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new: Added reduced_row_echelon method

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This commit is contained in:
Sayantan Santra 2023-05-26 00:43:33 -05:00
parent 2c5d7c4d77
commit d638e25388
Signed by: SinTan1729
GPG key ID: EB3E68BFBA25C85F
2 changed files with 75 additions and 15 deletions
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79
src/lib.rs
View file

@ -193,11 +193,13 @@ impl<T: Mul + Add + Sub> Matrix<T> {
// Cloning is necessary as we'll be doing row operations on it.
let mut rows = self.entries.clone();
let mut multiplier = T::one();
for i in 0..self.height() {
let h = self.height();
let w = self.width();
for i in 0..h {
// First check if the row has diagonal element 0, if yes, then swap.
if rows[i][i] == T::zero() {
let mut zero_column = true;
for j in (i + 1)..self.height() {
for j in (i + 1)..h {
if rows[j][i] != T::zero() {
rows.swap(i, j);
multiplier = T::zero() - multiplier;
@ -209,9 +211,9 @@ impl<T: Mul + Add + Sub> Matrix<T> {
return Ok(T::zero());
}
}
for j in (i + 1)..self.height() {
for j in (i + 1)..h {
let ratio = rows[j][i] / rows[i][i];
for k in i..self.width() {
for k in i..w {
rows[j][k] = rows[j][k] - rows[i][k] * ratio;
}
}
@ -225,7 +227,7 @@ impl<T: Mul + Add + Sub> Matrix<T> {
}
}
/// Return the row echelon form of a matrix over a field i.e. needs [`One`] and [`Div`] traits.
/// Returns the row echelon form of a matrix over a field i.e. needs [`One`] and [`Div`] traits.
/// # Example
/// ```
/// use matrix_basic::Matrix;
@ -242,12 +244,13 @@ impl<T: Mul + Add + Sub> Matrix<T> {
T: One,
T: PartialEq,
T: Div<Output = T>,
T: Display,
{
// Cloning is necessary as we'll be doing row operations on it.
let mut rows = self.entries.clone();
let mut offset = 0;
for i in 0..self.height() {
let h = self.height();
let w = self.width();
for i in 0..h {
// Check if all the rows below are 0
if i + offset >= self.width() {
break;
@ -255,7 +258,7 @@ impl<T: Mul + Add + Sub> Matrix<T> {
// First check if the row has diagonal element 0, if yes, then swap.
if rows[i][i + offset] == T::zero() {
let mut zero_column = true;
for j in (i + 1)..self.height() {
for j in (i + 1)..h {
if rows[j][i + offset] != T::zero() {
rows.swap(i, j);
zero_column = false;
@ -266,21 +269,65 @@ impl<T: Mul + Add + Sub> Matrix<T> {
offset += 1;
}
}
for j in (i + 1)..self.height() {
for j in (i + 1)..h {
let ratio = rows[j][i + offset] / rows[i][i + offset];
for k in (i + offset)..self.width() {
for k in (i + offset)..w {
rows[j][k] = rows[j][k] - rows[i][k] * ratio;
println!(
"{}, {}",
rows[j][k],
rows[i][k] * rows[j][i + offset] / rows[i][i + offset]
);
}
}
}
Matrix { entries: rows }
}
/// Returns the column echelon form of a matrix over a field i.e. needs [`One`] and [`Div`] traits.
/// It's just the transpose of the row echelon form of the transpose.
/// See [`row_echelon`](Self::row_echelon()) and [`transpose`](Self::transpose()).
pub fn column_echelon(&self) -> Self
where
T: Copy,
T: Mul<Output = T>,
T: Sub<Output = T>,
T: Zero,
T: One,
T: PartialEq,
T: Div<Output = T>,
{
self.transpose().row_echelon().transpose()
}
/// Returns the reduced row echelon form of a matrix over a field i.e. needs [`One`] and [`Div`] traits.
/// # Example
/// ```
/// use matrix_basic::Matrix;
/// let m = Matrix::from(vec![vec![1.0,2.0,3.0],vec![3.0,4.0,5.0]]).unwrap();
/// let n = Matrix::from(vec![vec![1.0,2.0,3.0], vec![0.0,1.0,2.0]]).unwrap();
/// assert_eq!(m.reduced_row_echelon(),n);
/// ```
pub fn reduced_row_echelon(&self) -> Self
where
T: Copy,
T: Mul<Output = T>,
T: Sub<Output = T>,
T: Zero,
T: One,
T: PartialEq,
T: Div<Output = T>,
{
let mut echelon = self.row_echelon();
let mut offset = 0;
for row in &mut echelon.entries {
while row[offset] == T::zero() {
offset += 1;
}
let divisor = row[offset];
for entry in row.iter_mut().skip(offset) {
*entry = *entry / divisor;
}
offset += 1;
}
echelon
}
/// Creates a zero matrix of a given size.
pub fn zero(height: usize, width: usize) -> Self
where
@ -317,6 +364,8 @@ impl<T: Mul + Add + Sub> Matrix<T> {
}
Matrix { entries: out }
}
// TODO: Canonical forms, eigenvalues, eigenvectors etc.
}
impl<T: Debug + Mul + Add + Sub> Display for Matrix<T> {

11
src/tests.rs
View file

@ -40,3 +40,14 @@ fn zero_one_test() {
assert_eq!(Matrix::<i32>::zero(2, 3), a);
assert_eq!(Matrix::<i32>::identity(2), b);
}
#[test]
fn echelon_test() {
let m = Matrix::from(vec![vec![1.0, 2.0, 3.0], vec![1.0, 0.0, 1.0]]).unwrap();
let a = Matrix::from(vec![vec![1.0, 2.0, 3.0], vec![0.0, -2.0, -2.0]]).unwrap();
let b = Matrix::from(vec![vec![1.0, 0.0, 0.0], vec![1.0, -2.0, 0.0]]).unwrap();
let c = Matrix::from(vec![vec![1.0, 2.0, 3.0], vec![0.0, 1.0, 1.0]]).unwrap();
assert_eq!(m.row_echelon(), a);
assert_eq!(m.column_echelon(), b);
assert_eq!(m.reduced_row_echelon(), c);
}