ml-matrix/matrix.js

Matrix manipulation and computation library

'use strict';

Object.defineProperty(exports, '__esModule', { value: true });

var isAnyArray = require('is-any-array');
var rescale = require('ml-array-rescale');

const indent = ' '.repeat(2);
const indentData = ' '.repeat(4);

/**
 * @this {Matrix}
 * @returns {string}
 */
function inspectMatrix() {
  return inspectMatrixWithOptions(this);
}

function inspectMatrixWithOptions(matrix, options = {}) {
  const {
    maxRows = 15,
    maxColumns = 10,
    maxNumSize = 8,
    padMinus = 'auto',
  } = options;
  return `${matrix.constructor.name} {
${indent}[
${indentData}${inspectData(matrix, maxRows, maxColumns, maxNumSize, padMinus)}
${indent}]
${indent}rows: ${matrix.rows}
${indent}columns: ${matrix.columns}
}`;
}

function inspectData(matrix, maxRows, maxColumns, maxNumSize, padMinus) {
  const { rows, columns } = matrix;
  const maxI = Math.min(rows, maxRows);
  const maxJ = Math.min(columns, maxColumns);
  const result = [];

  if (padMinus === 'auto') {
    padMinus = false;
    loop: for (let i = 0; i < maxI; i++) {
      for (let j = 0; j < maxJ; j++) {
        if (matrix.get(i, j) < 0) {
          padMinus = true;
          break loop;
        }
      }
    }
  }

  for (let i = 0; i < maxI; i++) {
    let line = [];
    for (let j = 0; j < maxJ; j++) {
      line.push(formatNumber(matrix.get(i, j), maxNumSize, padMinus));
    }
    result.push(`${line.join(' ')}`);
  }
  if (maxJ !== columns) {
    result[result.length - 1] += ` ... ${columns - maxColumns} more columns`;
  }
  if (maxI !== rows) {
    result.push(`... ${rows - maxRows} more rows`);
  }
  return result.join(`\n${indentData}`);
}

function formatNumber(num, maxNumSize, padMinus) {
  return (
    num >= 0 && padMinus
      ? ` ${formatNumber2(num, maxNumSize - 1)}`
      : formatNumber2(num, maxNumSize)
  ).padEnd(maxNumSize);
}

function formatNumber2(num, len) {
  // small.length numbers should be as is
  let str = num.toString();
  if (str.length <= len) return str;

  // (7)'0.00123' is better then (7)'1.23e-2'
  // (8)'0.000123' is worse then (7)'1.23e-3',
  let fix = num.toFixed(len);
  if (fix.length > len) {
    fix = num.toFixed(Math.max(0, len - (fix.length - len)));
  }
  if (
    fix.length <= len &&
    !fix.startsWith('0.000') &&
    !fix.startsWith('-0.000')
  ) {
    return fix;
  }

  // well, if it's still too long the user should've used longer numbers
  let exp = num.toExponential(len);
  if (exp.length > len) {
    exp = num.toExponential(Math.max(0, len - (exp.length - len)));
  }
  return exp.slice(0);
}

function installMathOperations(AbstractMatrix, Matrix) {
  AbstractMatrix.prototype.add = function add(value) {
    if (typeof value === 'number') return this.addS(value);
    return this.addM(value);
  };

  AbstractMatrix.prototype.addS = function addS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) + value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.addM = function addM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) + matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.add = function add(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.add(value);
  };

  AbstractMatrix.prototype.sub = function sub(value) {
    if (typeof value === 'number') return this.subS(value);
    return this.subM(value);
  };

  AbstractMatrix.prototype.subS = function subS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) - value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.subM = function subM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) - matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.sub = function sub(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.sub(value);
  };
  AbstractMatrix.prototype.subtract = AbstractMatrix.prototype.sub;
  AbstractMatrix.prototype.subtractS = AbstractMatrix.prototype.subS;
  AbstractMatrix.prototype.subtractM = AbstractMatrix.prototype.subM;
  AbstractMatrix.subtract = AbstractMatrix.sub;

  AbstractMatrix.prototype.mul = function mul(value) {
    if (typeof value === 'number') return this.mulS(value);
    return this.mulM(value);
  };

