math.hpp File Reference

Implements auto-diff enabled wrappers around their concrete tensor implementations. More...

#include "shape.hpp"
#include "tensorptr.hpp"
#include <iostream>
#include <vector>

Include dependency graph for math.hpp:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
struct	dl::DOF
	Wrapper around std::size_t to discern between var(TensorPtr, DOF) and var(TensorPtr, size_t). More...

Functions
TensorPtr	dl::pow (TensorPtr base, float exponent) noexcept
	Computes the exponent -th power of each element in base and returns the resulting tensor.
TensorPtr	dl::exp (TensorPtr x) noexcept
	Computes the elementwise x -th power of e.
TensorPtr	dl::log (TensorPtr x) noexcept
	Natural logarithm, \(\log_e(\,\cdot\,)\).
TensorPtr	dl::sqrt (TensorPtr x) noexcept
	Computes the elementwise square root of x .
TensorPtr	dl::rsqrt (TensorPtr x) noexcept
	Computes the reciprocal square root for each element in x.
TensorPtr	dl::mean (TensorPtr x) noexcept
	Mean.
TensorPtr	dl::mean (TensorPtr x, int dim, bool keepdim=false) noexcept
	Mean along a specified axis.
TensorPtr	dl::sum (TensorPtr x) noexcept
	Sum.
TensorPtr	dl::sum (TensorPtr x, int dim, bool keepdim=false) noexcept
	Sum along a specified axis.
TensorPtr	dl::min (TensorPtr x) noexcept
	Minimum.
TensorPtr	dl::min (TensorPtr x, int dim, bool keepdim=false) noexcept
	Minimum along a specified axis.
TensorPtr	dl::max (TensorPtr x) noexcept
	Maximum.
TensorPtr	dl::max (TensorPtr x, int dim, bool keepdim=false) noexcept
	Maximum along a specified axis.
TensorPtr	dl::max (TensorPtr x, TensorPtr y) noexcept
	Elementwise maximum.
TensorPtr	dl::var (TensorPtr x, DOF dof=DOF{1}) noexcept
	Variance.
TensorPtr	dl::var (TensorPtr x, int dim, DOF dof=DOF{1}) noexcept
	Variance along a specified axis.
TensorPtr	dl::erf (TensorPtr x) noexcept
	(Gauss) Error Function
TensorPtr	dl::relu (TensorPtr x) noexcept
TensorPtr	dl::operator+ (TensorPtr left, float right) noexcept
TensorPtr	dl::operator- (TensorPtr left, float right) noexcept
TensorPtr	dl::operator* (TensorPtr left, float right) noexcept
TensorPtr	dl::operator/ (TensorPtr left, float right) noexcept
TensorPtr	dl::operator+ (float left, TensorPtr right) noexcept
TensorPtr	dl::operator- (float left, TensorPtr right) noexcept
TensorPtr	dl::operator* (float left, TensorPtr right) noexcept
TensorPtr	dl::operator/ (float left, TensorPtr right) noexcept
TensorPtr	dl::operator+ (TensorPtr left, TensorPtr right) noexcept
TensorPtr	dl::operator- (TensorPtr left, TensorPtr right) noexcept
TensorPtr	dl::operator* (TensorPtr left, TensorPtr right) noexcept
TensorPtr	dl::operator/ (TensorPtr left, TensorPtr right) noexcept
TensorPtr	dl::fma (const TensorPtr &factor1, const TensorPtr &factor2, const TensorPtr &summand) noexcept
TensorPtr	dl::matmul (TensorPtr left, TensorPtr right) noexcept
TensorPtr	dl::transpose (TensorPtr x, std::vector< int > &&permutation) noexcept
	Transposes the given tensor at the specified coordinates.
TensorPtr	dl::softmax (TensorPtr x) noexcept
	Computes the softmax function of the input vector.
TensorPtr	dl::softmax (TensorPtr x, int dim) noexcept
std::ostream &	dl::operator<< (std::ostream &, const TensorPtr &tensor) noexcept
bool	dl::operator== (const TensorPtr &left, const TensorPtr &right) noexcept
bool	dl::allclose (const TensorPtr &left, const TensorPtr &right, float rtol=1e-5, float atol=1e-8) noexcept
size_t	dl::numEntries (const TensorPtr &tensor) noexcept
	Returns the number of entries in the tensor.
TensorPtr	dl::reshape (TensorPtr tensor, SShape shape) noexcept

Detailed Description

Implements auto-diff enabled wrappers around their concrete tensor implementations.

Definition in file math.hpp.

Function Documentation

numEntries()

size_t dl::numEntries ( const TensorPtr &  tensor )

noexcept

Returns the number of entries in the tensor.

This is equivalent to the product of the shape.

Parameters

tensor

The tensor to count the number of entries for.

Returns

size_t The number of entries in tensor.

softmax()

TensorPtr dl::softmax ( TensorPtr  x )

noexcept

Computes the softmax function of the input vector.

Let \(x \in \mathbb R^n\) be a vector, the softmax is defined as

\[ \text{softmax}\colon \mathbb R^n \to \mathbb R^n ~\text{via}~ x\mapsto \left(\frac{e^{x_i}}{\sum_{j=1}^n e^{x_j}}\right)_{1\leq i\leq n}. \]

Parameters

x	the input tensor.

Returns

TensorPtr the softmax of x .

transpose()

TensorPtr dl::transpose ( TensorPtr  x, std::vector< int > &&  permutation  )

noexcept

Transposes the given tensor at the specified coordinates.

Transposes the given tensor by permuting the dimensions. For example, if the input was a matrix, then \(x \in \mathbb{R}^n\times m\) the matrix transposition could be computed via dl::transpose(x, {0, 1});.

Parameters

x	the tensor to be tranposed.
permutation	the permutation to apply to the dimensions.

Returns

a new tensor with the permutation permutation applied to the dimensions.