NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
A Complete One-Module Learning Tutorial with Examples
Module Objective
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
1. Setup & Installation
pip install numpy torch
import numpy as np
import torch
print(f"NumPy version: {np.__version__}")
print(f"PyTorch version: {torch.__version__}")
Key Concept:
-np.array→torch.tensor
- Both are N-dimensional arrays, but PyTorch adds autograd & GPU support.
2. Creating Tensors (Arrays)
| Operation | NumPy | PyTorch |
|---|---|---|
| From list | np.array([1,2,3]) |
torch.tensor([1,2,3]) |
| Zeros | np.zeros((2,3)) |
torch.zeros(2,3) |
| Ones | np.ones((2,3)) |
torch.ones(2,3) |
| Range | np.arange(0,10,2) |
torch.arange(0,10,2) |
| Linspace | np.linspace(0,1,5) |
torch.linspace(0,1,5) |
| Random | np.random.rand(2,3) |
torch.rand(2,3) |
Example:
# NumPy
np_arr = np.array([[1, 2], [3, 4]])
np_zeros = np.zeros((2, 2))
np_rand = np.random.randn(2, 2)
# PyTorch
torch_arr = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
torch_zeros = torch.zeros(2, 2)
torch_rand = torch.randn(2, 2)
print("NumPy Array:\n", np_arr)
print("PyTorch Tensor:\n", torch_arr)
Note: Use
dtype=torch.float32for ML compatibility.
3. Data Types (dtype)
# NumPy
np_int = np.array([1, 2], dtype=np.int32)
np_float = np.array([1.0, 2.0], dtype=np.float64)
# PyTorch
torch_int = torch.tensor([1, 2], dtype=torch.int32)
torch_float = torch.tensor([1.0, 2.0], dtype=torch.float32) # Default for ML
Common PyTorch dtypes:
torch.float32 # float
torch.float64 # double
torch.int32 # int
torch.int64 # long
torch.bool
4. Shape, Size, Reshape
| Operation | NumPy | PyTorch |
|---|---|---|
| Shape | .shape |
.shape or .size() |
| Reshape | .reshape(2,3) |
.reshape(2,3) or .view(2,3) |
| Flatten | .flatten() |
.flatten() or .view(-1) |
Example:
x_np = np.arange(6)
x_torch = torch.arange(6)
print("Original:", x_torch)
print("Reshaped (view):", x_torch.view(2, 3))
print("Reshaped (reshape):", x_torch.reshape(2, 3))
print("Flattened:", x_torch.flatten())
.view()requires contiguous memory
.reshape()is more flexible (may copy)
5. Indexing & Slicing
arr = np.arange(10)
tensor = torch.arange(10)
# Same syntax!
print(arr[2:5]) # [2 3 4]
print(tensor[2:5]) # tensor([2, 3, 4])
# 2D indexing
mat_np = np.array([[1,2,3], [4,5,6]])
mat_torch = torch.tensor([[1,2,3], [4,5,6]])
print(mat_np[1, 2]) # 6
print(mat_torch[1, 2]) # 6
Advanced: Boolean masking
mask = tensor > 5
print(tensor[mask]) # tensor([6, 7, 8, 9])
6. Math Operations (Element-wise)
| Operation | NumPy | PyTorch |
|---|---|---|
| Add | + or np.add() |
+ or torch.add() |
| Multiply | * |
* |
| Power | ** or np.power() |
** or torch.pow() |
| sqrt, exp, log | np.sqrt(), etc. |
torch.sqrt(), etc. |
Example:
a = torch.tensor([1., 2., 3.])
b = torch.tensor([4., 5., 6.])
print(a + b) # tensor([5., 7., 9.])
print(a * b) # tensor([ 4., 10., 18.])
print(a ** 2) # tensor([1., 4., 9.])
print(torch.sqrt(a)) # tensor([1.0000, 1.4142, 1.7321])
7. Broadcasting (Same as NumPy!)
A = torch.randn(3, 1)
b = torch.tensor([[10], [20], [30]])
print(A + b)
# Works: b (3,1) broadcast to match A (3,1)
8. Matrix Operations
| Operation | NumPy | PyTorch |
|---|---|---|
| Transpose | .T |
.T or .transpose(0,1) |
| MatMul | @ or np.matmul() |
@ or torch.matmul() |
| Dot | np.dot() |
torch.dot() (1D only) |
Example:
A = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
B = torch.tensor([[5, 6], [7, 8]], dtype=torch.float32)
print("A @ B:\n", A @ B)
print("torch.matmul(A, B):\n", torch.matmul(A, B))
print("A.T:\n", A.T)
9. Aggregation (Sum, Mean, Max, etc.)
x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
print(x.sum()) # tensor(10.)
