Struct MatrixACA 

pub struct MatrixACA<T: Scalar> { /* private fields */ }

Adaptive Cross Approximation representation.

Stores a low-rank approximation A ~ U * diag(alpha) * V, where alpha[k] = 1/delta[k]. Implements AbstractMatrixCI for element-wise evaluation and submatrix extraction.

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![
    vec![1.0_f64, 2.0, 3.0],
    vec![4.0, 5.0, 6.0],
    vec![7.0, 8.0, 9.0],
]);

// Build ACA from a starting pivot
let mut aca = MatrixACA::from_matrix_with_pivot(&m, (1, 1)).unwrap();
assert_eq!(aca.rank(), 1);

// Add more pivots
aca.add_pivot(&m, (0, 0)).unwrap();
assert_eq!(aca.rank(), 2);

// Evaluate the approximation
let approx_11 = aca.evaluate(1, 1);
assert!((approx_11 - 5.0).abs() < 1e-10);

Implementations

impl<T: Scalar> MatrixACA<T>

pub fn new(nr: usize, nc: usize) -> Self

Create an empty MatrixACA for a matrix of given size

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA};

let aca = MatrixACA::<f64>::new(3, 4);
assert_eq!(aca.nrows(), 3);
assert_eq!(aca.ncols(), 4);
assert_eq!(aca.rank(), 0);
assert!(aca.is_empty());

pub fn from_matrix_with_pivot( a: &Matrix<T>, first_pivot: (usize, usize), ) -> Result<Self>

Create a MatrixACA from a matrix with an initial pivot

Returns an error if the pivot value is zero or near-zero.

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
assert_eq!(aca.rank(), 1);
assert_eq!(aca.row_indices(), &[0]);
assert_eq!(aca.col_indices(), &[0]);

pub fn npivots(&self) -> usize

Number of pivots

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
assert_eq!(aca.npivots(), 1);
aca.add_pivot(&m, (1, 1)).unwrap();
assert_eq!(aca.npivots(), 2);

pub fn u(&self) -> &Matrix<T>

Get reference to U matrix

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
let u = aca.u();
assert_eq!(u.nrows(), 2); // nrows of original matrix
assert_eq!(u.ncols(), 1); // one pivot

pub fn v(&self) -> &Matrix<T>

Get reference to V matrix

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
let v = aca.v();
assert_eq!(v.nrows(), 1); // one pivot
assert_eq!(v.ncols(), 2); // ncols of original matrix

pub fn alpha(&self) -> &[T]

Get reference to alpha values

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![2.0_f64, 1.0], vec![1.0, 3.0]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
let alpha = aca.alpha();
assert_eq!(alpha.len(), 1);
// alpha = 1 / pivot_value = 1 / m[0,0] = 0.5
assert!((alpha[0] - 0.5).abs() < 1e-10);

pub fn add_pivot_col(&mut self, a: &Matrix<T>, col_index: usize) -> Result<()>

Add a pivot column

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::<f64>::new(2, 2);
aca.add_pivot_col(&m, 0).unwrap();
assert_eq!(aca.u().ncols(), 1);

pub fn add_pivot_row(&mut self, a: &Matrix<T>, row_index: usize) -> Result<()>

Add a pivot row

Examples

use tensor4all_tcicore::{MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::<f64>::new(2, 2);
aca.add_pivot_col(&m, 0).unwrap();
aca.add_pivot_row(&m, 0).unwrap();
assert_eq!(aca.npivots(), 1);
assert_eq!(aca.v().nrows(), 1);

pub fn add_pivot(&mut self, a: &Matrix<T>, pivot: (usize, usize)) -> Result<()>

Add a pivot at the given position

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
aca.add_pivot(&m, (1, 1)).unwrap();
assert_eq!(aca.rank(), 2);
// Exact reconstruction at all positions
for i in 0..2 {
    for j in 0..2 {
        assert!((aca.evaluate(i, j) - m[[i, j]]).abs() < 1e-10);
    }
}

pub fn add_best_pivot(&mut self, a: &Matrix<T>) -> Result<(usize, usize)>

Add a pivot that maximizes the error using ACA heuristic

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![
    vec![1.0_f64, 2.0, 3.0],
    vec![4.0, 5.0, 6.0],
    vec![7.0, 8.0, 10.0],
]);
let mut aca = MatrixACA::<f64>::new(3, 3);
let (r, c) = aca.add_best_pivot(&m).unwrap();
assert!(r < 3);
assert!(c < 3);
assert_eq!(aca.rank(), 1);

pub fn set_cols(&mut self, new_pivot_rows: &Matrix<T>, permutation: &[usize])

Set columns with new pivot rows and permutation

Updates the column indices and V matrix according to the given permutation and new pivot row data.

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
// Identity permutation keeps columns the same
let pivot_rows = from_vec2d(vec![vec![1.0_f64, 2.0]]);
aca.set_cols(&pivot_rows, &[0, 1]);
assert_eq!(aca.col_indices(), &[0]);

pub fn set_rows(&mut self, new_pivot_cols: &Matrix<T>, permutation: &[usize])

Set rows with new pivot columns and permutation

Updates the row indices and U matrix according to the given permutation and new pivot column data.

Examples

use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let mut aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
// Identity permutation keeps rows the same
let pivot_cols = from_vec2d(vec![vec![1.0_f64], vec![3.0]]);
aca.set_rows(&pivot_cols, &[0, 1]);
assert_eq!(aca.row_indices(), &[0]);

Trait Implementations

impl<T: Scalar> AbstractMatrixCI<T> for MatrixACA<T>

fn nrows(&self) -> usize

Number of rows in the approximated matrix

fn ncols(&self) -> usize

Number of columns in the approximated matrix

fn rank(&self) -> usize

Current rank of the approximation (number of pivots)

fn row_indices(&self) -> &[usize]

Row indices selected as pivots (I set)

fn col_indices(&self) -> &[usize]

Column indices selected as pivots (J set)

fn evaluate(&self, i: usize, j: usize) -> T

Evaluate the approximation at position (i, j)

fn submatrix(&self, rows: &[usize], cols: &[usize]) -> Matrix<T>

Get a submatrix of the approximation

fn is_empty(&self) -> bool

Check if the approximation is empty (no pivots)

fn row(&self, i: usize) -> Vec<T>

Get a row of the approximation

fn col(&self, j: usize) -> Vec<T>

Get a column of the approximation

fn to_matrix(&self) -> Matrix<T>

Get the full approximated matrix

fn available_rows(&self) -> Vec<usize>

Get available row indices (rows without pivots)

fn available_cols(&self) -> Vec<usize>

Get available column indices (columns without pivots)

fn local_error( &self, a: &Matrix<T>, rows: &[usize], cols: &[usize], ) -> Matrix<T>

where T: Sub<Output = T>,

Compute local error |A - CI| for given indices

fn find_new_pivot(&self, a: &Matrix<T>) -> Result<((usize, usize), T)>

where T: Sub<Output = T>,

Find a new pivot that maximizes the local error

fn find_new_pivot_in( &self, a: &Matrix<T>, rows: &[usize], cols: &[usize], ) -> Result<((usize, usize), T)>

where T: Sub<Output = T>,

Find a new pivot in the given row/column subsets

impl<T: Clone + Scalar> Clone for MatrixACA<T>

fn clone(&self) -> MatrixACA<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + Scalar> Debug for MatrixACA<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.