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use nalgebra::{Dynamic, Matrix, VecStorage, U1};
use std::ops::{AddAssign, Mul, MulAssign};
pub type Complex = nalgebra::Complex<f64>;
pub type MatrixXc = Matrix<Complex, Dynamic, Dynamic, VecStorage<Complex, Dynamic, Dynamic>>;
pub type MatrixX = Matrix<f64, Dynamic, Dynamic, VecStorage<f64, Dynamic, Dynamic>>;
pub type VectorXc = Matrix<Complex, Dynamic, U1, VecStorage<Complex, Dynamic, U1>>;
pub type VectorX = Matrix<f64, Dynamic, U1, VecStorage<f64, Dynamic, U1>>;
pub enum Transpose {
NoTrans = 111,
Trans = 112,
ConjTrans = 113,
ConjNoTrans = 114,
}
pub trait Backend {
fn hadamard_product(a: &MatrixXc, b: &MatrixXc, c: &mut MatrixXc);
fn real(a: &MatrixXc, b: &mut MatrixX);
fn imag(a: &VectorXc, b: &mut VectorX);
fn pseudo_inverse_svd(matrix: MatrixXc, alpha: f64, result: &mut MatrixXc);
fn max_eigen_vector(matrix: MatrixXc) -> VectorXc;
fn matrix_add(alpha: f64, a: &MatrixX, beta: f64, b: &mut MatrixX);
fn matrix_mul(
trans_a: Transpose,
trans_b: Transpose,
alpha: Complex,
a: &MatrixXc,
b: &MatrixXc,
beta: Complex,
c: &mut MatrixXc,
);
fn matrix_mul_vec(
trans_a: Transpose,
alpha: Complex,
a: &MatrixXc,
b: &VectorXc,
beta: Complex,
c: &mut VectorXc,
);
fn vector_add(alpha: f64, a: &VectorX, b: &mut VectorX);
fn solve_ch(a: MatrixXc, b: &mut VectorXc) -> bool;
fn solve_g(a: MatrixX, b: &mut VectorX) -> bool;
fn dot(a: &VectorX, b: &VectorX) -> f64;
fn dot_c(a: &VectorXc, b: &VectorXc) -> Complex;
fn max_coefficient(a: &VectorX) -> f64;
fn max_coefficient_c(a: &VectorXc) -> f64;
fn concat_row(a: MatrixXc, b: &MatrixXc) -> MatrixXc;
fn concat_col(a: MatrixXc, b: &MatrixXc) -> MatrixXc;
}
pub struct NalgebraBackend {}
impl Backend for NalgebraBackend {
fn hadamard_product(a: &MatrixXc, b: &MatrixXc, c: &mut MatrixXc) {
*c = a.component_mul(b);
}
fn real(a: &MatrixXc, b: &mut MatrixX) {
*b = a.map(|x| x.re);
}
fn imag(a: &VectorXc, b: &mut VectorX) {
*b = a.map(|x| x.im);
}
fn pseudo_inverse_svd(matrix: MatrixXc, alpha: f64, result: &mut MatrixXc) {
let svd = matrix.svd(true, true);
let s_inv = MatrixXc::from_diagonal(
&svd.singular_values
.map(|s| Complex::new(s / (s * s + alpha * alpha), 0.)),
);
*result = match (&svd.v_t, &svd.u) {
(Some(v_t), Some(u)) => v_t.adjoint() * s_inv * u.adjoint(),
_ => unreachable!(),
};
}
fn max_eigen_vector(matrix: MatrixXc) -> VectorXc {
let eig = nalgebra::SymmetricEigen::new(matrix);
eig.eigenvectors.column(eig.eigenvalues.imax()).into()
}
fn matrix_add(alpha: f64, a: &MatrixX, beta: f64, b: &mut MatrixX) {
b.mul_assign(beta);
b.add_assign(a.mul(alpha));
}
fn matrix_mul(
trans_a: Transpose,
trans_b: Transpose,
alpha: Complex,
a: &MatrixXc,
b: &MatrixXc,
beta: Complex,
c: &mut MatrixXc,
) {
c.mul_assign(beta);
match (trans_a, trans_b) {
(Transpose::NoTrans, Transpose::NoTrans) => c.add_assign(a.mul(b).mul(alpha)),