print(x.sum(dim=0)) # tensor([4., 6.]) → column sum
print(x.sum(dim=1)) # tensor([3., 7.]) → row sum
print(x.mean(), x.std())
print(x.max(), x.argmax())
10. NumPy ↔ PyTorch Conversion
# NumPy → PyTorch
np_arr = np.array([[1, 2], [3, 4]])
torch_tensor = torch.from_numpy(np_arr) # Shares memory!
# PyTorch → NumPy
torch_tensor2 = torch.tensor([[5, 6], [7, 8]])
np_arr2 = torch_tensor2.numpy() # Shares memory (if on CPU)
Warning: Shared memory → changes in one affect the other!
np_arr[0,0] = 99
print(torch_tensor) # Changed too!
11. GPU Acceleration (PyTorch Only!)
if torch.cuda.is_available():
device = torch.device("cuda")
else:
device = torch.device("cpu")
x = torch.randn(1000, 1000, device=device)
y = torch.randn(1000, 1000, device=device)
%timeit x @ y # Much faster on GPU!
Move tensor to GPU:
x_cpu = torch.randn(3, 3)
x_gpu = x_cpu.to('cuda') # or .cuda()
x_back = x_gpu.to('cpu') # or .cpu()
12. Autograd: The Magic of PyTorch
x = torch.tensor([2.0], requires_grad=True)
y = x ** 2 + 3 * x + 1
y.backward() # Compute gradient
print(x.grad) # tensor([7.]) → dy/dx = 2x + 3
NumPy has no autograd → PyTorch enables deep learning.
13. Full Working Example: Linear Regression Step
# Data
X_np = np.array([[1], [2], [3], [4]], dtype=np.float32)
y_np = np.array([[2], [4], [6], [8]], dtype=np.float32)
# To PyTorch
X = torch.from_numpy(X_np)
y = torch.from_numpy(y_np)
# Model: y = w * x + b
w = torch.randn(1, requires_grad=True)
b = torch.randn(1, requires_grad=True)
lr = 0.01
for epoch in range(100):
y_pred = X @ w + b
loss = ((y_pred - y) ** 2).mean()
loss.backward()
with torch.no_grad():
w -= lr * w.grad
b -= lr * b.grad
w.grad.zero_()
b.grad.zero_()
print(f"Learned: y = {w.item():.2f}x + {b.item():.2f}")
Output:
y = 2.00x + 0.00→ Perfect fit!
Summary Cheat Sheet
| Concept | NumPy | PyTorch |
|---|---|---|
| Array | np.array() |
torch.tensor() |
| Zeros | np.zeros() |
torch.zeros() |
| Shape | .shape |
.shape |
| Reshape | .reshape() |
.reshape() / .view() |
| Transpose | .T |
.T |
| MatMul | @ |
@ |
| Sum | .sum(axis=) |
.sum(dim=) |
| GPU | ❌ | tensor.to('cuda') |
| Autograd | ❌ | requires_grad=True |
| Convert | — | torch.from_numpy(), .numpy() |
Practice Exercises
- Create a 3×3 identity matrix in both NumPy and PyTorch.
- Compute element-wise
sin(x) + cos(x)^2forx = [0, π/2, π]. - Perform matrix multiplication of two random 4×4 matrices on GPU.
- Convert a NumPy array to PyTorch, modify it, and see shared memory effect.
- Write a PyTorch version of
np.linalg.norm()using only basic ops.
Final Words
NumPy is great for scientific computing.
PyTorch is NumPy + autograd + GPU + deep learning.
You now have full fluency to move from NumPy → PyTorch!
Keep Learning:
Try torch.nn, DataLoader, and build your first neural net next!
End of Module
Mastered: Arrays → Tensors → Math → GPU → Autograd
Now go build something awesome! 🚀
Last updated: Nov 13, 2025
NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
NumPy → PyTorch: Math, Tensors, Arrays, Matrices & Vector Operations
A Complete One-Module Learning Tutorial with Examples
Module Objective
Master the transition from NumPy to PyTorch by understanding how core mathematical operations on arrays, matrices, and vectors map between the two libraries — with practical, runnable examples.
