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use alga::general::RealField;
use std::ops::{DivAssign, MulAssign};
use crate::allocator::Allocator;
use crate::base::dimension::{Dim, U1};
use crate::base::storage::Storage;
use crate::base::{DefaultAllocator, MatrixN, VectorN};
pub fn balance_parlett_reinsch<N: RealField, D: Dim>(m: &mut MatrixN<N, D>) -> VectorN<N, D>
where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
assert!(m.is_square(), "Unable to balance a non-square matrix.");
let dim = m.data.shape().0;
let radix: N = crate::convert(2.0f64);
let mut d = VectorN::from_element_generic(dim, U1, N::one());
let mut converged = false;
while !converged {
converged = true;
for i in 0..dim.value() {
let mut c = m.column(i).norm_squared();
let mut r = m.row(i).norm_squared();
let mut f = N::one();
let s = c + r;
c = c.sqrt();
r = r.sqrt();
if c.is_zero() || r.is_zero() {
continue;
}
while c < r / radix {
c *= radix;
r /= radix;
f *= radix;
}
while c >= r * radix {
c /= radix;
r *= radix;
f /= radix;
}
let eps: N = crate::convert(0.95);
if c * c + r * r < eps * s {
converged = false;
d[i] *= f;
m.column_mut(i).mul_assign(f);
m.row_mut(i).div_assign(f);
}
}
}
d
}
pub fn unbalance<N: RealField, D: Dim>(m: &mut MatrixN<N, D>, d: &VectorN<N, D>)
where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
assert!(m.is_square(), "Unable to unbalance a non-square matrix.");
assert_eq!(m.nrows(), d.len(), "Unbalancing: mismatched dimensions.");
for j in 0..d.len() {
let mut col = m.column_mut(j);
let denom = N::one() / d[j];
for i in 0..d.len() {
col[i] *= d[i] * denom;
}
}
}