229 lines
11 KiB
Rust
229 lines
11 KiB
Rust
use super::{diff_op_col, diff_op_row, Matrix, RowVector, SbpOperator1d, SbpOperator2d};
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use crate::Float;
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use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
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#[derive(Debug, Copy, Clone)]
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pub struct SBP8;
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impl SBP8 {
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#[rustfmt::skip]
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const HBLOCK: &'static [Float] = &[
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2.94890676177879e-01, 1.52572062389771e+00, 2.57452876984127e-01, 1.79811370149912e+00, 4.12708057760141e-01, 1.27848462301587e+00, 9.23295579805997e-01, 1.00933386085916e+00
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];
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#[rustfmt::skip]
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const DIAG: &'static [Float] = &[
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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
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];
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#[rustfmt::skip]
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const DIAG_MATRIX: RowVector<Float, 9> = Matrix::new([[
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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
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]]);
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#[rustfmt::skip]
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const BLOCK: &'static [&'static [Float]] = &[
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&[-1.69554360443190e+00, 2.24741246341404e+00, -3.38931922601500e-02, -7.81028168126749e-01, 2.54881486107905e-02, 3.43865227388873e-01, -8.62858162633335e-02, -2.00150583315761e-02],
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&[-4.34378988266985e-01, 0.00000000000000e+00, 9.18511925072956e-02, 4.94008626807984e-01, -2.46151762937235e-02, -1.86759403432935e-01, 5.27267838475813e-02, 7.16696483080115e-03],
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&[3.88218088704253e-02, -5.44329744454984e-01, 0.00000000000000e+00, 3.89516189693211e-01, 1.36433486528546e-01, 1.03290582800845e-01, -1.79720579323281e-01, 5.59882558852296e-02],
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&[1.28088632226564e-01, -4.19172130036008e-01, -5.57707021445779e-02, 0.00000000000000e+00, 1.24714160903055e-01, 2.81285212519100e-01, -3.94470423942641e-02, -1.96981310738430e-02],
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&[-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],
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&[-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],
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&[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],
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&[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],
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];
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#[rustfmt::skip]
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const BLOCK_MATRIX: Matrix<Float, 8, 12> = Matrix::new([
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[-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],
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[-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],
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[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],
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[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],
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[-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],
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[-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],
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[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],
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[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],
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]);
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#[rustfmt::skip]
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const BLOCKEND_MATRIX: Matrix<Float, 8, 12> = Matrix::new([
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[0.0035384016230155199, -0.037742950645498902, 0.19815049088886899, -0.79260196355547696, -0.0, 0.75166824372712304, -0.11941174319355199, 0.012224423573111201, -0.035091936128702303, 0.0142810403117803, 0.010833666120933699, -0.0058476727216045096],
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[-0.0, 0.0038681313433548601, -0.041260067662451799, 0.21661535522787201, -0.821713248844682, -0.0, 0.75587358166357999, -0.046018121340651898, -0.076822925360096897, -0.050113507756358401, 0.087129564256063705, -0.027558761526617698],
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[-0.0, -0.0, 0.0027934857464329702, -0.029797181295285, 0.094272792663829805, -0.54587651996612696, -0.0, 0.205756876210586, 0.39561116774840099, 0.020799982439143602, -0.22287532317150199, 0.079314719624520302],
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[-0.0, -0.0, -0.0, 0.0086536439119011006, -0.029896495621603899, 0.102950081118829, -0.63739245543855805, -0.0, 0.54336288636530095, 0.085109057027750595, -0.090998664615454999, 0.01821194725190089],
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[-0.0, -0.0, -0.0, -0.0, 0.019698131073842998, 0.039447042394264102, -0.28128521251909999, -0.124714160903055, -0.0, 0.055770702144577897, 0.41917213003600801, -0.128088632226564],
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[-0.0, -0.0, -0.0, -0.0, -0.055988255885229599, 0.179720579323281, -0.10329058280084499, -0.13643348652854601, -0.389516189693211, -0.0, 0.54432974445498405, -0.038821808870425301],
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[-0.0, -0.0, -0.0, -0.0, -0.0071669648308011497, -0.052726783847581303, 0.18675940343293501, 0.024615176293723499, -0.49400862680798402, -0.091851192507295606, -0.0, 0.43437898826698501],
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[-0.0, -0.0, -0.0, -0.0, 0.020015058331576099, 0.086285816263333495, -0.34386522738887298, -0.0254881486107905, 0.78102816812674902, 0.033893192260150001, -2.2474124634140402, 1.6955436044319001],
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]);
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}
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impl SbpOperator1d for SBP8 {
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fn diff(&self, prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>) {
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super::diff_op_1d_matrix(
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&Self::BLOCK_MATRIX,
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&Self::BLOCKEND_MATRIX,
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&Self::DIAG_MATRIX,
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super::OperatorType::Normal,
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prev,
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fut,
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)
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}
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fn h(&self) -> &'static [Float] {
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Self::HBLOCK
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}
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#[cfg(feature = "sparse")]
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fn diff_matrix(&self, n: usize) -> sprs::CsMat<Float> {
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super::sparse_from_block(
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Self::BLOCK,
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Self::DIAG,
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super::Symmetry::AntiSymmetric,
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super::OperatorType::Normal,
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n,
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)
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}
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#[cfg(feature = "sparse")]
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fn h_matrix(&self, n: usize) -> sprs::CsMat<Float> {
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super::h_matrix(Self::HBLOCK, n, self.is_h2())
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}
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}
