Warning
Pytorch tutorial

Pytorch is a numerical computation library with autograd capabilities. The following tutorial is to help refresh numpy basics and familiarize the student with the Pytorch numerical library. There are plenty high quality tutorials available online ranging from very basics to advanced concepts and state of the art implementations.

A good place to start would be here or the tutorial below which we will go through during class.

You can find a short presentation here for deep learning.

Make sure that you have Pytorch installed preferably with python3. You can do so by following the instructions from the getting started section. If you have a recent NVIDIA GPU then try to install the GPU version. In some cases the GPU can offer speedups of up to ~30x.

Numpy refresher

#!/usr/bin/env python
# coding: utf-8

# Tip: To execute a specific block of code from pycharm:
# a) open a python console (Tools -> python console),
# b) highlight code
# c) alt + shift + e to execute

import numpy as np

### Simple numerical manipulation recap. ###

# Numbers
a = 3; b = 2; c = 1
print("a: {}, b: {}, c: {}, a * b + c: {}".format(a,b,c, a * b + c))

# Tip: Use debugger to check the shapes and other attributes of the following vectors and matrices

# Vectors
a = np.array([10,40,20]); b = np.array([1,0.1,0.01]); c = 1.
print("a: {}, b: {}, c: {}, a * b + c: {}".format(a,b,c, a * b + c)) # Elementwise multiplication

a = np.array([[10,40,20]]); b = np.array([1,0.1,0.01]); c = 1.
print("a.shape: {}, b.shape: {}".format(a.shape, b.shape)) # Shapes of vectors as numpy sees it
print("a.T * b + c:") # Vector multiplication.
print(a.T * b + c)

# Matrices
A = np.eye(3); B = np.random.randn(3,3) # Identity and random 3x3 matrices

print("A: ")
print(A)

print("B: ")
print(B)

print("A * B: ")
print(A * B) # Elementwise multiplication

print("AB: ")
print(A @ B) # Matrix multiplication,  A @ B == A.dot(B) == np.matmul(A,B)

# Tip: There are various 'random' matrix types (normal, uniform, integer uniform, etc)

# Note:
# - Never use for loops to implement any sort of vector or matrix multiplication!
# - The difference between proper and sloppy implementation can be in several order of magnitudes of wait time.

# Practice (5 mins):
# 1) Make any [3x3] matrix M and [3x1] vector x. Multiply Q = Mx, Q = $x^T$M. Add x to M elementwise row by row with x (and then column by column).
# 2) Make an array a = [1,2,...30] (tip:use np.arange), b = [0,3,11,29]. Set the array a at positions indicated by vector b to 42 (tip:index a using b)
# 3) Make matrix B by tiling the first 5 elements of a 5 times vertically. Resultant matrix should have 5 row vectors which are [42,2,3,42,5] (tip: use np.tile)
# 4) Set last 2 columns of the last 2 rows of matrix B to zero

Pytorch basics

import torch
import numpy as np

### Pytorch Basics, use Debugger to inspect tensors (for finding out their shape and other attributes) ###

# Terminology: Tensor = any dimensional matrix

# Empty tensor of shape 5x3. Notice the initial values are (sometimes) whatever garbage was in memory.
x = torch.empty(5, 3)
print(x)

# Construct tensor directly from data
x = torch.tensor([5.5, 3])
print(x)

# Convert numpy arrays to pytorch
nparr = np.array([1,2])
x = torch.from_numpy(nparr)

# Convert pytorch arrays into numpy
nparr = x.numpy()

# Make operation using tensors (they support classic operators)
a = torch.tensor([3.])
b = torch.rand(1)
c = a + b # a + b = torch.add(a,b)
print("a: {}, b: {}, a + b: {}".format(a,b,c))

# Note, when performing operations make sure
# that the operands are of the same data type
a = torch.tensor(3)  # int64 type
b = torch.tensor(3.) # float32 type
print("atype: {}, btype: {}".format(a.dtype,b.dtype))

# ERROR, data type mismatch:
#print(a + b)

# Convert data type
b = torch.tensor(3., dtype=torch.int32) # Explicitly force datatype
b = b.long()
print(a + b)



# Make two tensors
a = torch.tensor(8., requires_grad=True)
b = torch.tensor(3., requires_grad=True)

# c tensor is a function of a,b
c = torch.exp((a / 2.) - b * b + 0.5)
print("c value before applying gradients: {}".format(c))

# Backwards pass
c.backward()

# Print gradients of individual tensors which contributed to c

# Move a,b towards the direction of greatest increase of c.
a = a + a.grad
b = b + b.grad
c = torch.exp((a / 2.) - b * b + 0.5)
print("c value after applying gradients: {}".format(c))

# If we don't want to track the history of operations then
# the torch.no_grad() context is used to create tensors and operations

# Note: Whenever we create a tensor or perform an operation requiring
# a gradient, a node is added to the operation graph in the background.
# This graph enables the backwards() pass to be called on any node and find all
# ancestor operations.

Simple regression

### Simple regressor: Optimizing bivariate rosenbrock function ###
### Rosenbrock function: f(x,y) = (a-x)^2 + b(y-x^2)^2 with global
### Min at (x,y) = (a,a^2). For a=1, b=100 this is (1,1)

# Clear all previous variables
import sys
sys.modules[__name__].__dict__.clear()

# Import everything
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F

# Define variables that we are minimizing
a = torch.tensor(1., requires_grad=False)
b = torch.tensor(100., requires_grad=False)
x = torch.randn(1, requires_grad=True)
y = torch.randn(1, requires_grad=True)

# Learning rate and iterations
lr = 0.001
iters = 10000

def rb_fun(x,y,a,b):
return (a - x) ** 2 + b * (y - x ** 2) ** 2

print("Initial values: x: {}, y: {}, f(x,y): {}".format(x,y,rb_fun(x,y,a,b)))

for i in range(iters):
# Forward pass:
loss = rb_fun(x,y,a,b)

# Backward pass
loss.backward()

x -= x.grad * lr
y -= y.grad * lr

# Manually zero the gradients after updating weights
print("Iteration: {}/{}, x,y: {},{}, loss: {}".format(i + 1, iters, x[0], y[0], loss[0]))