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use crate::traits::{LinalgScalar, Scalar};
use crate::matrix::vector::Vector;
use crate::Matrix;
impl<T: Scalar, const N: usize> Matrix<T, N, N> {
/// Sum of diagonal elements.
///
/// ```
/// use numeris::Matrix;
/// let m = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
/// assert_eq!(m.trace(), 5.0);
/// ```
pub fn trace(&self) -> T {
let mut sum = T::zero();
for i in 0..N {
sum = sum + self[(i, i)];
}
sum
}
/// Extract the diagonal as a vector.
///
/// ```
/// use numeris::Matrix;
/// let m = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
/// let d = m.diag();
/// assert_eq!(d[0], 1.0);
/// assert_eq!(d[1], 4.0);
/// ```
pub fn diag(&self) -> Vector<T, N> {
let mut v = Vector::zeros();
for i in 0..N {
v[i] = self[(i, i)];
}
v
}
/// Create a diagonal matrix from a vector.
///
/// ```
/// use numeris::{Matrix, Vector};
/// let v = Vector::from_array([2.0, 3.0]);
/// let m = Matrix::from_diag(&v);
/// assert_eq!(m[(0, 0)], 2.0);
/// assert_eq!(m[(1, 1)], 3.0);
/// assert_eq!(m[(0, 1)], 0.0);
/// ```
pub fn from_diag(v: &Vector<T, N>) -> Self {
let mut m = Self::zeros();
for i in 0..N {
m[(i, i)] = v[i];
}
m
}
/// Integer matrix power via repeated squaring.
///
/// `pow(0)` returns the identity matrix.
///
/// ```
/// use numeris::Matrix;
/// let m = Matrix::new([[1.0, 1.0], [0.0, 1.0]]);
/// let m3 = m.pow(3);
/// assert_eq!(m3[(0, 1)], 3.0); // upper-triangular power
/// assert_eq!(m.pow(0), Matrix::eye());
/// ```
pub fn pow(&self, mut n: u32) -> Self {
let mut result = Self::eye();
let mut base = *self;
while n > 0 {
if n & 1 == 1 {
result = result * base;
}
base = base * base;
n >>= 1;
}
result
}
/// Check if the matrix is symmetric (`A == A^T`).
///
/// ```
/// use numeris::Matrix;
/// let sym = Matrix::new([[1.0, 2.0], [2.0, 3.0]]);
/// assert!(sym.is_symmetric());
///
/// let asym = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
/// assert!(!asym.is_symmetric());
/// ```
pub fn is_symmetric(&self) -> bool {
for i in 0..N {
for j in (i + 1)..N {
if self[(i, j)] != self[(j, i)] {
return false;
}
}
}
true
}
}
impl<T: LinalgScalar, const N: usize> Matrix<T, N, N> {
/// Determinant via direct formulas for N<=4, Gaussian elimination otherwise.
///
/// ```
/// use numeris::Matrix;
/// let m = Matrix::new([[3.0_f64, 8.0], [4.0, 6.0]]);
/// assert!((m.det() - (-14.0)).abs() < 1e-12);
/// ```
pub fn det(&self) -> T {
// Direct formulas for small matrices — avoid full Gaussian elimination
if N == 1 {
return self.data[0][0];
}
if N == 2 {
// ad - bc (column-major: data[col][row])
return self.data[0][0] * self.data[1][1] - self.data[1][0] * self.data[0][1];
}
if N == 3 {
let a = self.data[0][0]; let b = self.data[1][0]; let c = self.data[2][0];
let d = self.data[0][1]; let e = self.data[1][1]; let f = self.data[2][1];
let g = self.data[0][2]; let h = self.data[1][2]; let i = self.data[2][2];
return a * (e * i - f * h) - b * (d * i - f * g) + c * (d * h - e * g);
}
if N == 4 {
// Sub-determinants from rows 0-1
let a00 = self.data[0][0]; let a01 = self.data[1][0];
let a02 = self.data[2][0]; let a03 = self.data[3][0];
let a10 = self.data[0][1]; let a11 = self.data[1][1];
let a12 = self.data[2][1]; let a13 = self.data[3][1];