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fn diff_op_row_local(prev: ndarray::ArrayView2<Float>, mut fut: ndarray::ArrayViewMut2<Float>) {
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/*
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let mut flipmatrix = SBP8::BLOCK_MATRIX;
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flipmatrix *= &-1.0;
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*/
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for (p, mut f) in prev
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.axis_iter(ndarray::Axis(0))
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.zip(fut.axis_iter_mut(ndarray::Axis(0)))
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{
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super::diff_op_1d_slice_matrix(
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&SBP8::BLOCK_MATRIX,
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&SBP8::BLOCKEND_MATRIX,
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//&flipmatrix,
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&SBP8::DIAG_MATRIX,
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super::OperatorType::Normal,
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p.as_slice().unwrap(),
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f.as_slice_mut().unwrap(),
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)
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}
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}
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fn diff_op_col_local(prev: ndarray::ArrayView2<Float>, fut: ndarray::ArrayViewMut2<Float>) {
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let optype = super::OperatorType::Normal;
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super::diff_op_col_matrix(
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&SBP8::BLOCK_MATRIX,
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&SBP8::BLOCKEND_MATRIX,
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&SBP8::DIAG_MATRIX,
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optype,
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prev,
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fut,
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)
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}
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impl SbpOperator2d for SBP8 {
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fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
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assert_eq!(prev.shape(), fut.shape());
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assert!(prev.shape()[1] >= 2 * SBP8::BLOCK.len());
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let symmetry = super::Symmetry::AntiSymmetric;
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let optype = super::OperatorType::Normal;
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match (prev.strides(), fut.strides()) {
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([_, 1], [_, 1]) => {
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//diff_op_row(SBP8::BLOCK, SBP8::DIAG, symmetry, optype)(prev, fut);
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diff_op_row_local(prev, fut);
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}
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([1, _], [1, _]) => {
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//diff_op_col(SBP8::BLOCK, SBP8::DIAG, symmetry, optype)(prev, fut);
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diff_op_col_local(prev, fut)
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}
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([_, _], [_, _]) => {
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// Fallback, work row by row
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for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
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SBP8.diff(r0, r1);
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}
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}
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_ => unreachable!("Should only be two elements in the strides vectors"),
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}
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}
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fn op_xi(&self) -> &dyn SbpOperator1d {
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&Self
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}
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fn op_eta(&self) -> &dyn SbpOperator1d {
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&Self
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}
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}
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#[test]
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fn test_trad8() {
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use super::testing::*;
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let nx = 32;
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let ny = 16;
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// Order one polynomial
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x + 2.0 * y,
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|_x, _y| 1.0,
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|_x, _y| 2.0,
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1e-4,
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);
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// Order two polynomial
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x * x + 0.5 * y * y,
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|x, _y| 2.0 * x,
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|_x, y| y,
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1e-4,
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);
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check_operator_on(SBP8, (ny, nx), |x, y| x * y, |_x, y| y, |x, _y| x, 1e-4);
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// Order three polynomials
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x * x * x + y * y * y / 6.0,
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|x, _y| 3.0 * x * x,
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|_x, y| y * y / 2.0,
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1e-4,
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);
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x * x * y + x * y * y / 2.0,
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|x, y| 2.0 * x * y + y * y / 2.0,
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|x, y| x * x + x * y,
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1e-4,
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);
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x.powi(3) + 2.0 * x.powi(2) * y + 3.0 * x * y.powi(2) + 4.0 * y.powi(3),
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|x, y| 3.0 * x.powi(2) + 4.0 * x * y + 3.0 * y.powi(2),
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|x, y| 2.0 * x.powi(2) + 6.0 * x * y + 12.0 * y.powi(2),
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1e-4,
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);
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// Order four polynomials
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check_operator_on(
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SBP8,
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(ny, nx),
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|x, y| x.powi(4) + x.powi(3) * y + x.powi(2) * y.powi(2) + x * y.powi(3) + y.powi(4),
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|x, y| 4.0 * x.powi(3) + 3.0 * x.powi(2) * y + 2.0 * x * y.powi(2) + y.powi(3),
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|x, y| x.powi(3) + 2.0 * x.powi(2) * y + 3.0 * x * y.powi(2) + 4.0 * y.powi(3),
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1e-4,
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);
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}
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#[test]
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fn block_equality() {
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let mut flipped_inverted = SBP8::BLOCK_MATRIX.flip();
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flipped_inverted *= -1.0;
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assert!(flipped_inverted
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.iter()
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.zip(SBP8::BLOCKEND_MATRIX.iter())
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.all(|(x, y)| (x - y).abs() < 1e-12))
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}
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