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//! Matrix addition.
use core::ops::Add;
use core::ops::AddAssign;
use crate::traits::Real;
use super::base::{Matrix, MatrixStorage};
// Add-assign by value
impl<T: Real> AddAssign<Matrix<T>> for Matrix<T> {
fn add_assign(&mut self, rhs: Matrix<T>) {
let n = self.n;
let m = self.m;
let lhs = core::mem::replace(self, Matrix::zeros(n, m));
*self = lhs + rhs;
}
}
// Matrix + Matrix (elementwise). If both are banded, keep banded with widened bandwidth; otherwise densify.
impl<T: Real> Add for Matrix<T> {
type Output = Matrix<T>;
fn add(self, rhs: Matrix<T>) -> Self::Output {
assert_eq!(self.n, rhs.n, "dimension mismatch in Matrix + Matrix");
assert_eq!(self.m, rhs.m, "dimension mismatch in Matrix + Matrix");
let n = self.n;
let m = self.m;
match (self, rhs) {
(
Matrix {
n: n1,
m: _,
data: _,
storage: MatrixStorage::Identity,
},
Matrix {
n: n2,
m: _,
data: _,
storage: MatrixStorage::Identity,
},
) => {
assert_eq!(n1, n2);
let mut data = vec![T::zero(); n * n];
for i in 0..n {
data[i * n + i] = T::one() + T::one();
}
Matrix {
n,
m: n,
data,
storage: MatrixStorage::Full,
}
}
(
Matrix {
data: a,
storage: MatrixStorage::Full,
..
},
Matrix {
data: b,
storage: MatrixStorage::Full,
..
},
) => {
let data = a.into_iter().zip(b).map(|(x, y)| x + y).collect();
Matrix {
n,
m,
data,
storage: MatrixStorage::Full,
}
}
(
Matrix {
data: a,
storage: MatrixStorage::Banded { ml, mu, .. },
..
},
Matrix {
data: b,
storage:
MatrixStorage::Banded {
ml: ml2, mu: mu2, ..
},
..
},
) => {
let ml_out = ml.max(ml2);
let mu_out = mu.max(mu2);
let rows_out = ml_out + mu_out + 1;
let mut out = Matrix {
n,
m: n,
data: vec![T::zero(); rows_out * n],
storage: MatrixStorage::Banded {
ml: ml_out,
mu: mu_out,
zero: T::zero(),
},
};
// First input accumulate
for j in 0..n {
for r in 0..(ml + mu + 1) {
let k = r as isize - mu as isize;
let i_signed = j as isize + k;
if i_signed >= 0 && (i_signed as usize) < n {
let row_out = (k + mu_out as isize) as usize;
out.data[row_out * n + j] += a[r * n + j];
}
}
}
// Second input accumulate
for j in 0..n {
for r in 0..(ml2 + mu2 + 1) {
let k = r as isize - mu2 as isize;
let i_signed = j as isize + k;
if i_signed >= 0 && (i_signed as usize) < n {
let row_out = (k + mu_out as isize) as usize;
out.data[row_out * n + j] += b[r * n + j];
}
}
}
out
}
// Mixed: densify
(
Matrix {
n: n1,
m: m1,
data: a,
storage: sa,
..
},
Matrix {
n: _n2,
m: _m2,
data: b,
storage: sb,
..
},
) => {
let aa = Matrix {
n: n1,
m: m1,
data: a,
storage: sa,
}
.to_dense_vec();
let bb = Matrix {
n: n1,
m: m1,
data: b,
storage: sb,
}
.to_dense_vec();
let data = aa.into_iter().zip(bb).map(|(x, y)| x + y).collect();
Matrix {
n: n1,
m: m1,
data,
storage: MatrixStorage::Full,
}
}
}
}
}
impl<T: Real> Matrix<T> {
/// Return a new matrix where each stored entry has `rhs` added. Off-band for banded becomes dense if rhs != 0.
