SummationByParts/sbp/src/operators/traditional8.rs

use super::{diff_op_col, diff_op_row, Matrix, RowVector, SbpOperator1d, SbpOperator2d};
use crate::Float;
use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};

#[derive(Debug, Copy, Clone)]
pub struct SBP8;

impl SBP8 {
    #[rustfmt::skip]
    const HBLOCK: &'static [Float] = &[
        2.94890676177879e-01, 1.52572062389771e+00, 2.57452876984127e-01, 1.79811370149912e+00, 4.12708057760141e-01, 1.27848462301587e+00, 9.23295579805997e-01, 1.00933386085916e+00
    ];
    #[rustfmt::skip]
    const DIAG: &'static [Float] = &[
        3.57142857142857e-03, -3.80952380952381e-02, 2.00000000000000e-01, -8.00000000000000e-01, -0.00000000000000e+00, 8.00000000000000e-01, -2.00000000000000e-01, 3.80952380952381e-02, -3.57142857142857e-03
    ];
    #[rustfmt::skip]
    const DIAG_MATRIX: RowVector<Float, 9> = Matrix::new([[
        3.57142857142857e-03, -3.80952380952381e-02, 2.00000000000000e-01, -8.00000000000000e-01, -0.00000000000000e+00, 8.00000000000000e-01, -2.00000000000000e-01, 3.80952380952381e-02, -3.57142857142857e-03
    ]]);
    #[rustfmt::skip]
    const BLOCK: &'static [&'static [Float]] = &[
        &[-1.69554360443190e+00, 2.24741246341404e+00, -3.38931922601500e-02, -7.81028168126749e-01, 2.54881486107905e-02, 3.43865227388873e-01, -8.62858162633335e-02, -2.00150583315761e-02],
        &[-4.34378988266985e-01, 0.00000000000000e+00, 9.18511925072956e-02, 4.94008626807984e-01, -2.46151762937235e-02, -1.86759403432935e-01, 5.27267838475813e-02, 7.16696483080115e-03],
        &[3.88218088704253e-02, -5.44329744454984e-01, 0.00000000000000e+00, 3.89516189693211e-01, 1.36433486528546e-01, 1.03290582800845e-01, -1.79720579323281e-01, 5.59882558852296e-02],
        &[1.28088632226564e-01, -4.19172130036008e-01, -5.57707021445779e-02, 0.00000000000000e+00, 1.24714160903055e-01, 2.81285212519100e-01, -3.94470423942641e-02, -1.96981310738430e-02],
        &[-1.82119472519009e-02, 9.09986646154550e-02, -8.51090570277506e-02, -5.43362886365301e-01, 0.00000000000000e+00, 6.37392455438558e-01, -1.02950081118829e-01, 2.98964956216039e-02, -8.65364391190110e-03],
        &[-7.93147196245203e-02, 2.22875323171502e-01, -2.07999824391436e-02, -3.95611167748401e-01, -2.05756876210586e-01, 0.00000000000000e+00, 5.45876519966127e-01, -9.42727926638298e-02, 2.97971812952850e-02, -2.79348574643297e-03],
        &[2.75587615266177e-02, -8.71295642560637e-02, 5.01135077563584e-02, 7.68229253600969e-02, 4.60181213406519e-02, -7.55873581663580e-01, 0.00000000000000e+00, 8.21713248844682e-01, -2.16615355227872e-01, 4.12600676624518e-02, -3.86813134335486e-03],
        &[5.84767272160451e-03, -1.08336661209337e-02, -1.42810403117803e-02, 3.50919361287023e-02, -1.22244235731112e-02, 1.19411743193552e-01, -7.51668243727123e-01, 0.00000000000000e+00, 7.92601963555477e-01, -1.98150490888869e-01, 3.77429506454989e-02, -3.53840162301552e-03],
    ];
    #[rustfmt::skip]
    const BLOCK_MATRIX: Matrix<Float, 8, 12> = Matrix::new([
        [-1.69554360443190e+00, 2.24741246341404e+00, -3.38931922601500e-02, -7.81028168126749e-01, 2.54881486107905e-02, 3.43865227388873e-01, -8.62858162633335e-02, -2.00150583315761e-02, 0.0, 0.0, 0.0, 0.0],
        [-4.34378988266985e-01, 0.00000000000000e+00, 9.18511925072956e-02, 4.94008626807984e-01, -2.46151762937235e-02, -1.86759403432935e-01, 5.27267838475813e-02, 7.16696483080115e-03, 0.0, 0.0, 0.0, 0.0],