1. Setup & Installation
pip install numpy torch
import numpy as np
import torch
print(f"NumPy version: {np.__version__}")
print(f"PyTorch version: {torch.__version__}")
Key Concept:
-np.array→torch.tensor
- Both are N-dimensional arrays, but PyTorch adds autograd & GPU support.
2. Creating Tensors (Arrays)
| Operation | NumPy | PyTorch |
|---|---|---|
| From list | np.array([1,2,3]) |
torch.tensor([1,2,3]) |
| Zeros | np.zeros((2,3)) |
torch.zeros(2,3) |
| Ones | np.ones((2,3)) |
torch.ones(2,3) |
| Range | np.arange(0,10,2) |
torch.arange(0,10,2) |
| Linspace | np.linspace(0,1,5) |
torch.linspace(0,1,5) |
| Random | np.random.rand(2,3) |
torch.rand(2,3) |
Example:
# NumPy
np_arr = np.array([[1, 2], [3, 4]])
np_zeros = np.zeros((2, 2))
np_rand = np.random.randn(2, 2)
# PyTorch
torch_arr = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
torch_zeros = torch.zeros(2, 2)
torch_rand = torch.randn(2, 2)
print("NumPy Array:\n", np_arr)
print("PyTorch Tensor:\n", torch_arr)
Note: Use
dtype=torch.float32for ML compatibility.
3. Data Types (dtype)
# NumPy
np_int = np.array([1, 2], dtype=np.int32)
np_float = np.array([1.0, 2.0], dtype=np.float64)
# PyTorch
torch_int = torch.tensor([1, 2], dtype=torch.int32)
torch_float = torch.tensor([1.0, 2.0], dtype=torch.float32) # Default for ML
Common PyTorch dtypes:
torch.float32 # float
torch.float64 # double
torch.int32 # int
torch.int64 # long
torch.bool
4. Shape, Size, Reshape
| Operation | NumPy | PyTorch |
|---|---|---|
| Shape | .shape |
.shape or .size() |
| Reshape | .reshape(2,3) |
.reshape(2,3) or .view(2,3) |
| Flatten | .flatten() |
.flatten() or .view(-1) |
Example:
x_np = np.arange(6)
x_torch = torch.arange(6)
print("Original:", x_torch)
print("Reshaped (view):", x_torch.view(2, 3))
print("Reshaped (reshape):", x_torch.reshape(2, 3))
print("Flattened:", x_torch.flatten())
.view()requires contiguous memory
.reshape()is more flexible (may copy)
5. Indexing & Slicing
arr = np.arange(10)
tensor = torch.arange(10)
# Same syntax!
print(arr[2:5]) # [2 3 4]
print(tensor[2:5]) # tensor([2, 3, 4])
# 2D indexing
mat_np = np.array([[1,2,3], [4,5,6]])
mat_torch = torch.tensor([[1,2,3], [4,5,6]])
print(mat_np[1, 2]) # 6
print(mat_torch[1, 2]) # 6
Advanced: Boolean masking
mask = tensor > 5
print(tensor[mask]) # tensor([6, 7, 8, 9])
6. Math Operations (Element-wise)
| Operation | NumPy | PyTorch |
|---|---|---|
| Add | + or np.add() |
+ or torch.add() |
| Multiply | * |
* |
| Power | ** or np.power() |
** or torch.pow() |
| sqrt, exp, log | np.sqrt(), etc. |
torch.sqrt(), etc. |
Example:
a = torch.tensor([1., 2., 3.])
b = torch.tensor([4., 5., 6.])
print(a + b) # tensor([5., 7., 9.])
print(a * b) # tensor([ 4., 10., 18.])
print(a ** 2) # tensor([1., 4., 9.])