  AbstractMatrix.prototype.mulS = function mulS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) * value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.mulM = function mulM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) * matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.mul = function mul(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.mul(value);
  };
  AbstractMatrix.prototype.multiply = AbstractMatrix.prototype.mul;
  AbstractMatrix.prototype.multiplyS = AbstractMatrix.prototype.mulS;
  AbstractMatrix.prototype.multiplyM = AbstractMatrix.prototype.mulM;
  AbstractMatrix.multiply = AbstractMatrix.mul;

  AbstractMatrix.prototype.div = function div(value) {
    if (typeof value === 'number') return this.divS(value);
    return this.divM(value);
  };

  AbstractMatrix.prototype.divS = function divS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) / value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.divM = function divM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) / matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.div = function div(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.div(value);
  };
  AbstractMatrix.prototype.divide = AbstractMatrix.prototype.div;
  AbstractMatrix.prototype.divideS = AbstractMatrix.prototype.divS;
  AbstractMatrix.prototype.divideM = AbstractMatrix.prototype.divM;
  AbstractMatrix.divide = AbstractMatrix.div;

  AbstractMatrix.prototype.mod = function mod(value) {
    if (typeof value === 'number') return this.modS(value);
    return this.modM(value);
  };

  AbstractMatrix.prototype.modS = function modS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) % value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.modM = function modM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) % matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.mod = function mod(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.mod(value);
  };
  AbstractMatrix.prototype.modulus = AbstractMatrix.prototype.mod;
  AbstractMatrix.prototype.modulusS = AbstractMatrix.prototype.modS;
  AbstractMatrix.prototype.modulusM = AbstractMatrix.prototype.modM;
  AbstractMatrix.modulus = AbstractMatrix.mod;

  AbstractMatrix.prototype.and = function and(value) {
    if (typeof value === 'number') return this.andS(value);
    return this.andM(value);
  };

  AbstractMatrix.prototype.andS = function andS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) & value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.andM = function andM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) & matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.and = function and(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.and(value);
  };

  AbstractMatrix.prototype.or = function or(value) {
    if (typeof value === 'number') return this.orS(value);
    return this.orM(value);
  };

  AbstractMatrix.prototype.orS = function orS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) | value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.orM = function orM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) | matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.or = function or(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.or(value);
  };

  AbstractMatrix.prototype.xor = function xor(value) {
    if (typeof value === 'number') return this.xorS(value);
    return this.xorM(value);
  };

  AbstractMatrix.prototype.xorS = function xorS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) ^ value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.xorM = function xorM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) ^ matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.xor = function xor(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.xor(value);
  };

  AbstractMatrix.prototype.leftShift = function leftShift(value) {
    if (typeof value === 'number') return this.leftShiftS(value);
    return this.leftShiftM(value);
  };

  AbstractMatrix.prototype.leftShiftS = function leftShiftS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) << value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.leftShiftM = function leftShiftM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) << matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.leftShift = function leftShift(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.leftShift(value);
  };

  AbstractMatrix.prototype.signPropagatingRightShift = function signPropagatingRightShift(value) {
    if (typeof value === 'number') return this.signPropagatingRightShiftS(value);
    return this.signPropagatingRightShiftM(value);
  };

  AbstractMatrix.prototype.signPropagatingRightShiftS = function signPropagatingRightShiftS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) >> value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.signPropagatingRightShiftM = function signPropagatingRightShiftM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) >> matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.signPropagatingRightShift = function signPropagatingRightShift(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.signPropagatingRightShift(value);
  };

  AbstractMatrix.prototype.rightShift = function rightShift(value) {
    if (typeof value === 'number') return this.rightShiftS(value);
    return this.rightShiftM(value);
  };

  AbstractMatrix.prototype.rightShiftS = function rightShiftS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) >>> value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.rightShiftM = function rightShiftM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) >>> matrix.get(i, j));
      }
    }
    return this;
  };

  AbstractMatrix.rightShift = function rightShift(matrix, value) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.rightShift(value);
  };
  AbstractMatrix.prototype.zeroFillRightShift = AbstractMatrix.prototype.rightShift;
  AbstractMatrix.prototype.zeroFillRightShiftS = AbstractMatrix.prototype.rightShiftS;
  AbstractMatrix.prototype.zeroFillRightShiftM = AbstractMatrix.prototype.rightShiftM;
  AbstractMatrix.zeroFillRightShift = AbstractMatrix.rightShift;

  AbstractMatrix.prototype.not = function not() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, ~(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.not = function not(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.not();
  };

  AbstractMatrix.prototype.abs = function abs() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.abs(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.abs = function abs(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.abs();
  };