(Transpose::NoTrans, Transpose::Trans) => c.add_assign(a.mul(b.transpose()).mul(alpha)),
(Transpose::NoTrans, Transpose::ConjTrans) => {
c.add_assign(a.mul(b.adjoint()).mul(alpha))
}
(Transpose::NoTrans, Transpose::ConjNoTrans) => {
c.add_assign(a.mul(b.conjugate()).mul(alpha))
}
(Transpose::Trans, Transpose::NoTrans) => c.add_assign(a.transpose().mul(b).mul(alpha)),
(Transpose::Trans, Transpose::Trans) => {
c.add_assign(a.transpose().mul(b.transpose()).mul(alpha))
}
(Transpose::Trans, Transpose::ConjTrans) => {
c.add_assign(a.transpose().mul(b.adjoint()).mul(alpha))
}
(Transpose::Trans, Transpose::ConjNoTrans) => {
c.add_assign(a.transpose().mul(b.conjugate()).mul(alpha))
}
(Transpose::ConjTrans, Transpose::NoTrans) => {
c.add_assign(a.adjoint().mul(b).mul(alpha))
}
(Transpose::ConjTrans, Transpose::Trans) => {
c.add_assign(a.adjoint().mul(b.transpose()).mul(alpha))
}
(Transpose::ConjTrans, Transpose::ConjTrans) => {
c.add_assign(a.adjoint().mul(b.adjoint()).mul(alpha))
}
(Transpose::ConjTrans, Transpose::ConjNoTrans) => {
c.add_assign(a.adjoint().mul(b.conjugate()).mul(alpha))
}
(Transpose::ConjNoTrans, Transpose::NoTrans) => {
c.add_assign(a.conjugate().mul(b).mul(alpha))
}
(Transpose::ConjNoTrans, Transpose::Trans) => {
c.add_assign(a.conjugate().mul(b.transpose()).mul(alpha))
}
(Transpose::ConjNoTrans, Transpose::ConjTrans) => {
c.add_assign(a.conjugate().mul(b.adjoint()).mul(alpha))
}
(Transpose::ConjNoTrans, Transpose::ConjNoTrans) => {
c.add_assign(a.conjugate().mul(b.conjugate()).mul(alpha))
}
};
}
fn matrix_mul_vec(
trans_a: Transpose,
alpha: Complex,
a: &MatrixXc,
b: &VectorXc,
beta: Complex,
c: &mut VectorXc,
) {
c.mul_assign(beta);
match trans_a {
Transpose::NoTrans => c.add_assign(a.mul(b).mul(alpha)),
Transpose::Trans => c.add_assign(a.transpose().mul(b).mul(alpha)),
Transpose::ConjTrans => c.add_assign(a.adjoint().mul(b).mul(alpha)),
Transpose::ConjNoTrans => c.add_assign(a.conjugate().mul(b).mul(alpha)),
};
}
fn vector_add(alpha: f64, a: &VectorX, b: &mut VectorX) {
b.add_assign(a.mul(alpha));
}
fn solve_ch(a: MatrixXc, b: &mut VectorXc) -> bool {
a.qr().solve_mut(b)
}
fn solve_g(a: MatrixX, b: &mut VectorX) -> bool {
a.qr().solve_mut(b)
}
fn dot(a: &VectorX, b: &VectorX) -> f64 {
a.dot(b)
}
fn dot_c(a: &VectorXc, b: &VectorXc) -> Complex {
a.dot(b)
}
fn max_coefficient(a: &VectorX) -> f64 {
a.camax()
}
fn max_coefficient_c(a: &VectorXc) -> f64 {
a.camax()
}
fn concat_row(a: MatrixXc, b: &MatrixXc) -> MatrixXc {
let arows = a.nrows();
let acols = a.ncols();
let mut new_mat = a.resize(arows + b.nrows(), acols, Default::default());
new_mat
.slice_mut((arows, 0), (b.nrows(), b.ncols()))
.copy_from(b);
new_mat
}
fn concat_col(a: MatrixXc, b: &MatrixXc) -> MatrixXc {
let arows = a.nrows();
let acols = a.ncols();
let mut new_mat = a.resize(arows, acols + b.ncols(), Default::default());
new_mat
.slice_mut((0, acols), (b.nrows(), b.ncols()))
.copy_from(b);
new_mat
}
}
