From af651601e72b0a69ea18ec255c42bcccd430224b Mon Sep 17 00:00:00 2001
From: htoopyae <htoopyae5@gmail.com>
Date: Thu, 18 Oct 2018 20:26:16 +0630
Subject: [PATCH] Linear Algebra: Determinal of Matrix Added

---
 .eslintrc                                     |  3 +-
 src/algorithms/index.js                       |  4 +-
 src/algorithms/linear algebra/index.js        |  5 ++
 .../linear algebra/matrix_determinant.js      | 66 +++++++++++++++++++
 .../linear algebra/testMatrixDeterminant.js   | 37 +++++++++++
 5 files changed, 113 insertions(+), 2 deletions(-)
 create mode 100644 src/algorithms/linear algebra/index.js
 create mode 100644 src/algorithms/linear algebra/matrix_determinant.js
 create mode 100644 test/algorithms/linear algebra/testMatrixDeterminant.js

diff --git a/.eslintrc b/.eslintrc
index 262dafce..4aa0b3b1 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -8,6 +8,7 @@
     "no-param-reassign": "off",
     "class-methods-use-this": "off",
     "no-bitwise": "off",
-    "no-continue": "off"
+    "no-continue": "off",
+    "no-plusplus": "off"
   }
 }
diff --git a/src/algorithms/index.js b/src/algorithms/index.js
index 2335cebb..21cefea8 100644
--- a/src/algorithms/index.js
+++ b/src/algorithms/index.js
@@ -3,11 +3,13 @@ const math = require('./math');
 const string = require('./string');
 const search = require('./search');
 const sort = require('./sort');
+const linearAlgebra = require('./linear algebra');
 
 module.exports = {
   geometry,
   math,
   string,
   search,
-  sort
+  sort,
+  linearAlgebra
 };
diff --git a/src/algorithms/linear algebra/index.js b/src/algorithms/linear algebra/index.js
new file mode 100644
index 00000000..a5e231c7
--- /dev/null
+++ b/src/algorithms/linear algebra/index.js	
@@ -0,0 +1,5 @@
+const matrixDeterminant = require('./matrix_determinant');
+
+module.exports = {
+  matrixDeterminant
+};
diff --git a/src/algorithms/linear algebra/matrix_determinant.js b/src/algorithms/linear algebra/matrix_determinant.js
new file mode 100644
index 00000000..54e0b45c
--- /dev/null
+++ b/src/algorithms/linear algebra/matrix_determinant.js	
@@ -0,0 +1,66 @@
+/**
+ * Determinant of a square matrix
+ * @param  {Array}  mat input matrix
+ * @param  {Number} n   no. of rows
+ * @return {Number}     determinant
+ */
+const create2dArr = (len) => {
+  const arr = [];
+  for (let i = 0; i < len; i++) {
+    arr.push([]);
+  }
+  return arr;
+};
+
+const getCoMatrix = (mat, p, q, len) => {
+  let i = 0;
+  let j = 0;
+  const coMatrix = create2dArr(len);
+
+  for (let row = 0; row < len; row++) {
+    for (let col = 0; col < len; col++) {
+      // copy into temporary matrix
+      if (row !== p && col !== q) {
+        coMatrix[i][j++] = mat[row][col];
+
+        // one row filled, go to next one
+        if (j === len - 1) {
+          j = 0;
+          i++;
+        }
+      }
+    }
+  }
+
+  return coMatrix;
+};
+
+const matrixDeterminant = (mat, len) => {
+  let D = 0;
+  // to store co matrices
+  let coMat;
+  // to toggle signs
+  let sign = 1;
+
+  // check whether it is square or not
+  if (len !== mat[0].length) {
+    throw new Error('Not a square matrix!');
+  }
+
+  // base case: if matrix contains single element
+  if (len === 1) { return mat[0][0]; }
+
+  // iterate for each element of first row
+  for (let f = 0; f < len; f++) {
+    // get co matrix
+    coMat = getCoMatrix(mat, 0, f, len);
+    D += sign * mat[0][f] * matrixDeterminant(coMat, len - 1);
+
+    // toggle sign
+    sign = -sign;
+  }
+
+  return D;
+};
+
+module.exports = matrixDeterminant;
diff --git a/test/algorithms/linear algebra/testMatrixDeterminant.js b/test/algorithms/linear algebra/testMatrixDeterminant.js
new file mode 100644
index 00000000..19e4f5de
--- /dev/null
+++ b/test/algorithms/linear algebra/testMatrixDeterminant.js	
@@ -0,0 +1,37 @@
+/* eslint-env mocha */
+const matrixDeterminant = require('../../../src').algorithms.linearAlgebra.matrixDeterminant;
+
+const assert = require('assert');
+
+const matOK1 = [
+  [1, 2, 3],
+  [8, 9, 4],
+  [7, 6, 5]
+];
+
+const matOK2 = [
+  [1, 2, 3, 8],
+  [8, 9, 4, 1],
+  [7, 6, 5, 3],
+  [2, 4, 5, 6]
+];
+
+const matNotOK = [
+  [1, 2],
+  [3, 4],
+  [5, 6]
+];
+
+describe('Determinant of Matrix', () => {
+  it('should throw an error if the matrix is not a square', () => {
+    assert.throws(() => matrixDeterminant(matNotOK, matNotOK.length));
+  });
+
+  it('should return appropriate determinant for 3x3 matrix', () => {
+    assert.equal(matrixDeterminant(matOK1, matOK1.length), -48);
+  });
+
+  it('should return appropriate determinant for 4x4 matrix', () => {
+    assert.equal(matrixDeterminant(matOK2, matOK2.length), 347);
+  });
+});