bempp 0.2.0

Boundary element method library.
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//! FMM tools
use crate::assembly::common::SparseMatrixData;
use crate::function::SerialFunctionSpace;
use crate::quadrature::simplex_rules::simplex_rule;
use crate::traits::FunctionSpace;
use ndelement::traits::FiniteElement;
use ndelement::types::ReferenceCellType;
use ndgrid::traits::{GeometryMap, Grid};
use rlst::CsrMatrix;
use rlst::{
    rlst_dynamic_array2, rlst_dynamic_array4, Array, BaseArray, MatrixInverse, RandomAccessByRef,
    RandomAccessMut, RawAccess, RlstScalar, Shape, VectorContainer,
};

/// Generate an array of all the quadrature points
pub fn get_all_quadrature_points<
    T: RlstScalar<Real = T> + MatrixInverse,
    G: Grid<T = T, EntityDescriptor = ReferenceCellType> + Sync,
>(
    npts: usize,
    grid: &G,
) -> Array<T, BaseArray<T, VectorContainer<T>, 2>, 2> {
    // TODO: remove hardcoding of triangle in this function
    let qrule = simplex_rule(ReferenceCellType::Triangle, npts).unwrap();
    let mut qpoints = rlst_dynamic_array2!(T, [npts, 2]);
    for i in 0..npts {
        for j in 0..2 {
            *qpoints.get_mut([i, j]).unwrap() =
                num::cast::<f64, T>(qrule.points[2 * i + j]).unwrap();
        }
    }

    let evaluator = grid.geometry_map(ReferenceCellType::Triangle, qpoints.data());

    let mut all_points = rlst_dynamic_array2!(
        T,
        [
            npts * grid.entity_count(ReferenceCellType::Triangle),
            grid.geometry_dim()
        ]
    );
    let mut points = vec![num::cast::<f64, T>(0.0).unwrap(); npts * grid.geometry_dim()];

    for cell in 0..grid.entity_count(ReferenceCellType::Triangle) {
        evaluator.points(cell, &mut points);
        for j in 0..grid.geometry_dim() {
            for i in 0..npts {
                *all_points.get_mut([cell * npts + i, j]).unwrap() = points[j * npts + i];
            }
        }
    }
    all_points
}

/// Generate a dense matrix mapping between basis functions and quadrature points
pub fn basis_to_quadrature_into_dense<
    const BLOCKSIZE: usize,
    T: RlstScalar + MatrixInverse,
    G: Grid<T = T::Real, EntityDescriptor = ReferenceCellType> + Sync,
>(
    output: &mut Array<T, BaseArray<T, VectorContainer<T>, 2>, 2>,
    npts: usize,
    space: &SerialFunctionSpace<'_, T, G>,
) {
    let sparse_matrix = basis_to_quadrature::<BLOCKSIZE, T, G>(output.shape(), npts, space);
    let data = sparse_matrix.data;
    let rows = sparse_matrix.rows;
    let cols = sparse_matrix.cols;
    for ((i, j), value) in rows.iter().zip(cols.iter()).zip(data.iter()) {
        *output.get_mut([*i, *j]).unwrap() += *value;
    }
}

/// Generate a CSR matrix mapping between basis functions and quadrature points
pub fn basis_to_quadrature_into_csr<
    const BLOCKSIZE: usize,
    T: RlstScalar + MatrixInverse,
    G: Grid<T = T::Real, EntityDescriptor = ReferenceCellType> + Sync,
>(
    npts: usize,
    space: &SerialFunctionSpace<'_, T, G>,
) -> CsrMatrix<T> {
    let grid = space.grid();
    let ncells = grid
        .entity_types(2)
        .iter()
        .map(|&i| grid.entity_count(i))
        .sum::<usize>();
    let shape = [ncells * npts, space.global_size()];
    let sparse_matrix = basis_to_quadrature::<BLOCKSIZE, T, G>(shape, npts, space);

    CsrMatrix::<T>::from_aij(
        sparse_matrix.shape,
        &sparse_matrix.rows,
        &sparse_matrix.cols,
        &sparse_matrix.data,
    )
    .unwrap()
}

