test_Direct.cpp File Reference

Unit tests for block-sparse LU factorization in Solver/Direct.hpp. More...

#include "doctest.h"
#include "DNDS/Defines.hpp"
#include "DNDS/MPI.hpp"
#include "Solver/Direct.hpp"
#include <Eigen/Dense>
#include <iostream>
#include <iomanip>
#include <vector>
#include <memory>
#include <cmath>

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Classes
struct	TestBlockLU
struct	TestBlockLDLT

Macros
#define	DOCTEST_CONFIG_IMPLEMENT

Typedefs
using	Block = Eigen::Matrix< real, BS, BS >
using	BVec = Eigen::Vector< real, BS >
using	tVec = std::vector< BVec >
using	tBase = Direct::LocalLUBase< TestBlockLU, Block, tVec >
using	tLDLTBase = Direct::LocalLDLTBase< TestBlockLDLT, Block, tVec >

Functions
	TEST_CASE ("Direct 2D periodic: symbolic factorization has fill-in")
	TEST_CASE ("Direct 2D periodic: MatMul is correct")
	TEST_CASE ("Direct 2D periodic: complete LU solve is exact")
symLU0	ObtainSymmetricSymbolicFactorization (adj, {0, NCells}, 0)
	fill2DLaplacian (luOrig)
tVec	x_known (NCells)
tVec	b (NCells)
tVec	x_ilu (NCells)
tVec	Ax_ilu (NCells)
	for (int i=0;i< NCells;i++)
luOrig	MatMul (x_known, b)
	fill2DLaplacian (luILU)
luILU	InPlaceDecompose ()
luILU	Solve (b, x_ilu)
	fill2DLaplacian (luMul)
luMul	MatMul (x_ilu, Ax_ilu)
	fill2DLaplacian (luA)
symM	ObtainSymmetricSymbolicFactorization (adj, {0, NCells}, iluCode)
	fill2DLaplacian (luM)
tVec	x (NCells)
tVec	r (NCells)
tVec	z (NCells)
tVec	Ax (NCells)
	TEST_CASE ("Direct 2D periodic: ILU(1) converges faster than ILU(0) as preconditioner")
	TEST_CASE ("Direct 2D periodic LDLT: MatMul matches LU MatMul for symmetric system")
	TEST_CASE ("Direct 2D periodic LDLT: complete decompose + solve is exact")
int	main (int argc, char **argv)

Variables
auto	adj = build2DPeriodicAdj()
auto	symLUorig = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)
TestBlockLU	luOrig (symLUorig, NCells)
TestBlockLU	luILU (symLU0, NCells)
auto	symLUmul = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)
TestBlockLU	luMul (symLUmul, NCells)
real	residualNorm = 0
real	bNorm = 0
real	relResidual = residualNorm / bNorm
TestBlockLU	luA (symA, NCells)
auto	symM = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)
TestBlockLU	luM (symM, NCells)
real	err = 0

Detailed Description

Unit tests for block-sparse LU factorization in Solver/Direct.hpp.

Tests a 2D periodic Laplacian with 2x2 blocks on an NxN grid: A = 5-point stencil with periodic boundary (4 neighbors per cell). Each cell (i,j) connects to (i±1,j) and (i,j±1) with wrap-around. Diag = 4*I + delta*diag(i,2i), off-diag = -I (non-symmetric diag to exercise the full LU, not just LDLT).

Verifies:

• SerialSymLUStructure: symbolic factorization with fill-in
• LocalLUBase: MatMul (A*x == b), InPlaceDecompose, Solve (A^{-1}b == x)
• ILU(0): approximate solve, residual reduction
• Complete LU (iluCode=-1): exact solve
• ILU(1): intermediate fill, better than ILU(0)

Definition in file test_Direct.cpp.

Macro Definition Documentation

DOCTEST_CONFIG_IMPLEMENT

#define DOCTEST_CONFIG_IMPLEMENT

Definition at line 19 of file test_Direct.cpp.

Typedef Documentation

Block

using Block = Eigen::Matrix<real, BS, BS>

Definition at line 35 of file test_Direct.cpp.

BVec

using BVec = Eigen::Vector<real, BS>

Definition at line 36 of file test_Direct.cpp.

tBase

using tBase = Direct::LocalLUBase<TestBlockLU, Block, tVec>

Definition at line 43 of file test_Direct.cpp.

tLDLTBase

using tLDLTBase = Direct::LocalLDLTBase<TestBlockLDLT, Block, tVec>

Definition at line 360 of file test_Direct.cpp.

tVec

using tVec = std::vector<BVec>

Definition at line 42 of file test_Direct.cpp.

