Numpy

NumPy

What I do

I provide fundamental numerical computing capabilities for Python through powerful N-dimensional array objects and mathematical functions. I enable efficient array operations, linear algebra computations, random number generation, Fourier transforms, and statistical calculations. I am the backbone of scientific computing in Python and serve as the foundation for pandas, scikit-learn, and other data science libraries.

When to use me

• Performing numerical computations on large datasets
• Working with multi-dimensional arrays and matrices
• Implementing mathematical and statistical operations
• Linear algebra operations (matrix multiplication, eigenvalues, decompositions)
• Random sampling and probability distributions
• Signal processing and Fourier analysis
• Image processing (as multi-dimensional arrays)
• Performance-critical numerical code

Core Concepts

Arrays

• ndarray: N-dimensional array object with homogeneous data types
• Shape: Dimensions of the array (e.g., (1000, 50) for 1000 rows, 50 columns)
• Data Types: int8-uint64, float16-float128, complex, bool, object
• Memory Layout: C-contiguous (row-major) or Fortran-contiguous (column-major)

Array Creation

• From scratch: np.zeros(), np.ones(), np.empty(), np.arange(), np.linspace()
• From data: np.array(), np.asarray(), np.fromfunction()
• Random arrays: np.random.rand(), np.random.randint(), np.random.randn()
• Special matrices: np.eye(), np.identity(), np.diag()

Indexing and Slicing

• Basic indexing: Single element arr[0, 0], slices arr[1:5, :]
• Boolean indexing: arr[arr > 0] for filtering
• Fancy indexing: arr[[0, 2, 5]] for multiple indices
• Advanced indexing: Integer arrays arr[np.newaxis, :]

Broadcasting

• Automatic expansion of arrays with different shapes for element-wise operations
• Rule 1: Dimensions match from right to left
• Rule 2: Dimensions of size 1 can be stretched to match
• Enables vectorized operations without explicit loops

Vectorization

• ufuncs: Universal functions for element-wise operations (np.add, np.multiply)
• Reduction operations: np.sum(), np.mean(), np.max(), np.min()
• Accumulation: np.cumsum(), np.cumprod()
• Sorting: np.sort(), np.argsort(), np.partition()

Code Examples (Python)

import numpy as np

# Array creation
arr = np.array([1, 2, 3, 4, 5])
zeros = np.zeros((3, 4)) 3), dtype=int)
arange = np.arange(0, 10, 2)
linspace = np.linspace(0, 1, 100)
random = np.random.rand(1000)
random_normal = np.random.randn(1000)
random_int = np.random.randint(0, 100, (5, 5))
identity = np.eye(3)
diagonal = np.diag([1, 2, 3])

# Array properties
arr.shape  # (5,) or (rows, cols)
arr.dtype  # dtype('int64')
arr.ndim  # Number of dimensions
arr.size  # Total elements
arr.nbytes  # Memory usage in bytes

# Reshaping
arr = np.arange(12)
reshaped = arr.reshape(3, 4)
flattened = reshaped.ravel()
transposed = reshaped.T
newaxis = arr[:, np.newaxis]

# Indexing
arr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
arr[0, 0]  # First element: 1
arr[0]  # First row: [1, 2, 3]
arr[:, 0]  # First column: [1, 4, 7]
arr[1:3, 1:3]  # Sub-array
arr[arr > 5]  # Boolean indexing: [6, 7, 8, 9]
arr[[0, 2], [0, 2]]  # Fancy indexing: [1, 9]

# Mathematical operations
arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])
np.add(arr1, arr2)  # [5, 7, 9]
np.multiply(arr1, arr2)  # [4, 10, 18]
np.divide(arr1, arr2)  # [0.25, 0.4, 0.5]
np.power(arr1, 2)  # [1, 4, 9]
np.sqrt(arr1)  # [1.0, 1.414, 1.732]
np.exp(arr1)  # [2.718, 7.389, 20.086]
np.log(arr1)  # [0.0, 0.693, 1.099]

# Broadcasting
arr1 = np.array([[1], [2], [3]])  # (3, 1)
arr2 = np.array([4, 5, 6])  # (3,)
result = arr1 + arr2  # [[5, 6, 7], [6, 7, 8], [7, 8, 9]]

