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use num_traits::{NumOps, Zero}; pub(crate) fn det_correlation_matrix<T: Clone + NumOps + Zero>(mat: &[Vec<T>]) -> T { let dim = mat[0].len(); let num = mat.len(); let mut cor = Vec::new(); for i in 0..num { let mut column = Vec::new(); for j in 0..num { let mut c = T::zero(); for k in 0..dim { c = c + mat[i][k].clone() * mat[j][k].clone(); } column.push(c); } cor.push(column); } det(&cor) } pub(crate) fn dot<T: Clone + NumOps + Zero>(x: &[T], y: &[T]) -> T { x.iter() .zip(y.iter()) .map(|(a, b)| a.clone() * b.clone()) .fold(T::zero(), |sum, c| sum + c) } pub(crate) fn sub<T: Clone + NumOps + Zero>(x: &[T], y: &[T]) -> Vec<T> { x.iter() .zip(y.iter()) .map(|(a, b)| a.clone() - b.clone()) .collect() } pub(crate) fn min_max_index_each_axis<T: Clone + Zero + PartialOrd>( points: &[Vec<T>], ) -> Vec<(usize, usize)> { let dim = points[0].len(); let mut min_index = vec![0; dim]; let mut max_index = vec![0; dim]; let mut min = vec![T::zero(); dim]; let mut max = vec![T::zero(); dim]; for (index, point) in points.iter().enumerate() { for (j, element) in point.iter().enumerate() { if index == 0 || *element < min[j] { min[j] = element.clone(); min_index[j] = index; } if index == 0 || *element > max[j] { max[j] = element.clone(); max_index[j] = index; } } } min_index.into_iter().zip(max_index.into_iter()).collect() } pub(crate) fn is_same_dimension<T>(points: &[Vec<T>]) -> bool { if points.len() == 0 { return true; } let dim = points[0].len(); if points.iter().skip(1).find(|p| p.len() != dim).is_some() { false } else { true } } pub(crate) fn det<T: NumOps + Clone>(m: &[Vec<T>]) -> T { let row_dim = m.len(); let column_dim = m[0].len(); assert_eq!(row_dim, column_dim); match column_dim { 1 => m[0][0].clone(), 2 => det_2x2(m), 3 => det_3x3(m), 4 => det_4x4(m), _ => { unimplemented!("matrix size should be less than 4 dim to calcurate determinant for now") } } } fn det_2x2<T: NumOps + Clone>(m: &[Vec<T>]) -> T { m[0][0].clone() * m[1][1].clone() - m[0][1].clone() * m[1][0].clone() } #[rustfmt::skip] fn det_3x3<T: NumOps+Clone>(m: &[Vec<T>]) -> T { m[0][0].clone() * (m[1][1].clone() * m[2][2].clone() - m[1][2].clone() * m[2][1].clone()) - m[1][0].clone() * (m[0][1].clone() * m[2][2].clone() - m[0][2].clone() * m[2][1].clone()) + m[2][0].clone() * (m[0][1].clone() * m[1][2].clone() - m[0][2].clone() * m[1][1].clone()) } #[rustfmt::skip] fn det_4x4<T: NumOps + Clone>(m: &[Vec<T>]) -> T { m[0][0].clone() * ( m[1][1].clone() * m[2][2].clone() * m[3][3].clone() + m[1][2].clone() * m[2][3].clone() * m[3][1].clone() + m[1][3].clone() * m[2][1].clone() * m[3][2].clone() - m[1][3].clone() * m[2][2].clone() * m[3][1].clone() - m[1][2].clone() * m[2][1].clone() * m[3][3].clone() - m[1][1].clone() * m[2][3].clone() * m[3][2].clone()) - m[1][0].clone() * ( m[0][1].clone() * m[2][2].clone() * m[3][3].clone() + m[0][2].clone() * m[2][3].clone() * m[3][1].clone() + m[0][3].clone() * m[2][1].clone() * m[3][2].clone() - m[0][3].clone() * m[2][2].clone() * m[3][1].clone() - m[0][2].clone() * m[2][1].clone() * m[3][3].clone() - m[0][1].clone() * m[2][3].clone() * m[3][2].clone()) + m[2][0].clone() * ( m[0][1].clone() * m[1][2].clone() * m[3][3].clone() + m[0][2].clone() * m[1][3].clone() * m[3][1].clone() + m[0][3].clone() * m[1][1].clone() * m[3][2].clone() - m[0][3].clone() * m[1][2].clone() * m[3][1].clone() - m[0][2].clone() * m[1][1].clone() * m[3][3].clone() - m[0][1].clone() * m[1][3].clone() * m[3][2].clone()) - m[3][0].clone() * ( m[0][1].clone() * m[1][2].clone() * m[2][3].clone() + m[0][2].clone() * m[1][3].clone() * m[2][1].clone() + m[0][3].clone() * m[1][1].clone() * m[2][2].clone() - m[0][3].clone() * m[1][2].clone() * m[2][1].clone() - m[0][2].clone() * m[1][1].clone() * m[2][3].clone() - m[0][1].clone() * m[1][3].clone() * m[2][2].clone()) } #[test] fn det_4x4_test() { let r1 = vec![1., 2., 3., 4.]; let r2 = vec![5., 6., 7., 8.]; let r3 = vec![9., 10., 11., 12.]; let r4 = vec![13., 14., 15., 16.]; assert_eq!(det(&[r1, r2, r3, r4]), 0.); let r1 = vec![1., 2., 3., 1.]; let r2 = vec![6., 6., 7., 1.]; let r3 = vec![9., 11., 11., 1.]; let r4 = vec![15., 14., 15., 1.]; assert_eq!(det(&[r1, r2, r3, r4]), -4.); let r1 = vec![1., 1., 1., 1.]; let r2 = vec![1., 2., 2., 1.]; let r3 = vec![1., 2., 3., 1.]; let r4 = vec![1., 1., 1., 2.]; assert_eq!(det(&[r1, r2, r3, r4]), 1.); }