{"version":3,"file":"ml-pls.js","sources":["../node_modules/is-any-array/lib-esm/index.js","../node_modules/ml-array-max/lib-es6/index.js","../node_modules/ml-array-min/lib-es6/index.js","../node_modules/ml-array-rescale/lib-es6/index.js","../node_modules/ml-matrix/src/inspect.js","../node_modules/ml-matrix/src/mathOperations.js","../node_modules/ml-matrix/src/util.js","../node_modules/ml-matrix/src/stat.js","../node_modules/ml-matrix/src/matrix.js","../node_modules/ml-matrix/src/wrap/WrapperMatrix2D.js","../node_modules/ml-matrix/src/dc/lu.js","../node_modules/ml-matrix/src/dc/util.js","../node_modules/ml-matrix/src/dc/qr.js","../node_modules/ml-matrix/src/dc/svd.js","../node_modules/ml-matrix/src/decompositions.js","../node_modules/ml-matrix/src/dc/nipals.js","../src/util/utils.js","../src/PLS.js","../src/KOPLS.js","../node_modules/ml-confusion-matrix/src/index.js","../node_modules/ml-cross-validation/src/getFolds.js","../node_modules/ml-array-sum/lib-es6/index.js","../node_modules/ml-array-mean/lib-es6/index.js","../node_modules/ml-roc-multiclass/lib-esm/getAuc.js","../node_modules/ml-roc-multiclass/lib-esm/utilities/getThresholds.js","../node_modules/ml-roc-multiclass/lib-esm/getBinaryClassifiers.js","../node_modules/ml-roc-multiclass/lib-esm/utilities/getClasses.js","../node_modules/ml-roc-multiclass/lib-esm/utilities/getClassesPairs.js","../node_modules/ml-roc-multiclass/lib-esm/utilities/getSelectedResults.js","../node_modules/ml-roc-multiclass/lib-esm/getRocCurve.js","../src/oplsNipals.js","../src/util/tss.js","../src/OPLS.js"],"sourcesContent":["const toString = Object.prototype.toString;\n/**\n * Checks if an object is an instance of an Array (array or typed array).\n *\n * @param {any} value - Object to check.\n * @returns {boolean} True if the object is an array.\n */\nexport function isAnyArray(value) {\n    return toString.call(value).endsWith('Array]');\n}\n//# sourceMappingURL=index.js.map","import { isAnyArray } from 'is-any-array';\n\nfunction max(input) {\n  var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n  if (!isAnyArray(input)) {\n    throw new TypeError('input must be an array');\n  }\n\n  if (input.length === 0) {\n    throw new TypeError('input must not be empty');\n  }\n\n  var _options$fromIndex = options.fromIndex,\n      fromIndex = _options$fromIndex === void 0 ? 0 : _options$fromIndex,\n      _options$toIndex = options.toIndex,\n      toIndex = _options$toIndex === void 0 ? input.length : _options$toIndex;\n\n  if (fromIndex < 0 || fromIndex >= input.length || !Number.isInteger(fromIndex)) {\n    throw new Error('fromIndex must be a positive integer smaller than length');\n  }\n\n  if (toIndex <= fromIndex || toIndex > input.length || !Number.isInteger(toIndex)) {\n    throw new Error('toIndex must be an integer greater than fromIndex and at most equal to length');\n  }\n\n  var maxValue = input[fromIndex];\n\n  for (var i = fromIndex + 1; i < toIndex; i++) {\n    if (input[i] > maxValue) maxValue = input[i];\n  }\n\n  return maxValue;\n}\n\nexport { max as default };\n","import { isAnyArray } from 'is-any-array';\n\nfunction min(input) {\n  var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n  if (!isAnyArray(input)) {\n    throw new TypeError('input must be an array');\n  }\n\n  if (input.length === 0) {\n    throw new TypeError('input must not be empty');\n  }\n\n  var _options$fromIndex = options.fromIndex,\n      fromIndex = _options$fromIndex === void 0 ? 0 : _options$fromIndex,\n      _options$toIndex = options.toIndex,\n      toIndex = _options$toIndex === void 0 ? input.length : _options$toIndex;\n\n  if (fromIndex < 0 || fromIndex >= input.length || !Number.isInteger(fromIndex)) {\n    throw new Error('fromIndex must be a positive integer smaller than length');\n  }\n\n  if (toIndex <= fromIndex || toIndex > input.length || !Number.isInteger(toIndex)) {\n    throw new Error('toIndex must be an integer greater than fromIndex and at most equal to length');\n  }\n\n  var minValue = input[fromIndex];\n\n  for (var i = fromIndex + 1; i < toIndex; i++) {\n    if (input[i] < minValue) minValue = input[i];\n  }\n\n  return minValue;\n}\n\nexport { min as default };\n","import { isAnyArray } from 'is-any-array';\nimport max from 'ml-array-max';\nimport min from 'ml-array-min';\n\nfunction rescale(input) {\n  var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n  if (!isAnyArray(input)) {\n    throw new TypeError('input must be an array');\n  } else if (input.length === 0) {\n    throw new TypeError('input must not be empty');\n  }\n\n  var output;\n\n  if (options.output !== undefined) {\n    if (!isAnyArray(options.output)) {\n      throw new TypeError('output option must be an array if specified');\n    }\n\n    output = options.output;\n  } else {\n    output = new Array(input.length);\n  }\n\n  var currentMin = min(input);\n  var currentMax = max(input);\n\n  if (currentMin === currentMax) {\n    throw new RangeError('minimum and maximum input values are equal. Cannot rescale a constant array');\n  }\n\n  var _options$min = options.min,\n      minValue = _options$min === void 0 ? options.autoMinMax ? currentMin : 0 : _options$min,\n      _options$max = options.max,\n      maxValue = _options$max === void 0 ? options.autoMinMax ? currentMax : 1 : _options$max;\n\n  if (minValue >= maxValue) {\n    throw new RangeError('min option must be smaller than max option');\n  }\n\n  var factor = (maxValue - minValue) / (currentMax - currentMin);\n\n  for (var i = 0; i < input.length; i++) {\n    output[i] = (input[i] - currentMin) * factor + minValue;\n  }\n\n  return output;\n}\n\nexport { rescale as default };\n","const indent = ' '.repeat(2);\nconst indentData = ' '.repeat(4);\n\nexport function inspectMatrix() {\n  return inspectMatrixWithOptions(this);\n}\n\nexport function inspectMatrixWithOptions(matrix, options = {}) {\n  const {\n    maxRows = 15,\n    maxColumns = 10,\n    maxNumSize = 8,\n    padMinus = 'auto',\n  } = options;\n  return `${matrix.constructor.name} {\n${indent}[\n${indentData}${inspectData(matrix, maxRows, maxColumns, maxNumSize, padMinus)}\n${indent}]\n${indent}rows: ${matrix.rows}\n${indent}columns: ${matrix.columns}\n}`;\n}\n\nfunction inspectData(matrix, maxRows, maxColumns, maxNumSize, padMinus) {\n  const { rows, columns } = matrix;\n  const maxI = Math.min(rows, maxRows);\n  const maxJ = Math.min(columns, maxColumns);\n  const result = [];\n\n  if (padMinus === 'auto') {\n    padMinus = false;\n    loop: for (let i = 0; i < maxI; i++) {\n      for (let j = 0; j < maxJ; j++) {\n        if (matrix.get(i, j) < 0) {\n          padMinus = true;\n          break loop;\n        }\n      }\n    }\n  }\n\n  for (let i = 0; i < maxI; i++) {\n    let line = [];\n    for (let j = 0; j < maxJ; j++) {\n      line.push(formatNumber(matrix.get(i, j), maxNumSize, padMinus));\n    }\n    result.push(`${line.join(' ')}`);\n  }\n  if (maxJ !== columns) {\n    result[result.length - 1] += ` ... ${columns - maxColumns} more columns`;\n  }\n  if (maxI !