 1]│
# ├────┼────┼────┤ ==> ├──────┼──────┼──────┤
# │ t0 │ t1 │ t2 │ │[1,-1]│[1, 0]│[1, 1]│
# └────┴────┴────┘ └──────┴──────┴──────┘
t0 = x[1, -1]
y0 = x[0, -1]
k1 = dt * f(t0, y0)
k2 = dt * f(t0 + dt / 2, y0 + 1 / 2 * k1)
k3 = dt * f(t0 + dt / 2, y0 + 1 / 2 * k2)
k4 = dt * f(t0 + dt, y0 + k3)
yn_1 = y0 + 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
return yn_1
F = kex.kscan(kernel_size=(2, 3), relative=True, padding=((0, 1))) # kernel size = 3
F[0:1, 1:] = rk4
F[0, 0] = ic
# compile the solver
solver = jax.jit(F.__call__)
y = solver(x)[0, :]
plt.plot(t, y, '-o', label='rk4')
plt.plot(t, jnp.exp(t), '-o', label='analytical')
plt.legend()
```