Function Documentation

Ax()

tVec Ax

(

NCells

)

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Ax_ilu()

tVec Ax_ilu

(

NCells

)

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b()

tVec b

(

NCells

)

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fill2DLaplacian() [1/5]

fill2DLaplacian

(

luA

)

fill2DLaplacian() [2/5]

fill2DLaplacian

(

luILU

)

fill2DLaplacian() [3/5]

fill2DLaplacian

(

luM

)

fill2DLaplacian() [4/5]

fill2DLaplacian

(

luMul

)

fill2DLaplacian() [5/5]

fill2DLaplacian

(

luOrig

)

for()

for

(

)

Definition at line 239 of file test_Direct.cpp.

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InPlaceDecompose()

luM InPlaceDecompose

(

)

main()

int main	(	int	argc,
		char **	argv
	)

Definition at line 514 of file test_Direct.cpp.

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MatMul() [1/2]

luMul MatMul	(	x_ilu	,
		Ax_ilu
	)

MatMul() [2/2]

luOrig MatMul	(	x_known	,
		b
	)

ObtainSymmetricSymbolicFactorization() [1/2]

symA ObtainSymmetricSymbolicFactorization	(	adj	,
		{0, NCells}	,
		0
	)

ObtainSymmetricSymbolicFactorization() [2/2]

symM ObtainSymmetricSymbolicFactorization	(	adj	,
		{0, NCells}	,
		iluCode
	)

r()

tVec r

(

NCells

)

Solve()

luILU Solve	(	b	,
		x_ilu
	)

TEST_CASE() [1/6]

TEST_CASE

(

"Direct 2D periodic LDLT: complete decompose + solve is exact"

)

Definition at line 474 of file test_Direct.cpp.

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TEST_CASE() [2/6]

TEST_CASE

(

"Direct 2D periodic LDLT: MatMul matches LU MatMul for symmetric system"

)

Definition at line 438 of file test_Direct.cpp.

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TEST_CASE() [3/6]

TEST_CASE

(

"Direct 2D periodic: complete LU solve is exact"

)

Definition at line 191 of file test_Direct.cpp.

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TEST_CASE() [4/6]

TEST_CASE

(

"Direct 2D periodic: ILU(1) converges faster than ILU(0) as preconditioner"

)

Definition at line 321 of file test_Direct.cpp.

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TEST_CASE() [5/6]

TEST_CASE

(

"Direct 2D periodic: MatMul is correct"

)

Definition at line 153 of file test_Direct.cpp.

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TEST_CASE() [6/6]

TEST_CASE

(

"Direct 2D periodic: symbolic factorization has fill-in"

)

Definition at line 137 of file test_Direct.cpp.

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x()

tVec x

(

NCells

)

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x_ilu()

tVec x_ilu

(

NCells

)

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x_known()

tVec x_known

(

NCells

)

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z()

tVec z

(

NCells

)

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Variable Documentation

adj

auto adj = build2DPeriodicAdj()

Definition at line 229 of file test_Direct.cpp.

bNorm

bNorm = 0

Definition at line 265 of file test_Direct.cpp.

err

real err = 0

Definition at line 315 of file test_Direct.cpp.

luA

TestBlockLU luA(symA, NCells)	(	symA	,
		NCells
	)

luILU

TestBlockLU luILU(symLU0, NCells)	(	symLU0	,
		NCells
	)

luM

TestBlockLU luM(symM, NCells)	(	symM	,
		NCells
	)

luMul

TestBlockLU luMul(symLUmul, NCells)	(	symLUmul	,
		NCells
	)

luOrig

TestBlockLU luOrig(symLUorig, NCells)	(	symLUorig	,
		NCells
	)

relResidual

real relResidual = residualNorm / bNorm

Definition at line 274 of file test_Direct.cpp.

residualNorm

residualNorm = 0

Definition at line 265 of file test_Direct.cpp.

symLUmul

auto symLUmul = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)

Definition at line 259 of file test_Direct.cpp.

symLUorig

auto symLUorig = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)

Definition at line 233 of file test_Direct.cpp.

symM

auto symM = std::make_shared<Direct::SerialSymLUStructure>(g_mpi, NCells)

Definition at line 295 of file test_Direct.cpp.