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AbstractMatrixCI

tensor4all_tcicore::traits

Trait AbstractMatrixCI 

Source 
pub trait AbstractMatrixCI<T: Scalar>: Sized {

Show 16 methods    // Required methods
    fn nrows(&self) -> usize;
    fn ncols(&self) -> usize;
    fn rank(&self) -> usize;
    fn row_indices(&self) -> &[usize];
    fn col_indices(&self) -> &[usize];
    fn evaluate(&self, i: usize, j: usize) -> T;
    fn submatrix(&self, rows: &[usize], cols: &[usize]) -> Matrix<T>;

    // Provided methods
    fn is_empty(&self) -> bool { ... }
    fn row(&self, i: usize) -> Vec<T> { ... }
    fn col(&self, j: usize) -> Vec<T> { ... }
    fn to_matrix(&self) -> Matrix<T> { ... }
    fn available_rows(&self) -> Vec<usize> { ... }
    fn available_cols(&self) -> Vec<usize> { ... }
    fn local_error(
        &self,
        a: &Matrix<T>,
        rows: &[usize],
        cols: &[usize],
    ) -> Matrix<T>
       where T: Sub<Output = T> { ... }
    fn find_new_pivot(&self, a: &Matrix<T>) -> Result<((usize, usize), T)>
       where T: Sub<Output = T> { ... }
    fn find_new_pivot_in(
        &self,
        a: &Matrix<T>,
        rows: &[usize],
        cols: &[usize],
    ) -> Result<((usize, usize), T)>
       where T: Sub<Output = T> { ... }

}
Expand description

Common interface for matrix cross interpolation objects.

Implementors provide low-rank approximations of matrices via selected pivot rows and columns. This trait unifies the API for MatrixLUCI and MatrixACA.

§Examples

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

let m = from_vec2d(vec![
    vec![1.0_f64, 2.0],
    vec![3.0, 4.0],
]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();

// All AbstractMatrixCI methods are available:
assert_eq!(ci.nrows(), 2);
assert_eq!(ci.ncols(), 2);
assert!(ci.rank() >= 1);
assert!(!ci.is_empty());

// Full reconstruction
let full = ci.to_matrix();
for i in 0..2 {
    for j in 0..2 {
        assert!((full[[i, j]] - m[[i, j]]).abs() < 1e-10);
    }
}

Required Methods§

Source

fn nrows(&self) -> usize

Number of rows in the approximated matrix

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0], vec![5.0, 6.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
assert_eq!(ci.nrows(), 3);
Source

fn ncols(&self) -> usize

Number of columns in the approximated matrix

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0, 3.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
assert_eq!(ci.ncols(), 3);
Source

fn rank(&self) -> usize

Current rank of the approximation (number of pivots)

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
assert!(ci.rank() >= 1);
assert!(ci.rank() <= 2);
Source

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

Row indices selected as pivots (I set)

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let rows = ci.row_indices();
assert_eq!(rows.len(), ci.rank());
for &r in rows {
    assert!(r < ci.nrows());
}
Source

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

Column indices selected as pivots (J set)

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let cols = ci.col_indices();
assert_eq!(cols.len(), ci.rank());
for &c in cols {
    assert!(c < ci.ncols());
}
Source

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

Evaluate the approximation at position (i, j)

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
assert!((ci.evaluate(0, 0) - 1.0).abs() < 1e-10);
assert!((ci.evaluate(1, 1) - 4.0).abs() < 1e-10);
Source

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

Get a submatrix of the approximation

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, 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],
]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let sub = ci.submatrix(&[0, 2], &[1]);
assert_eq!(sub.nrows(), 2);
assert_eq!(sub.ncols(), 1);
assert!((sub[[0, 0]] - 2.0).abs() < 1e-10);
assert!((sub[[1, 0]] - 8.0).abs() < 1e-10);

Provided Methods§

Source

fn is_empty(&self) -> bool

Check if the approximation is empty (no pivots)

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixACA};

let aca = MatrixACA::<f64>::new(2, 2);
assert!(aca.is_empty());
Source

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

Get a row of the approximation

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let row0 = ci.row(0);
assert_eq!(row0.len(), 2);
assert!((row0[0] - 1.0).abs() < 1e-10);
assert!((row0[1] - 2.0).abs() < 1e-10);
Source

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

Get a column of the approximation

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let col1 = ci.col(1);
assert_eq!(col1.len(), 2);
assert!((col1[0] - 2.0).abs() < 1e-10);
assert!((col1[1] - 4.0).abs() < 1e-10);
Source

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

Get the full approximated matrix

§Examples
use tensor4all_tcicore::{AbstractMatrixCI, MatrixLUCI, from_vec2d};

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0]]);
let ci = MatrixLUCI::from_matrix(&m, None).unwrap();
let full = ci.to_matrix();
assert_eq!(full.nrows(), 2);
assert_eq!(full.ncols(), 2);
for i in 0..2 {
    for j in 0..2 {
        assert!((full[[i, j]] - m[[i, j]]).abs() < 1e-10);
    }
}
Source

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

Get available row indices (rows without pivots)

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

let m = from_vec2d(vec![vec![1.0_f64, 2.0], vec![3.0, 4.0], vec![5.0, 6.0]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (1, 0)).unwrap();
let avail = aca.available_rows();
// Row 1 was used as pivot, so 0 and 2 remain
assert_eq!(avail, vec![0, 2]);
Source

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

Get available column indices (columns without pivots)

§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]]);
let aca = MatrixACA::from_matrix_with_pivot(&m, (0, 1)).unwrap();
let avail = aca.available_cols();
// Column 1 was used as pivot, so 0 and 2 remain
assert_eq!(avail, vec![0, 2]);
Source

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

§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 aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
let err = aca.local_error(&m, &[1, 2], &[1, 2]);
// Error at pivot position (0,0) would be zero; off-pivot may be non-zero
assert_eq!(err.nrows(), 2);
assert_eq!(err.ncols(), 2);
Source

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

§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 aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
let ((r, c), err_val) = aca.find_new_pivot(&m).unwrap();
// New pivot must be in available rows/cols (not row 0 or col 0)
assert_ne!(r, 0);
assert_ne!(c, 0);
Source

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

§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 aca = MatrixACA::from_matrix_with_pivot(&m, (0, 0)).unwrap();
// Search only in rows [1,2] and cols [1,2]
let ((r, c), _) = aca.find_new_pivot_in(&m, &[1, 2], &[1, 2]).unwrap();
assert!(r == 1 || r == 2);
assert!(c == 1 || c == 2);

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§