        [3.88218088704253e-02, -5.44329744454984e-01, 0.00000000000000e+00, 3.89516189693211e-01, 1.36433486528546e-01, 1.03290582800845e-01, -1.79720579323281e-01, 5.59882558852296e-02, 0.0, 0.0, 0.0, 0.0],
        [1.28088632226564e-01, -4.19172130036008e-01, -5.57707021445779e-02, 0.00000000000000e+00, 1.24714160903055e-01, 2.81285212519100e-01, -3.94470423942641e-02, -1.96981310738430e-02, 0.0, 0.0, 0.0, 0.0],
        [-1.82119472519009e-02, 9.09986646154550e-02, -8.51090570277506e-02, -5.43362886365301e-01, 0.00000000000000e+00, 6.37392455438558e-01, -1.02950081118829e-01, 2.98964956216039e-02, -8.65364391190110e-03, 0.0, 0.0, 0.0],
        [-7.93147196245203e-02, 2.22875323171502e-01, -2.07999824391436e-02, -3.95611167748401e-01, -2.05756876210586e-01, 0.00000000000000e+00, 5.45876519966127e-01, -9.42727926638298e-02, 2.97971812952850e-02, -2.79348574643297e-03, 0.0, 0.0],
        [2.75587615266177e-02, -8.71295642560637e-02, 5.01135077563584e-02, 7.68229253600969e-02, 4.60181213406519e-02, -7.55873581663580e-01, 0.00000000000000e+00, 8.21713248844682e-01, -2.16615355227872e-01, 4.12600676624518e-02, -3.86813134335486e-03, 0.0],
        [5.84767272160451e-03, -1.08336661209337e-02, -1.42810403117803e-02, 3.50919361287023e-02, -1.22244235731112e-02, 1.19411743193552e-01, -7.51668243727123e-01, 0.00000000000000e+00, 7.92601963555477e-01, -1.98150490888869e-01, 3.77429506454989e-02, -3.53840162301552e-03],
    ]);
    #[rustfmt::skip]
    const BLOCKEND_MATRIX: Matrix<Float, 8, 12> = Matrix::new([
        [0.0035384016230155199,   -0.037742950645498902,   0.19815049088886899,   -0.79260196355547696,   -0.0,   0.75166824372712304,   -0.11941174319355199,   0.012224423573111201,   -0.035091936128702303,   0.0142810403117803,   0.010833666120933699,   -0.0058476727216045096],
        [-0.0,   0.0038681313433548601,   -0.041260067662451799,   0.21661535522787201,   -0.821713248844682,   -0.0,   0.75587358166357999,   -0.046018121340651898,   -0.076822925360096897,   -0.050113507756358401,   0.087129564256063705,   -0.027558761526617698],
        [-0.0,   -0.0,   0.0027934857464329702,   -0.029797181295285,   0.094272792663829805,   -0.54587651996612696,   -0.0,   0.205756876210586,   0.39561116774840099,   0.020799982439143602,   -0.22287532317150199,   0.079314719624520302],
        [-0.0,   -0.0,   -0.0,   0.0086536439119011006,   -0.029896495621603899,   0.102950081118829,   -0.63739245543855805,   -0.0,   0.54336288636530095,   0.085109057027750595,   -0.090998664615454999,   0.01821194725190089],
        [-0.0,   -0.0,   -0.0,   -0.0,   0.019698131073842998,   0.039447042394264102,   -0.28128521251909999,   -0.124714160903055,   -0.0,   0.055770702144577897,   0.41917213003600801,   -0.128088632226564],
        [-0.0,   -0.0,   -0.0,   -0.0,   -0.055988255885229599,   0.179720579323281,   -0.10329058280084499,   -0.13643348652854601,   -0.389516189693211,   -0.0,   0.54432974445498405,   -0.038821808870425301],
        [-0.0,   -0.0,   -0.0,   -0.0,   -0.0071669648308011497,   -0.052726783847581303,   0.18675940343293501,   0.024615176293723499,   -0.49400862680798402,   -0.091851192507295606,   -0.0,   0.43437898826698501],
        [-0.0,   -0.0,   -0.0,   -0.0,   0.020015058331576099,   0.086285816263333495,   -0.34386522738887298,   -0.0254881486107905,   0.78102816812674902,   0.033893192260150001,   -2.2474124634140402,   1.6955436044319001],
    ]);
}

