PyTorch Library

3.

Tensor Operations and Manipulation

3.1.

Indexing and Slicing

3.1.1.

3.1.1.1.

Single Element Access

3.1.1.2.

Multi-dimensional Indexing

3.1.2.

Slicing Operations

3.1.2.1.

3.1.2.2.

3.1.2.3.

Negative Indexing

3.1.3.

Advanced Indexing

3.1.3.1.

Boolean Indexing

3.1.3.2.

3.1.3.3.

3.1.4.

Conditional Selection

3.1.4.1.

3.1.4.2.

torch.masked_select()

3.2.

Tensor Shape Manipulation

3.2.1.

Reshaping Operations

3.2.1.1.

torch.reshape()

3.2.1.2.

3.2.1.3.

Automatic Size Inference

3.2.2.

Dimension Manipulation

3.2.2.1.

torch.squeeze()

3.2.2.2.

torch.unsqueeze()

3.2.2.3.

Adding and Removing Dimensions

3.2.3.

Transposition and Permutation

3.2.3.1.

torch.transpose()

3.2.3.2.

torch.permute()

3.2.3.3.

Matrix Transposition

3.2.4.

Flattening Operations

3.2.4.1.

torch.flatten()

3.2.4.2.

Multi-dimensional Flattening

3.2.5.

Expansion and Repetition

3.2.5.1.

3.2.5.2.

3.2.5.3.

Broadcasting vs Expansion

3.3.

Joining and Splitting Tensors

3.3.1.

Concatenation Operations

3.3.1.1.

3.3.1.2.

Concatenation Along Different Axes

3.3.2.

Stacking Operations

3.3.2.1.

3.3.2.2.

Creating New Dimensions

3.3.3.

Splitting Operations

3.3.3.1.

3.3.3.2.

3.3.3.3.

3.3.4.

Gathering and Scattering

3.3.4.1.

3.3.4.2.

torch.scatter()

3.3.4.3.

Index-based Operations

3.4.

Mathematical Operations

3.4.1.

Element-wise Arithmetic

3.4.1.1.

Addition and Subtraction

3.4.1.2.

Multiplication and Division

3.4.1.3.

Power and Root Operations

3.4.1.4.

Modular Arithmetic

3.4.2.

Trigonometric Functions

3.4.2.1.

Basic Trigonometric Functions

3.4.2.2.

Inverse Trigonometric Functions

3.4.2.3.

Hyperbolic Functions

3.4.3.

Exponential and Logarithmic Functions

3.4.3.1.

3.4.3.2.

3.4.3.3.

3.4.3.4.

3.4.4.

Rounding and Ceiling Functions

3.4.4.1.

3.4.4.2.

3.4.4.3.

3.4.4.4.

3.4.5.

Statistical Functions

3.4.5.1.

3.4.5.2.

3.4.5.3.

3.5.

Reduction Operations

3.5.1.

3.5.1.1.

3.5.1.2.

Dimension-specific Sums

3.5.1.3.

Cumulative Sums

3.5.2.

Mean and Average

3.5.2.1.

3.5.2.2.

Weighted Averages

3.5.3.

Variance and Standard Deviation

3.5.3.1.

3.5.3.2.

3.5.3.3.

Bessel's Correction

3.5.4.

Min and Max Operations

3.5.4.1.

3.5.4.2.

3.5.4.3.

3.5.4.4.

3.5.5.

Product Operations

3.5.5.1.

3.5.5.2.

torch.cumprod()

3.5.6.

Norm Calculations

3.5.6.1.

3.5.6.2.

Different Norm Types

3.6.

Comparison Operations

3.6.1.

Element-wise Comparisons

3.6.1.1.

3.6.1.2.

3.6.1.3.

3.6.1.4.

3.6.1.5.

3.6.1.6.

3.6.2.

Logical Operations

3.6.2.1.

torch.logical_and()

3.6.2.2.

torch.logical_or()

3.6.2.3.

torch.logical_not()

3.6.2.4.

torch.logical_xor()

3.6.3.

Sorting Operations

3.6.3.1.

3.6.3.2.

torch.argsort()

3.6.3.3.

3.7.

Linear Algebra Operations

3.7.1.

Matrix Multiplication

3.7.1.1.

3.7.1.2.

3.7.1.3.

3.7.1.4.

Batch Matrix Multiplication

3.7.2.

Vector Operations

3.7.2.1.

3.7.2.2.

3.7.2.3.

3.7.3.

Matrix Decomposition

3.7.3.1.

3.7.3.2.

QR Decomposition

3.7.3.3.

Cholesky Decomposition

3.7.4.

Eigenvalue Operations

3.7.4.1.

3.7.4.2.

3.7.5.

Linear System Solving

3.7.5.1.

3.7.5.2.

Matrix Inversion

3.7.5.3.

Determinant Calculation

3.8.

3.8.1.

Broadcasting Rules

3.8.1.1.

Dimension Compatibility

3.8.1.2.

Size Compatibility

3.8.2.

Broadcasting in Practice

3.8.2.1.

Automatic Broadcasting

3.8.2.2.

Manual Broadcasting

3.8.3.

Common Broadcasting Patterns

3.8.3.1.

Vector-Matrix Operations

3.8.3.2.

Batch Operations

3.8.4.

Broadcasting Limitations

3.8.4.1.

Memory Considerations

3.8.4.2.

Performance Implications

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2. Tensors: The Foundation

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4. Automatic Differentiation