== rows) {\n    result.push(`... ${rows - maxRows} more rows`);\n  }\n  return result.join(`\\n${indentData}`);\n}\n\nfunction formatNumber(num, maxNumSize, padMinus) {\n  return (\n    num >= 0 && padMinus\n      ? ` ${formatNumber2(num, maxNumSize - 1)}`\n      : formatNumber2(num, maxNumSize)\n  ).padEnd(maxNumSize);\n}\n\nfunction formatNumber2(num, len) {\n  // small.length numbers should be as is\n  let str = num.toString();\n  if (str.length <= len) return str;\n\n  // (7)'0.00123' is better then (7)'1.23e-2'\n  // (8)'0.000123' is worse then (7)'1.23e-3',\n  let fix = num.toFixed(len);\n  if (fix.length > len) {\n    fix = num.toFixed(Math.max(0, len - (fix.length - len)));\n  }\n  if (\n    fix.length <= len &&\n    !fix.startsWith('0.000') &&\n    !fix.startsWith('-0.000')\n  ) {\n    return fix;\n  }\n\n  // well, if it's still too long the user should've used longer numbers\n  let exp = num.toExponential(len);\n  if (exp.length > len) {\n    exp = num.toExponential(Math.max(0, len - (exp.length - len)));\n  }\n  return exp.slice(0);\n}\n","export function installMathOperations(AbstractMatrix, Matrix) {\n  AbstractMatrix.prototype.add = function add(value) {\n    if (typeof value === 'number') return this.addS(value);\n    return this.addM(value);\n  };\n\n  AbstractMatrix.prototype.addS = function addS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) + value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.addM = function addM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) + matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.add = function add(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.add(value);\n  };\n\n  AbstractMatrix.prototype.sub = function sub(value) {\n    if (typeof value === 'number') return this.subS(value);\n    return this.subM(value);\n  };\n\n  AbstractMatrix.prototype.subS = function subS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) - value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.subM = function subM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) - matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.sub = function sub(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.sub(value);\n  };\n  AbstractMatrix.prototype.subtract = AbstractMatrix.prototype.sub;\n  AbstractMatrix.prototype.subtractS = AbstractMatrix.prototype.subS;\n  AbstractMatrix.prototype.subtractM = AbstractMatrix.prototype.subM;\n  AbstractMatrix.subtract = AbstractMatrix.sub;\n\n  AbstractMatrix.prototype.mul = function mul(value) {\n    if (typeof value === 'number') return this.mulS(value);\n    return this.mulM(value);\n  };\n\n  AbstractMatrix.prototype.mulS = function mulS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) * value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.mulM = function mulM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) * matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.mul = function mul(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.mul(value);\n  };\n  AbstractMatrix.prototype.multiply = AbstractMatrix.prototype.mul;\n  AbstractMatrix.prototype.multiplyS = AbstractMatrix.prototype.mulS;\n  AbstractMatrix.prototype.multiplyM = AbstractMatrix.prototype.mulM;\n  AbstractMatrix.multiply = AbstractMatrix.mul;\n\n  AbstractMatrix.prototype.div = function div(value) {\n    if (typeof value === 'number') return this.divS(value);\n    return this.divM(value);\n  };\n\n  AbstractMatrix.prototype.divS = function divS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) / value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.divM = function divM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) / matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.div = function div(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.div(value);\n  };\n  AbstractMatrix.prototype.divide = AbstractMatrix.prototype.div;\n  AbstractMatrix.prototype.divideS = AbstractMatrix.prototype.divS;\n  AbstractMatrix.prototype.divideM = AbstractMatrix.prototype.divM;\n  AbstractMatrix.divide = AbstractMatrix.div;\n\n  AbstractMatrix.prototype.mod = function mod(value) {\n    if (typeof value === 'number') return this.modS(value);\n    return this.modM(value);\n  };\n\n  AbstractMatrix.prototype.modS = function modS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) % value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.modM = function modM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) % matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.mod = function mod(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.mod(value);\n  };\n  AbstractMatrix.prototype.modulus = AbstractMatrix.prototype.mod;\n  AbstractMatrix.prototype.modulusS = AbstractMatrix.prototype.modS;\n  AbstractMatrix.prototype.modulusM = AbstractMatrix.prototype.modM;\n  AbstractMatrix.modulus = AbstractMatrix.mod;\n\n  AbstractMatrix.prototype.and = function and(value) {\n    if (typeof value === 'number') return this.andS(value);\n    return this.andM(value);\n  };\n\n  AbstractMatrix.prototype.andS = function andS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) & value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.andM = function andM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) & matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.and = function and(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.and(value);\n  };\n\n  AbstractMatrix.prototype.or = function or(value) {\n    if (typeof value === 'number') return this.orS(value);\n    return this.orM(value);\n  };\n\n  AbstractMatrix.prototype.orS = function orS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) | value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.orM = function orM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) | matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.or = function or(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.or(value);\n  };\n\n  AbstractMatrix.prototype.xor = function xor(value) {\n    if (typeof value === 'number') return this.xorS(value);\n    return this.xorM(value);\n  };\n\n  AbstractMatrix.prototype.xorS = function xorS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) ^ value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.xorM = function xorM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) ^ matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.xor = function xor(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.xor(value);\n  };\n\n  AbstractMatrix.prototype.leftShift = function leftShift(value) {\n    if (typeof value === 'number') return this.leftShiftS(value);\n    return this.leftShiftM(value);\n  };\n\n  AbstractMatrix.prototype.leftShiftS = function leftShiftS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) << value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.leftShiftM = function leftShiftM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) << matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.leftShift = function leftShift(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.leftShift(value);\n  };\n\n  AbstractMatrix.prototype.signPropagatingRightShift = function signPropagatingRightShift(value) {\n    if (typeof value === 'number') return this.signPropagatingRightShiftS(value);\n    return this.signPropagatingRightShiftM(value);\n  };\n\n  