A utility class for common math functions on tensors. More...

#include <TensorFunc.h>

Collaboration diagram for txeo::TensorFunc< T >:

Public Member Functions
	TensorFunc (const TensorFunc &)=delete

	TensorFunc (TensorFunc &&)=delete

TensorFunc &	operator= (const TensorFunc &)=default

TensorFunc &	operator= (TensorFunc &&)=delete

	~TensorFunc ()=default

Static Public Member Functions
static txeo::Tensor< T >	power_elem (const txeo::Tensor< T > &tensor, const T &exponent)
	Returns the element-wise potentiation of a tensor.

static txeo::Tensor< T > &	power_elem_by (txeo::Tensor< T > &tensor, const T &exponent)
	Performs element-wise potentiation of the tensor (in-place)

static txeo::Tensor< T >	square (const txeo::Tensor< T > &tensor)
	Computes the element-wise square of a tensor.

static txeo::Tensor< T > &	square_by (txeo::Tensor< T > &tensor)
	Computes the element-wise square of a tensor in-place.

static txeo::Tensor< T >	sqrt (const txeo::Tensor< T > &tensor)
	Computes the element-wise square root of a tensor.

static txeo::Tensor< T > &	sqrt_by (txeo::Tensor< T > &tensor)
	Computes the element-wise square root of a tensor in-place.

static txeo::Tensor< T >	abs (const txeo::Tensor< T > &tensor)
	Computes the element-wise absolute value of a tensor.

static txeo::Tensor< T > &	abs_by (txeo::Tensor< T > &tensor)
	Computes the element-wise absolute value of a tensor in-place.

static txeo::Tensor< T >	permute (const txeo::Tensor< T > &tensor, const std::vector< size_t > &axes)
	Permutes the axes of a tensor.

static txeo::Tensor< T > &	permute_by (txeo::Tensor< T > &tensor, const std::vector< size_t > &axes)
	Permutes the axes of a tensor in-place.

static txeo::Tensor< T > &	normalize_by (txeo::Tensor< T > &tensor, size_t axis, txeo::NormalizationType type)
	Normalizes the input tensor along a specified axis in-place.

static txeo::Tensor< T >	normalize (const txeo::Tensor< T > &tensor, size_t axis, txeo::NormalizationType type)
	Creates a normalized copy of the input tensor along a specified axis.

static std::vector< std::function< T(const T &)> >	make_normalize_functions (const txeo::Tensor< T > &tensor, size_t axis, txeo::NormalizationType type)
	Construct the normalization functions for each dimension of the specified axis.

static Tensor< T > &	normalize_by (txeo::Tensor< T > &tensor, txeo::NormalizationType type)
	Normalizes the entire tensor in-place (global normalization)

static txeo::Tensor< T >	normalize (const txeo::Tensor< T > &tensor, txeo::NormalizationType type)
	Creates a normalized copy of the entire tensor (global normalization)

static std::function< T(const T &)>	make_normalize_function (const txeo::Tensor< T > &tensor, txeo::NormalizationType type)
	Construct the normalization function for the elements of the specified tensor.

static txeo::Matrix< T >	transpose (const txeo::Matrix< T > &matrix)
	Transposes a matrix.

static txeo::Matrix< T > &	transpose_by (txeo::Matrix< T > &matrix)
	Transposes a matrix in-place.

static txeo::Matrix< T >	compute_gram_matrix (const txeo::Matrix< T > &matrix)
	Computes the Gram matrix ( \(A^TA\)) of the input matrix.

Detailed Description

template<typename T>
class txeo::TensorFunc< T >

A utility class for common math functions on tensors.

This class provides static methods for common tensor functions, such as square.

Template Parameters

T	The data type of the tensor elements (e.g., int, double).

Definition at line 27 of file TensorFunc.h.

Constructor & Destructor Documentation

◆ TensorFunc() [1/2]

template<typename T >

txeo::TensorFunc< T >::TensorFunc ( const TensorFunc< T > & )

delete

◆ TensorFunc() [2/2]

template<typename T >

txeo::TensorFunc< T >::TensorFunc ( TensorFunc< T > && )

delete

◆ ~TensorFunc()

template<typename T >

txeo::TensorFunc< T >::~TensorFunc ( )

default

Member Function Documentation

◆ abs()

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::abs ( const txeo::Tensor< T > & tensor )

static

Computes the element-wise absolute value of a tensor.

