85 lines
2.7 KiB
Rust
85 lines
2.7 KiB
Rust
//! Functions for balancing a matrix.
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use simba::scalar::RealField;
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use std::ops::{DivAssign, MulAssign};
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use crate::allocator::Allocator;
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use crate::base::dimension::Dim;
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use crate::base::{Const, DefaultAllocator, OMatrix, OVector};
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/// Applies in-place a modified Parlett and Reinsch matrix balancing with 2-norm to the matrix and returns
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/// the corresponding diagonal transformation.
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///
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/// See <https://arxiv.org/pdf/1401.5766.pdf>
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pub fn balance_parlett_reinsch<T: RealField, D: Dim>(matrix: &mut OMatrix<T, D, D>) -> OVector<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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assert!(matrix.is_square(), "Unable to balance a non-square matrix.");
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let dim = matrix.shape_generic().0;
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let radix: T = crate::convert(2.0f64);
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let mut d = OVector::from_element_generic(dim, Const::<1>, T::one());
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let mut converged = false;
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while !converged {
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converged = true;
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for i in 0..dim.value() {
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let mut n_col = matrix.column(i).norm_squared();
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let mut n_row = matrix.row(i).norm_squared();
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let mut f = T::one();
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let s = n_col.clone() + n_row.clone();
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n_col = n_col.sqrt();
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n_row = n_row.sqrt();
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if n_col.clone().is_zero() || n_row.clone().is_zero() {
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continue;
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}
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while n_col.clone() < n_row.clone() / radix.clone() {
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n_col *= radix.clone();
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n_row /= radix.clone();
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f *= radix.clone();
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}
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while n_col.clone() >= n_row.clone() * radix.clone() {
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n_col /= radix.clone();
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n_row *= radix.clone();
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f /= radix.clone();
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}
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let eps: T = crate::convert(0.95);
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#[allow(clippy::suspicious_operation_groupings)]
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if n_col.clone() * n_col + n_row.clone() * n_row < eps * s {
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converged = false;
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d[i] *= f.clone();
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matrix.column_mut(i).mul_assign(f.clone());
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matrix.row_mut(i).div_assign(f.clone());
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}
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}
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}
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d
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}
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/// Computes in-place `D * m * D.inverse()`, where `D` is the matrix with diagonal `d`.
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pub fn unbalance<T: RealField, D: Dim>(m: &mut OMatrix<T, D, D>, d: &OVector<T, D>)
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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assert!(m.is_square(), "Unable to unbalance a non-square matrix.");
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assert_eq!(m.nrows(), d.len(), "Unbalancing: mismatched dimensions.");
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for j in 0..d.len() {
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let mut col = m.column_mut(j);
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let denom = T::one() / d[j].clone();
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for i in 0..d.len() {
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col[i] *= d[i].clone() * denom.clone();
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}
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}
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}
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