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use crate::traits::{LinalgScalar, Scalar};
use super::vector::DynVector;
use super::DynMatrix;
impl<T: Scalar> DynMatrix<T> {
/// Sum of diagonal elements.
///
/// ```
/// use numeris::DynMatrix;
/// let m = DynMatrix::from_rows(2, 2, &[1.0, 2.0, 3.0, 4.0]);
/// assert_eq!(m.trace(), 5.0);
/// ```
pub fn trace(&self) -> T {
let n = self.nrows.min(self.ncols);
let mut sum = T::zero();
for i in 0..n {
sum = sum + self[(i, i)];
}
sum
}
/// Extract the diagonal as a `DynVector`.
///
/// ```
/// use numeris::DynMatrix;
/// let m = DynMatrix::from_rows(2, 2, &[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) -> DynVector<T> {
let n = self.nrows.min(self.ncols);
let mut data = alloc::vec::Vec::with_capacity(n);
for i in 0..n {
data.push(self[(i, i)]);
}
DynVector::from_vec(data)
}
/// Create a square diagonal matrix from a vector.
///
/// ```
/// use numeris::{DynMatrix, DynVector};
/// let v = DynVector::from_slice(&[2.0, 3.0]);
/// let m = DynMatrix::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: &DynVector<T>) -> Self {
let n = v.len();
let mut m = Self::zeros(n, n);
for i in 0..n {
m[(i, i)] = v[i];
}
m
}
/// Integer matrix power via repeated squaring.
///
/// `pow(0)` returns the identity matrix. Panics if not square.
///
/// ```
/// use numeris::DynMatrix;
/// let m = DynMatrix::from_rows(2, 2, &[1.0, 1.0, 0.0, 1.0]);
/// let m3 = m.pow(3);
/// assert_eq!(m3[(0, 1)], 3.0);
/// ```
pub fn pow(&self, mut n: u32) -> Self {
assert!(self.is_square(), "pow requires a square matrix");
let sz = self.nrows;
let mut result = Self::eye(sz);
let mut base = self.clone();
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::DynMatrix;
/// let sym = DynMatrix::from_rows(2, 2, &[1.0, 2.0, 2.0, 3.0]);
/// assert!(sym.is_symmetric());
/// ```
pub fn is_symmetric(&self) -> bool {
if !self.is_square() {
return false;
}
let n = self.nrows;
for i in 0..n {
for j in (i + 1)..n {
if self[(i, j)] != self[(j, i)] {
return false;
}
}
}
true
}
}
impl<T: LinalgScalar> DynMatrix<T> {
/// Determinant via Gaussian elimination with partial pivoting.
///
/// Panics if the matrix is not square.
///
/// ```
/// use numeris::DynMatrix;
/// let m = DynMatrix::from_rows(2, 2, &[3.0_f64, 8.0, 4.0, 6.0]);
/// assert!((m.det() - (-14.0)).abs() < 1e-12);
/// ```
pub fn det(&self) -> T {
assert!(self.is_square(), "determinant requires a square matrix");
let n = self.nrows;
let mut a = self.clone();
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 {
a.swap_rows(col, max_row);
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 = DynMatrix::from_rows(2, 2, &[1.0, 2.0, 3.0, 4.0]);
assert_eq!(m.trace(), 5.0);
let id = DynMatrix::<f64>::eye(3);
assert_eq!(id.trace(), 3.0);
}
#[test]
fn diag_and_from_diag() {
let m = DynMatrix::from_fn(3, 3, |i, j| (i * 3 + j + 1) as f64);
let d = m.diag();
assert_eq!(d[0], 1.0);
assert_eq!(d[1], 5.0);
assert_eq!(d[2], 9.0);
let m2 = DynMatrix::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 = DynMatrix::from_rows(2, 2, &[1.0, 1.0, 0.0, 1.0]);
let m0 = m.pow(0);
assert_eq!(m0, DynMatrix::<f64>::eye(2));
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 = DynMatrix::from_rows(2, 2, &[1.0, 2.0, 2.0, 3.0]);
assert!(sym.is_symmetric());
let asym = DynMatrix::from_rows(2, 2, &[1.0, 2.0, 3.0, 4.0]);
assert!(!asym.is_symmetric());
let rect = DynMatrix::from_rows(2, 3, &[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]);
assert!(!rect.is_symmetric());
}
#[test]
fn det_2x2() {
let m = DynMatrix::from_rows(2, 2, &[3.0_f64, 8.0, 4.0, 6.0]);
assert!((m.det() - (-14.0)).abs() < 1e-12);
}
#[test]
fn det_3x3() {
let m = DynMatrix::from_rows(
3,
3,
&[6.0_f64, 1.0, 1.0, 4.0, -2.0, 5.0, 2.0, 8.0, 7.0],
);
assert!((m.det() - (-306.0)).abs() < 1e-10);
}
#[test]
fn det_identity() {
let id = DynMatrix::<f64>::eye(4);
assert!((id.det() - 1.0).abs() < 1e-12);
}
#[test]
fn det_singular() {
let m = DynMatrix::from_rows(2, 2, &[1.0_f64, 2.0, 2.0, 4.0]);
assert!(m.det().abs() < 1e-12);
}
}