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pub use crate::conjugate_gradient::ConjugateGradient;
use ndarray::ArcArray1;
use ndarray::ArcArray2;
pub type S = f64;
pub type M = ArcArray2<S>;
pub type V = ArcArray1<S>;
#[cfg(test)]
mod tests {
use crate::conjugate_gradient::ConjugateGradient;
use crate::inspect;
use crate::last;
use crate::utils::make_3x3_pd_system_1;
use crate::utils::make_3x3_psd_system;
use crate::utils::{LinearSystem, M, V};
extern crate nalgebra as na;
use eigenvalues::algorithms::lanczos::HermitianLanczos;
use eigenvalues::SpectrumTarget;
use na::{DMatrix, DVector, Dynamic};
use ndarray::rcarr1;
use ndarray::rcarr2;
use quickcheck::{quickcheck, TestResult};
use streaming_iterator::StreamingIterator;
pub fn solve_approximately(p: LinearSystem) -> V {
let solution = ConjugateGradient::for_problem(&p).take(20);
last(solution.map(|s| s.x_k.clone()))
.expect("ConjugateGradient should always return a solution.")
}
pub fn show_progress(p: LinearSystem) {
let cg_iter = ConjugateGradient::for_problem(&p).take(20);
let mut cg_print_iter = inspect(cg_iter, |result| {
let res = result.a.dot(&result.solution) - &result.b;
let res_norm = res.dot(&res);
println!(
"r_k2 = {:.10}, ||Ax - b ||_2^2 = {:.5}, for x = {:.4}, and Ax - b = {:.5}",
res_norm,
res_norm,
result.solution,
result.a.dot(&result.solution) - &result.b,
);
});
while let Some(_cgi) = cg_print_iter.next() {}
}
#[test]
fn test_alt_eig() {
let dm = DMatrix::from_row_slice(3, 3, &[3.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 2.0]);
println!("dm: {}", dm);
let high = HermitianLanczos::new(dm.clone(), 3, SpectrumTarget::Highest)
.unwrap()
.eigenvalues[(0, 0)];
println!("high: {}", &high);
assert!((high - 3.).abs() < 0.001);
}
fn eigvals(m: &M) -> Result<DVector<f64>, String> {
let shape = m.shape();
let h = shape[0];
let w = shape[1];
assert_eq!(h, w);
let elems = m.reshape(h * w).to_vec();
let dm = na::DMatrix::from_vec_generic(Dynamic::new(h), Dynamic::new(w), elems);
Ok(
HermitianLanczos::new(dm.clone(), 3, SpectrumTarget::Highest)?
.eigenvalues
.clone(),
)
}
fn test_arbitrary_3x3_psd(vs: Vec<u16>, b: Vec<u16>) -> TestResult {
if b.len().pow(2) != vs.len() || b.len() != 3 {
return TestResult::discard();
}
let vs = rcarr1(&vs).reshape((3, 3)).map(|i| *i as f64).into_shared();
let b = rcarr1(&b).map(|i| *i as f64).into_shared();
let p = make_3x3_psd_system(vs, b);
let eigvals = eigvals(&p.a).expect(&format!("Failed to compute eigenvalues for {}", &p.a));
if !eigvals.iter().all(|ev| &1e-8 < ev && ev < &1e9) {
return TestResult::discard();
}
println!("eigvals of a: {}", eigvals);
println!("a: {}", p.a);
println!("b: {}", p.b);
let x = solve_approximately(p.clone());
let res = p.a.dot(&x) - &p.b;
let res_square_norm = res.dot(&res);
println!("x: {}", x);
show_progress(p.clone());
TestResult::from_bool(res_square_norm < 1e-40)
}
quickcheck! {
fn prop(vs: Vec<u16>, b: Vec<u16>) -> TestResult {
test_arbitrary_3x3_psd(vs, b)
}
}
#[test]
fn cg_simple_test() {
let p = make_3x3_pd_system_1();
println!("Problem is: {:?}", p);
show_progress(p.clone());
let x = solve_approximately(p.clone());
let r = p.a.dot(&x) - p.b;
println!("Residual is: {}", r);
let res_square_norm = r.dot(&r);
println!("Residual squared norm is: {}", res_square_norm);
assert!(res_square_norm < 1e-10);
}
#[test]
fn cg_simple_passed() {
let p = LinearSystem {
a: rcarr2(&[[1.0, 0.5, 0.0], [0.5, 1.0, 0.5], [0.0, 0.5, 1.0]]),
b: rcarr1(&[0.0, 1., 0.]),
x0: None,
};
println!("Problem is: {:?}", p);
show_progress(p.clone());
println!("done showing");
let x = solve_approximately(p.clone());
let r = p.a.dot(&x) - p.b;
println!("Residual is: {}", r);
let res_square_norm = r.dot(&r);
println!("Residual squared norm is: {}", res_square_norm);
assert!(res_square_norm < 1e-10);
}
#[test]
fn cg_zero_x() {
let result = test_arbitrary_3x3_psd(vec![0, 0, 1, 1, 0, 0, 0, 1, 0], vec![0, 0, 0]);
assert!(!result.is_failure());
assert!(!result.is_error());
}
#[ignore]
#[test]
fn cg_rank_one_v() {
let result = test_arbitrary_3x3_psd(vec![0, 0, 0, 0, 0, 0, 1, 43, 8124], vec![0, 0, 1]);
assert!(!result.is_failure());
assert!(!result.is_error());
}
#[test]
fn cg_horribly_conditioned() {
let result =
test_arbitrary_3x3_psd(vec![0, 0, 0, 0, 0, 1, 101, 4654, 53693], vec![0, 0, 6]);
assert!(!result.is_failure());
assert!(!result.is_error());
}
}