impl SbpOperator1d for SBP8 {
    fn diff(&self, prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>) {
        super::diff_op_1d(
            Self::BLOCK,
            Self::DIAG,
            super::Symmetry::AntiSymmetric,
            super::OperatorType::Normal,
            prev,
            fut,
        )
    }

    fn h(&self) -> &'static [Float] {
        Self::HBLOCK
    }

    #[cfg(feature = "sparse")]
    fn diff_matrix(&self, n: usize) -> sprs::CsMat<Float> {
        super::sparse_from_block(
            Self::BLOCK,
            Self::DIAG,
            super::Symmetry::AntiSymmetric,
            super::OperatorType::Normal,
            n,
        )
    }
    #[cfg(feature = "sparse")]
    fn h_matrix(&self, n: usize) -> sprs::CsMat<Float> {
        super::h_matrix(Self::HBLOCK, n, self.is_h2())
    }
}

fn diff_op_row_local(prev: ndarray::ArrayView2<Float>, mut fut: ndarray::ArrayViewMut2<Float>) {
    /*
    let mut flipmatrix = SBP8::BLOCK_MATRIX;
    flipmatrix *= &-1.0;
    */

    for (p, mut f) in prev
        .axis_iter(ndarray::Axis(0))
        .zip(fut.axis_iter_mut(ndarray::Axis(0)))
    {
        super::diff_op_1d_slice_matrix(
            &SBP8::BLOCK_MATRIX,
            &SBP8::BLOCKEND_MATRIX,
            //&flipmatrix,
            &SBP8::DIAG_MATRIX,
            super::OperatorType::Normal,
            p.as_slice().unwrap(),
            f.as_slice_mut().unwrap(),
        )
    }
}

impl SbpOperator2d for SBP8 {
    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
        assert_eq!(prev.shape(), fut.shape());
        assert!(prev.shape()[1] >= 2 * SBP8::BLOCK.len());

        let symmetry = super::Symmetry::AntiSymmetric;
        let optype = super::OperatorType::Normal;

        match (prev.strides(), fut.strides()) {
            ([_, 1], [_, 1]) => {
                //diff_op_row(SBP8::BLOCK, SBP8::DIAG, symmetry, optype)(prev, fut);
                diff_op_row_local(prev, fut);
            }
            ([1, _], [1, _]) => {
                diff_op_col(SBP8::BLOCK, SBP8::DIAG, symmetry, optype)(prev, fut);
            }
            ([_, _], [_, _]) => {
                // Fallback, work row by row
                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
                    SBP8.diff(r0, r1);
                }
            }
            _ => unreachable!("Should only be two elements in the strides vectors"),
        }
    }
    fn op_xi(&self) -> &dyn SbpOperator1d {
        &Self
    }
    fn op_eta(&self) -> &dyn SbpOperator1d {
        &Self
    }
}

#[test]
fn test_trad8() {
    use super::testing::*;
    let nx = 32;
    let ny = 16;

    // Order one polynomial
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x + 2.0 * y,
        |_x, _y| 1.0,
        |_x, _y| 2.0,
        1e-4,
    );

    // Order two polynomial
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x * x + 0.5 * y * y,
        |x, _y| 2.0 * x,
        |_x, y| y,
        1e-4,
    );
    check_operator_on(SBP8, (ny, nx), |x, y| x * y, |_x, y| y, |x, _y| x, 1e-4);

    // Order three polynomials
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x * x * x + y * y * y / 6.0,
        |x, _y| 3.0 * x * x,
        |_x, y| y * y / 2.0,
        1e-4,
    );
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x * x * y + x * y * y / 2.0,
        |x, y| 2.0 * x * y + y * y / 2.0,
        |x, y| x * x + x * y,
        1e-4,
    );
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x.powi(3) + 2.0 * x.powi(2) * y + 3.0 * x * y.powi(2) + 4.0 * y.powi(3),
        |x, y| 3.0 * x.powi(2) + 4.0 * x * y + 3.0 * y.powi(2),
        |x, y| 2.0 * x.powi(2) + 6.0 * x * y + 12.0 * y.powi(2),
        1e-4,
    );

    // Order four polynomials
    check_operator_on(
        SBP8,
        (ny, nx),
        |x, y| x.powi(4) + x.powi(3) * y + x.powi(2) * y.powi(2) + x * y.powi(3) + y.powi(4),
        |x, y| 4.0 * x.powi(3) + 3.0 * x.powi(2) * y + 2.0 * x * y.powi(2) + y.powi(3),
        |x, y| x.powi(3) + 2.0 * x.powi(2) * y + 3.0 * x * y.powi(2) + 4.0 * y.powi(3),
        1e-4,
    );
}

#[test]
fn block_equality() {
    let mut flipped_inverted = SBP8::BLOCK_MATRIX.flip();
    flipped_inverted *= &-1.0;

    assert!(flipped_inverted
        .iter()
        .zip(SBP8::BLOCKEND_MATRIX.iter())
        .all(|(x, y)| (x - y).abs() < 1e-12))
}