/*
    Matrix Class
    Created By Davenchy
    twitter: @fadi_davenchy
*/

const Matrix = (function() {
  class Matrix {
    constructor(r=3, c=3, i=0) {
      // create matrix
      if (Array.isArray(r)) this.matrix = r.map(c => c.slice(0));
      else if (r instanceof Matrix) this.copyOf(r);
      else this.matrix = Matrix.generateArray(r, c, i);

      // check the matrix
      const rows = this.matrix.length;
      const columns = this.matrix[0].length;
      const columnsLength = this.matrix.filter(c => c.length === columns).length;
      if (columnsLength !== rows) throw new Error(`each column must have the same number of values: ${rows}`);
    }

    reset(i=0) {
      this.matrix = Matrix.generateArray(this.rows, this.columns, i);
      return this;
    }

    copyOf(m) {
      this.matrix = m.matrix.map(c => c.slice(0));
      return this;
    }

    clone() {
      return new Matrix(this.matrix);
    }

    toString() {
      return this.matrix.map(c => c.join('\t')).join('\n');
    }

    isEqualTo(m2) {
      if (!m2 instanceof Matrix) throw new Error('need matrix to compare to');
      const m1 = this;
      if (m1.rows !== m2.rows || m1.columns !== m2.columns) return  false;
      m1.loop(({ i, j, value }) => {
        if (m2.getValue(i, j) !== value) return false;
      });
      return true;
    }

    get isSquare() {
      return this.rows === this.columns;
    }

    get isInversable() {
      return this.determinate !== 0;
    }

    get determinate() {
      const m = this.clone();
      if (!m.isSquare) throw new Error('matrix must be a square matrix');
      const M = m.getValue.bind(m);
      // handle (1x1) Matrix
      if (m.rows === 1) return M(1, 1);
      // handle (2x2) Matrix
      if (m.rows === 2) return M(1, 1) * M(2, 2) - M(1, 2) * M(2, 1);
      // handle (3x3) or more Matrices
      if (m.rows >= 3) {
        let sum = 0;
        for (let i = 1; i <= m.rows; i++) {
          const det = m.clone().reduce(1, i).determinate;
          sum += Math.pow(-1, i - 1) * M(1, i) * det;
        }
        return sum;
      }
      return;
    }

    get rows() {
      return this.matrix.length;
    }

    get columns() {
      return this.matrix[0].length;
    }

    get type() {
      return `(${this.rows} x ${this.columns})`
    }

    setColumn(n, c=[]) {
      if (c.length !== this.rows) throw new Error(`column must has ${this.rows} value(s)`);
      if (n > this.columns || n <= 0) throw new Error(`column number must be in range [1, ${this.columns}]`);
      this.matrix.forEach((col, i) => {
        col[n - 1] = c[i];
      });
      return this;
    }

    addColumn(c=[]) {
      if (c.length !== this.rows) throw new Error(`column must has ${this.rows} value(s)`);
      this.matrix.forEach((col, i) => {
        col.push(c[i]);
      });
      return this;
    }

    getColumn(c=1) {
      if (c > this.columns || c <= 0) throw new Error(`column number must be in range [1, ${this.columns}]`);
      return this.matrix.map(r => r[c - 1]);
    }

    removeColumn(c) {
      if (c > this.columns || c <= 0) throw new Error(`column number must be in range [1, ${this.columns}]`);
      this.matrix.forEach(r => r.splice(c - 1, 1));
      return this;
    }

    setRow(n, r=[]) {
      if (r.length !== this.columns) throw new Error(`row must has ${this.columns} value(s)`);
      if (n > this.rows || n <= 0) throw new Error(`row number must be in range [1, ${this.rows}]`);
      this.matrix[n - 1] = r;
      return this;
    }

    addRow(r=[]) {
      if (r.length !== this.columns) throw new Error(`row must has ${this.columns} value(s)`);
      this.matrix.push(r);
      return this;
    }

    getRow(r=1) {
      if (r > this.rows || r <= 0) throw new Error(`row number must be in range [1, ${this.rows}]`);
      return this.matrix[r - 1].slice(0);
    }

    removeRow(r) {
      if (r > this.rows || r <= 0) throw new Error(`row number must be in range [1, ${this.rows}]`);
      this.matrix.splice(r - 1, 1);
      return this;
    }