  AbstractMatrix.prototype.acos = function acos() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.acos(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.acos = function acos(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.acos();
  };

  AbstractMatrix.prototype.acosh = function acosh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.acosh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.acosh = function acosh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.acosh();
  };

  AbstractMatrix.prototype.asin = function asin() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.asin(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.asin = function asin(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.asin();
  };

  AbstractMatrix.prototype.asinh = function asinh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.asinh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.asinh = function asinh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.asinh();
  };

  AbstractMatrix.prototype.atan = function atan() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.atan(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.atan = function atan(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.atan();
  };

  AbstractMatrix.prototype.atanh = function atanh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.atanh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.atanh = function atanh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.atanh();
  };

  AbstractMatrix.prototype.cbrt = function cbrt() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.cbrt(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.cbrt = function cbrt(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.cbrt();
  };

  AbstractMatrix.prototype.ceil = function ceil() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.ceil(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.ceil = function ceil(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.ceil();
  };

  AbstractMatrix.prototype.clz32 = function clz32() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.clz32(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.clz32 = function clz32(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.clz32();
  };

  AbstractMatrix.prototype.cos = function cos() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.cos(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.cos = function cos(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.cos();
  };

  AbstractMatrix.prototype.cosh = function cosh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.cosh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.cosh = function cosh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.cosh();
  };

  AbstractMatrix.prototype.exp = function exp() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.exp(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.exp = function exp(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.exp();
  };

  AbstractMatrix.prototype.expm1 = function expm1() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.expm1(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.expm1 = function expm1(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.expm1();
  };

  AbstractMatrix.prototype.floor = function floor() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.floor(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.floor = function floor(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.floor();
  };

  AbstractMatrix.prototype.fround = function fround() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.fround(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.fround = function fround(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.fround();
  };

  AbstractMatrix.prototype.log = function log() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.log(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.log = function log(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.log();
  };

  AbstractMatrix.prototype.log1p = function log1p() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.log1p(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.log1p = function log1p(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.log1p();
  };

  AbstractMatrix.prototype.log10 = function log10() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.log10(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.log10 = function log10(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.log10();
  };

  AbstractMatrix.prototype.log2 = function log2() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.log2(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.log2 = function log2(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.log2();
  };

  AbstractMatrix.prototype.round = function round() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.round(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.round = function round(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.round();
  };

  AbstractMatrix.prototype.sign = function sign() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.sign(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.sign = function sign(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.sign();
  };

  AbstractMatrix.prototype.sin = function sin() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.sin(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.sin = function sin(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.sin();
  };

  AbstractMatrix.prototype.sinh = function sinh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.sinh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.sinh = function sinh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.sinh();
  };

  AbstractMatrix.prototype.sqrt = function sqrt() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.sqrt(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.sqrt = function sqrt(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.sqrt();
  };

  AbstractMatrix.prototype.tan = function tan() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.tan(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.tan = function tan(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.tan();
  };

  AbstractMatrix.prototype.tanh = function tanh() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.tanh(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.tanh = function tanh(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.tanh();
  };

  AbstractMatrix.prototype.trunc = function trunc() {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, Math.trunc(this.get(i, j)));
      }
    }
    return this;
  };

  AbstractMatrix.trunc = function trunc(matrix) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.trunc();
  };

  AbstractMatrix.pow = function pow(matrix, arg0) {
    const newMatrix = new Matrix(matrix);
    return newMatrix.pow(arg0);
  };

  AbstractMatrix.prototype.pow = function pow(value) {
    if (typeof value === 'number') return this.powS(value);
    return this.powM(value);
  };

  AbstractMatrix.prototype.powS = function powS(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) ** value);
      }
    }
    return this;
  };

  AbstractMatrix.prototype.powM = function powM(matrix) {
    matrix = Matrix.checkMatrix(matrix);
    if (this.rows !== matrix.rows ||
      this.columns !== matrix.columns) {
      throw new RangeError('Matrices dimensions must be equal');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) ** matrix.get(i, j));
      }
    }
    return this;
  };
}

/**
 * @private
 * Check that a row index is not out of bounds
 * @param {Matrix} matrix
 * @param {number} index
 * @param {boolean} [outer]
 */
function checkRowIndex(matrix, index, outer) {
  let max = outer ? matrix.rows : matrix.rows - 1;
  if (index < 0 || index > max) {
    throw new RangeError('Row index out of range');
  }
}