Parameters

tensor The input tensor to be modified.

Example Usage:

txeo::Tensor<int> tensor({3}, {-1, 2, -3});
TensorOp<int>::abs_by(tensor);
// tensor = [1, 2, 3]

◆ abs_by()

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::abs_by ( txeo::Tensor< T > & tensor )

static

Computes the element-wise absolute value of a tensor in-place.

Parameters

tensor The input tensor to be modified.

Example Usage:

txeo::Tensor<int> tensor({3}, {-1, 2, -3});
TensorOp<int>::abs_by(tensor);
// tensor = [1, 2, 3]

◆ compute_gram_matrix()

template<typename T >

static txeo::Matrix< T > txeo::TensorFunc< T >::compute_gram_matrix ( const txeo::Matrix< T > & matrix )

static

Computes the Gram matrix ( \(A^TA\)) of the input matrix.

Parameters

matrix Input matrix where rows represent samples and columns represent features

Returns: New matrix containing the Gram matrix (square matrix of size n x n, where n is the number of columns)

Exceptions

TensorFuncError

The Gram matrix is calculated as the matrix product of the transpose of the input matrix with the original matrix. This produces a symmetric positive semi-definite matrix where each element (i,j) represents the inner product of column i and column j from the original matrix.

Example Usage:

// Create a 2x3 matrix (2 samples, 3 features)
txeo::Matrix<double> A(2, 3, {1.0, 2.0, 3.0,
                              4.0, 5.0, 6.0});
 
// Compute Gram matrix (will be 3x3)
auto G = txeo::Matrix<double>::compute_gram_matrix(A);
 
// Resulting Gram matrix:
// [17.0  22.0  27.0]
// [22.0  29.0  36.0]
// [27.0  36.0  45.0]
 
// Verify diagonal elements (squared norms of columns)
assert(G(0,0) == 1.0*1.0 + 4.0*4.0); // 17.0
assert(G(1,1) == 2.0*2.0 + 5.0*5.0); // 29.0
assert(G(2,2) == 3.0*3.0 + 6.0*6.0); // 45.0

Note: Common applications include covariance matrices in statistics and kernel methods in machine learning.

◆ make_normalize_function()

template<typename T >

static std::function< T(const T &)> txeo::TensorFunc< T >::make_normalize_function	(	const txeo::Tensor< T > &	tensor,
		txeo::NormalizationType	type
	)

static

Construct the normalization function for the elements of the specified tensor.

Parameters

tensor	Tensor to be inspected
type	NOrmalization type

Returns: std::function<T(const T &)>

Exceptions

std::TensorFuncError

◆ make_normalize_functions()

template<typename T >

static std::vector< std::function< T(const T &)> > txeo::TensorFunc< T >::make_normalize_functions	(	const txeo::Tensor< T > &	tensor,
		size_t	axis,
		txeo::NormalizationType	type
	)

static

Construct the normalization functions for each dimension of the specified axis.

Parameters

tensor	Tensor to be inspected
axis	Axis from which the normalization functions will be computed
type	NOrmalization type

Returns: std::vector<std::function<T(const T &)>>

Exceptions

std::TensorFuncError

◆ normalize() [1/2]

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::normalize	(	const txeo::Tensor< T > &	tensor,
		size_t	axis,
		txeo::NormalizationType	type
	)

static

Creates a normalized copy of the input tensor along a specified axis.

Parameters

tensor	The input tensor to normalize
axis	The dimension along which to apply normalization
type	The normalization method (MIN_MAX or Z_SCORE)

Returns: New tensor containing normalized values

Exceptions

std::TensorFuncError

Example Usage:

// Example: Min-max normalization of a vector
txeo::Tensor<float> vec({2.0f, 4.0f, 6.0f}); // min=2, max=6
auto normalized = TensorFunc<float>::normalize(vec, 0, txeo::NormalizationType::MIN_MAX);
// normalized contains [0.0, 0.5, 1.0]

◆ normalize() [2/2]

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::normalize	(	const txeo::Tensor< T > &	tensor,
		txeo::NormalizationType	type
	)

static

Creates a normalized copy of the entire tensor (global normalization)

