Crate russell_lab

Russell - Rust Scientific Library

lab: Matrix-vector laboratory including linear algebra tools

Example - Cholesky factorization

use russell_lab::{cholesky_factor, Matrix, StrError};

fn main() -> Result<(), StrError> {
    // set matrix
    let a = Matrix::from(&[
        [  4.0,  12.0, -16.0],
        [ 12.0,  37.0, -43.0],
        [-16.0, -43.0,  98.0],
    ]);

    // perform factorization
    let m = a.nrow();
    let mut l = Matrix::new(m, m);
    cholesky_factor(&mut l, &a)?;

    // compare with solution
    let l_correct = "┌          ┐\n\
                     │  2  0  0 │\n\
                     │  6  1  0 │\n\
                     │ -8  5  3 │\n\
                     └          ┘";
    assert_eq!(format!("{}", l), l_correct);
    Ok(())
}

Structs

NumMatrix

Implements a matrix with numeric components for linear algebra

NumVector

Implements a vector with numeric components for linear algebra

Stopwatch

Assists in measuring computation time

Enums

NormMat

Options to compute matrix norm

NormVec

Options to compute vector norm

Traits

AsArray1D

Defines a trait to handle 1D arrays

AsArray2D

Defines a trait to handle 2D arrays

Functions

add_matrices

Performs the addition of two matrices

add_vectors

Performs the addition of two vectors

boxcar

Implements the boxcar function

cholesky_factor

Performs the Cholesky factorization of a symmetric positive-definite matrix

complex_add_matrices

Performs the addition of two matrices

complex_add_vectors

Performs the addition of two vectors

complex_copy_vector

Copies vector (complex version)

complex_mat_mat_mul

Performs the matrix-matrix multiplication resulting in a matrix (complex version)

complex_mat_zip

Zips two arrays (real and imag) to make a new ComplexMatrix

complex_matrix_norm

Computes the matrix norm (complex version)

complex_vec_zip

Zips two arrays (real and imag) to make a new ComplexVector

copy_matrix

Copies matrix

copy_vector

Copies vector

desc

Returns package description

eigen_decomp

Performs the eigen-decomposition of a square matrix

eigen_decomp_lr

Performs the eigen-decomposition of a square matrix (left and right)

format_nanoseconds

Returns a nice string representing the value in nanoseconds

generate2d

Generates 2d points (meshgrid)

generate3d

Generates 3d points (function over meshgrid)

heaviside

Implements the Heaviside step function (derivative of ramp(x))

inner

Performs the inner (dot) product between two vectors resulting in a scalar value

inverse

Computes the inverse of a square matrix and returns its determinant

logistic

Implements the standard logistic function

logistic_deriv

Returns the first derivative of the standard logistic function

mat_mat_mul

Performs the matrix-matrix multiplication resulting in a matrix

mat_max_abs_diff

Finds the maximum absolute difference between the components of two matrices

mat_sum_cols

Sums the columns of a matrix

mat_sum_rows

Sums the rows of a matrix

mat_t_mat_mul

Performs the matrix(transposed)-matrix multiplication resulting in a matrix

mat_vec_mul

Performs the matrix-vector multiplication resulting in a vector

matrix_norm

Computes the matrix norm

outer

Performs the outer (tensor) product between two vectors resulting in a matrix

pseudo_inverse

Computes the pseudo-inverse matrix

ramp

scale_matrix

Scales matrix

scale_vector

Scales vector

sign

Implements the sign function

smooth_ramp

Implements a smooth ramp function

smooth_ramp_deriv

Returns the first derivative of smooth_ramp

smooth_ramp_deriv2

Returns the second derivative of smooth_ramp

solve_lin_sys

Solves a general linear system (real numbers)

sort2

Sorts 2 values

sort3

Sorts 3 values

sort4

Sorts 4 values

suq_cos

Implements the superquadric auxiliary involving cos(x)

suq_sin

Implements the superquadric function involving sin(x)

sv_decomp

Computes the singular value decomposition (SVD) of a matrix

update_matrix

Updates matrix based on another matrix (axpy)

update_vector

Updates vector based on another vector (axpy)

vec_mat_mul

Performs the vector-matrix multiplication resulting in a vector

vec_max_abs_diff

Finds the maximum absolute difference between the components of two vectors

vector_norm

Returns the vector norm

Type Definitions

ComplexMatrix

ComplexMatrix is an alias to NumMatrix and is used in most functions that call OpenBLAS

ComplexVector

ComplexVector is an alias to NumVector and is used in most functions that call OpenBLAS

Matrix

Matrix is an alias to NumMatrix and is used in most functions that call OpenBLAS

StrError

Defines a type alias for the error type as a static string

Vector

Vector is an alias to NumVector and is used in most functions that call OpenBLAS