linalg.hpp File Reference

Minimal linear algebra helpers for Arr (transpose, matmul, Cholesky, inverse, etc.). More...

#include <ellalgo/arr.hpp>
#include <random>

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Functions
Arr	transpose (const Arr &a)
	Transpose a 2D matrix.
Arr	flatten (const Arr &a)
	Flatten a matrix or vector into a 1D array.
Arr	diagonal (const Arr &a)
	Extract the diagonal of a square matrix.
double	trace (const Arr &a)
	Compute the trace of a square matrix (sum of diagonal elements).
double	norm (const Arr &a)
	Compute the Frobenius norm of an array.
Arr	matmul (const Arr &A, const Arr &B)
	Multiply two matrices: A * B.
Arr	cholesky (const Arr &A)
	Cholesky decomposition: A = L * L^T for SPD matrices.
Arr	inv (const Arr &A)
	Compute the inverse of a symmetric positive definite matrix via Cholesky.
std::mt19937_64 &	global_rng ()
	Get the global Mersenne Twister random number generator.
void	random_seed (unsigned seed)
	Seed the global random number generator.
Arr	randn (size_t n)
	Generate a vector of standard normal random numbers.
std::pair< Arr, Arr >	meshgrid (const Arr &x, const Arr &y)
	Create 2D meshgrid arrays from 1D coordinate vectors.
Arr	stack (const Arr &a, const Arr &b, int=0)
	Stack two 1D arrays as rows into a 2D matrix.

Detailed Description

Minimal linear algebra helpers for Arr (transpose, matmul, Cholesky, inverse, etc.).

Function Documentation

cholesky()

Arr cholesky ( const Arr &  A )

inline

Cholesky decomposition: A = L * L^T for SPD matrices.

\[ A = LL^T, \quad L_{jj} = \sqrt{A_{jj} - \sum_{k=1}^{j-1} L_{jk}^2}, \quad L_{ij} = \frac{1}{L_{jj}}\Bigl(A_{ij} - \sum_{k=1}^{j-1} L_{ik} L_{jk}\Bigr) \]

Parameters

A	Symmetric positive definite matrix

Returns

Lower-triangular Cholesky factor L

diagonal()

Arr diagonal ( const Arr &  a )

inline

Extract the diagonal of a square matrix.

Parameters

a	Input square matrix

Returns

1D array containing diagonal elements

flatten()

Arr flatten ( const Arr &  a )

inline

Flatten a matrix or vector into a 1D array.

Parameters

a	Input array

Returns

Flattened 1D array

global_rng()

std::mt19937_64 & global_rng ( )

inline

Get the global Mersenne Twister random number generator.

Returns

Reference to the global RNG

inv()

Arr inv ( const Arr &  A )

inline

Compute the inverse of a symmetric positive definite matrix via Cholesky.

Computes \(A^{-1}\) by solving \(LY = I\) (forward substitution) then \(L^T X = Y\) (back substitution).

Parameters

A	SPD matrix

Returns

Inverse matrix

matmul()

Arr matmul ( const Arr &  A, const Arr &  B  )

inline

Multiply two matrices: A * B.

\[ (AB)_{ij} = \sum_{k=1}^{p} A_{ik} B_{kj} \]

Parameters

A	Left matrix (m x k)
B	Right matrix (k x n)

Returns

Result matrix (m x n)

meshgrid()

std::pair< Arr, Arr > meshgrid ( const Arr &  x, const Arr &  y  )

inline

Create 2D meshgrid arrays from 1D coordinate vectors.

Parameters

x	1D x-coordinates
y	1D y-coordinates

Returns

Pair of 2D arrays (XX, YY)

norm()

double norm ( const Arr &  a )

inline

Compute the Frobenius norm of an array.

\( \|A\|_F = \sqrt{\sum_{i}\sum_{j} A_{ij}^2} \)

Parameters

a	Input array

Returns

Frobenius norm

randn()

Arr randn ( size_t  n )

inline

Generate a vector of standard normal random numbers.

Parameters

n	Number of elements

Returns

1D array of i.i.d. N(0,1) samples

random_seed()

void random_seed ( unsigned  seed )

inline

Seed the global random number generator.

Parameters

seed	The seed value

stack()

Arr stack ( const Arr &  a, const Arr &  b, int  = 0  )

inline

Stack two 1D arrays as rows into a 2D matrix.

Parameters

a	First row
b	Second row

Returns

2D matrix with two rows

trace()

double trace ( const Arr &  a )

inline

Compute the trace of a square matrix (sum of diagonal elements).

\( \operatorname{tr}(A) = \sum_{i=1}^{n} A_{ii} \)

Parameters

a	Input square matrix

Returns

Trace value

transpose()

Arr transpose ( const Arr &  a )

inline

Transpose a 2D matrix.

Minimal linear algebra helpers for Arr, replacing xtensor-blas operations. For small FIR/correlation problems, naive O(n^3) is sufficient.

\[ (A^T)_{ij} = A_{ji} \]

Parameters

a	Input matrix

Returns

Transposed matrix