# Reductions
arr = np.array([1, 2, 3, 4, 5])
np.sum(arr)  # 15
np.mean(arr)  # 3.0
np.std(arr)  # 1.414...
np.var(arr)  # 2.0
np.min(arr)  # 1
np.max(arr)  # 5
np.argmax(arr)  # 4
np.median(arr)  # 3.0
np.percentile(arr, 75)  # 4.0

# Axis-based operations
matrix = np.array([[1, 2, 3], [4, 5, 6]])
np.sum(matrix, axis=0)  # Column sums: [5, 7, 9]
np.sum(matrix, axis=1)  # Row sums: [6, 15]
np.mean(matrix, axis=1)  # Row means: [2.0, 5.0]

# Linear algebra
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
np.dot(A, B)  # Matrix multiplication
A @ B  # Same as above
np.linalg.det(A)  # Determinant: -2
np.linalg.inv(A)  # Inverse
np.linalg.eig(A)  # Eigenvalues and eigenvectors
np.linalg.solve(A, np.array([5, 6]))  # Solve Ax = b
np.linalg.svd(A)  # Singular value decomposition
np.linalg.qr(A)  # QR decomposition
np.linalg.norm(A)  # Matrix/vector norm

# Random number generation
np.random.seed(42)  # Set seed
np.random.rand(5)  # Uniform [0, 1)
np.random.randn(5)  # Standard normal
np.random.randint(0, 10, 5)  # Random integers
np.random.uniform(0, 1, 5)  # Explicit uniform
np.random.normal(0, 1, 5)  # Explicit normal
np.random.choice([1, 2, 3, 4, 5], 3, replace=False)  # Without replacement
np.random.permutation(5)  # Permutation

# Distributions
np.random.binomial(10, 0.5, 100)  # Binomial
np.random.poisson(5, 100)  # Poisson
np.random.exponential(1, 100)  # Exponential
np.random.uniform(0, 1, 100)  # Uniform
np.random.normal(0, 1, 100)  # Normal

# Sorting
arr = np.array([3, 1, 4, 1, 5, 9, 2])
np.sort(arr)  # Sorted array
np.argsort(arr)  # Indices
np.partition(arr, 3)  # Partition around 3rd element

# Set operations
arr1 = np.array([1, 2, 3, 4, 5])
arr2 = np.array([3, 4, 5, 6, 7])
np.union1d(arr1, arr2)  # [1, 2, 3, 4, 5, 6, 7]
np.intersect1d(arr1, arr2)  # [3, 4, 5]
np.setdiff1d(arr1, arr2)  # [1, 2]

Best Practices

1. Use vectorization: Replace Python loops with NumPy vectorized operations for 10-100x speedup.

2. Pre-allocate arrays: Create arrays with known sizes before loops instead of appending.

3. Use appropriate dtypes: Choose smaller dtypes (float32 instead of float64) when precision permits.

4. Avoid copies: Use views (reshape, strides) instead of copies when possible.

5. Use in-place operations: arr += 5 instead of arr = arr + 5 to avoid temporary arrays.

6. Leverage broadcasting: Write clean code that broadcasts instead of explicit tiling.

7. Use np.newaxis: Create proper dimensions for broadcasting.

8. Memory-mapped arrays: For large datasets, use np.memmap to avoid loading everything into memory.

Common Patterns

Pattern 1: Efficient Loop Replacement

# Instead of this:
result = []
for i in range(len(data)):
    if data[i] > 0:
        result.append(data[i] ** 2)

# Use this:
result = data[data > 0] ** 2

Pattern 2: Moving Average Calculation

def moving_average(arr, window):
    """Calculate moving average using convolution."""
    kernel = np.ones(window) / window
    return np.convolve(arr, kernel, mode='valid')

# Or using rolling window:
def rolling_mean(arr, window):
    return np.array([arr[max(0,i):i+1].mean() 
                     for i in range(len(arr))])

Pattern 3: Distance Matrix Computation

def compute_distance_matrix(X, metric='euclidean'):
    """Compute pairwise distances efficiently."""
    # euclidean: ||a - b||^2 = ||a||^2 + ||b||^2 - 2*a.b
    X_sq = np.sum(X**2, axis=1)
    dist_sq = X_sq[:, np.newaxis] + X_sq[np.newaxis, :] - 2 @ X @ X.T
    dist_sq = np.maximum(dist_sq, 0)  # Numerical precision
    if metric == 'euclidean':
        return np.sqrt(dist_sq)
    return dist_sq