AbstractMatrix.prototype.signPropagatingRightShiftS = function signPropagatingRightShiftS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) >> value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.signPropagatingRightShiftM = function signPropagatingRightShiftM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) >> matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.signPropagatingRightShift = function signPropagatingRightShift(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.signPropagatingRightShift(value);\n  };\n\n  AbstractMatrix.prototype.rightShift = function rightShift(value) {\n    if (typeof value === 'number') return this.rightShiftS(value);\n    return this.rightShiftM(value);\n  };\n\n  AbstractMatrix.prototype.rightShiftS = function rightShiftS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) >>> value);\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.rightShiftM = function rightShiftM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) >>> matrix.get(i, j));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.rightShift = function rightShift(matrix, value) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.rightShift(value);\n  };\n  AbstractMatrix.prototype.zeroFillRightShift = AbstractMatrix.prototype.rightShift;\n  AbstractMatrix.prototype.zeroFillRightShiftS = AbstractMatrix.prototype.rightShiftS;\n  AbstractMatrix.prototype.zeroFillRightShiftM = AbstractMatrix.prototype.rightShiftM;\n  AbstractMatrix.zeroFillRightShift = AbstractMatrix.rightShift;\n\n  AbstractMatrix.prototype.not = function not() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, ~(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.not = function not(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.not();\n  };\n\n  AbstractMatrix.prototype.abs = function abs() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.abs(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.abs = function abs(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.abs();\n  };\n\n  AbstractMatrix.prototype.acos = function acos() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.acos(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.acos = function acos(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.acos();\n  };\n\n  AbstractMatrix.prototype.acosh = function acosh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.acosh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.acosh = function acosh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.acosh();\n  };\n\n  AbstractMatrix.prototype.asin = function asin() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.asin(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.asin = function asin(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.asin();\n  };\n\n  AbstractMatrix.prototype.asinh = function asinh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.asinh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.asinh = function asinh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.asinh();\n  };\n\n  AbstractMatrix.prototype.atan = function atan() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.atan(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.atan = function atan(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.atan();\n  };\n\n  AbstractMatrix.prototype.atanh = function atanh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.atanh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.atanh = function atanh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.atanh();\n  };\n\n  AbstractMatrix.prototype.cbrt = function cbrt() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.cbrt(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.cbrt = function cbrt(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.cbrt();\n  };\n\n  AbstractMatrix.prototype.ceil = function ceil() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.ceil(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.ceil = function ceil(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.ceil();\n  };\n\n  AbstractMatrix.prototype.clz32 = function clz32() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.clz32(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.clz32 = function clz32(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.clz32();\n  };\n\n  AbstractMatrix.prototype.cos = function cos() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.cos(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.cos = function cos(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.cos();\n  };\n\n  AbstractMatrix.prototype.cosh = function cosh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.cosh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.cosh = function cosh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.cosh();\n  };\n\n  AbstractMatrix.prototype.exp = function exp() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.exp(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.exp = function exp(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.exp();\n  };\n\n  AbstractMatrix.prototype.expm1 = function expm1() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.expm1(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.expm1 = function expm1(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.expm1();\n  };\n\n  AbstractMatrix.prototype.floor = function floor() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.floor(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.floor = function floor(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.floor();\n  };\n\n  AbstractMatrix.prototype.fround = function fround() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.fround(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.fround = function fround(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.fround();\n  };\n\n  AbstractMatrix.prototype.log = function log() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.log(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.log = function log(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.log();\n  };\n\n  AbstractMatrix.prototype.log1p = function log1p() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.log1p(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.log1p = function log1p(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.log1p();\n  };\n\n  AbstractMatrix.prototype.log10 = function log10() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.log10(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.log10 = function log10(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.log10();\n  };\n\n  AbstractMatrix.prototype.log2 = function log2() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.log2(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.log2 = function log2(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.log2();\n  };\n\n  AbstractMatrix.prototype.round = function round() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.round(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.round = function round(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.round();\n  };\n\n  AbstractMatrix.prototype.sign = function