/**
 * @private
 * Check that a column index is not out of bounds
 * @param {Matrix} matrix
 * @param {number} index
 * @param {boolean} [outer]
 */
function checkColumnIndex(matrix, index, outer) {
  let max = outer ? matrix.columns : matrix.columns - 1;
  if (index < 0 || index > max) {
    throw new RangeError('Column index out of range');
  }
}

/**
 * @private
 * Check that the provided vector is an array with the right length
 * @param {Matrix} matrix
 * @param {Array|Matrix} vector
 * @return {Array}
 * @throws {RangeError}
 */
function checkRowVector(matrix, vector) {
  if (vector.to1DArray) {
    vector = vector.to1DArray();
  }
  if (vector.length !== matrix.columns) {
    throw new RangeError(
      'vector size must be the same as the number of columns',
    );
  }
  return vector;
}

/**
 * @private
 * Check that the provided vector is an array with the right length
 * @param {Matrix} matrix
 * @param {Array|Matrix} vector
 * @return {Array}
 * @throws {RangeError}
 */
function checkColumnVector(matrix, vector) {
  if (vector.to1DArray) {
    vector = vector.to1DArray();
  }
  if (vector.length !== matrix.rows) {
    throw new RangeError('vector size must be the same as the number of rows');
  }
  return vector;
}

function checkRowIndices(matrix, rowIndices) {
  if (!isAnyArray.isAnyArray(rowIndices)) {
    throw new TypeError('row indices must be an array');
  }

  for (let i = 0; i < rowIndices.length; i++) {
    if (rowIndices[i] < 0 || rowIndices[i] >= matrix.rows) {
      throw new RangeError('row indices are out of range');
    }
  }
}

function checkColumnIndices(matrix, columnIndices) {
  if (!isAnyArray.isAnyArray(columnIndices)) {
    throw new TypeError('column indices must be an array');
  }

  for (let i = 0; i < columnIndices.length; i++) {
    if (columnIndices[i] < 0 || columnIndices[i] >= matrix.columns) {
      throw new RangeError('column indices are out of range');
    }
  }
}

function checkRange(matrix, startRow, endRow, startColumn, endColumn) {
  if (arguments.length !== 5) {
    throw new RangeError('expected 4 arguments');
  }
  checkNumber('startRow', startRow);
  checkNumber('endRow', endRow);
  checkNumber('startColumn', startColumn);
  checkNumber('endColumn', endColumn);
  if (
    startRow > endRow ||
    startColumn > endColumn ||
    startRow < 0 ||
    startRow >= matrix.rows ||
    endRow < 0 ||
    endRow >= matrix.rows ||
    startColumn < 0 ||
    startColumn >= matrix.columns ||
    endColumn < 0 ||
    endColumn >= matrix.columns
  ) {
    throw new RangeError('Submatrix indices are out of range');
  }
}

function newArray(length, value = 0) {
  let array = [];
  for (let i = 0; i < length; i++) {
    array.push(value);
  }
  return array;
}

function checkNumber(name, value) {
  if (typeof value !== 'number') {
    throw new TypeError(`${name} must be a number`);
  }
}

function checkNonEmpty(matrix) {
  if (matrix.isEmpty()) {
    throw new Error('Empty matrix has no elements to index');
  }
}

function sumByRow(matrix) {
  let sum = newArray(matrix.rows);
  for (let i = 0; i < matrix.rows; ++i) {
    for (let j = 0; j < matrix.columns; ++j) {
      sum[i] += matrix.get(i, j);
    }
  }
  return sum;
}

function sumByColumn(matrix) {
  let sum = newArray(matrix.columns);
  for (let i = 0; i < matrix.rows; ++i) {
    for (let j = 0; j < matrix.columns; ++j) {
      sum[j] += matrix.get(i, j);
    }
  }
  return sum;
}

function sumAll(matrix) {
  let v = 0;
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      v += matrix.get(i, j);
    }
  }
  return v;
}

function productByRow(matrix) {
  let sum = newArray(matrix.rows, 1);
  for (let i = 0; i < matrix.rows; ++i) {
    for (let j = 0; j < matrix.columns; ++j) {
      sum[i] *= matrix.get(i, j);
    }
  }
  return sum;
}

function productByColumn(matrix) {
  let sum = newArray(matrix.columns, 1);
  for (let i = 0; i < matrix.rows; ++i) {
    for (let j = 0; j < matrix.columns; ++j) {
      sum[j] *= matrix.get(i, j);
    }
  }
  return sum;
}

