matrix.test.js

var assert = require('assert');
var numbers = require('../index.js');
var matrix = numbers.matrix;

suite('numbers', function () {

  console.log('\n\n\033[34mTesting Matrix Mathematics\033[0m');

  test('should create a deep copy of a matrix', function (done) {
    var input = [
      [1, 2],
      [2, 1]
    ];

    var copy = matrix.deepCopy(input);

    assert.notEqual(input, copy);

    assert.throws(
      function () {
        matrix.deepCopy([1, 2]);
      },
      /Input cannot be a vector./
    );

    done();
  });

  test('should be able to tell if a matrix is square', function (done) {
    assert.equal(matrix.isSquare([
      [1, 2],
      [3, 4]
    ]), true);
    assert.equal(matrix.isSquare([
      [1, 2, 3],
      [4, 5, 6]
    ]), false);
    assert.equal(matrix.isSquare([
      [1, 2, 3],
      [4, 5, 6],
      [7, 8, 9]
    ]), true);
    assert.equal(matrix.isSquare([
      [1, 2],
      [3, 4, 5]
    ]), false);
    assert.equal(matrix.isSquare([
      [1, 2, 3],
      [4, 5],
      [6, 7, 8]
    ]), false);

    done();
  });

  test('should return sum of two matrices', function (done) {
    var arrA = [
      [0, 1, 2],
      [3, 4, 5]
    ];

    var arrB = [
      [6, 7, 8],
      [9, 10, 11]
    ];

    var arrC = [
      [6, 8, 10],
      [12, 14, 16]
    ];

    var res = matrix.addition(arrA, arrB);

    assert.deepEqual(arrC, res);
    done();
  });

  test('should return sum of two vectors', function (done) {
    var arrA = [0, 1, 2];
    var arrB = [3, 4, 5];

    var arrC = [3, 5, 7];

    var res = matrix.addition(arrA, arrB);

    assert.deepEqual(arrC, res);
    done();
  });

  test('should return difference of two vectors', function (done) {
    var arrA = [0, 1, 2];
    var arrB = [3, 4, 5];
    var expected1 = [-3, -3, -3];
    var res = matrix.subtraction(arrA, arrB);

    assert.deepEqual(expected1, res);
    done();
  });

  test('should returned scaled matrix', function (done) {
    var array = [
      [0, 1, 2],
      [3, 4, 5]
    ];
    var scalar = 5;

    var res = matrix.scalar(array, scalar);

    assert.deepEqual([
      [0, 5, 10],
      [15, 20, 25]
    ], res);
    done();
  });

  test('should return transposed matrix', function (done) {
    var array = [
      [0, 1, 2],
      [3, 4, 5]
    ];

    var transposed = [
      [0, 3],
      [1, 4],
      [2, 5]
    ];

    var res = matrix.transpose(array);

    assert.deepEqual(transposed, res);
    done();
  });

  test('should return identity matrix of dimension n', function (done) {
    var identity = [
      [1, 0, 0],
      [0, 1, 0],
      [0, 0, 1]
    ];
    var res = matrix.identity(3);

    assert.deepEqual(identity, res);
    done();
  });

  test('should return dot product of two vectors', function (done) {
    var vectorA = [0, 1, 2, 3];
    var vectorB = [-1, 2, 4, 6];

    var res = matrix.dotproduct(vectorA, vectorB);

    assert.equal(28, res);
    done();
  });

  test('should return product of two matrices', function (done) {
    var matrixA = [
      [0, 1, 2],
      [3, 4, 5]
    ];
    var matrixB = [
      [0, 3],
      [1, 4],
      [2, 5]
    ];

    var res = matrix.multiply(matrixA, matrixB);

    assert.deepEqual([
      [5, 14],
      [14, 50]
    ], res);
    done();
  });

  test('should return product of matrix and a vector', function (done) {
    var matrixA = [
      [0, 1, 2],
      [3, 4, 5]
    ];
    var matrixB = [
      [0],
      [1],
      [2]
    ];

    var res = matrix.multiply(matrixA, matrixB);

    assert.deepEqual([
      [5],
      [14]
    ], res);
    done();
  });

  test('should return determinant of matrix', function (done) {

    var m0 = [
      [1]
    ];

    var res0 = matrix.determinant(m0);
    assert.equal(1, res0);