print(torch.sqrt(a)) # tensor([1.0000, 1.4142, 1.7321])
7. Broadcasting (Same as NumPy!)
A = torch.randn(3, 1)
b = torch.tensor([[10], [20], [30]])
print(A + b)
# Works: b (3,1) broadcast to match A (3,1)
8. Matrix Operations
| Operation | NumPy | PyTorch |
|---|---|---|
| Transpose | .T |
.T or .transpose(0,1) |
| MatMul | @ or np.matmul() |
@ or torch.matmul() |
| Dot | np.dot() |
torch.dot() (1D only) |
Example:
A = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
B = torch.tensor([[5, 6], [7, 8]], dtype=torch.float32)
print("A @ B:\n", A @ B)
print("torch.matmul(A, B):\n", torch.matmul(A, B))
print("A.T:\n", A.T)
9. Aggregation (Sum, Mean, Max, etc.)
x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float32)
print(x.sum()) # tensor(10.)
print(x.sum(dim=0)) # tensor([4., 6.]) → column sum
print(x.sum(dim=1)) # tensor([3., 7.]) → row sum
print(x.mean(), x.std())
print(x.max(), x.argmax())
10. NumPy ↔ PyTorch Conversion
# NumPy → PyTorch
np_arr = np.array([[1, 2], [3, 4]])
torch_tensor = torch.from_numpy(np_arr) # Shares memory!
# PyTorch → NumPy
torch_tensor2 = torch.tensor([[5, 6], [7, 8]])
np_arr2 = torch_tensor2.numpy() # Shares memory (if on CPU)
Warning: Shared memory → changes in one affect the other!
np_arr[0,0] = 99
print(torch_tensor) # Changed too!
11. GPU Acceleration (PyTorch Only!)
if torch.cuda.is_available():
device = torch.device("cuda")
else:
device = torch.device("cpu")
x = torch.randn(1000, 1000, device=device)
y = torch.randn(1000, 1000, device=device)
%timeit x @ y # Much faster on GPU!
Move tensor to GPU:
x_cpu = torch.randn(3, 3)
x_gpu = x_cpu.to('cuda') # or .cuda()
x_back = x_gpu.to('cpu') # or .cpu()
12. Autograd: The Magic of PyTorch
x = torch.tensor([2.0], requires_grad=True)
y = x ** 2 + 3 * x + 1
y.backward() # Compute gradient
print(x.grad) # tensor([7.]) → dy/dx = 2x + 3
NumPy has no autograd → PyTorch enables deep learning.
13. Full Working Example: Linear Regression Step
# Data
X_np = np.array([[1], [2], [3], [4]], dtype=np.float32)
y_np = np.array([[2], [4], [6], [8]], dtype=np.float32)
# To PyTorch
X = torch.from_numpy(X_np)
y = torch.from_numpy(y_np)
# Model: y = w * x + b
w = torch.randn(1, requires_grad=True)
b = torch.randn(1, requires_grad=True)
lr = 0.01
for epoch in range(100):
y_pred = X @ w + b
loss = ((y_pred - y) ** 2).mean()
loss.backward()
with torch.no_grad():
w -= lr * w.grad
b -= lr * b.grad
w.grad.zero_()
b.grad.zero_()
print(f"Learned: y = {w.item():.2f}x + {b.item():.2f}")
Output:
y = 2.00x + 0.00→ Perfect fit!
Summary Cheat Sheet
| Concept | NumPy | PyTorch |
|---|---|---|
| Array | np.array() |
torch.tensor() |
| Zeros | np.zeros() |
torch.zeros() |
| Shape | .shape |
.shape |
| Reshape | .reshape() |
.reshape() / .view() |
| Transpose | .T |
.T |
| MatMul | @ |
@ |
| Sum | .sum(axis=) |
.sum(dim=) |
| GPU | ❌ | tensor.to('cuda') |
| Autograd | ❌ | requires_grad=True |
| Convert | — | torch.from_numpy(), .numpy() |
Practice Exercises
- Create a 3×3 identity matrix in both NumPy and PyTorch.
- Compute element-wise
sin(x) + cos(x)^2forx = [0, π/2, π]. - Perform matrix multiplication of two random 4×4 matrices on GPU.
- Convert a NumPy array to PyTorch, modify it, and see shared memory effect.
- Write a PyTorch version of
np.linalg.norm()using only basic ops.
Final Words
NumPy is great for scientific computing.
PyTorch is NumPy + autograd + GPU + deep learning.
You now have full fluency to move from NumPy → PyTorch!
Keep Learning:
Try torch.nn, DataLoader, and build your first neural net next!
End of Module
Mastered: Arrays → Tensors → Math → GPU → Autograd
Now go build something awesome! 🚀
Last updated: Nov 13, 2025