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//! Matrix subtraction.
use core::ops::{Sub, SubAssign};
use super::base::{Matrix, MatrixStorage};
use crate::traits::Real;
// Matrix - Matrix
impl<T: Real> Sub for Matrix<T> {
type Output = Matrix<T>;
fn sub(self, rhs: Matrix<T>) -> Self::Output {
match (self, rhs) {
(
Matrix {
n: n1,
storage: MatrixStorage::Identity,
..
},
Matrix {
n: n2,
storage: MatrixStorage::Identity,
..
},
) => {
assert_eq!(n1, n2, "dimension mismatch in Matrix - Matrix");
Matrix {
n: n1,
m: n1,
data: vec![T::zero(); n1 * n1],
storage: MatrixStorage::Full,
}
}
(
Matrix {
n,
data: mut a,
storage: MatrixStorage::Full,
..
},
Matrix {
n: n2,
data: b,
storage: MatrixStorage::Full,
..
},
) => {
assert_eq!(n, n2, "dimension mismatch in Matrix - Matrix");
for (x, y) in a.iter_mut().zip(b.iter()) {
*x -= *y;
}
Matrix {
n,
m: n,
data: a,
storage: MatrixStorage::Full,
}
}
(
Matrix {
n,
data: a,
storage: MatrixStorage::Banded { ml, mu, .. },
..
},
Matrix {
n: n2,
data: b,
storage:
MatrixStorage::Banded {
ml: ml2, mu: mu2, ..
},
..
},
) => {
assert_eq!(n, n2, "dimension mismatch in Matrix - Matrix");
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(),
},
};
// Add first banded
for j in 0..n {
for r in 0..(ml + mu + 1) {
let k = r as isize - mu as isize; // i - j for first
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];
}
}
}
// Subtract second banded
for j in 0..n {
for r in 0..(ml2 + mu2 + 1) {
let k = r as isize - mu2 as isize; // i - j for second
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 storage: densify
(
Matrix {
n: n1,
data: a,
storage: sa,
..
},
Matrix {
n: n2,
data: b,
storage: sb,
..
},
) => {
assert_eq!(n1, n2, "dimension mismatch in Matrix - Matrix");
let to_full = |n: usize, data: Vec<T>, storage: MatrixStorage<T>| -> Vec<T> {
match storage {
MatrixStorage::Full => data,
MatrixStorage::Identity => {
let mut d = vec![T::zero(); n * n];
for i in 0..n {
d[i * n + i] = T::one();
}
d
}
MatrixStorage::Banded { ml, mu, .. } => {
let mut d = vec![T::zero(); n * n];
for j in 0..n {
for r in 0..(ml + mu + 1) {
let k = r as isize - mu as isize; // i - j
let i_signed = j as isize + k;
if i_signed >= 0 && (i_signed as usize) < n {
let i = i_signed as usize;
d[i * n + j] += data[r * n + j];
}
}
}
d
}
}
};
let aa = to_full(n1, a, sa);
let bb = to_full(n2, b, sb);
let data = aa.into_iter().zip(bb).map(|(x, y)| x - y).collect();
Matrix {
n: n1,
m: n1,
data,
storage: MatrixStorage::Full,
}
}
}
}
}
// For scalars, use `component_sub`.
// Sub-assign by value
impl<T: Real> SubAssign<Matrix<T>> for Matrix<T> {
fn sub_assign(&mut self, rhs: Matrix<T>) {
let n = self.n;
let lhs = core::mem::replace(self, Matrix::zeros(n, n));
*self = lhs - rhs;
}
}
// Sub-assign by reference (clones rhs)
impl<T: Real> SubAssign<&Matrix<T>> for Matrix<T> {
fn sub_assign(&mut self, rhs: &Matrix<T>) {
let n = self.n;
let lhs = core::mem::replace(self, Matrix::zeros(n, n));
*self = lhs - rhs.clone();
}
}
impl<T: Real> Matrix<T> {
/// Return a new matrix where each stored entry has `rhs` subtracted. Off-band handling similar to add.
pub fn component_sub(mut self, rhs: T) -> Self {
match &mut self.storage {
MatrixStorage::Identity => {
let n = self.n;
let mut data = vec![T::zero() - rhs; n * n];
for i in 0..n {
data[i * n + i] = T::one() - rhs;
}
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![T::zero() - 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,
}
}
}
}
}
}
#[cfg(test)]
mod tests {
use crate::linalg::matrix::Matrix;
#[test]
fn sub_scalar_full() {
let m: Matrix<f64> = Matrix::from_vec(2, 2, vec![1.0, 2.0, 3.0, 4.0]);
let r = m.component_sub(1.0);
assert_eq!(r[(0, 0)], 0.0);
assert_eq!(r[(0, 1)], 1.0);
assert_eq!(r[(1, 0)], 2.0);
assert_eq!(r[(1, 1)], 3.0);
}
#[test]
fn sub_scalar_banded_zero_keeps_banded() {
let m: Matrix<f64> = Matrix::banded(3, 1, 1);
let r = m.component_sub(0.0);
for i in 0..3 {
for j in 0..3 {
assert_eq!(r[(i, j)], 0.0);
}
}
}
#[test]
fn sub_matrix_full_full() {
let a: Matrix<f64> = Matrix::from_vec(2, 2, vec![1.0, 2.0, 3.0, 4.0]);
let b: Matrix<f64> = Matrix::from_vec(2, 2, vec![4.0, 3.0, 2.0, 1.0]);
let r = a - b;
assert_eq!(r[(0, 0)], -3.0);
assert_eq!(r[(0, 1)], -1.0);
assert_eq!(r[(1, 0)], 1.0);
assert_eq!(r[(1, 1)], 3.0);
}
#[test]
fn sub_matrix_banded_banded() {
// 3x3, ml=1, mu=0 and 0,1
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)], -1.0);
assert_eq!(r[(1, 1)], -1.0);
assert_eq!(r[(2, 2)], -1.0);
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);
}
}