function productAll(matrix) {
  let v = 1;
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      v *= matrix.get(i, j);
    }
  }
  return v;
}

function varianceByRow(matrix, unbiased, mean) {
  const rows = matrix.rows;
  const cols = matrix.columns;
  const variance = [];

  for (let i = 0; i < rows; i++) {
    let sum1 = 0;
    let sum2 = 0;
    let x = 0;
    for (let j = 0; j < cols; j++) {
      x = matrix.get(i, j) - mean[i];
      sum1 += x;
      sum2 += x * x;
    }
    if (unbiased) {
      variance.push((sum2 - (sum1 * sum1) / cols) / (cols - 1));
    } else {
      variance.push((sum2 - (sum1 * sum1) / cols) / cols);
    }
  }
  return variance;
}

function varianceByColumn(matrix, unbiased, mean) {
  const rows = matrix.rows;
  const cols = matrix.columns;
  const variance = [];

  for (let j = 0; j < cols; j++) {
    let sum1 = 0;
    let sum2 = 0;
    let x = 0;
    for (let i = 0; i < rows; i++) {
      x = matrix.get(i, j) - mean[j];
      sum1 += x;
      sum2 += x * x;
    }
    if (unbiased) {
      variance.push((sum2 - (sum1 * sum1) / rows) / (rows - 1));
    } else {
      variance.push((sum2 - (sum1 * sum1) / rows) / rows);
    }
  }
  return variance;
}

function varianceAll(matrix, unbiased, mean) {
  const rows = matrix.rows;
  const cols = matrix.columns;
  const size = rows * cols;

  let sum1 = 0;
  let sum2 = 0;
  let x = 0;
  for (let i = 0; i < rows; i++) {
    for (let j = 0; j < cols; j++) {
      x = matrix.get(i, j) - mean;
      sum1 += x;
      sum2 += x * x;
    }
  }
  if (unbiased) {
    return (sum2 - (sum1 * sum1) / size) / (size - 1);
  } else {
    return (sum2 - (sum1 * sum1) / size) / size;
  }
}

function centerByRow(matrix, mean) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) - mean[i]);
    }
  }
}

function centerByColumn(matrix, mean) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) - mean[j]);
    }
  }
}

function centerAll(matrix, mean) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) - mean);
    }
  }
}

function getScaleByRow(matrix) {
  const scale = [];
  for (let i = 0; i < matrix.rows; i++) {
    let sum = 0;
    for (let j = 0; j < matrix.columns; j++) {
      sum += matrix.get(i, j) ** 2 / (matrix.columns - 1);
    }
    scale.push(Math.sqrt(sum));
  }
  return scale;
}

function scaleByRow(matrix, scale) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) / scale[i]);
    }
  }
}

function getScaleByColumn(matrix) {
  const scale = [];
  for (let j = 0; j < matrix.columns; j++) {
    let sum = 0;
    for (let i = 0; i < matrix.rows; i++) {
      sum += matrix.get(i, j) ** 2 / (matrix.rows - 1);
    }
    scale.push(Math.sqrt(sum));
  }
  return scale;
}

function scaleByColumn(matrix, scale) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) / scale[j]);
    }
  }
}

function getScaleAll(matrix) {
  const divider = matrix.size - 1;
  let sum = 0;
  for (let j = 0; j < matrix.columns; j++) {
    for (let i = 0; i < matrix.rows; i++) {
      sum += matrix.get(i, j) ** 2 / divider;
    }
  }
  return Math.sqrt(sum);
}

function scaleAll(matrix, scale) {
  for (let i = 0; i < matrix.rows; i++) {
    for (let j = 0; j < matrix.columns; j++) {
      matrix.set(i, j, matrix.get(i, j) / scale);
    }
  }
}

class AbstractMatrix {
  static from1DArray(newRows, newColumns, newData) {
    let length = newRows * newColumns;
    if (length !== newData.length) {
      throw new RangeError('data length does not match given dimensions');
    }
    let newMatrix = new Matrix(newRows, newColumns);
    for (let row = 0; row < newRows; row++) {
      for (let column = 0; column < newColumns; column++) {
        newMatrix.set(row, column, newData[row * newColumns + column]);
      }
    }
    return newMatrix;
  }

  static rowVector(newData) {
    let vector = new Matrix(1, newData.length);
    for (let i = 0; i < newData.length; i++) {
      vector.set(0, i, newData[i]);
    }
    return vector;
  }

