luDecomposition

import karasux.linear_algebra.matrix : isClose;
enum N = 4;

immutable m = Matrix!(N, N).fromRows([
    [5.0, 6.0, 7.0, 8.0],
    [10.0, 21.0, 24.0, 27.0],
    [15.0, 54.0, 73.0, 81.0],
    [25.0, 84.0, 179.0, 211.0],
]);
immutable lu = m.luDecomposition();

immutable inverse = lu.createInverse();
auto result = typeof(lu).Mat();
result.mul(inverse, m);
assert(result.isUnitMatrix);

import karasux.linear_algebra.vector : isClose;
enum N = 4;

immutable m = Matrix!(N, N).fromRows([
    [5.0, 6.0, 7.0, 8.0],
    [10.0, 21.0, 24.0, 27.0],
    [15.0, 54.0, 73.0, 81.0],
    [25.0, 84.0, 179.0, 211.0],
]);
immutable lu = m.luDecomposition();

immutable y = typeof(lu).Vec([3.0, 5.0, 4.0, -5.0]);
immutable x = lu.solve(y);

typeof(lu).Vec result;
result.mul(m, x);
assert(result.isClose(y));