Parameters

tensor	The input tensor to normalize
type	The normalization method (MIN_MAX or Z_SCORE)

Returns: New tensor containing normalized values

Exceptions

std::TensorFuncError

Example Usage:

// Example: Global Z-score normalization
txeo::Tensor<float> cube({{{1.0f, 2.0f}, {3.0f, 4.0f}}, {{5.0f, 6.0f}, {7.0f, 8.0f}}});
auto result = TensorFunc<float>::normalize(cube, txeo::NormalizationType::Z_SCORE);
// result contains values with μ=4.5 and σ=2.449

◆ normalize_by() [1/2]

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::normalize_by	(	txeo::Tensor< T > &	tensor,
		size_t	axis,
		txeo::NormalizationType	type
	)

static

Normalizes the input tensor along a specified axis in-place.

Parameters

[in,out]	tensor	The tensor to be normalized (modified in-place)
	axis	The dimension along which to apply normalization
	type	The normalization method from NormalizationType enum: MIN_MAX: Scales values to [0, 1] range Z_SCORE: Standardizes to mean=0, std=1

Returns: Reference to the modified input tensor

Exceptions

std::TensorFuncError

Example Usage:

// Example: Z-score normalization along columns (axis=1)
txeo::Tensor<double> matrix({{1.0, 2.0}, {3.0, 4.0}}); // 2x2 matrix
TensorFunc<double>::normalize_by(matrix, 1, txeo::NormalizationType::Z_SCORE);
// Column 0 becomes [-1.0, 1.0], Column 1 becomes [-1.0, 1.0]

◆ normalize_by() [2/2]

template<typename T >

static Tensor< T > & txeo::TensorFunc< T >::normalize_by	(	txeo::Tensor< T > &	tensor,
		txeo::NormalizationType	type
	)

static

Normalizes the entire tensor in-place (global normalization)

Parameters

[in,out]	tensor	The tensor to be normalized (modified in-place)
	type	The normalization method (MIN_MAX or Z_SCORE)

Returns: Reference to the modified input tensor

Exceptions

std::TensorFuncError

Example Usage:

// Example: Global min-max normalization
txeo::Tensor<double> data({{10.0, 20.0}, {30.0, 40.0}}); // min=10, max=40
TensorFunc<double>::normalize_by(data, txeo::NormalizationType::MIN_MAX);
// data now contains [[0.0, 0.333], [0.666, 1.0]]

◆ operator=() [1/2]

template<typename T >

TensorFunc & txeo::TensorFunc< T >::operator= ( const TensorFunc< T > & )

default

◆ operator=() [2/2]

template<typename T >

TensorFunc & txeo::TensorFunc< T >::operator= ( TensorFunc< T > && )

delete

◆ permute()

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::permute	(	const txeo::Tensor< T > &	tensor,
		const std::vector< size_t > &	axes
	)

static

Permutes the axes of a tensor.

Parameters

tensor	The input tensor.
axes	The new order of the tensor axes. Must be a valid permutation of the tensor's dimensions.

Returns: A new tensor with the axes permuted.

Exceptions

std::invalid_argument If the axes are invalid (e.g., size mismatch or out of range).

Example Usage:

txeo::Tensor<int> tensor({2, 3, 4}, {
    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
    13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
});
 // The new postion of axis 1 is zero, of axis 2 is one and of axis zero is 2
auto result = TensorFunc<int>::permute(tensor, {1, 2, 0});
// result shape: (3, 4, 2)

◆ permute_by()

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::permute_by	(	txeo::Tensor< T > &	tensor,
		const std::vector< size_t > &	axes
	)

static

Permutes the axes of a tensor in-place.

Parameters

tensor	The input tensor to be modified.
axes	The new order of axes. Must be a valid permutation of the tensor's dimensions.

Returns: A reference to the modified tensor.

Exceptions

std::TensorFuncError

Example Usage:

txeo::Tensor<int> tensor({2, 3, 4}, {
    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
    13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
});
 // The new postion of axis 1 is zero, of axis 2 is one and of axis zero is 2
TensorFunc<int>::permute_by(tensor, {1, 2, 0});
// tensor shape after permutation: (3, 4, 2)

◆ power_elem()

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::power_elem	(	const txeo::Tensor< T > &	tensor,
		const T &	exponent
	)

static

Returns the element-wise potentiation of a tensor.

