Flux/test/test_lu.cpp

#include "test_common.h"

#include "./utils/utils.h"           // brings in vector.h, matrix.h, etc.
#include "./numerics/matmul.h"       // numerics::matmul

#include "./decomp/lu.h"

//#include <chrono>


TEST_CASE(LU_Solve_Vector_Basic) {
    using T = double;

    // A * x = b  with exact solution x = [1, 1, 2]^T
    utils::Matrix<T> A(3,3, T{0});
    A(0,0)=2;  A(0,1)=1;  A(0,2)=1;
    A(1,0)=4;  A(1,1)=-6; A(1,2)=0;
    A(2,0)=-2; A(2,1)=7;  A(2,2)=2;

    utils::Vector<T> b(3, T{0});
    b[0]=5; b[1]=-2; b[2]=9;

    decomp::LUdcmpd lu(A);
    auto x = lu.solve(b);

    utils::Vector<T> x_true(3, T{0});
    x_true[0]=1; x_true[1]=1; x_true[2]=2;

    CHECK( (x.nearly_equal(x_true,1e-12)), "LU solve (vector RHS) failed" );
}

TEST_CASE(LU_Solve_MatrixRHS_TwoColumns) {
    using T = double;

    // Same A, solve two RHS at once
    utils::Matrix<T> A(3,3, T{0});
    A(0,0)=2;  A(0,1)=1;  A(0,2)=1;
    A(1,0)=4;  A(1,1)=-6; A(1,2)=0;
    A(2,0)=-2; A(2,1)=7;  A(2,2)=2;

    utils::Matrix<T> B(3,2, T{0});
    // First column b1 (same as previous test)
    B(0,0)=5;  B(1,0)=-2; B(2,0)=9;
    // Second column b2 → choose solution x2 = [0, 2, 1]^T
    // Compute b2 = A * x2 by hand:
    // Row0: 2*0 + 1*2 + 1*1 = 3
    // Row1: 4*0 -6*2 + 0*1 = -12
    // Row2: -2*0 +7*2 + 2*1 = 16
    B(0,1)=3;  B(1,1)=-12; B(2,1)=16;

    decomp::LUdcmpd lu(A);
    auto X = lu.solve(B);

    // Check A*X ≈ B
    auto AX = numerics::matmul(A, X);
    CHECK( AX.nearly_equal(B, 1e-12), "A * X does not match B for matrix RHS" );
}


TEST_CASE(LU_Determinant_Known) {
    using T = double;

    // Determinant of:
    // [[1,2,3],[0,1,4],[5,6,0]] is 1
    utils::Matrix<T> A(3,3, T{0});
    A(0,0)=1; A(0,1)=2; A(0,2)=3;
    A(1,0)=0; A(1,1)=1; A(1,2)=4;
    A(2,0)=5; A(2,1)=6; A(2,2)=0;

    decomp::LUdcmpd lu(A);
    T det = lu.det();
    CHECK( std::fabs(det - T{1}) < 1e-12, "det(A) should be 1" );
}

TEST_CASE(LU_Pivoting_Handles_Zero_Leading) {
    using T = double;

    // Requires pivoting (A(0,0)=0); system has solution x=[1,2]^T, b = A*x = [2,3]^T
    utils::Matrix<T> A(2,2, T{0});
    A(0,0)=0; A(0,1)=1;
    A(1,0)=1; A(1,1)=1;

    utils::Vector<T> b(2, T{0});
    b[0]=2; b[1]=3;

    decomp::LUdcmpd lu(A);
    auto x = lu.solve(b);

    utils::Vector<T> x_true(2, T{0}); x_true[0]=1; x_true[1]=2;
    CHECK( (x.nearly_equal(x_true,1e-12)), "Pivoting failed on zero-leading matrix" );
}

TEST_CASE(LU_Input_Unchanged_By_NonInplace_Path) {
    using T = double;

    utils::Matrix<T> A(4,4, T{0});
    for (uint64_t i=0;i<4;++i) {
        for (uint64_t j=0;j<4;++j) {
            A(i,j) = (i==j) ? 3.0 : 0.1 * ((i+1)*(j+2) % 5 + 1);
        }
    }
    utils::Matrix<T> A_copy = A;

    decomp::LUdcmpd lu(A); // constructor should not mutate input A
    CHECK( A.nearly_equal(A_copy, 0.0), "LU constructor modified input matrix" );

    // Also check solve doesn't mutate RHS copy when using out-of-place convenience
    utils::Vector<T> b(4, 0.0);
    for (uint64_t i=0;i<4;++i) b[i] = double(i+1);
    auto b_copy = b;

    auto x = lu.solve(b);
    (void)x;
    CHECK( (b.nearly_equal(b_copy, 1e-300)), "solve(b) modified its input vector" );
}

TEST_CASE(LU_Inplace_Equals_OutOfPlace_Solve_Vector) {
    using T = double;

    utils::Matrix<T> A(3,3, T{0});
    A(0,0)=4;  A(0,1)=1;  A(0,2)=2;
    A(1,0)=0;  A(1,1)=3;  A(1,2)=-1;
    A(2,0)=0;  A(2,1)=0;  A(2,2)=2;

    utils::Vector<T> b(3, T{0}); b[0]=7; b[1]=5; b[2]=4;

    decomp::LUdcmpd lu(A);

    auto x1 = lu.solve(b);
    utils::Vector<T> x2(3, T{0});
    lu.inplace_solve(b, x2);

    CHECK( (x1.nearly_equal(x2,1e-12)), "inplace_solve(b,x) differs from solve(b)" );
}

TEST_CASE(LU_Singular_Throws) {
    using T = double;

    // Singular (row2 = 2 * row1)
    utils::Matrix<T> S(2,2, T{0});
    S(0,0)=1; S(0,1)=2;
    S(1,0)=2; S(1,1)=4;

    bool threw=false;
    try {
        decomp::LUdcmpd lu(S);
        (void)lu;
    } catch (const std::runtime_error&) { threw = true; }
    CHECK(threw, "LU should throw on singular matrix");
}

TEST_CASE(LU_NonSquare_Throws) {
    using T = double;

    utils::Matrix<T> A(3,2, T{0});
    bool threw = false;
    try {
        decomp::LUdcmpd lu(A);
        (void)lu;
    } catch (const std::runtime_error&) { threw = true; }
    CHECK(threw, "LU should throw on non-square input");
}

TEST_CASE(LU_Inverse_RoundTrip) {
    using T = double;

    // Build a strictly diagonally dominant 5x5
    utils::Matrix<T> A(5,5, T{0});
    for (uint64_t i=0;i<5;++i) {
        T rowsum = 0;
        for (uint64_t j=0;j<5;++j) {
            if (i==j) continue;
            A(i,j) = T(0.01 * double(1 + ((i+2)*(j+3)) % 7));
            rowsum += std::fabs(A(i,j));
        }
        A(i,i) = rowsum + T{1};
    }

    decomp::LUdcmpd lu(A);
    auto Ainv = lu.inverse();

    utils::Md I(5,5, 0.0);
    for (uint64_t i=0;i<I.rows();++i) I(i,i)=1.0;

    auto L = numerics::matmul(A, Ainv);
    auto R = numerics::matmul(Ainv, A);

    CHECK(L.nearly_equal(I, 1e-10), "A * inverse(A) not close to I");
    CHECK(R.nearly_equal(I, 1e-10), "inverse(A) * A not close to I");
}