sign() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.sign(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.sign = function sign(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.sign();\n  };\n\n  AbstractMatrix.prototype.sin = function sin() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.sin(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.sin = function sin(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.sin();\n  };\n\n  AbstractMatrix.prototype.sinh = function sinh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.sinh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.sinh = function sinh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.sinh();\n  };\n\n  AbstractMatrix.prototype.sqrt = function sqrt() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.sqrt(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.sqrt = function sqrt(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.sqrt();\n  };\n\n  AbstractMatrix.prototype.tan = function tan() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.tan(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.tan = function tan(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.tan();\n  };\n\n  AbstractMatrix.prototype.tanh = function tanh() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.tanh(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.tanh = function tanh(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.tanh();\n  };\n\n  AbstractMatrix.prototype.trunc = function trunc() {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.trunc(this.get(i, j)));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.trunc = function trunc(matrix) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.trunc();\n  };\n\n  AbstractMatrix.pow = function pow(matrix, arg0) {\n    const newMatrix = new Matrix(matrix);\n    return newMatrix.pow(arg0);\n  };\n\n  AbstractMatrix.prototype.pow = function pow(value) {\n    if (typeof value === 'number') return this.powS(value);\n    return this.powM(value);\n  };\n\n  AbstractMatrix.prototype.powS = function powS(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.pow(this.get(i, j), value));\n      }\n    }\n    return this;\n  };\n\n  AbstractMatrix.prototype.powM = function powM(matrix) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (this.rows !== matrix.rows ||\n      this.columns !== matrix.columns) {\n      throw new RangeError('Matrices dimensions must be equal');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, Math.pow(this.get(i, j), matrix.get(i, j)));\n      }\n    }\n    return this;\n  };\n}\n","import { isAnyArray } from 'is-any-array';\n\n/**\n * @private\n * Check that a row index is not out of bounds\n * @param {Matrix} matrix\n * @param {number} index\n * @param {boolean} [outer]\n */\nexport function checkRowIndex(matrix, index, outer) {\n  let max = outer ? matrix.rows : matrix.rows - 1;\n  if (index < 0 || index > max) {\n    throw new RangeError('Row index out of range');\n  }\n}\n\n/**\n * @private\n * Check that a column index is not out of bounds\n * @param {Matrix} matrix\n * @param {number} index\n * @param {boolean} [outer]\n */\nexport function checkColumnIndex(matrix, index, outer) {\n  let max = outer ? matrix.columns : matrix.columns - 1;\n  if (index < 0 || index > max) {\n    throw new RangeError('Column index out of range');\n  }\n}\n\n/**\n * @private\n * Check that the provided vector is an array with the right length\n * @param {Matrix} matrix\n * @param {Array|Matrix} vector\n * @return {Array}\n * @throws {RangeError}\n */\nexport function checkRowVector(matrix, vector) {\n  if (vector.to1DArray) {\n    vector = vector.to1DArray();\n  }\n  if (vector.length !== matrix.columns) {\n    throw new RangeError(\n      'vector size must be the same as the number of columns',\n    );\n  }\n  return vector;\n}\n\n/**\n * @private\n * Check that the provided vector is an array with the right length\n * @param {Matrix} matrix\n * @param {Array|Matrix} vector\n * @return {Array}\n * @throws {RangeError}\n */\nexport function checkColumnVector(matrix, vector) {\n  if (vector.to1DArray) {\n    vector = vector.to1DArray();\n  }\n  if (vector.length !== matrix.rows) {\n    throw new RangeError('vector size must be the same as the number of rows');\n  }\n  return vector;\n}\n\nexport function checkRowIndices(matrix, rowIndices) {\n  if (!isAnyArray(rowIndices)) {\n    throw new TypeError('row indices must be an array');\n  }\n\n  for (let i = 0; i < rowIndices.length; i++) {\n    if (rowIndices[i] < 0 || rowIndices[i] >= matrix.rows) {\n      throw new RangeError('row indices are out of range');\n    }\n  }\n}\n\nexport function checkColumnIndices(matrix, columnIndices) {\n  if (!isAnyArray(columnIndices)) {\n    throw new TypeError('column indices must be an array');\n  }\n\n  for (let i = 0; i < columnIndices.length; i++) {\n    if (columnIndices[i] < 0 || columnIndices[i] >= matrix.columns) {\n      throw new RangeError('column indices are out of range');\n    }\n  }\n}\n\nexport function checkRange(matrix, startRow, endRow, startColumn, endColumn) {\n  if (arguments.length !== 5) {\n    throw new RangeError('expected 4 arguments');\n  }\n  checkNumber('startRow', startRow);\n  checkNumber('endRow', endRow);\n  checkNumber('startColumn', startColumn);\n  checkNumber('endColumn', endColumn);\n  if (\n    startRow > endRow ||\n    startColumn > endColumn ||\n    startRow < 0 ||\n    startRow >= matrix.rows ||\n    endRow < 0 ||\n    endRow >= matrix.rows ||\n    startColumn < 0 ||\n    startColumn >= matrix.columns ||\n    endColumn < 0 ||\n    endColumn >= matrix.columns\n  ) {\n    throw new RangeError('Submatrix indices are out of range');\n  }\n}\n\nexport function newArray(length, value = 0) {\n  let array = [];\n  for (let i = 0; i < length; i++) {\n    array.push(value);\n  }\n  return array;\n}\n\nfunction checkNumber(name, value) {\n  if (typeof value !== 'number') {\n    throw new TypeError(`${name} must be a number`);\n  }\n}\n\nexport function checkNonEmpty(matrix) {\n  if (matrix.isEmpty()) {\n    throw new Error('Empty matrix has no elements to index');\n  }\n}\n","import { newArray } from './util';\n\nexport function sumByRow(matrix) {\n  let sum = newArray(matrix.rows);\n  for (let i = 0; i < matrix.rows; ++i) {\n    for (let j = 0; j < matrix.columns; ++j) {\n      sum[i] += matrix.get(i, j);\n    }\n  }\n  return sum;\n}\n\nexport function sumByColumn(matrix) {\n  let sum = newArray(matrix.columns);\n  for (let i = 0; i < matrix.rows; ++i) {\n    for (let j = 0; j < matrix.columns; ++j) {\n      sum[j] += matrix.get(i, j);\n    }\n  }\n  return sum;\n}\n\nexport function sumAll(matrix) {\n  let v = 0;\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      v += matrix.get(i, j);\n    }\n  }\n  return v;\n}\n\nexport function productByRow(matrix) {\n  let sum = newArray(matrix.rows, 1);\n  for (let i = 0; i < matrix.rows; ++i) {\n    for (let j = 0; j < matrix.columns; ++j) {\n      sum[i] *= matrix.get(i, j);\n    }\n  }\n  return sum;\n}\n\nexport function productByColumn(matrix) {\n  let sum = newArray(matrix.columns, 1);\n  for (let i = 0; i < matrix.rows; ++i) {\n    for (let j = 0; j < matrix.columns; ++j) {\n      