faer 0.24.0

linear algebra library
Documentation 
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use crate::internal_prelude::*;
/// kronecker product of two matrices
///
/// the kronecker product of two matrices $A$ and $B$ is a block matrix
/// $B$ with the following structure:
///
/// ```text
/// C = [ a[(0, 0)] * B    , a[(0, 1)] * B    , ... , a[(0, n-1)] * B    ]
///     [ a[(1, 0)] * B    , a[(1, 1)] * B    , ... , a[(1, n-1)] * B    ]
///     [ ...              , ...              , ... , ...              ]
///     [ a[(m-1, 0)] * B  , a[(m-1, 1)] * B  , ... , a[(m-1, n-1)] * B  ]
/// ```
///
/// # panics
///
/// panics if `dst` does not have the correct dimensions. the dimensions
/// of `dst` must be `A.nrows() * B.nrows()` by `A.ncols() * B.ncols()`.
///
/// # example
///
/// ```
/// use faer::linalg::kron::kron;
/// use faer::{Mat, mat};
/// let a = mat![[1.0, 2.0], [3.0, 4.0]];
/// let b = mat![[0.0, 5.0], [6.0, 7.0]];
/// let c = mat![
/// 	[0.0, 5.0, 0.0, 10.0],
/// 	[6.0, 7.0, 12.0, 14.0],
/// 	[0.0, 15.0, 0.0, 20.0],
/// 	[18.0, 21.0, 24.0, 28.0],
/// ];
/// let mut dst = Mat::zeros(4, 4);
/// kron(dst.as_mut(), a.as_ref(), b.as_ref());
/// assert_eq!(dst, c);
/// ```
#[track_caller]
pub fn kron<T: ComplexField>(
	dst: MatMut<'_, T>,
	lhs: MatRef<'_, impl Conjugate<Canonical = T>>,
	rhs: MatRef<'_, impl Conjugate<Canonical = T>>,
) {
	let mut dst = dst;
	let mut lhs = lhs;
	let mut rhs = rhs;
	if dst.col_stride().unsigned_abs() < dst.row_stride().unsigned_abs() {
		dst = dst.transpose_mut();
		lhs = lhs.transpose();
		rhs = rhs.transpose();
	}
	Assert!(Some(dst.nrows()) == lhs.nrows().checked_mul(rhs.nrows()));
	Assert!(Some(dst.ncols()) == lhs.ncols().checked_mul(rhs.ncols()));
	for lhs_j in 0..lhs.ncols() {
		for lhs_i in 0..lhs.nrows() {
			let lhs_val = &Conj::apply(lhs.at(lhs_i, lhs_j));
			let mut dst = dst.rb_mut().submatrix_mut(
				lhs_i * rhs.nrows(),
				lhs_j * rhs.ncols(),
				rhs.nrows(),
				rhs.ncols(),
			);
			for rhs_j in 0..rhs.ncols() {
				for rhs_i in 0..rhs.nrows() {
					unsafe {
						let rhs_val =
							Conj::apply(rhs.at_unchecked(rhs_i, rhs_j));
						*dst.rb_mut().at_mut_unchecked(rhs_i, rhs_j) =
							lhs_val * rhs_val;
					}
				}
			}
		}
	}
}
#[cfg(test)]
mod tests {
	use super::kron;
	use crate::{Col, Mat, Row, assert};
	#[test]
	fn test_kron_ones() {
		for (m, n, p, q) in [(2, 3, 4, 5), (3, 2, 5, 4), (1, 1, 1, 1)] {
			let a = Mat::from_fn(m, n, |_, _| 1 as f64);
			let b = Mat::from_fn(p, q, |_, _| 1 as f64);
			let expected = Mat::from_fn(m * p, n * q, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(a.nrows() * b.nrows(), a.ncols() * b.ncols());
			kron(out.as_mut(), a.as_ref(), b.as_ref());
			assert!(out == expected);
		}
		for (m, n, p) in [(2, 3, 4), (3, 2, 5), (1, 1, 1)] {
			let a = Mat::from_fn(m, n, |_, _| 1 as f64);
			let b = Col::from_fn(p, |_| 1 as f64);
			let expected = Mat::from_fn(m * p, n, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(a.nrows() * b.nrows(), a.ncols() * b.ncols());
			kron(out.as_mut(), a.as_ref(), b.as_ref().as_mat());
			assert!(out == expected);
			let mut out =
				Mat::zeros(b.nrows() * a.nrows(), b.ncols() * a.ncols());
			kron(out.as_mut(), b.as_ref().as_mat(), a.as_ref());
			assert!(out == expected);
			let a = Mat::from_fn(m, n, |_, _| 1 as f64);
			let b = Row::from_fn(p, |_| 1 as f64);
			let expected = Mat::from_fn(m, n * p, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(a.nrows() * b.nrows(), a.ncols() * b.ncols());
			kron(out.as_mut(), a.as_ref(), b.as_ref().as_mat());
			assert!(out == expected);
			let mut out =
				Mat::zeros(b.nrows() * a.nrows(), b.ncols() * a.ncols());
			kron(out.as_mut(), b.as_ref().as_mat(), a.as_ref());
			assert!(out == expected);
		}
		for (m, n) in [(2, 3), (3, 2), (1, 1)] {
			let a = Row::from_fn(m, |_| 1 as f64);
			let b = Col::from_fn(n, |_| 1 as f64);
			let expected = Mat::from_fn(n, m, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(a.nrows() * b.nrows(), a.ncols() * b.ncols());
			kron(out.as_mut(), a.as_ref().as_mat(), b.as_ref().as_mat());
			assert!(out == expected);
			let mut out =
				Mat::zeros(b.nrows() * a.nrows(), b.ncols() * a.ncols());
			kron(out.as_mut(), b.as_ref().as_mat(), a.as_ref().as_mat());
			assert!(out == expected);
			let c = Row::from_fn(n, |_| 1 as f64);
			let expected = Mat::from_fn(1, m * n, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(a.nrows() * c.nrows(), a.ncols() * c.ncols());
			kron(out.as_mut(), a.as_ref().as_mat(), c.as_ref().as_mat());
			assert!(out == expected);
			let d = Col::from_fn(m, |_| 1 as f64);
			let expected = Mat::from_fn(m * n, 1, |_, _| 1 as f64);
			let mut out =
				Mat::zeros(d.nrows() * b.nrows(), d.ncols() * b.ncols());
			kron(out.as_mut(), d.as_ref().as_mat(), b.as_ref().as_mat());
			assert!(out == expected);
		}
	}
}