pub fn component_add(mut self, rhs: T) -> Self {
match &mut self.storage {
MatrixStorage::Identity => {
// I + c -> Full with diag 1+c and off-diag c
let n = self.n;
let mut data = vec![rhs; n * n];
for i in 0..n {
data[i * n + i] = rhs + T::one();
}
Matrix {
n,
m: n,
data,
storage: MatrixStorage::Full,
}
}
MatrixStorage::Full => {
for v in &mut self.data {
*v += rhs;
}
self
}
MatrixStorage::Banded { ml, mu, .. } => {
let n = self.n;
if rhs == T::zero() {
self
} else {
let rows = *ml + *mu + 1;
let mut dense = vec![rhs; n * n];
for j in 0..n {
for r in 0..rows {
let k = r as isize - *mu as isize;
let i_signed = j as isize + k;
if i_signed >= 0 && (i_signed as usize) < n {
let i = i_signed as usize;
let val = self.data[r * n + j];
dense[i * n + j] = val + rhs;
}
}
}
Matrix {
n,
m: n,
data: dense,
storage: MatrixStorage::Full,
}
}
}
MatrixStorage::Sparse { coords, zero } => {
let n = self.n;
let m = self.m;
if rhs == T::zero() {
Matrix {
n,
m,
data: Vec::new(),
storage: MatrixStorage::Sparse {
coords: coords.clone(),
zero: *zero,
},
}
} else {
let mut dense = vec![rhs; n * m];
for &(r, c, v) in coords.iter() {
dense[r * m + c] += v;
}
Matrix {
n,
m,
data: dense,
storage: MatrixStorage::Full,
}
}
}
}
}
}
#[cfg(test)]
mod tests {
use crate::linalg::matrix::Matrix;
#[test]
fn add_scalar_full() {
let mut m: Matrix<f64> = Matrix::full(2, 2);
m[(0, 0)] = 1.0;
m[(0, 1)] = 2.0;
m[(1, 0)] = 3.0;
m[(1, 1)] = 4.0;
let r = m.component_add(1.0);
assert_eq!(r[(0, 0)], 2.0);
assert_eq!(r[(0, 1)], 3.0);
assert_eq!(r[(1, 0)], 4.0);
assert_eq!(r[(1, 1)], 5.0);
}
#[test]
fn add_scalar_banded_zero_keeps_banded() {
let m: Matrix<f64> = Matrix::banded(3, 1, 1);
let r = m.component_add(0.0);
for i in 0..3 {
for j in 0..3 {
assert_eq!(r[(i, j)], 0.0);
}
}
}
#[test]
fn add_matrix_full_full() {
let mut a: Matrix<f64> = Matrix::full(2, 2);
a[(0, 0)] = 1.0;
a[(0, 1)] = 2.0;
a[(1, 0)] = 3.0;
a[(1, 1)] = 4.0;
let mut b: Matrix<f64> = Matrix::full(2, 2);
b[(0, 0)] = 4.0;
b[(0, 1)] = 3.0;
b[(1, 0)] = 2.0;
b[(1, 1)] = 1.0;
let r = a + b;
assert_eq!(r[(0, 0)], 5.0);
assert_eq!(r[(0, 1)], 5.0);
assert_eq!(r[(1, 0)], 5.0);
assert_eq!(r[(1, 1)], 5.0);
}
#[test]
fn add_matrix_banded_banded() {
// 3x3, ml=1, mu=0 (lower tri without main above)
let mut a: Matrix<f64> = Matrix::banded(3, 1, 0);
let mut b: Matrix<f64> = Matrix::banded(3, 0, 1);
// set a main and lower
a[(0, 0)] = 1.0;
a[(1, 1)] = 1.0;
a[(2, 2)] = 1.0;
a[(1, 0)] = 1.0;
a[(2, 1)] = 1.0;
// set b main and upper
b[(0, 0)] = 2.0;
b[(1, 1)] = 2.0;
b[(2, 2)] = 2.0;
b[(0, 1)] = 2.0;
b[(1, 2)] = 2.0;
let r = a + b;
// Check entries of the resulting tri-diagonal
assert_eq!(r[(0, 0)], 3.0);
assert_eq!(r[(1, 1)], 3.0);
assert_eq!(r[(2, 2)], 3.0);
assert_eq!(r[(1, 0)], 1.0);
assert_eq!(r[(2, 1)], 1.0);
assert_eq!(r[(0, 1)], 2.0);
assert_eq!(r[(1, 2)], 2.0);
assert_eq!(r[(0, 2)], 0.0);
}
#[test]
fn add_sparse_sparse_densifies_with_summed_values() {
let a = Matrix::sparse_from_triplets(2, 2, vec![(0, 0, 1.0), (0, 0, 2.0)]);
let b = Matrix::sparse_from_triplets(2, 2, vec![(0, 1, 3.0), (1, 1, 4.0)]);
let r = a + b;
assert_eq!(r[(0, 0)], 3.0);
assert_eq!(r[(0, 1)], 3.0);
assert_eq!(r[(1, 1)], 4.0);
}
#[test]
fn add_scalar_zero_keeps_sparse() {
let m = Matrix::sparse_from_triplets(2, 2, vec![(0, 1, 2.0)]);
let r = m.component_add(0.0);
assert_eq!(r[(0, 1)], 2.0);
assert_eq!(r[(1, 0)], 0.0);
}
}