sum[j] *= matrix.get(i, j);\n    }\n  }\n  return sum;\n}\n\nexport function productAll(matrix) {\n  let v = 1;\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      v *= matrix.get(i, j);\n    }\n  }\n  return v;\n}\n\nexport function varianceByRow(matrix, unbiased, mean) {\n  const rows = matrix.rows;\n  const cols = matrix.columns;\n  const variance = [];\n\n  for (let i = 0; i < rows; i++) {\n    let sum1 = 0;\n    let sum2 = 0;\n    let x = 0;\n    for (let j = 0; j < cols; j++) {\n      x = matrix.get(i, j) - mean[i];\n      sum1 += x;\n      sum2 += x * x;\n    }\n    if (unbiased) {\n      variance.push((sum2 - (sum1 * sum1) / cols) / (cols - 1));\n    } else {\n      variance.push((sum2 - (sum1 * sum1) / cols) / cols);\n    }\n  }\n  return variance;\n}\n\nexport function varianceByColumn(matrix, unbiased, mean) {\n  const rows = matrix.rows;\n  const cols = matrix.columns;\n  const variance = [];\n\n  for (let j = 0; j < cols; j++) {\n    let sum1 = 0;\n    let sum2 = 0;\n    let x = 0;\n    for (let i = 0; i < rows; i++) {\n      x = matrix.get(i, j) - mean[j];\n      sum1 += x;\n      sum2 += x * x;\n    }\n    if (unbiased) {\n      variance.push((sum2 - (sum1 * sum1) / rows) / (rows - 1));\n    } else {\n      variance.push((sum2 - (sum1 * sum1) / rows) / rows);\n    }\n  }\n  return variance;\n}\n\nexport function varianceAll(matrix, unbiased, mean) {\n  const rows = matrix.rows;\n  const cols = matrix.columns;\n  const size = rows * cols;\n\n  let sum1 = 0;\n  let sum2 = 0;\n  let x = 0;\n  for (let i = 0; i < rows; i++) {\n    for (let j = 0; j < cols; j++) {\n      x = matrix.get(i, j) - mean;\n      sum1 += x;\n      sum2 += x * x;\n    }\n  }\n  if (unbiased) {\n    return (sum2 - (sum1 * sum1) / size) / (size - 1);\n  } else {\n    return (sum2 - (sum1 * sum1) / size) / size;\n  }\n}\n\nexport function centerByRow(matrix, mean) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) - mean[i]);\n    }\n  }\n}\n\nexport function centerByColumn(matrix, mean) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) - mean[j]);\n    }\n  }\n}\n\nexport function centerAll(matrix, mean) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) - mean);\n    }\n  }\n}\n\nexport function getScaleByRow(matrix) {\n  const scale = [];\n  for (let i = 0; i < matrix.rows; i++) {\n    let sum = 0;\n    for (let j = 0; j < matrix.columns; j++) {\n      sum += Math.pow(matrix.get(i, j), 2) / (matrix.columns - 1);\n    }\n    scale.push(Math.sqrt(sum));\n  }\n  return scale;\n}\n\nexport function scaleByRow(matrix, scale) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) / scale[i]);\n    }\n  }\n}\n\nexport function getScaleByColumn(matrix) {\n  const scale = [];\n  for (let j = 0; j < matrix.columns; j++) {\n    let sum = 0;\n    for (let i = 0; i < matrix.rows; i++) {\n      sum += Math.pow(matrix.get(i, j), 2) / (matrix.rows - 1);\n    }\n    scale.push(Math.sqrt(sum));\n  }\n  return scale;\n}\n\nexport function scaleByColumn(matrix, scale) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) / scale[j]);\n    }\n  }\n}\n\nexport function getScaleAll(matrix) {\n  const divider = matrix.size - 1;\n  let sum = 0;\n  for (let j = 0; j < matrix.columns; j++) {\n    for (let i = 0; i < matrix.rows; i++) {\n      sum += Math.pow(matrix.get(i, j), 2) / divider;\n    }\n  }\n  return Math.sqrt(sum);\n}\n\nexport function scaleAll(matrix, scale) {\n  for (let i = 0; i < matrix.rows; i++) {\n    for (let j = 0; j < matrix.columns; j++) {\n      matrix.set(i, j, matrix.get(i, j) / scale);\n    }\n  }\n}\n","import { isAnyArray } from 'is-any-array';\nimport rescale from 'ml-array-rescale';\n\nimport { inspectMatrix, inspectMatrixWithOptions } from './inspect';\nimport { installMathOperations } from './mathOperations';\nimport {\n  sumByRow,\n  sumByColumn,\n  sumAll,\n  productByRow,\n  productByColumn,\n  productAll,\n  varianceByRow,\n  varianceByColumn,\n  varianceAll,\n  centerByRow,\n  centerByColumn,\n  centerAll,\n  scaleByRow,\n  scaleByColumn,\n  scaleAll,\n  getScaleByRow,\n  getScaleByColumn,\n  getScaleAll,\n} from './stat';\nimport {\n  checkRowVector,\n  checkRowIndex,\n  checkColumnIndex,\n  checkColumnVector,\n  checkRange,\n  checkNonEmpty,\n  checkRowIndices,\n  checkColumnIndices,\n} from './util';\n\nexport class AbstractMatrix {\n  static from1DArray(newRows, newColumns, newData) {\n    let length = newRows * newColumns;\n    if (length !== newData.length) {\n      throw new RangeError('data length does not match given dimensions');\n    }\n    let newMatrix = new Matrix(newRows, newColumns);\n    for (let row = 0; row < newRows; row++) {\n      for (let column = 0; column < newColumns; column++) {\n        newMatrix.set(row, column, newData[row * newColumns + column]);\n      }\n    }\n    return newMatrix;\n  }\n\n  static rowVector(newData) {\n    let vector = new Matrix(1, newData.length);\n    for (let i = 0; i < newData.length; i++) {\n      vector.set(0, i, newData[i]);\n    }\n    return vector;\n  }\n\n  static columnVector(newData) {\n    let vector = new Matrix(newData.length, 1);\n    for (let i = 0; i < newData.length; i++) {\n      vector.set(i, 0, newData[i]);\n    }\n    return vector;\n  }\n\n  static zeros(rows, columns) {\n    return new Matrix(rows, columns);\n  }\n\n  static ones(rows, columns) {\n    return new Matrix(rows, columns).fill(1);\n  }\n\n  static rand(rows, columns, options = {}) {\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { random = Math.random } = options;\n    let matrix = new Matrix(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        matrix.set(i, j, random());\n      }\n    }\n    return matrix;\n  }\n\n  static randInt(rows, columns, options = {}) {\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { min = 0, max = 1000, random = Math.random } = options;\n    if (!Number.isInteger(min)) throw new TypeError('min must be an integer');\n    if (!Number.isInteger(max)) throw new TypeError('max must be an integer');\n    if (min >= max) throw new RangeError('min must be smaller than max');\n    let interval = max - min;\n    let matrix = new Matrix(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        let value = min + Math.round(random() * interval);\n        matrix.set(i, j, value);\n      }\n    }\n    return matrix;\n  }\n\n  static eye(rows, columns, value) {\n    if (columns === undefined) columns = rows;\n    if (value === undefined) value = 1;\n    let min = Math.min(rows, columns);\n    let matrix = this.zeros(rows, columns);\n    for (let i = 0; i < min; i++) {\n      matrix.set(i, i, value);\n    }\n    return matrix;\n  }\n\n  static diag(data, rows, columns) {\n    let l = data.length;\n    if (rows === undefined) rows = l;\n    if (columns === undefined) columns = rows;\n    let min = Math.min(l, rows, columns);\n    let matrix = this.zeros(rows, columns);\n    for (let i = 0; i < min; i++) {\n      matrix.set(i, i, data[i]);\n    }\n    return matrix;\n  }\n\n  static min(matrix1, matrix2) {\n    matrix1 = this.checkMatrix(matrix1);\n    matrix2 = this.checkMatrix(matrix2);\n    let rows = matrix1.rows;\n    let columns = matrix1.columns;\n    let result = new Matrix(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        result.set(i, j, Math.min(matrix1.get(i, j), matrix2.get(i, j)));\n      }\n    }\n    return result;\n  }\n\n  static max(matrix1, matrix2) {\n    matrix1 = this.checkMatrix(matrix1);\n    matrix2 = this.checkMatrix(matrix2);\n    let rows = matrix1.rows;\n    let columns = matrix1.columns;\n    let result = new this(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        result.set(i, j, Math.max(matrix1.get(i, j), matrix2.get(i, j)));\n      }\n    }\n    return result;\n  }\n\n  static checkMatrix(value) {\n    return AbstractMatrix.isMatrix(value) ? value : new Matrix(value);\n  }\n\n  static isMatrix(value) {\n    return value != null && value.klass === 'Matrix';\n  }\n\n  get size() {\n    return this.rows * this.columns;\n  }\n\n  apply(callback) {\n    if (typeof callback !