forked from M-Labs/nalgebra
81 lines
2.3 KiB
Rust
81 lines
2.3 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, U1};
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use crate::base::storage::Storage;
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use crate::base::{DefaultAllocator, MatrixN, VectorN};
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/// Applies in-place a modified Parlett and Reinsch matrix balancing with 2-norm to the matrix `m` 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<N: RealField, D: Dim>(m: &mut MatrixN<N, D>) -> VectorN<N, D>
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where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
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assert!(m.is_square(), "Unable to balance a non-square matrix.");
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let dim = m.data.shape().0;
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let radix: N = crate::convert(2.0f64);
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let mut d = VectorN::from_element_generic(dim, U1, N::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 c = m.column(i).norm_squared();
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let mut r = m.row(i).norm_squared();
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let mut f = N::one();
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let s = c + r;
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c = c.sqrt();
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r = r.sqrt();
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if c.is_zero() || r.is_zero() {
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continue;
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}
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while c < r / radix {
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c *= radix;
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r /= radix;
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f *= radix;
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}
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while c >= r * radix {
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c /= radix;
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r *= radix;
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f /= radix;
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}
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let eps: N = crate::convert(0.95);
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if c * c + r * r < eps * s {
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converged = false;
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d[i] *= f;
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m.column_mut(i).mul_assign(f);
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m.row_mut(i).div_assign(f);
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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<N: RealField, D: Dim>(m: &mut MatrixN<N, D>, d: &VectorN<N, D>)
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where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
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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 = N::one() / d[j];
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for i in 0..d.len() {
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col[i] *= d[i] * denom;
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}
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}
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}
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