  static columnVector(newData) {
    let vector = new Matrix(newData.length, 1);
    for (let i = 0; i < newData.length; i++) {
      vector.set(i, 0, newData[i]);
    }
    return vector;
  }

  static zeros(rows, columns) {
    return new Matrix(rows, columns);
  }

  static ones(rows, columns) {
    return new Matrix(rows, columns).fill(1);
  }

  static rand(rows, columns, options = {}) {
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { random = Math.random } = options;
    let matrix = new Matrix(rows, columns);
    for (let i = 0; i < rows; i++) {
      for (let j = 0; j < columns; j++) {
        matrix.set(i, j, random());
      }
    }
    return matrix;
  }

  static randInt(rows, columns, options = {}) {
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { min = 0, max = 1000, random = Math.random } = options;
    if (!Number.isInteger(min)) throw new TypeError('min must be an integer');
    if (!Number.isInteger(max)) throw new TypeError('max must be an integer');
    if (min >= max) throw new RangeError('min must be smaller than max');
    let interval = max - min;
    let matrix = new Matrix(rows, columns);
    for (let i = 0; i < rows; i++) {
      for (let j = 0; j < columns; j++) {
        let value = min + Math.round(random() * interval);
        matrix.set(i, j, value);
      }
    }
    return matrix;
  }

  static eye(rows, columns, value) {
    if (columns === undefined) columns = rows;
    if (value === undefined) value = 1;
    let min = Math.min(rows, columns);
    let matrix = this.zeros(rows, columns);
    for (let i = 0; i < min; i++) {
      matrix.set(i, i, value);
    }
    return matrix;
  }

  static diag(data, rows, columns) {
    let l = data.length;
    if (rows === undefined) rows = l;
    if (columns === undefined) columns = rows;
    let min = Math.min(l, rows, columns);
    let matrix = this.zeros(rows, columns);
    for (let i = 0; i < min; i++) {
      matrix.set(i, i, data[i]);
    }
    return matrix;
  }

  static min(matrix1, matrix2) {
    matrix1 = this.checkMatrix(matrix1);
    matrix2 = this.checkMatrix(matrix2);
    let rows = matrix1.rows;
    let columns = matrix1.columns;
    let result = new Matrix(rows, columns);
    for (let i = 0; i < rows; i++) {
      for (let j = 0; j < columns; j++) {
        result.set(i, j, Math.min(matrix1.get(i, j), matrix2.get(i, j)));
      }
    }
    return result;
  }

  static max(matrix1, matrix2) {
    matrix1 = this.checkMatrix(matrix1);
    matrix2 = this.checkMatrix(matrix2);
    let rows = matrix1.rows;
    let columns = matrix1.columns;
    let result = new this(rows, columns);
    for (let i = 0; i < rows; i++) {
      for (let j = 0; j < columns; j++) {
        result.set(i, j, Math.max(matrix1.get(i, j), matrix2.get(i, j)));
      }
    }
    return result;
  }

  static checkMatrix(value) {
    return AbstractMatrix.isMatrix(value) ? value : new Matrix(value);
  }

  static isMatrix(value) {
    return value != null && value.klass === 'Matrix';
  }

  get size() {
    return this.rows * this.columns;
  }

  apply(callback) {
    if (typeof callback !== 'function') {
      throw new TypeError('callback must be a function');
    }
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        callback.call(this, i, j);
      }
    }
    return this;
  }

  to1DArray() {
    let array = [];
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        array.push(this.get(i, j));
      }
    }
    return array;
  }

  to2DArray() {
    let copy = [];
    for (let i = 0; i < this.rows; i++) {
      copy.push([]);
      for (let j = 0; j < this.columns; j++) {
        copy[i].push(this.get(i, j));
      }
    }
    return copy;
  }

  toJSON() {
    return this.to2DArray();
  }

  isRowVector() {
    return this.rows === 1;
  }

  isColumnVector() {
    return this.columns === 1;
  }

  isVector() {
    return this.rows === 1 || this.columns === 1;
  }

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

  isEmpty() {
    return this.rows === 0 || this.columns === 0;
  }

  isSymmetric() {
    if (this.isSquare()) {
      for (let i = 0; i < this.rows; i++) {
        for (let j = 0; j <= i; j++) {
          if (this.get(i, j) !== this.get(j, i)) {
            return false;
          }
        }
      }
      return true;
    }
    return false;
  }

