faer 0.24.0

linear algebra library
Documentation 
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use super::LINEAR_IMPL_THRESHOLD;
use crate::internal_prelude::*;
#[inline(always)]
fn sum_simd<'N, T: ComplexField>(
	data: ColRef<'_, T, Dim<'N>, ContiguousFwd>,
) -> T {
	struct Impl<'a, 'N, T: ComplexField> {
		data: ColRef<'a, T, Dim<'N>, ContiguousFwd>,
	}
	impl<'N, T: ComplexField> pulp::WithSimd for Impl<'_, 'N, T> {
		type Output = T;

		#[inline(always)]
		fn with_simd<S: pulp::Simd>(self, simd: S) -> Self::Output {
			let Self { data } = self;
			let simd = SimdCtx::<T, S>::new(T::simd_ctx(simd), data.nrows());
			let mut acc = [simd.zero(); 4];
			simd_iter!(for (IDX, i) in [simd.batch_indices(); 4] {
				let x = simd.read(data, i);
				acc[IDX] = simd.add(acc[IDX], x);
			});
			let acc0 = simd.add(acc[0], acc[1]);
			let acc2 = simd.add(acc[2], acc[3]);
			let acc0 = simd.add(acc0, acc2);
			simd.reduce_sum(acc0)
		}
	}
	dispatch!(Impl { data }, Impl, T)
}
fn sum_simd_pairwise_rows<T: ComplexField>(
	data: ColRef<'_, T, usize, ContiguousFwd>,
) -> T {
	if data.nrows() <= LINEAR_IMPL_THRESHOLD {
		with_dim!(N, data.nrows());
		sum_simd(data.as_row_shape(N))
	} else {
		let split_point = ((data.nrows() + 1) / 2).next_power_of_two();
		let (head, tail) = data.split_at_row(split_point);
		let acc0 = sum_simd_pairwise_rows(head);
		let acc1 = sum_simd_pairwise_rows(tail);
		acc0 + acc1
	}
}
fn sum_simd_pairwise_cols<T: ComplexField>(
	data: MatRef<'_, T, usize, usize, ContiguousFwd>,
) -> T {
	if data.ncols() == 1 {
		sum_simd_pairwise_rows(data.col(0))
	} else {
		let split_point = ((data.ncols() + 1) / 2).next_power_of_two();
		let (head, tail) = data.split_at_col(split_point);
		let acc0 = sum_simd_pairwise_cols(head);
		let acc1 = sum_simd_pairwise_cols(tail);
		acc0 + acc1
	}
}
pub fn sum<T: ComplexField>(mut mat: MatRef<'_, T>) -> T {
	if mat.ncols() > 1 && mat.col_stride().unsigned_abs() == 1 {
		mat = mat.transpose();
	}
	if mat.row_stride() < 0 {
		mat = mat.reverse_rows();
	}
	if mat.nrows() == 0 || mat.ncols() == 0 {
		zero()
	} else {
		let m = mat.nrows();
		let n = mat.ncols();
		if const { T::SIMD_CAPABILITIES.is_simd() } {
			if let Some(mat) = mat.try_as_col_major() {
				return sum_simd_pairwise_cols(mat);
			}
		}
		let mut acc = zero();
		for j in 0..n {
			for i in 0..m {
				acc += &mat[(i, j)];
			}
		}
		acc
	}
}
#[cfg(test)]
mod tests {
	use super::*;
	use crate::{Col, Mat, assert};
	#[test]
	fn test_sum_real() {
		let relative_err =
			|a: f64, b: f64| (a - b).abs() / f64::max(a.abs(), b.abs());
		for (m, n) in [(9, 10), (1023, 1024), (42, 1)] {
			for factor in [0.0, 1.0, 1e30, 1e250, 1e-30, 1e-250] {
				let mat = Mat::from_fn(m, n, |i, j| factor * ((i + j) as f64));
				let mut target = 0.0;
				zip!(mat.rb()).for_each(|unzip!(x)| {
					target += x;
				});
				if factor == 0.0 {
					assert!(sum(mat.rb()) == target);
				} else {
					assert!(relative_err(sum(mat.rb()), target) < 1e-13);
				}
			}
		}
		let col = Col::from_fn(10000000, |_| 0.3);
		let target = 0.3 * 10000000.0f64;
		assert!(relative_err(sum(col.as_mat()), target) < 1e-14);
	}
	#[test]
	fn test_sum_cplx() {
		let relative_err =
			|a: c64, b: c64| (a - b).abs() / f64::max(a.abs(), b.abs());
		for (m, n) in [(9, 10), (1023, 5), (42, 1)] {
			for factor in [0.0, 1.0, 1e30, 1e250, 1e-30, 1e-250] {
				let mat = Mat::from_fn(m, n, |i, j| {
					let i = i as isize;
					let j = j as isize;
					c64::new(
						factor * ((i + j) as f64),
						factor * ((i - j) as f64),
					)
				});
				let mut target = c64::ZERO;
				zip!(mat.rb()).for_each(|unzip!(x)| {
					target += x;
				});
				if factor == 0.0 {
					assert!(sum(mat.rb()) == target);
				} else {
					assert!(relative_err(sum(mat.rb()), target) < 1e-14);
				}
			}
		}
	}
}