    var m1 = [
      [2, 3],
      [6, 7]
    ];

    var res1 = matrix.determinant(m1);
    assert.equal(-4, res1);

    var m2 = [
      [0, 1, 2],
      [3, 4, 5],
      [6, 7, 8]
    ];

    var res2 = matrix.determinant(m2);
    assert.equal(0, res2);

    done();
  });

  test('should throw an error for calculating the determinant of a non-square matrix', function (done) {
    var m3 = [
      [3, -7, 8, 9, -6],
      [0, 2, -5, 7, 3],
      [0, 0, 1, 5, 0],
      [0, 0, 0, -2, 0]
    ];

    assert.throws(function () {
        matrix.determinant(m3);
      },
      /Matrix must be square./
    );
    done();
  });

  test('should throw an error if trying to get LU decomposition of non-square matrix', function (done) {
    assert.throws(
      function () {
        matrix.lupDecomposition([
          [1, 2, 3],
          [4, 5, 6]
        ]);
      },
      /Matrix must be square./
    );

    done();
  });

  test('should return the LU decomposition of a matrix', function (done) {
    var inputMatrix = [
      [1, 0, 0, 2],
      [2, -2, 0, 5],
      [1, -2, -2, 3],
      [5, -3, -5, 2]
    ];
    var firstLup = matrix.lupDecomposition(inputMatrix);

    assert.deepEqual(matrix.multiply(firstLup[0], firstLup[1]),
      matrix.multiply(firstLup[2], inputMatrix));

    var secondInputMatrix = [
      [1, 0, 0, 2],
      [1, -2, 0, 5],
      [1, -2, 0, 3],
      [1, -3, -5, 0]
    ];
    var secondLup = matrix.lupDecomposition(secondInputMatrix);

    assert.deepEqual(matrix.multiply(secondLup[0], secondLup[1]),
      matrix.multiply(secondLup[2], secondInputMatrix));

    done();
  });

  test('should return a new vector that has been rotated by the transformation matrix', function (done) {
    var vectorA = [
      [0],
      [1]
    ];
    var degree = 90;

    var res = matrix.rotate(vectorA, degree, 'clockwise');

    assert.equal((res[0][0] > (1 - numbers.EPSILON)), true);
    assert.equal((res[0][0] < (1 + numbers.EPSILON)), true);
    assert.equal((res[1][0] > (0 - numbers.EPSILON)), true);
    assert.equal((res[1][0] < (0 + numbers.EPSILON)), true);
    done();
  });

  test('should throw an error if a vector larger than two is given for rotation', function (done) {
    var vectorA = [
      [0],
      [1],
      [2]
    ];
    var degree = 90;

    assert.throws(
      function () {
        matrix.rotate(vectorA, degree, 'clockwise');
      },
      /Only two dimensional operations are supported at this time/
    );
    done();
  });

  test('should return a new vector that has been scaled by the transformation matrix', function (done) {
    var vectorA = [
      [2],
      [5]
    ];
    var sx = 10;
    var sy = 5;
    var expected = [
      [20],
      [25]
    ];

    var res = matrix.scale(vectorA, sx, sy);

    assert.deepEqual(expected, res);
    done();
  });

  test('should throw an error if a vector larger than two is given for scaling', function (done) {
    var vectorA = [
      [0],
      [1],
      [2]
    ];
    var sx = 10;
    var sy = 5;

    assert.throws(
      function () {
        matrix.scale(vectorA, sx, sy);
      },
      /Only two dimensional operations are supported at this time/
    );
    done();
  });

  test('should return a new vector that has been sheared in the x direction by the transformation matrix', function (done) {
    var vectorA = [
      [2],
      [5]
    ];
    var k = 10;
    var direction = "xaxis";
    var expected = [
      [52],
      [5]
    ];

    var res = matrix.shear(vectorA, k, direction);

    assert.deepEqual(expected, res);
    done();
  });

  test('should return a new vector that has been sheared in the y direction by the transformation matrix', function (done) {
    var vectorA = [
      [2],
      [5]
    ];
    var k = 10;
    var direction = "yaxis";
    var expected = [
      [2],
      [25]
    ];

    var res = matrix.shear(vectorA, k, direction);

    assert.deepEqual(expected, res);
    done();
  });