== 'function') {\n      throw new TypeError('callback must be a function');\n    }\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        callback.call(this, i, j);\n      }\n    }\n    return this;\n  }\n\n  to1DArray() {\n    let array = [];\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        array.push(this.get(i, j));\n      }\n    }\n    return array;\n  }\n\n  to2DArray() {\n    let copy = [];\n    for (let i = 0; i < this.rows; i++) {\n      copy.push([]);\n      for (let j = 0; j < this.columns; j++) {\n        copy[i].push(this.get(i, j));\n      }\n    }\n    return copy;\n  }\n\n  toJSON() {\n    return this.to2DArray();\n  }\n\n  isRowVector() {\n    return this.rows === 1;\n  }\n\n  isColumnVector() {\n    return this.columns === 1;\n  }\n\n  isVector() {\n    return this.rows === 1 || this.columns === 1;\n  }\n\n  isSquare() {\n    return this.rows === this.columns;\n  }\n\n  isEmpty() {\n    return this.rows === 0 || this.columns === 0;\n  }\n\n  isSymmetric() {\n    if (this.isSquare()) {\n      for (let i = 0; i < this.rows; i++) {\n        for (let j = 0; j <= i; j++) {\n          if (this.get(i, j) !== this.get(j, i)) {\n            return false;\n          }\n        }\n      }\n      return true;\n    }\n    return false;\n  }\n\n  isEchelonForm() {\n    let i = 0;\n    let j = 0;\n    let previousColumn = -1;\n    let isEchelonForm = true;\n    let checked = false;\n    while (i < this.rows && isEchelonForm) {\n      j = 0;\n      checked = false;\n      while (j < this.columns && checked === false) {\n        if (this.get(i, j) === 0) {\n          j++;\n        } else if (this.get(i, j) === 1 && j > previousColumn) {\n          checked = true;\n          previousColumn = j;\n        } else {\n          isEchelonForm = false;\n          checked = true;\n        }\n      }\n      i++;\n    }\n    return isEchelonForm;\n  }\n\n  isReducedEchelonForm() {\n    let i = 0;\n    let j = 0;\n    let previousColumn = -1;\n    let isReducedEchelonForm = true;\n    let checked = false;\n    while (i < this.rows && isReducedEchelonForm) {\n      j = 0;\n      checked = false;\n      while (j < this.columns && checked === false) {\n        if (this.get(i, j) === 0) {\n          j++;\n        } else if (this.get(i, j) === 1 && j > previousColumn) {\n          checked = true;\n          previousColumn = j;\n        } else {\n          isReducedEchelonForm = false;\n          checked = true;\n        }\n      }\n      for (let k = j + 1; k < this.rows; k++) {\n        if (this.get(i, k) !== 0) {\n          isReducedEchelonForm = false;\n        }\n      }\n      i++;\n    }\n    return isReducedEchelonForm;\n  }\n\n  echelonForm() {\n    let result = this.clone();\n    let h = 0;\n    let k = 0;\n    while (h < result.rows && k < result.columns) {\n      let iMax = h;\n      for (let i = h; i < result.rows; i++) {\n        if (result.get(i, k) > result.get(iMax, k)) {\n          iMax = i;\n        }\n      }\n      if (result.get(iMax, k) === 0) {\n        k++;\n      } else {\n        result.swapRows(h, iMax);\n        let tmp = result.get(h, k);\n        for (let j = k; j < result.columns; j++) {\n          result.set(h, j, result.get(h, j) / tmp);\n        }\n        for (let i = h + 1; i < result.rows; i++) {\n          let factor = result.get(i, k) / result.get(h, k);\n          result.set(i, k, 0);\n          for (let j = k + 1; j < result.columns; j++) {\n            result.set(i, j, result.get(i, j) - result.get(h, j) * factor);\n          }\n        }\n        h++;\n        k++;\n      }\n    }\n    return result;\n  }\n\n  reducedEchelonForm() {\n    let result = this.echelonForm();\n    let m = result.columns;\n    let n = result.rows;\n    let h = n - 1;\n    while (h >= 0) {\n      if (result.maxRow(h) === 0) {\n        h--;\n      } else {\n        let p = 0;\n        let pivot = false;\n        while (p < n && pivot === false) {\n          if (result.get(h, p) === 1) {\n            pivot = true;\n          } else {\n            p++;\n          }\n        }\n        for (let i = 0; i < h; i++) {\n          let factor = result.get(i, p);\n          for (let j = p; j < m; j++) {\n            let tmp = result.get(i, j) - factor * result.get(h, j);\n            result.set(i, j, tmp);\n          }\n        }\n        h--;\n      }\n    }\n    return result;\n  }\n\n  set() {\n    throw new Error('set method is unimplemented');\n  }\n\n  get() {\n    throw new Error('get method is unimplemented');\n  }\n\n  repeat(options = {}) {\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { rows = 1, columns = 1 } = options;\n    if (!Number.isInteger(rows) || rows <= 0) {\n      throw new TypeError('rows must be a positive integer');\n    }\n    if (!Number.isInteger(columns) || columns <= 0) {\n      throw new TypeError('columns must be a positive integer');\n    }\n    let matrix = new Matrix(this.rows * rows, this.columns * columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        matrix.setSubMatrix(this, this.rows * i, this.columns * j);\n      }\n    }\n    return matrix;\n  }\n\n  fill(value) {\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, value);\n      }\n    }\n    return this;\n  }\n\n  neg() {\n    return this.mulS(-1);\n  }\n\n  getRow(index) {\n    checkRowIndex(this, index);\n    let row = [];\n    for (let i = 0; i < this.columns; i++) {\n      row.push(this.get(index, i));\n    }\n    return row;\n  }\n\n  getRowVector(index) {\n    return Matrix.rowVector(this.getRow(index));\n  }\n\n  setRow(index, array) {\n    checkRowIndex(this, index);\n    array = checkRowVector(this, array);\n    for (let i = 0; i < this.columns; i++) {\n      this.set(index, i, array[i]);\n    }\n    return this;\n  }\n\n  swapRows(row1, row2) {\n    checkRowIndex(this, row1);\n    checkRowIndex(this, row2);\n    for (let i = 0; i < this.columns; i++) {\n      let temp = this.get(row1, i);\n      this.set(row1, i, this.get(row2, i));\n      this.set(row2, i, temp);\n    }\n    return this;\n  }\n\n  getColumn(index) {\n    checkColumnIndex(this, index);\n    let column = [];\n    for (let i = 0; i < this.rows; i++) {\n      column.push(this.get(i, index));\n    }\n    return column;\n  }\n\n  getColumnVector(index) {\n    return Matrix.columnVector(this.getColumn(index));\n  }\n\n  