use na::dimension::{Const, Dynamic};
use na::{DMatrix, EuclideanNorm, Norm, OMatrix};
use nl::GE;
use num_complex::Complex;
use simba::scalar::ComplexField;
use std::cmp;

use crate::proptest::*;
use proptest::{prop_assert, proptest};

proptest! {
    #[test]
    fn ge(n in PROPTEST_MATRIX_DIM) {
        let n = cmp::max(1, cmp::min(n, 10));
        let a = DMatrix::<f64>::new_random(n, n);
        let b = DMatrix::<f64>::new_random(n, n);
        let a_condition_no = a.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&a)));
        let b_condition_no = b.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&b)));

        if a_condition_no.unwrap_or(200000.0) < 10.0 && b_condition_no.unwrap_or(200000.0) < 10.0 {
        let a_c =a.clone().map(|x| Complex::new(x, 0.0));
        let b_c = b.clone().map(|x| Complex::new(x, 0.0));

        let ge = GE::new(a.clone(), b.clone());
        let (vsl,vsr) = ge.clone().eigenvectors();
        let eigenvalues = ge.clone().eigenvalues();

        for i in 0..n {
            let left_eigenvector = &vsl.column(i);
            prop_assert!(relative_eq!((left_eigenvector.transpose()*&a_c - left_eigenvector.transpose()*&b_c*eigenvalues[i]).map(|x| x.modulus()), OMatrix::zeros_generic(Const::<1>,Dynamic::new(n)) ,epsilon = 1.0e-7));

            let right_eigenvector = &vsr.column(i);
            prop_assert!(relative_eq!((&a_c*right_eigenvector - &b_c*right_eigenvector*eigenvalues[i]).map(|x| x.modulus()), OMatrix::zeros_generic(Dynamic::new(n), Const::<1>) ,epsilon = 1.0e-7));
           };
        };
    }

    #[test]
    fn ge_static(a in matrix4(), b in matrix4()) {
        let a_condition_no = a.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&a)));
        let b_condition_no = b.clone().try_inverse().and_then(|x| Some(EuclideanNorm.norm(&x)* EuclideanNorm.norm(&b)));

        if a_condition_no.unwrap_or(200000.0) < 10.0 && b_condition_no.unwrap_or(200000.0) < 10.0{
        let ge = GE::new(a.clone(), b.clone());
        let a_c =a.clone().map(|x| Complex::new(x, 0.0));
        let b_c = b.clone().map(|x| Complex::new(x, 0.0));
        let (vsl,vsr) = ge.eigenvectors();
        let eigenvalues = ge.eigenvalues();

        for i in 0..4 {
                let left_eigenvector = &vsl.column(i);
                prop_assert!(relative_eq!((left_eigenvector.transpose()*&a_c - left_eigenvector.transpose()*&b_c*eigenvalues[i]).map(|x| x.modulus()), OMatrix::zeros_generic(Const::<1>,Const::<4>) ,epsilon = 1.0e-7));

                let right_eigenvector = &vsr.column(i);
                prop_assert!(relative_eq!((&a_c*right_eigenvector - &b_c*right_eigenvector*eigenvalues[i]).map(|x| x.modulus()), OMatrix::zeros_generic(Const::<4>, Const::<1>) ,epsilon = 1.0e-7));
            };
        };
    }
}