  isDistance() {
    if (!this.isSymmetric()) return false;

    for (let i = 0; i < this.rows; i++) {
      if (this.get(i, i) !== 0) return false;
    }

    return true;
  }

  isEchelonForm() {
    let i = 0;
    let j = 0;
    let previousColumn = -1;
    let isEchelonForm = true;
    let checked = false;
    while (i < this.rows && isEchelonForm) {
      j = 0;
      checked = false;
      while (j < this.columns && checked === false) {
        if (this.get(i, j) === 0) {
          j++;
        } else if (this.get(i, j) === 1 && j > previousColumn) {
          checked = true;
          previousColumn = j;
        } else {
          isEchelonForm = false;
          checked = true;
        }
      }
      i++;
    }
    return isEchelonForm;
  }

  isReducedEchelonForm() {
    let i = 0;
    let j = 0;
    let previousColumn = -1;
    let isReducedEchelonForm = true;
    let checked = false;
    while (i < this.rows && isReducedEchelonForm) {
      j = 0;
      checked = false;
      while (j < this.columns && checked === false) {
        if (this.get(i, j) === 0) {
          j++;
        } else if (this.get(i, j) === 1 && j > previousColumn) {
          checked = true;
          previousColumn = j;
        } else {
          isReducedEchelonForm = false;
          checked = true;
        }
      }
      for (let k = j + 1; k < this.rows; k++) {
        if (this.get(i, k) !== 0) {
          isReducedEchelonForm = false;
        }
      }
      i++;
    }
    return isReducedEchelonForm;
  }

  echelonForm() {
    let result = this.clone();
    let h = 0;
    let k = 0;
    while (h < result.rows && k < result.columns) {
      let iMax = h;
      for (let i = h; i < result.rows; i++) {
        if (result.get(i, k) > result.get(iMax, k)) {
          iMax = i;
        }
      }
      if (result.get(iMax, k) === 0) {
        k++;
      } else {
        result.swapRows(h, iMax);
        let tmp = result.get(h, k);
        for (let j = k; j < result.columns; j++) {
          result.set(h, j, result.get(h, j) / tmp);
        }
        for (let i = h + 1; i < result.rows; i++) {
          let factor = result.get(i, k) / result.get(h, k);
          result.set(i, k, 0);
          for (let j = k + 1; j < result.columns; j++) {
            result.set(i, j, result.get(i, j) - result.get(h, j) * factor);
          }
        }
        h++;
        k++;
      }
    }
    return result;
  }

  reducedEchelonForm() {
    let result = this.echelonForm();
    let m = result.columns;
    let n = result.rows;
    let h = n - 1;
    while (h >= 0) {
      if (result.maxRow(h) === 0) {
        h--;
      } else {
        let p = 0;
        let pivot = false;
        while (p < n && pivot === false) {
          if (result.get(h, p) === 1) {
            pivot = true;
          } else {
            p++;
          }
        }
        for (let i = 0; i < h; i++) {
          let factor = result.get(i, p);
          for (let j = p; j < m; j++) {
            let tmp = result.get(i, j) - factor * result.get(h, j);
            result.set(i, j, tmp);
          }
        }
        h--;
      }
    }
    return result;
  }

  set() {
    throw new Error('set method is unimplemented');
  }

  get() {
    throw new Error('get method is unimplemented');
  }

  repeat(options = {}) {
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { rows = 1, columns = 1 } = options;
    if (!Number.isInteger(rows) || rows <= 0) {
      throw new TypeError('rows must be a positive integer');
    }
    if (!Number.isInteger(columns) || columns <= 0) {
      throw new TypeError('columns must be a positive integer');
    }
    let matrix = new Matrix(this.rows * rows, this.columns * columns);
    for (let i = 0; i < rows; i++) {
      for (let j = 0; j < columns; j++) {
        matrix.setSubMatrix(this, this.rows * i, this.columns * j);
      }
    }
    return matrix;
  }

  fill(value) {
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, value);
      }
    }
    return this;
  }

  neg() {
    return this.mulS(-1);
  }

  getRow(index) {
    checkRowIndex(this, index);
    let row = [];
    for (let i = 0; i < this.columns; i++) {
      row.push(this.get(index, i));
    }
    return row;
  }