    setValue(r=1, c=1, v) {
      this.matrix[r-1][c-1] = v;
      return this;
    }

    getValue(r=1, c=1) {
      if (r <= 0 || r > this.rows || c <= 0 || c > this.cols) return;
      return this.matrix[r-1][c-1];
    }

    loop(cb) {
      const self = this;
      const { rows, columns } = this;
      let counter = 0;
      for(let i = 1; i <= rows; i++)
        for(let j = 1; j <= columns; j++) {
          const tools = {
            self, i, j,
            clone: self.clone(),
            sign: Math.pow(-1, counter),
            counter: counter++,
            value: self.getValue(i, j),
            setValue: v => self.setValue(i, j, v),
            column: self.getColumn(j),
            row: self.getRow(i),
          }

          try { tools.determinate = self.determinate; }
          catch (_) { tools.determinate = null; }
          tools.reduce = () => tools.clone.reduce(i, j);
          tools.inverse = () => tools.clone.inverse();
          tools.transpose = () => tools.clone.transpose();
          tools.adjacency = () => tools.clone.adjacency();
          tools.identity = () => tools.clone.identity();

          cb(tools);
        }
      return this;
    }

    multiply(...matrices) {
      const m1 = this;
      matrices.forEach(m2 => {
        if (m1.columns !== m2.rows) throw new Error('can not multiply the 2 matrices');
        const temp = new Matrix(m1.rows, m2.columns);
        temp.loop(({i, j, setValue}) => {
          const product = Matrix.vectorDotProduct(m1.getRow(i), m2.getColumn(j));
          setValue(product);
        });
        m1.copyOf(temp);
      });
      return this;
    }

    addNumber (n) {
      const self = this;
      const { rows, columns } = this;
      this.loop(t => t.setValue(t.value + n));
      return this;
    }

    subtractNumber (n) {
      const self = this;
      const { rows, columns } = this;
      this.loop(t => t.setValue(t.value - n));
      return this;
    }

    multiplyNumber (n) {
      const self = this;
      const { rows, columns } = this;
      this.loop(t => t.setValue(t.value * n));
      return this;
    }

    divideNumber (n) {
      if (n === 0) throw new Error('can not divide by zero');
      const self = this;
      const { rows, columns } = this;
      this.loop(t => t.setValue(t.value / n));
      return this;
    }

    transpose() {
      const mat = Array(this.columns).fill(0);
      this.matrix = mat.map((r, i) => this.getColumn(i + 1));
      return this;
    }

    inverse () {
      const delta = Math.pow(this.determinate, -1);
      this.adjacency().multiplyNumber(delta);
      return this;
    }

    adjacency() {
      if (!this.isInversable) throw new Error('matrix determinate value equal to zero');
      if (!this.isSquare) throw new Error('must be a square matrix');

      // 1x1 Matrix
      if (this.rows === 1) this.setValue(1, 1, Math.pow(this.getValue(1, 1), -1));
      // 2x2 Matrix
      else if (this.rows === 2) {
        const temp = this.getValue(1, 1);
        this.setValue(1, 2, this.getValue(1, 2) * -1);
        this.setValue(2, 1, this.getValue(2, 1) * -1);
        this.setValue(1, 1, this.getValue(2, 2));
        this.setValue(2, 2, temp);
      }
      // 3x3 or more Matrices
      else if (this.rows >= 3) {
        const temp = this.clone().reset();
        this.loop(({i, j, reduce, sign}) => {
          temp.setValue(i, j, reduce().determinate * sign)
        }).copyOf(temp.transpose());
      }

      return this;
    }

    identity () {
      const m = this;
      if (!m.isSquare) throw new Error('must be a square matrix');
      const n = m.rows;
      const i = new Matrix(n, n);
      for (let a = 1; a <= n; a++) {
        i.setValue(a, a, 1);
      }
      return i;
    }

    reduce (r, c) {
      this.removeRow(r).removeColumn(c);
      return this;
    }
  }

  Matrix.generateArray = (r = 3, c = 3, i = 0) => Array(r).fill().map(r => Array(c).fill().map(c => i));
  Matrix.vectorDotProduct = (a, b) => {
    if (a.length !== b.length) throw new Error(`length of 'a' not equal length of 'b'`)
    return a.map((x, i) => x * b[i]).reduce((a, b) => a + b);
  }

  return Matrix;
})();