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arrays
dimensionality reduction
ND arrays
1D arrays
data transformation

From ND to 1D arrays

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Introduction

Converting multidimensional (ND) arrays to one-dimensional (1D) arrays — called flattening or raveling — is one of the most common array operations in scientific computing. Machine learning models typically expect 1D feature vectors, many C libraries require contiguous 1D buffers, and serialization formats work with flat sequences. NumPy provides several methods to flatten arrays, each with different memory and performance characteristics.

Method 1: ndarray.flatten()

flatten() always returns a copy of the data as a contiguous 1D array:

python
1import numpy as np
2
3arr = np.array([[1, 2, 3],
4                [4, 5, 6]])
5
6flat = arr.flatten()
7print(flat)        # [1 2 3 4 5 6]
8print(flat.shape)  # (6,)
9
10# Modifying the flattened array does NOT affect the original
11flat[0] = 99
12print(arr[0, 0])   # 1 — unchanged

Row-major vs Column-major Order

python
1arr = np.array([[1, 2, 3],
2                [4, 5, 6]])
3
4# 'C' order (row-major, default) — reads across rows
5print(arr.flatten('C'))  # [1 2 3 4 5 6]
6
7# 'F' order (column-major, Fortran order) — reads down columns
8print(arr.flatten('F'))  # [1 4 2 5 3 6]
9
10# 'A' order — 'F' if array is Fortran-contiguous, else 'C'
11# 'K' order — flattens in memory layout order

Method 2: ndarray.ravel()

ravel() returns a 1D view when possible, avoiding a copy:

python
1arr = np.array([[1, 2, 3],
2                [4, 5, 6]])
3
4raveled = arr.ravel()
5print(raveled)  # [1 2 3 4 5 6]
6
7# Modifying the raveled array DOES affect the original (it's a view)
8raveled[0] = 99
9print(arr[0, 0])  # 99 — changed!

ravel() is faster and more memory-efficient than flatten() because it avoids copying data when the array is already contiguous. Use flatten() when you need an independent copy.

python
1arr = np.array([[1, 2, 3],
2                [4, 5, 6]])
3
4# ravel returns a view (no copy) for C-contiguous arrays
5r = arr.ravel()
6print(np.shares_memory(arr, r))  # True
7
8# flatten always copies
9f = arr.flatten()
10print(np.shares_memory(arr, f))  # False

Method 3: ndarray.reshape(-1)

reshape(-1) reshapes to 1D, returning a view when possible (same behavior as ravel()):

python
1arr = np.array([[1, 2, 3],
2                [4, 5, 6]])
3
4flat = arr.reshape(-1)
5print(flat)  # [1 2 3 4 5 6]
6
7# The -1 tells NumPy to infer the size
8# Equivalent to arr.reshape(arr.size)

reshape(-1) is commonly used in machine learning pipelines where you chain multiple reshape operations:

python
1# Flatten a batch of images: (32, 28, 28) → (32, 784)
2images = np.random.rand(32, 28, 28)
3flat_images = images.reshape(32, -1)
4print(flat_images.shape)  # (32, 784)

Method 4: np.concatenate or np.hstack

For flattening a list of arrays into one 1D array:

python
1arrays = [np.array([1, 2]), np.array([3, 4, 5]), np.array([6])]
2
3flat = np.concatenate(arrays)
4print(flat)  # [1 2 3 4 5 6]
5
6# For 2D arrays, flatten each first
7matrices = [np.array([[1, 2], [3, 4]]), np.array([[5, 6]])]
8flat = np.concatenate([m.ravel() for m in matrices])
9print(flat)  # [1 2 3 4 5 6]

Higher-Dimensional Arrays

All methods work on arrays of any dimensionality:

python
1# 3D array (e.g., RGB image)
2arr_3d = np.arange(24).reshape(2, 3, 4)
3print(arr_3d.shape)           # (2, 3, 4)
4print(arr_3d.flatten().shape) # (24,)
5print(arr_3d.ravel().shape)   # (24,)
6
7# 4D array (e.g., batch of images)
8arr_4d = np.zeros((10, 3, 32, 32))
9print(arr_4d.flatten().shape)  # (30720,)

Comparison of Methods

MethodReturns CopySpeedWhen to Use
flatten()AlwaysSlowerNeed independent copy
ravel()Only if neededFastestRead-only or safe mutation
reshape(-1)Only if neededFastChaining reshape operations
np.concatenateAlwaysModerateMerging multiple arrays

Flattening in Other Languages

Python Lists (No NumPy)

python
1# Nested list flattening
2nested = [[1, 2, 3], [4, 5], [6]]
3
4# List comprehension
5flat = [x for sublist in nested for x in sublist]
6print(flat)  # [1, 2, 3, 4, 5, 6]
7
8# itertools.chain
9from itertools import chain
10flat = list(chain.from_iterable(nested))

PyTorch

python
1import torch
2
3tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])
4flat = tensor.flatten()        # Returns a view when possible
5flat = tensor.reshape(-1)      # Equivalent
6flat = tensor.view(-1)         # Requires contiguous memory

Common Pitfalls

  • Unintended mutation with ravel(): Since ravel() returns a view, modifying the result modifies the original array. Use flatten() if you need an independent copy.
  • Non-contiguous arrays: Transposed or sliced arrays may not be contiguous in memory. ravel() and reshape(-1) will silently make a copy in these cases. Check with arr.flags['C_CONTIGUOUS'].
  • Order matters for ML: Most frameworks expect row-major ('C') order. If you flatten a Fortran-order array with the default 'C' order, the element sequence may be unexpected. Explicitly pass order='C' or order='F'.
  • Memory with large arrays: flatten() on a 10 GB array allocates another 10 GB. Use ravel() to avoid the copy, or process the array in chunks.
  • Nested Python lists vs NumPy: np.array(nested_list).flatten() only works if the nested list is rectangular (all sublists have the same length). For ragged lists, use itertools.chain.from_iterable.

Summary

  • Use arr.ravel() for the fastest, memory-efficient flattening (returns a view when possible)
  • Use arr.flatten() when you need a guaranteed independent copy
  • Use arr.reshape(-1) when chaining with other reshape operations
  • The default order is row-major ('C') — elements are read across rows first
  • For non-NumPy nested lists, use list comprehensions or itertools.chain.from_iterable
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