let a20 = self.data[0][2]; let a21 = self.data[1][2];
let a22 = self.data[2][2]; let a23 = self.data[3][2];
let a30 = self.data[0][3]; let a31 = self.data[1][3];
let a32 = self.data[2][3]; let a33 = self.data[3][3];
let s0 = a00 * a11 - a01 * a10;
let s1 = a00 * a12 - a02 * a10;
let s2 = a00 * a13 - a03 * a10;
let s3 = a01 * a12 - a02 * a11;
let s4 = a01 * a13 - a03 * a11;
let s5 = a02 * a13 - a03 * a12;
let c0 = a20 * a31 - a21 * a30;
let c1 = a20 * a32 - a22 * a30;
let c2 = a20 * a33 - a23 * a30;
let c3 = a21 * a32 - a22 * a31;
let c4 = a21 * a33 - a23 * a31;
let c5 = a22 * a33 - a23 * a32;
return s0 * c5 - s1 * c4 + s2 * c3 + s3 * c2 - s4 * c1 + s5 * c0;
}
// General case: Gaussian elimination with partial pivoting
let mut a = *self;
let mut sign = T::one();
for col in 0..N {
let mut max_row = col;
let mut max_val = a[(col, col)].modulus();
for row in (col + 1)..N {
let val = a[(row, col)].modulus();
if val > max_val {
max_val = val;
max_row = row;
}
}
if max_val < T::lepsilon() {
return T::zero();
}
if max_row != col {
for j in 0..N {
let tmp = a[(col, j)];
a[(col, j)] = a[(max_row, j)];
a[(max_row, j)] = tmp;
}
sign = T::zero() - sign;
}
let pivot = a[(col, col)];
for row in (col + 1)..N {
let factor = a[(row, col)] / pivot;
for j in (col + 1)..N {
let val = a[(col, j)];
a[(row, j)] = a[(row, j)] - factor * val;
}
a[(row, col)] = T::zero();
}
}
let mut det = sign;
for i in 0..N {
det = det * a[(i, i)];
}
det
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn trace() {
let m = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
assert_eq!(m.trace(), 5.0);
let id: Matrix<f64, 3, 3> = Matrix::eye();
assert_eq!(id.trace(), 3.0);
}
#[test]
fn trace_integer() {
let m = Matrix::new([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assert_eq!(m.trace(), 15);
}
#[test]
fn diag_and_from_diag() {
let m = Matrix::new([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]);
let d = m.diag();
assert_eq!(d[0], 1.0);
assert_eq!(d[1], 5.0);
assert_eq!(d[2], 9.0);
let m2 = Matrix::from_diag(&d);
assert_eq!(m2[(0, 0)], 1.0);
assert_eq!(m2[(1, 1)], 5.0);
assert_eq!(m2[(2, 2)], 9.0);
assert_eq!(m2[(0, 1)], 0.0);
}
#[test]
fn pow() {
let m = Matrix::new([[1.0, 1.0], [0.0, 1.0]]);
let m0 = m.pow(0);
assert_eq!(m0, Matrix::eye());
let m1 = m.pow(1);
assert_eq!(m1, m);
let m3 = m.pow(3);
assert_eq!(m3[(0, 0)], 1.0);
assert_eq!(m3[(0, 1)], 3.0);
assert_eq!(m3[(1, 0)], 0.0);
assert_eq!(m3[(1, 1)], 1.0);
}
#[test]
fn is_symmetric() {
let sym = Matrix::new([[1.0, 2.0, 3.0], [2.0, 5.0, 6.0], [3.0, 6.0, 9.0]]);
assert!(sym.is_symmetric());
let asym = Matrix::new([[1.0, 2.0], [3.0, 4.0]]);
assert!(!asym.is_symmetric());
let id: Matrix<f64, 3, 3> = Matrix::eye();
assert!(id.is_symmetric());
}
#[test]
fn det_2x2() {
let m = Matrix::new([[3.0_f64, 8.0], [4.0, 6.0]]);
let d = m.det();
assert!((d - (-14.0)).abs() < 1e-12);
}
#[test]
fn det_3x3() {
let m = Matrix::new([[6.0_f64, 1.0, 1.0], [4.0, -2.0, 5.0], [2.0, 8.0, 7.0]]);
let d = m.det();
assert!((d - (-306.0)).abs() < 1e-10);
}
#[test]
fn det_identity() {
let id: Matrix<f64, 4, 4> = Matrix::eye();
assert!((id.det() - 1.0).abs() < 1e-12);
}
#[test]
fn det_singular() {
let m = Matrix::new([[1.0_f64, 2.0], [2.0, 4.0]]);
assert!(m.det().abs() < 1e-12);
}
}