setColumn(index, array) {\n    checkColumnIndex(this, index);\n    array = checkColumnVector(this, array);\n    for (let i = 0; i < this.rows; i++) {\n      this.set(i, index, array[i]);\n    }\n    return this;\n  }\n\n  swapColumns(column1, column2) {\n    checkColumnIndex(this, column1);\n    checkColumnIndex(this, column2);\n    for (let i = 0; i < this.rows; i++) {\n      let temp = this.get(i, column1);\n      this.set(i, column1, this.get(i, column2));\n      this.set(i, column2, temp);\n    }\n    return this;\n  }\n\n  addRowVector(vector) {\n    vector = checkRowVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) + vector[j]);\n      }\n    }\n    return this;\n  }\n\n  subRowVector(vector) {\n    vector = checkRowVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) - vector[j]);\n      }\n    }\n    return this;\n  }\n\n  mulRowVector(vector) {\n    vector = checkRowVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) * vector[j]);\n      }\n    }\n    return this;\n  }\n\n  divRowVector(vector) {\n    vector = checkRowVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) / vector[j]);\n      }\n    }\n    return this;\n  }\n\n  addColumnVector(vector) {\n    vector = checkColumnVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) + vector[i]);\n      }\n    }\n    return this;\n  }\n\n  subColumnVector(vector) {\n    vector = checkColumnVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) - vector[i]);\n      }\n    }\n    return this;\n  }\n\n  mulColumnVector(vector) {\n    vector = checkColumnVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) * vector[i]);\n      }\n    }\n    return this;\n  }\n\n  divColumnVector(vector) {\n    vector = checkColumnVector(this, vector);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        this.set(i, j, this.get(i, j) / vector[i]);\n      }\n    }\n    return this;\n  }\n\n  mulRow(index, value) {\n    checkRowIndex(this, index);\n    for (let i = 0; i < this.columns; i++) {\n      this.set(index, i, this.get(index, i) * value);\n    }\n    return this;\n  }\n\n  mulColumn(index, value) {\n    checkColumnIndex(this, index);\n    for (let i = 0; i < this.rows; i++) {\n      this.set(i, index, this.get(i, index) * value);\n    }\n    return this;\n  }\n\n  max(by) {\n    if (this.isEmpty()) {\n      return NaN;\n    }\n    switch (by) {\n      case 'row': {\n        const max = new Array(this.rows).fill(Number.NEGATIVE_INFINITY);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) > max[row]) {\n              max[row] = this.get(row, column);\n            }\n          }\n        }\n        return max;\n      }\n      case 'column': {\n        const max = new Array(this.columns).fill(Number.NEGATIVE_INFINITY);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) > max[column]) {\n              max[column] = this.get(row, column);\n            }\n          }\n        }\n        return max;\n      }\n      case undefined: {\n        let max = this.get(0, 0);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) > max) {\n              max = this.get(row, column);\n            }\n          }\n        }\n        return max;\n      }\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  maxIndex() {\n    checkNonEmpty(this);\n    let v = this.get(0, 0);\n    let idx = [0, 0];\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        if (this.get(i, j) > v) {\n          v = this.get(i, j);\n          idx[0] = i;\n          idx[1] = j;\n        }\n      }\n    }\n    return idx;\n  }\n\n  min(by) {\n    if (this.isEmpty()) {\n      return NaN;\n    }\n\n    switch (by) {\n      case 'row': {\n        const min = new Array(this.rows).fill(Number.POSITIVE_INFINITY);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) < min[row]) {\n              min[row] = this.get(row, column);\n            }\n          }\n        }\n        return min;\n      }\n      case 'column': {\n        const min = new Array(this.columns).fill(Number.POSITIVE_INFINITY);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) < min[column]) {\n              min[column] = this.get(row, column);\n            }\n          }\n        }\n        return min;\n      }\n      case undefined: {\n        let min = this.get(0, 0);\n        for (let row = 0; row < this.rows; row++) {\n          for (let column = 0; column < this.columns; column++) {\n            if (this.get(row, column) < min) {\n              min = this.get(row, column);\n            }\n          }\n        }\n        return min;\n      }\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  minIndex() {\n    checkNonEmpty(this);\n    let v = this.get(0, 0);\n    let idx = [0, 0];\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        if (this.get(i, j) < v) {\n          v = this.get(i, j);\n          idx[0] = i;\n          idx[1] = j;\n        }\n      }\n    }\n    return idx;\n  }\n\n  maxRow(row) {\n    checkRowIndex(this, row);\n    if (this.isEmpty()) {\n      return NaN;\n    }\n    let v = this.get(row, 0);\n    for (let i = 1; i < this.columns; i++) {\n      if (this.get(row, i) > v) {\n        v = this.get(row, i);\n      }\n    }\n    return v;\n  }\n\n  maxRowIndex(row) {\n    checkRowIndex(this, row);\n    checkNonEmpty(this);\n    let v = this.get(row, 0);\n    let idx = [row, 0];\n    for (let i = 1; i < this.columns; i++) {\n      if (this.get(row, i) > v) {\n        v = this.get(row, i);\n        idx[1] = i;\n      }\n    }\n    return idx;\n  }\n\n  minRow(row) {\n    checkRowIndex(this, row);\n    if (this.isEmpty()) {\n      return NaN;\n    }\n    let v = this.get(row, 0);\n    for (let i = 1; i < this.columns; i++) {\n      if (this.get(row, i) < v) {\n        v = this.get(row, i);\n      }\n    }\n    return v;\n  }\n\n  minRowIndex(row) {\n    checkRowIndex(this, row);\n    checkNonEmpty(this);\n    let v = this.get(row, 0);\n    let idx = [row, 0];\n    for (let i = 1; i < this.columns; i++) {\n      if (this.get(row, i) < v) {\n        v = this.get(row, i);\n        idx[1] = i;\n      }\n    }\n    return idx;\n  }\n\n  maxColumn(column) {\n    checkColumnIndex(this, column);\n    if (this.isEmpty()) {\n      return NaN;\n    }\n    let v = this.get(0, column);\n    for (let i = 1; i < this.rows; i++) {\n      if (this.get(i, column) > v) {\n        v = this.get(i, column);\n      }\n    }\n    return v;\n  }\n\n  maxColumnIndex(column) {\n    checkColumnIndex(this, column);\n    checkNonEmpty(this);\n    let v = this.get(0, column);\n    let idx = [0, column];\n    for (let i = 1; i < this.rows; i++) {\n      if (this.get(i, column) > v) {\n        v = this.get(i, column);\n        idx[0] = i;\n      }\n    }\n    return idx;\n  }\n\n  minColumn(column) {\n    checkColumnIndex(this, column);\n    if (this.isEmpty()) {\n      return NaN;\n    }\n    let v = this.get(0, column);\n    for (let i = 1; i < this.rows; i++) {\n      if (this.get(i, column) < v) {\n        v = this.get(i, column);\n      }\n    }\n    return v;\n  }\n\n  minColumnIndex(column) {\n    checkColumnIndex(this, column);\n    checkNonEmpty(this);\n    let v = this.get(0, column);\n    let idx = [0, column];\n    for (let i = 1; i < this.rows; i++) {\n      if (this.get(i, column) < v) {\n        v = this.get(i, column);\n        idx[0] = i;\n      }\n    }\n    return idx;\n  }\n\n  diag() {\n    let min = Math.min(this.rows, this.columns);\n    let diag = [];\n    for (let i = 0; i < min; i++) {\n      diag.push(this.get(i, i));\n    }\n    return diag;\n  }\n\n  norm(type = 'frobenius') {\n    let result = 0;\n    if (type === 'max') {\n      return this.max();\n    } else if (type === 'frobenius') {\n      for (let i = 0; i < this.rows; i++) {\n        for (let j = 0; j < this.columns; j++) {\n          result = result + this.get(i, j) * this.get(i, j);\n        }\n      }\n      return Math.sqrt(result);\n    } else {\n      throw new RangeError(`unknown norm type: ${type}`);\n    }\n  }\n\n  cumulativeSum() {\n    let sum = 0;\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        sum += this.get(i, j);\n        this.set(i, j, sum);\n      }\n    }\n    return this;\n  }\n\n  dot(vector2) {\n    if (AbstractMatrix.isMatrix(vector2)) vector2 = vector2.to1DArray();\n    let vector1 = this.to1DArray();\n    if (vector1.length !