/// Generate a dense transpose matrix mapping between basis functions and quadrature points
pub fn transpose_basis_to_quadrature_into_dense<
    const BLOCKSIZE: usize,
    T: RlstScalar + MatrixInverse,
    G: Grid<T = T::Real, EntityDescriptor = ReferenceCellType> + Sync,
>(
    output: &mut Array<T, BaseArray<T, VectorContainer<T>, 2>, 2>,
    npts: usize,
    space: &SerialFunctionSpace<'_, T, G>,
) {
    let shape = [output.shape()[1], output.shape()[0]];
    let sparse_matrix = basis_to_quadrature::<BLOCKSIZE, T, G>(shape, npts, space);
    let data = sparse_matrix.data;
    let rows = sparse_matrix.rows;
    let cols = sparse_matrix.cols;
    for ((i, j), value) in rows.iter().zip(cols.iter()).zip(data.iter()) {
        *output.get_mut([*j, *i]).unwrap() += *value;
    }
}

/// Generate a CSR transpose matrix mapping between basis functions and quadrature points
pub fn transpose_basis_to_quadrature_into_csr<
    const BLOCKSIZE: usize,
    T: RlstScalar + MatrixInverse,
    G: Grid<T = T::Real, EntityDescriptor = ReferenceCellType> + Sync,
>(
    npts: usize,
    space: &SerialFunctionSpace<'_, T, G>,
) -> CsrMatrix<T> {
    let grid = space.grid();
    let ncells = grid
        .entity_types(2)
        .iter()
        .map(|&i| grid.entity_count(i))
        .sum::<usize>();
    let shape = [ncells * npts, space.global_size()];
    let sparse_matrix = basis_to_quadrature::<BLOCKSIZE, T, G>(shape, npts, space);

    CsrMatrix::<T>::from_aij(
        [space.global_size(), ncells * npts],
        &sparse_matrix.cols,
        &sparse_matrix.rows,
        &sparse_matrix.data,
    )
    .unwrap()
}

fn basis_to_quadrature<
    const BLOCKSIZE: usize,
    T: RlstScalar + MatrixInverse,
    G: Grid<T = T::Real, EntityDescriptor = ReferenceCellType> + Sync,
>(
    shape: [usize; 2],
    npts: usize,
    space: &SerialFunctionSpace<'_, T, G>,
) -> SparseMatrixData<T> {
    if !space.is_serial() {
        panic!("Dense assembly can only be used for function spaces stored in serial");
    }
    let grid = space.grid();
    let ncells = grid
        .entity_types(2)
        .iter()
        .map(|&i| grid.entity_count(i))
        .sum::<usize>();
    if shape[0] != ncells * npts || shape[1] != space.global_size() {
        panic!("Matrix has wrong shape");
    }

    // TODO: pass cell types into this function
    let qrule = simplex_rule(ReferenceCellType::Triangle, npts).unwrap();
    let mut qpoints = rlst_dynamic_array2!(T::Real, [npts, 2]);
    for i in 0..npts {
        for j in 0..2 {
            *qpoints.get_mut([i, j]).unwrap() =
                num::cast::<f64, T::Real>(qrule.points[2 * i + j]).unwrap();
        }
    }
    let qweights = qrule
        .weights
        .iter()
        .map(|w| num::cast::<f64, T>(*w).unwrap())
        .collect::<Vec<_>>();

    let mut table = rlst_dynamic_array4!(
        T,
        space
            .element(ReferenceCellType::Triangle)
            .tabulate_array_shape(0, npts)
    );
    space
        .element(ReferenceCellType::Triangle)
        .tabulate(&qpoints, 0, &mut table);

    let mut output = SparseMatrixData::<T>::new_known_size(
        shape,
        ncells * space.element(ReferenceCellType::Triangle).dim() * npts,
    );
    debug_assert!(qpoints.shape()[0] == npts);

    let evaluator = grid.geometry_map(ReferenceCellType::Triangle, qpoints.data());
    let npts = qweights.len();

    let mut jacobians = vec![
        num::cast::<f64, T::Real>(0.0).unwrap();
        grid.geometry_dim() * grid.topology_dim() * npts
    ];
    let mut jdets = vec![num::cast::<f64, T::Real>(0.0).unwrap(); npts];
    let mut normals = vec![num::cast::<f64, T::Real>(0.0).unwrap(); grid.geometry_dim() * npts];

    // TODO: batch this?
    for cell in 0..ncells {
        let cell_dofs = space.cell_dofs(cell).unwrap();
        evaluator.jacobians_dets_normals(cell, &mut jacobians, &mut jdets, &mut normals);
        for (qindex, w) in qweights.iter().enumerate() {
            for (i, dof) in cell_dofs.iter().enumerate() {
                output.rows.push(cell * npts + qindex);
                output.cols.push(*dof);
                output.data.push(
                    num::cast::<T::Real, T>(jdets[qindex]).unwrap()
                        * *w
                        * *table.get([0, qindex, i, 0]).unwrap(),
                );
            }
        }
    }
    output
}