Parameters

tensor	Tensor to be powered
exponent	Exponent of the potentiation

Returns: txeo::Tensor<T> Result

Example Usage:

txeo::Tensor<float> a({3}, {2.0f, 3.0f, 4.0f});

auto b = TensorOp<float>::power_elem(a, 2.0f); // Result: [4.0f, 9.0f, 16.0f]

◆ power_elem_by()

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::power_elem_by	(	txeo::Tensor< T > &	tensor,
		const T &	exponent
	)

static

Performs element-wise potentiation of the tensor (in-place)

Parameters

tensor	Tensor to be modified
exponent	Exponent of the potentiation

Example Usage:

txeo::Tensor<double> a({2}, {3.0, 4.0});

TensorOp<double>::power_elem_by(a, 3.0); // a becomes [27.0, 64.0]

◆ sqrt()

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::sqrt ( const txeo::Tensor< T > & tensor )

static

Computes the element-wise square root of a tensor.

Parameters

tensor The input tensor.

Returns: A new tensor containing the square root values.

Example Usage:

txeo::Tensor<double> tensor({3}, {1.0, 4.0, 9.0});
auto result = TensorOp<double>::sqrt(tensor);
// result = [1.0, 2.0, 3.0]

◆ sqrt_by()

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::sqrt_by ( txeo::Tensor< T > & tensor )

static

Computes the element-wise square root of a tensor in-place.

Parameters

tensor The input tensor to be modified.

Example Usage:

txeo::Tensor<double> tensor({3}, {1.0, 4.0, 9.0});
TensorOp<double>::sqrt_by(tensor);
// tensor = [1.0, 2.0, 3.0]

◆ square()

template<typename T >

static txeo::Tensor< T > txeo::TensorFunc< T >::square ( const txeo::Tensor< T > & tensor )

static

Computes the element-wise square of a tensor.

Parameters

tensor The input tensor.

Returns: A new tensor containing the squared values.

Example Usage:

txeo::Tensor<int> tensor({3}, {1, 2, 3});
auto result = TensorOp<int>::square(tensor);
// result = [1, 4, 9]

◆ square_by()

template<typename T >

static txeo::Tensor< T > & txeo::TensorFunc< T >::square_by ( txeo::Tensor< T > & tensor )

static

Computes the element-wise square of a tensor in-place.

Parameters

tensor The input tensor to be modified.

Example Usage:

txeo::Tensor<int> tensor({3}, {1, 2, 3});
TensorOp<int>::square_by(tensor);
// tensor = [1, 4, 9]

◆ transpose()

template<typename T >

static txeo::Matrix< T > txeo::TensorFunc< T >::transpose ( const txeo::Matrix< T > & matrix )

static

Transposes a matrix.

Parameters

matrix The input matrix.

Returns: A new matrix that is the transpose of the input matrix.

Example Usage:

txeo::Matrix<int> matrix(2, 3, {1, 2, 3, 4, 5, 6});
auto result = TensorFunc<int>::transpose(matrix);
// result shape: (3, 2)

◆ transpose_by()

template<typename T >

static txeo::Matrix< T > & txeo::TensorFunc< T >::transpose_by ( txeo::Matrix< T > & matrix )

static

Transposes a matrix in-place.

Parameters

matrix The input matrix to be modified.

Returns: A reference to the modified matrix.

Example Usage:

txeo::Matrix<int> matrix(2, 3, {1, 2, 3, 4, 5, 6});
TensorFunc<int>::transpose_by(matrix);
// matrix shape after transpose: (3, 2)

The documentation for this class was generated from the following files:

include/txeo/Matrix.h
include/txeo/TensorFunc.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ TensorFunc() [1/2]

◆ TensorFunc() [2/2]

◆ ~TensorFunc()

Member Function Documentation

◆ abs()

◆ abs_by()

◆ compute_gram_matrix()

◆ make_normalize_function()

◆ make_normalize_functions()

◆ normalize() [1/2]

◆ normalize() [2/2]

◆ normalize_by() [1/2]

◆ normalize_by() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ permute()

◆ permute_by()

◆ power_elem()

◆ power_elem_by()

◆ sqrt()

◆ sqrt_by()

◆ square()

◆ square_by()

◆ transpose()

◆ transpose_by()