  test('should throw an error if a vector larger than two is given for shearing', function (done) {
    var vectorA = [
      [0],
      [1],
      [2]
    ];
    var k = 10;
    var direction = "yaxis";

    assert.throws(
      function () {
        matrix.shear(vectorA, k, direction);
      },
      /Only two dimensional operations are supported at this time/
    );
    done();
  });

  test('should return a new vector that has been transformed by the affine transformation matrix', function (done) {
    var vectorA = [
      [2],
      [5]
    ];
    var tx = 10;
    var ty = 10;
    var expected = [
      [12],
      [15]
    ];

    var res = matrix.affine(vectorA, tx, ty);

    assert.deepEqual(expected, res);
    done();
  });

  test('should throw an error if a vector larger than two is given for the affine transform', function (done) {
    var vectorA = [
      [0],
      [1],
      [2]
    ];
    var tx = 10;
    var ty = 10;

    assert.throws(
      function () {
        matrix.affine(vectorA, tx, ty);
      },
      /Only two dimensional operations are supported at this time/
    );

    done();
  });

  test('should return a new matrix that has a scaled row for the rowScale function', function (done) {
    var m = [
      [0, 1, 2],
      [3, -1, 5],
      [1, 2, 5]
    ];

    var expected1 = [
      [0, 0, 0],
      [3, -1, 5],
      [1, 2, 5]
    ];
    var res1 = matrix.rowScale(m, 0, 0);

    assert.deepEqual(res1, expected1);


    var expected2 = [
      [0, 1, 2],
      [-6, 2, -10],
      [1, 2, 5]
    ];
    var res2 = matrix.rowScale(m, 1, -2);

    assert.deepEqual(res2, expected2);


    done();
  });

  test('should return a new matrix that has rows changed with the rowSwitch function', function (done) {
    var m = [
      [0, 1, 2],
      [3, -1, 5],
      [1, 2, 5]
    ];

    var expected1 = [
      [3, -1, 5],
      [0, 1, 2],
      [1, 2, 5]
    ];
    var res1 = matrix.rowSwitch(m, 0, 1);

    assert.deepEqual(res1, expected1);

    var res2 = matrix.rowScale(m, 1, 1);

    assert.deepEqual(res2, m);


    done();
  });
  test('should return a new matrix that has a multiple of one row added to another using the rowAddMultiple function', function (done) {
    var m = [
      [0, 1, 2],
      [3, -1, 5],
      [1, 2, 5]
    ];

    var expected1 = [
      [0, 1, 2],
      [3, 1, 9],
      [1, 2, 5]
    ];
    var res1 = matrix.rowAddMultiple(m, 0, 1, 2);

    assert.deepEqual(res1, expected1);

    var res2 = matrix.rowScale(m, 1, 1, 0);

    assert.deepEqual(res2, m);


    done();
  });

  test('should row reduce the given matrix for a given epsilon', function (done) {
    var m1 = [
      [0, 1, 2],
      [3, -1, 5],
      [1, 2, 5]
    ];

    var m2 = [
      [2, -1, 0],
      [-1, 2, -1],
      [0, -1, 2]
    ];

    var expected1 = [
      [1, 0, 0],
      [0, 1, 0],
      [0, 0, 1]
    ];

    var res1 = matrix.GaussJordanEliminate(m1);
    var res2 = matrix.GaussJordanEliminate(m2);
    var res3 = matrix.rowReduce(m2, 0.01);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected1);
    assert.deepEqual(res3, expected1);

    done();
  });

  test('should row reduce the given matrix for a given epsilon', function (done) {
    var m1 = [
      [0, 1],
      [1, 2]
    ];

    var expected1 = [
      [-2, 1],
      [1, 0]
    ];

    var m2 = [
      [1, 3, 3],
      [1, 4, 3],
      [1, 3, 4]
    ];

    var expected2 = [
      [7, -3, -3],
      [-1, 1, 0],
      [-1, 0, 1]
    ];

    var res1 = matrix.inverse(m1);
    var res2 = matrix.inverse(m2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);

    done();
  });

  test('should reorder columns', function (done) {
    var m1 = [
      [1, 2, 3],
      [4, 5, 6],
      [7, 8, 9]
    ];

    var expected1 = [
      [2, 3, 1],
      [5, 6, 4],
      [8, 9, 7]
    ];

