smartcore/src/linalg/svd.rs

use crate::linalg::{Matrix};

#[derive(Debug, Clone)]
pub struct SVD<M: Matrix> {
    pub U: M,
    pub V: M,
    pub s: Vec<f64>,
    full: bool,
    m: usize,
    n: usize,
    tol: f64
}

impl<M: Matrix> SVD<M> {
    pub fn new(U: M, V: M, s: Vec<f64>) -> SVD<M> {
        let m = U.shape().0;
        let n = V.shape().0;     
        let full = s.len() == m.min(n);   
        let tol = 0.5 * ((m + n) as f64 + 1.).sqrt() * s[0] * std::f64::EPSILON;
        SVD {
            U: U,
            V: V,
            s: s,
            full: full,
            m: m,
            n: n,
            tol: tol
        }
    }

    pub fn solve(&self, mut b: M) -> M {
        let p = b.shape().1;

        if self.U.shape().0 != b.shape().0 {
            panic!("Dimensions do not agree. U.nrows should equal b.nrows but is {}, {}", self.U.shape().0, b.shape().0);
        }

        for k in 0..p {
            let mut tmp = vec![0f64; self.n];
            for j in 0..self.n {
                let mut r = 0f64;
                if self.s[j] > self.tol {
                    for i in 0..self.m {
                        r += self.U.get(i, j) * b.get(i, k);
                    }
                    r /= self.s[j];
                }
                tmp[j] = r;
            }

            for j in 0..self.n {
                let mut r = 0.0;
                for jj in 0..self.n {
                    r += self.V.get(j, jj) * tmp[jj];
                }
                b.set(j, k, r);
            }
        }

        b
    }
}

#[cfg(test)]
mod tests {    
    use super::*; 
    use crate::linalg::naive::dense_matrix::DenseMatrix;

    #[test]
    fn decompose_symmetric() { 

        let A = DenseMatrix::from_array(&[
            &[0.9000, 0.4000, 0.7000],
            &[0.4000, 0.5000, 0.3000],
            &[0.7000, 0.3000, 0.8000]]);

        let s = vec![1.7498382, 0.3165784, 0.1335834];

        let U = DenseMatrix::from_array(&[
            &[0.6881997, -0.07121225, 0.7220180],
            &[0.3700456, 0.89044952, -0.2648886],
            &[0.6240573, -0.44947578, -0.639158]
        ]);

        let V = DenseMatrix::from_array(&[
            &[0.6881997, -0.07121225, 0.7220180],
            &[0.3700456, 0.89044952, -0.2648886],
            &[0.6240573, -0.44947578, -0.6391588]
        ]);

        let svd = A.svd();

        assert!(V.abs().approximate_eq(&svd.V.abs(), 1e-4));
        assert!(U.abs().approximate_eq(&svd.U.abs(), 1e-4));
        for i in 0..s.len() {
            assert!((s[i] - svd.s[i]).abs() < 1e-4);
        }

    }

    #[test]
    fn decompose_asymmetric() { 

        let A = DenseMatrix::from_array(&[
            &[1.19720880, -1.8391378, 0.3019585, -1.1165701, -1.7210814, 0.4918882, -0.04247433],
            &[0.06605075, 1.0315583, 0.8294362, -0.3646043, -1.6038017, -0.9188110, -0.63760340],
            &[-1.02637715, 1.0747931, -0.8089055, -0.4726863, -0.2064826, -0.3325532, 0.17966051],
            &[-1.45817729, -0.8942353, 0.3459245, 1.5068363, -2.0180708, -0.3696350, -1.19575563],
            &[-0.07318103, -0.2783787, 1.2237598, 0.1995332, 0.2545336, -0.1392502, -1.88207227],
            &[0.88248425, -0.9360321, 0.1393172, 0.1393281, -0.3277873, -0.5553013, 1.63805985],
            &[0.12641406, -0.8710055, -0.2712301, 0.2296515, 1.1781535, -0.2158704, -0.27529472]
        ]);

        let s = vec![3.8589375, 3.4396766, 2.6487176, 2.2317399, 1.5165054, 0.8109055, 0.2706515];

        let U = DenseMatrix::from_array(&[
            &[-0.3082776, 0.77676231, 0.01330514, 0.23231424, -0.47682758, 0.13927109, 0.02640713],
            &[-0.4013477, -0.09112050, 0.48754440, 0.47371793, 0.40636608, 0.24600706, -0.37796295],
            &[0.0599719, -0.31406586, 0.45428229, -0.08071283, -0.38432597, 0.57320261, 0.45673993],
            &[-0.7694214, -0.12681435, -0.05536793, -0.62189972, -0.02075522, -0.01724911, -0.03681864],
            &[-0.3319069, -0.17984404, -0.54466777, 0.45335157, 0.19377726, 0.12333423, 0.55003852],
            &[0.1259351, 0.49087824, 0.16349687, -0.32080176, 0.64828744, 0.20643772, 0.38812467],
            &[0.1491884, 0.01768604, -0.47884363, -0.14108924, 0.03922507, 0.73034065, -0.43965505]
        ]);

        let V = DenseMatrix::from_array(&[
            &[-0.2122609, -0.54650056, 0.08071332, -0.43239135, -0.2925067, 0.1414550, 0.59769207],
            &[-0.1943605, 0.63132116, -0.54059857, -0.37089970, -0.1363031, 0.2892641, 0.17774114],
            &[0.3031265, -0.06182488, 0.18579097, -0.38606409, -0.5364911, 0.2983466, -0.58642548],
            &[0.1844063, 0.24425278, 0.25923756, 0.59043765, -0.4435443, 0.3959057, 0.37019098],
            &[-0.7164205, 0.30694911, 0.58264743, -0.07458095, -0.1142140, -0.1311972, -0.13124764],
            &[-0.1103067, -0.10633600, 0.18257905, -0.03638501, 0.5722925, 0.7784398, -0.09153611],
            &[-0.5156083, -0.36573746, -0.47613340, 0.41342817, -0.2659765, 0.1654796, -0.32346758]
        ]);        

        let svd = A.svd();

        assert!(V.abs().approximate_eq(&svd.V.abs(), 1e-4));
        assert!(U.abs().approximate_eq(&svd.U.abs(), 1e-4));
        for i in 0..s.len() {
            assert!((s[i] - svd.s[i]).abs() < 1e-4);
        }

    }

    #[test]
    fn solve() { 

            let mut a = DenseMatrix::from_array(&[&[0.9, 0.4, 0.7], &[0.4, 0.5, 0.3], &[0.7, 0.3, 0.8]]);
            let b = DenseMatrix::from_array(&[&[0.5, 0.2],&[0.5, 0.8], &[0.5, 0.3]]);
            let expected_w = DenseMatrix::from_array(&[
                &[-0.20, -1.28],
                &[0.87, 2.22],
                &[0.47, 0.66]
            ]);
            let w = a.svd_solve_mut(b);  
            assert!(w.approximate_eq(&expected_w, 1e-2));            
    }
    
}