multicalc 0.7.2

Calculus, autodiff, nonlinear least squares and linear algebra in pure safe no_std Rust
Documentation 
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use multicalc::linear_algebra::{Matrix, Vector};

// ----- construction & access -----

#[test]
fn construct_and_access() {
    let v = Vector::new([1.0, 2.0, 3.0]);
    assert_eq!(v[0], 1.0);
    assert_eq!(v.into_array(), [1.0, 2.0, 3.0]);

    let mut w = Vector::from([4.0, 5.0]);
    w[1] = 9.0;
    assert_eq!(w, Vector::new([4.0, 9.0]));

    let z: Vector<3> = Vector::zeros();
    assert_eq!(z, Vector::new([0.0, 0.0, 0.0]));

    assert_eq!(
        Vector::<4>::from_fn(|i| i as f64),
        Vector::new([0.0, 1.0, 2.0, 3.0])
    );

    let mut m = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
    assert_eq!(m[(1, 0)], 3.0);
    m[(0, 1)] = 7.0;
    assert_eq!(m[(0, 1)], 7.0);

    let id: Matrix<3, 3> = Matrix::identity();
    assert_eq!(
        id.into_array(),
        [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
    );

    assert_eq!(
        Matrix::<2, 2>::from_fn(|r, c| (r * 2 + c) as f64),
        Matrix::new([[0.0, 1.0], [2.0, 3.0]])
    );
}

#[test]
fn try_from_slice_length() {
    assert_eq!(
        Vector::<3>::try_from_slice(&[1.0, 2.0, 3.0]),
        Some(Vector::new([1.0, 2.0, 3.0]))
    );
    assert!(Vector::<3>::try_from_slice(&[1.0, 2.0]).is_none());

    assert_eq!(
        Matrix::<2, 2>::try_from_row_slice(&[1.0, 2.0, 3.0, 4.0]),
        Some(Matrix::new([[1.0, 2.0], [3.0, 4.0]]))
    );
    assert!(Matrix::<2, 2>::try_from_row_slice(&[1.0, 2.0, 3.0]).is_none());
}

// ----- vector arithmetic -----

#[test]
fn vector_arithmetic() {
    let a = Vector::new([1.0, 2.0, 3.0]);
    let b = Vector::new([4.0, 5.0, 6.0]);

    assert_eq!(a + b, Vector::new([5.0, 7.0, 9.0]));
    assert_eq!(b - a, Vector::new([3.0, 3.0, 3.0]));
    assert_eq!(-a, Vector::new([-1.0, -2.0, -3.0]));
    assert_eq!(a * 2.0, a.scale(2.0));
    assert_eq!(a.scale(2.0), Vector::new([2.0, 4.0, 6.0]));

    let mut c = a;
    c += b;
    assert_eq!(c, a + b);
    c -= b;
    assert_eq!(c, a);
}

#[test]
fn vector_dot_and_norm() {
    let a: Vector<3> = Vector::new([1.0, 2.0, 3.0]);
    let b: Vector<3> = Vector::new([4.0, 5.0, 6.0]);
    assert_eq!(a.dot(b), 32.0);
    assert!((a.dot(b) - b.dot(a)).abs() < 1e-12); // symmetry
    assert_eq!(Vector::new([1.0, 0.0]).dot(Vector::new([0.0, 1.0])), 0.0); // orthogonal

    let empty: Vector<0> = Vector::zeros();
    assert_eq!(empty.dot(empty), 0.0);

    let v: Vector<2> = Vector::new([3.0, 4.0]);
    assert_eq!(v.norm(), 5.0);
    assert!((v.norm_squared() - v.norm() * v.norm()).abs() < 1e-12);

    let z: Vector<3> = Vector::zeros();
    assert_eq!(z.norm(), 0.0);
    assert!(Vector::new([f64::INFINITY, 0.0]).norm().is_infinite());
}

// ----- cross products & scalar triple -----

#[test]
fn vector_cross_3d() {
    let x = Vector::new([1.0, 0.0, 0.0]);
    let y = Vector::new([0.0, 1.0, 0.0]);
    let z = Vector::new([0.0, 0.0, 1.0]);
    assert_eq!(x.cross(y), z);
    assert_eq!(y.cross(z), x);
    assert_eq!(z.cross(x), y);
    assert_eq!(x.cross(y), -(y.cross(x))); // anti-commutativity

    let a = Vector::new([1.0, 2.0, 3.0]);
    let b = Vector::new([4.0, 5.0, 6.0]);
    let axb = a.cross(b);
    assert_eq!(a.dot(axb), 0.0); // orthogonal to both inputs
    assert_eq!(b.dot(axb), 0.0);
}

#[test]
fn vector_cross_2d_and_scalar_triple() {
    assert_eq!(Vector::new([1.0, 0.0]).cross(Vector::new([0.0, 1.0])), 1.0);
    let a: Vector<2> = Vector::new([2.0, 3.0]);
    let b: Vector<2> = Vector::new([5.0, 7.0]);
    assert!((a.cross(b) + b.cross(a)).abs() < 1e-12); // anti-commutativity
    assert_eq!(a.cross(a), 0.0); // parallel

    let x = Vector::new([1.0, 0.0, 0.0]);
    let y = Vector::new([0.0, 1.0, 0.0]);
    let z = Vector::new([0.0, 0.0, 1.0]);
    assert_eq!(x.scalar_triple(y, z), 1.0);

    let p: Vector<3> = Vector::new([1.0, 2.0, 3.0]);
    let q: Vector<3> = Vector::new([0.0, 1.0, 4.0]);
    let r: Vector<3> = Vector::new([5.0, 6.0, 0.0]);
    assert!((p.scalar_triple(q, r) - q.scalar_triple(r, p)).abs() < 1e-12); // cyclic
    let m = Matrix::new([p.into_array(), q.into_array(), r.into_array()]);
    assert!((p.scalar_triple(q, r) - m.determinant()).abs() < 1e-12); // == det([p; q; r])
}