  getRowVector(index) {
    return Matrix.rowVector(this.getRow(index));
  }

  setRow(index, array) {
    checkRowIndex(this, index);
    array = checkRowVector(this, array);
    for (let i = 0; i < this.columns; i++) {
      this.set(index, i, array[i]);
    }
    return this;
  }

  swapRows(row1, row2) {
    checkRowIndex(this, row1);
    checkRowIndex(this, row2);
    for (let i = 0; i < this.columns; i++) {
      let temp = this.get(row1, i);
      this.set(row1, i, this.get(row2, i));
      this.set(row2, i, temp);
    }
    return this;
  }

  getColumn(index) {
    checkColumnIndex(this, index);
    let column = [];
    for (let i = 0; i < this.rows; i++) {
      column.push(this.get(i, index));
    }
    return column;
  }

  getColumnVector(index) {
    return Matrix.columnVector(this.getColumn(index));
  }

  setColumn(index, array) {
    checkColumnIndex(this, index);
    array = checkColumnVector(this, array);
    for (let i = 0; i < this.rows; i++) {
      this.set(i, index, array[i]);
    }
    return this;
  }

  swapColumns(column1, column2) {
    checkColumnIndex(this, column1);
    checkColumnIndex(this, column2);
    for (let i = 0; i < this.rows; i++) {
      let temp = this.get(i, column1);
      this.set(i, column1, this.get(i, column2));
      this.set(i, column2, temp);
    }
    return this;
  }

  addRowVector(vector) {
    vector = checkRowVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) + vector[j]);
      }
    }
    return this;
  }

  subRowVector(vector) {
    vector = checkRowVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) - vector[j]);
      }
    }
    return this;
  }

  mulRowVector(vector) {
    vector = checkRowVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) * vector[j]);
      }
    }
    return this;
  }

  divRowVector(vector) {
    vector = checkRowVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) / vector[j]);
      }
    }
    return this;
  }

  addColumnVector(vector) {
    vector = checkColumnVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) + vector[i]);
      }
    }
    return this;
  }

  subColumnVector(vector) {
    vector = checkColumnVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) - vector[i]);
      }
    }
    return this;
  }

  mulColumnVector(vector) {
    vector = checkColumnVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) * vector[i]);
      }
    }
    return this;
  }

  divColumnVector(vector) {
    vector = checkColumnVector(this, vector);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        this.set(i, j, this.get(i, j) / vector[i]);
      }
    }
    return this;
  }

  mulRow(index, value) {
    checkRowIndex(this, index);
    for (let i = 0; i < this.columns; i++) {
      this.set(index, i, this.get(index, i) * value);
    }
    return this;
  }

  mulColumn(index, value) {
    checkColumnIndex(this, index);
    for (let i = 0; i < this.rows; i++) {
      this.set(i, index, this.get(i, index) * value);
    }
    return this;
  }

  max(by) {
    if (this.isEmpty()) {
      return NaN;
    }
    switch (by) {
      case 'row': {
        const max = new Array(this.rows).fill(Number.NEGATIVE_INFINITY);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) > max[row]) {
              max[row] = this.get(row, column);
            }
          }
        }
        return max;
      }
      case 'column': {
        const max = new Array(this.columns).fill(Number.NEGATIVE_INFINITY);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) > max[column]) {
              max[column] = this.get(row, column);
            }
          }
        }
        return max;
      }
      case undefined: {
        let max = this.get(0, 0);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) > max) {
              max = this.get(row, column);
            }
          }
        }
        return max;
      }
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  maxIndex() {
    checkNonEmpty(this);
    let v = this.get(0, 0);
    let idx = [0, 0];
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        if (this.get(i, j) > v) {
          v = this.get(i, j);
          idx[0] = i;
          idx[1] = j;
        }
      }
    }
    return idx;
  }

  min(by) {
    if (this.isEmpty()) {
      return NaN;
    }

    switch (by) {
      case 'row': {
        const min = new Array(this.rows).fill(Number.POSITIVE_INFINITY);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) < min[row]) {
              min[row] = this.get(row, column);
            }
          }
        }
        return min;
      }
      case 'column': {
        const min = new Array(this.columns).fill(Number.POSITIVE_INFINITY);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) < min[column]) {
              min[column] = this.get(row, column);
            }
          }
        }
        return min;
      }
      case undefined: {
        let min = this.get(0, 0);
        for (let row = 0; row < this.rows; row++) {
          for (let column = 0; column < this.columns; column++) {
            if (this.get(row, column) < min) {
              min = this.get(row