    var m2 = [
      [20, 3],
      [17, 5]
    ];

    var expected2 = [
      [3, 20],
      [5, 17]
    ];

    var res1 = matrix.reorderCols(m1, [1, 2, 0]);
    var res2 = matrix.reorderCols(m2, [1, 0]);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should reorder rows', function (done) {
    var m1 = [
      [1, 2, 3],
      [4, 5, 6],
      [7, 8, 9]
    ];

    var expected1 = [
      [7, 8, 9],
      [1, 2, 3],
      [4, 5, 6]
    ];

    var m2 = [
      [20, 3],
      [17, 5]
    ];

    var expected2 = [
      [17, 5],
      [20, 3]
    ];

    var res1 = matrix.reorderRows(m1, [2, 0, 1]);
    var res2 = matrix.reorderRows(m2, [1, 0]);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should reverse columns and rows', function (done) {
    var m1 = [
      [2, 5, 7],
      [10, 4, 6],
      [0, 1, 0]
    ];

    var expected1 = [
      [0, 1, 0],
      [6, 4, 10],
      [7, 5, 2]
    ];

    var res1 = matrix.reverseRows(matrix.reverseCols(m1));

    assert.deepEqual(res1, expected1);
    done();
  });

  test('should produce a matrix of zeros', function (done) {
    var n1 = 3;
    var m1 = 2;

    var expected1 = [
      [0, 0],
      [0, 0],
      [0, 0]
    ];

    var res1 = matrix.zeros(n1, m1);

    assert.deepEqual(res1, expected1);
    done();
  });

  test('should get a column', function (done) {
    var m1 = [
      [10, 2, 5],
      [5, 2, 42],
      [7, 6, 4],
      [4, 11, 89]
    ];

    var expected1 = [5, 42, 4, 89];

    var res1 = matrix.getCol(m1, 2);

    assert.deepEqual(res1, expected1);
    done();
  });

  test('should create a zigzag matrix', function (done) {
    var n1 = 4;
    var corner1 = 'TL';
    var dir1 = 'V';

    var expected1 = [
      [1, 3, 4, 10],
      [2, 5, 9, 11],
      [6, 8, 12, 15],
      [7, 13, 14, 16]
    ];

    var res1 = matrix.zigzag(n1, corner1, dir1);

    assert.deepEqual(res1, expected1);
    done();
  });

  test('should calculate a vector norm', function (done) {
    var v1 = [-100, 5, -12, 20, 83];
    var p1 = Infinity;
    var p2 = -Infinity;

    var v2 = [1, 1, 1, 1];
    var p3 = 2;

    var expected1 = 100;
    var expected2 = 5;
    var expected3 = 2;

    var res1 = matrix.vectorNorm(v1, p1);
    var res2 = matrix.vectorNorm(v1, p2);
    var res3 = matrix.vectorNorm(v2, p3);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    assert.deepEqual(res3, expected3);
    done();
  });

  test('should calculate a matrix norm', function (done) {
    var m1 = [
      [1, -3, 2],
      [-4, 6, -5],
      [7, -9, -8],
      [-10, 12, 11]
    ];
    var p1 = Infinity;
    var p2 = -Infinity;
    var p3 = 1;
    var p4 = -1;

    var m2 = [
      [1, 0, 0, 0],
      [0, 1, 0, 0],
      [0, 0, 1, 0],
      [0, 0, 0, 1]
    ];
    var p5 = null;

    var expected1 = 33;
    var expected2 = 6;
    var expected3 = 30;
    var expected4 = 22;
    var expected5 = 2;

    var res1 = matrix.matrixNorm(m1, p1);
    var res2 = matrix.matrixNorm(m1, p2);
    var res3 = matrix.matrixNorm(m1, p3);
    var res4 = matrix.matrixNorm(m1, p4);
    var res5 = matrix.matrixNorm(m2, p5);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    assert.deepEqual(res3, expected3);
    assert.deepEqual(res4, expected4);
    assert.deepEqual(res5, expected5);
    done();
  });

  test('should test for upper bandwidth', function (done) {
    var m1 = [
      [1, 2, 0, 0],
      [5, 4, 3, 0],
      [8, 2, 1, 5],
      [1, 2, 5, 4]
    ];
    var m2 = [
      [1, 0, 0, 0, 0],
      [1, 3, 3, 0, 0],
      [1, 3, 3, 3, 0]
    ];
    var q1 = 1;
    var q2 = 0;

