From d0e27ea7da8769418459a7f07f16d53f7218f8c5 Mon Sep 17 00:00:00 2001
From: Filip Znachor <filip@znachor.cz>
Date: Thu, 13 Oct 2022 18:57:40 +0200
Subject: [PATCH] Added matrix diagonal method and upper/lower triangular form
 check

---
 __tests__/matrix.ts | 38 +++++++++++++++++++++++++++++++-------
 matrix.ts           | 22 +++++++++++++++++++++-
 2 files changed, 52 insertions(+), 8 deletions(-)

diff --git a/__tests__/matrix.ts b/__tests__/matrix.ts
index e048765..5b1f4de 100644
--- a/__tests__/matrix.ts
+++ b/__tests__/matrix.ts
@@ -1,4 +1,4 @@
-import { GaussianElimination, Matrix } from "../matrix";
+import { GaussianElimination, Matrix, TriangularForm } from "../matrix";
 
 let A = new Matrix(
 	[1, 2, 3],
@@ -16,19 +16,19 @@ let C = new Matrix(
 	[ 32, 77 ]
 );
 
-test('A = B.transpose', () => {
+test('Transpose (A, B)', () => {
 	expect(A.eq(B.transpose())).toBe(true);
 });
 
-test('B = A.transpose', () => {
+test('Transpose (B, A)', () => {
 	expect(B.eq(A.transpose())).toBe(true);
 });
 
-test('A * B = C', () => {
+test('Multiply (A, B, C)', () => {
 	expect(A.mul(B).eq(C)).toBe(true);
 });
 
-test('B * A != C', () => {
+test('Multiply (B, A, C)', () => {
 	expect(B.mul(A).eq(C)).toBe(false);
 });
 
@@ -48,7 +48,7 @@ let D_solved = new Matrix(
 	[0, 0, 0, 0, 0]
 );
 
-test('D - Gaussian elimination', () => {
+test('Gaussian elimination (D)', () => {
 	expect(D.solve().eq(D_solved)).toBe(true);
 });
 
@@ -64,6 +64,30 @@ let E_solved = new Matrix(
 	[0, -3, -2]
 );
 
-test('E - Gaussian elimination', () => {
+test('Gaussian elimination (E)', () => {
 	expect(E.solve().eq(E_solved)).toBe(true);
+});
+
+let F = new Matrix(
+	[1, 1, 1],
+	[0, 2, 4],
+	[0, 0, 5],
+);
+
+let G = new Matrix(
+	[1, 0, 0],
+	[5, 2, 0],
+	[4, 8, 5],
+);
+
+test('Upper triangular matrix (F)', () => {
+	expect(F.is_triangular()).toBe(true);
+});
+
+test('Upper triangular matrix (A)', () => {
+	expect(A.is_triangular()).toBe(false);
+});
+
+test('Lower triangular matrix (G)', () => {
+	expect(G.is_triangular(TriangularForm.LOWER)).toBe(true);
 });
\ No newline at end of file
diff --git a/matrix.ts b/matrix.ts
index d679d3a..fdec8d6 100644
--- a/matrix.ts
+++ b/matrix.ts
@@ -1,6 +1,8 @@
 
 export type RawMatrix = number[][];
 
+export enum TriangularForm {UPPER, LOWER};
+
 export class Matrix {
 
 	rows!: number;
@@ -98,6 +100,14 @@ export class Matrix {
 		return new_matrix;
 	}
 
+	diagonal() {
+		let diagonal: number[] = [];
+		for(let i=0; i<Math.min(this.rows, this.cols); i++) {
+			diagonal.push(this.matrix[i][i]);
+		}
+		return diagonal;
+	}
+
 	eq(other_matrix: Matrix) {
 		if(this.rows != other_matrix.rows || this.cols != other_matrix.cols) return false;
 		for(let i=0; i<this.rows; i++) {
@@ -108,7 +118,7 @@ export class Matrix {
 		return true;
 	}
 
-	in_stepped_shape() {
+	is_in_elchelon_form() {
 		let pivot_index = -1;
 		for(let i=0; i<this.rows; i++) {
 			for(let j=0; j<this.cols; j++) {
@@ -122,6 +132,16 @@ export class Matrix {
 		return true;
 	}
 
+	is_triangular(form: TriangularForm = TriangularForm.UPPER) {
+		for(let i=0; i<Math.min(this.rows, this.cols); i++) {
+			for(let j=0; j<i; j++) {
+				if(this.matrix[i][j] !== 0 && form == TriangularForm.UPPER) return false;
+				if(this.matrix[j][i] !== 0 && form == TriangularForm.LOWER) return false;
+			}
+		}
+		return true;
+	}
+
 	pivots() {
 		let pivots: number[] = [];
 		for(let i=0; i<this.rows; i++) {