    var expected1 = true;
    var expected2 = false;

    var res1 = matrix.isUpperBand(m1, q1);
    var res2 = matrix.isUpperBand(m2, q2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for lower bandwidth', function (done) {
    var m1 = [
      [1, 2, 3, 5],
      [5, 4, 3, 0],
      [0, 2, 1, 5],
      [0, 0, 5, 4]
    ];
    var m2 = [
      [1, 3, 4, 5, 9],
      [0, 3, 3, 0, 0],
      [0, 0, 3, 3, 0],
      [0, 0, 1, 3, 3]
    ];
    var q1 = 1;
    var q2 = 0;

    var expected1 = true;
    var expected2 = false;

    var res1 = matrix.isLowerBand(m1, q1);
    var res2 = matrix.isLowerBand(m2, q2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for weak row diagonal dominance', function (done) {
    var m1 = [
      [3, -2, 1],
      [1, -3, 2],
      [-1, 2, 4]
    ];
    var m2 = [
      [-2, 2, 1],
      [1, 3, 2],
      [1, -2, 0]
    ];

    var expected1 = true;
    var expected2 = false;

    var res1 = matrix.isRowDD(m1);
    var res2 = matrix.isRowDD(m2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for strict row diagonal dominance', function (done) {
    var m1 = [
      [3, -2, 1],
      [1, -3, 2],
      [-1, 2, 4]
    ];
    var m2 = [
      [-4, 2, 1],
      [1, 6, 2],
      [1, -2, 5]
    ];

    var expected1 = false;
    var expected2 = true;

    var res1 = matrix.isStrictlyRowDD(m1);
    var res2 = matrix.isStrictlyRowDD(m2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for weak column diagonal dominance', function (done) {
    var m1 = [
      [3, -2, 1],
      [1, -3, 2],
      [-1, 2, 4]
    ];
    var m2 = [
      [-4, 1, 1],
      [2, 3, 2],
      [2, -1, 5]
    ];

    var expected1 = false;
    var expected2 = true;

    var res1 = matrix.isColumnDD(m1);
    var res2 = matrix.isColumnDD(m2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for strict column diagonal dominance', function (done) {
    var m1 = [
      [-4, 2, 1],
      [1, 6, 2],
      [1, -2, 5]
    ];
    var m2 = [
      [-4, 1, 1],
      [2, 3, 2],
      [2, -1, 5]
    ];

    var expected1 = true;
    var expected2 = false;

    var res1 = matrix.isStrictlyColumnDD(m1);
    var res2 = matrix.isStrictlyColumnDD(m2);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for applying a function to each element of a matrix', function (done) {
    var m1 = [
      [-1, 0, 5],
      [2, 3, 18],
      [42, 0, 3]
    ];
    var m2 = [
      [-5, 2],
      [2, 3],
      [11, -1]
    ];
    var addOne = function (x) {
      return x + 1;
    };

    var expected1 = [
      [0, 1, 6],
      [3, 4, 19],
      [43, 1, 4]
    ];
    var expected2 = [
      [-4, 3],
      [3, 4],
      [12, 0]
    ];

    var res1 = matrix.map(m1, addOne);
    var res2 = matrix.map(m2, addOne);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });

  test('should test for applying a function to each element of a matrix with addition parameters', function (done) {
    var m1 = [
      [1, 3, 5],
      [-1, -7, 2],
      [5, 5, 4]
    ];
    var m2 = [
      [-10, 3],
      [4, 9],
      [100, 0]
    ];
    var scaleAndAddOne = function (x, alpha) {
      return alpha * x + 1;
    };

    var expected1 = [
      [3, 7, 11],
      [-1, -13, 5],
      [11, 11, 9]
    ];
    var expected2 = [
      [-29, 10],
      [13, 28],
      [301, 1]
    ];

    var res1 = matrix.mapMulti(m1, scaleAndAddOne, 2);
    var res2 = matrix.mapMulti(m2, scaleAndAddOne, 3);

    assert.deepEqual(res1, expected1);
    assert.deepEqual(res2, expected2);
    done();
  });
});