== vector2.length) {\n      throw new RangeError('vectors do not have the same size');\n    }\n    let dot = 0;\n    for (let i = 0; i < vector1.length; i++) {\n      dot += vector1[i] * vector2[i];\n    }\n    return dot;\n  }\n\n  mmul(other) {\n    other = Matrix.checkMatrix(other);\n\n    let m = this.rows;\n    let n = this.columns;\n    let p = other.columns;\n\n    let result = new Matrix(m, p);\n\n    let Bcolj = new Float64Array(n);\n    for (let j = 0; j < p; j++) {\n      for (let k = 0; k < n; k++) {\n        Bcolj[k] = other.get(k, j);\n      }\n\n      for (let i = 0; i < m; i++) {\n        let s = 0;\n        for (let k = 0; k < n; k++) {\n          s += this.get(i, k) * Bcolj[k];\n        }\n\n        result.set(i, j, s);\n      }\n    }\n    return result;\n  }\n\n  strassen2x2(other) {\n    other = Matrix.checkMatrix(other);\n    let result = new Matrix(2, 2);\n    const a11 = this.get(0, 0);\n    const b11 = other.get(0, 0);\n    const a12 = this.get(0, 1);\n    const b12 = other.get(0, 1);\n    const a21 = this.get(1, 0);\n    const b21 = other.get(1, 0);\n    const a22 = this.get(1, 1);\n    const b22 = other.get(1, 1);\n\n    // Compute intermediate values.\n    const m1 = (a11 + a22) * (b11 + b22);\n    const m2 = (a21 + a22) * b11;\n    const m3 = a11 * (b12 - b22);\n    const m4 = a22 * (b21 - b11);\n    const m5 = (a11 + a12) * b22;\n    const m6 = (a21 - a11) * (b11 + b12);\n    const m7 = (a12 - a22) * (b21 + b22);\n\n    // Combine intermediate values into the output.\n    const c00 = m1 + m4 - m5 + m7;\n    const c01 = m3 + m5;\n    const c10 = m2 + m4;\n    const c11 = m1 - m2 + m3 + m6;\n\n    result.set(0, 0, c00);\n    result.set(0, 1, c01);\n    result.set(1, 0, c10);\n    result.set(1, 1, c11);\n    return result;\n  }\n\n  strassen3x3(other) {\n    other = Matrix.checkMatrix(other);\n    let result = new Matrix(3, 3);\n\n    const a00 = this.get(0, 0);\n    const a01 = this.get(0, 1);\n    const a02 = this.get(0, 2);\n    const a10 = this.get(1, 0);\n    const a11 = this.get(1, 1);\n    const a12 = this.get(1, 2);\n    const a20 = this.get(2, 0);\n    const a21 = this.get(2, 1);\n    const a22 = this.get(2, 2);\n\n    const b00 = other.get(0, 0);\n    const b01 = other.get(0, 1);\n    const b02 = other.get(0, 2);\n    const b10 = other.get(1, 0);\n    const b11 = other.get(1, 1);\n    const b12 = other.get(1, 2);\n    const b20 = other.get(2, 0);\n    const b21 = other.get(2, 1);\n    const b22 = other.get(2, 2);\n\n    const m1 = (a00 + a01 + a02 - a10 - a11 - a21 - a22) * b11;\n    const m2 = (a00 - a10) * (-b01 + b11);\n    const m3 = a11 * (-b00 + b01 + b10 - b11 - b12 - b20 + b22);\n    const m4 = (-a00 + a10 + a11) * (b00 - b01 + b11);\n    const m5 = (a10 + a11) * (-b00 + b01);\n    const m6 = a00 * b00;\n    const m7 = (-a00 + a20 + a21) * (b00 - b02 + b12);\n    const m8 = (-a00 + a20) * (b02 - b12);\n    const m9 = (a20 + a21) * (-b00 + b02);\n    const m10 = (a00 + a01 + a02 - a11 - a12 - a20 - a21) * b12;\n    const m11 = a21 * (-b00 + b02 + b10 - b11 - b12 - b20 + b21);\n    const m12 = (-a02 + a21 + a22) * (b11 + b20 - b21);\n    const m13 = (a02 - a22) * (b11 - b21);\n    const m14 = a02 * b20;\n    const m15 = (a21 + a22) * (-b20 + b21);\n    const m16 = (-a02 + a11 + a12) * (b12 + b20 - b22);\n    const m17 = (a02 - a12) * (b12 - b22);\n    const m18 = (a11 + a12) * (-b20 + b22);\n    const m19 = a01 * b10;\n    const m20 = a12 * b21;\n    const m21 = a10 * b02;\n    const m22 = a20 * b01;\n    const m23 = a22 * b22;\n\n    const c00 = m6 + m14 + m19;\n    const c01 = m1 + m4 + m5 + m6 + m12 + m14 + m15;\n    const c02 = m6 + m7 + m9 + m10 + m14 + m16 + m18;\n    const c10 = m2 + m3 + m4 + m6 + m14 + m16 + m17;\n    const c11 = m2 + m4 + m5 + m6 + m20;\n    const c12 = m14 + m16 + m17 + m18 + m21;\n    const c20 = m6 + m7 + m8 + m11 + m12 + m13 + m14;\n    const c21 = m12 + m13 + m14 + m15 + m22;\n    const c22 = m6 + m7 + m8 + m9 + m23;\n\n    result.set(0, 0, c00);\n    result.set(0, 1, c01);\n    result.set(0, 2, c02);\n    result.set(1, 0, c10);\n    result.set(1, 1, c11);\n    result.set(1, 2, c12);\n    result.set(2, 0, c20);\n    result.set(2, 1, c21);\n    result.set(2, 2, c22);\n    return result;\n  }\n\n  mmulStrassen(y) {\n    y = Matrix.checkMatrix(y);\n    let x = this.clone();\n    let r1 = x.rows;\n    let c1 = x.columns;\n    let r2 = y.rows;\n    let c2 = y.columns;\n    if (c1 !== r2) {\n      // eslint-disable-next-line no-console\n      console.warn(\n        `Multiplying ${r1} x ${c1} and ${r2} x ${c2} matrix: dimensions do not match.`,\n      );\n    }\n\n    // Put a matrix into the top left of a matrix of zeros.\n    // `rows` and `cols` are the dimensions of the output matrix.\n    function embed(mat, rows, cols) {\n      let r = mat.rows;\n      let c = mat.columns;\n      if (r === rows && c === cols) {\n        return mat;\n      } else {\n        let resultat = AbstractMatrix.zeros(rows, cols);\n        resultat = resultat.setSubMatrix(mat, 0, 0);\n        return resultat;\n      }\n    }\n\n    // Make sure both matrices are the same size.\n    // This is exclusively for simplicity:\n    // this algorithm can be implemented with matrices of different sizes.\n\n    let r = Math.max(r1, r2);\n    let c = Math.max(c1, c2);\n    x = embed(x, r, c);\n    y = embed(y, r, c);\n\n    // Our recursive multiplication function.\n    function blockMult(a, b, rows, cols) {\n      // For small matrices, resort to naive multiplication.\n      if (rows <= 512 || cols <= 512) {\n        return a.mmul(b); // a is equivalent to this\n      }\n\n      // Apply dynamic padding.\n      if (rows % 2 === 1 && cols % 2 === 1) {\n        a = embed(a, rows + 1, cols + 1);\n        b = embed(b, rows + 1, cols + 1);\n      } else if (rows % 2 === 1) {\n        a = embed(a, rows + 1, cols);\n        b = embed(b, rows + 1, cols);\n      } else if (cols % 2 === 1) {\n        a = embed(a, rows, cols + 1);\n        b = embed(b, rows, cols + 1);\n      }\n\n      let halfRows = parseInt(a.rows / 2, 10);\n      let halfCols = parseInt(a.columns / 2, 10);\n      // Subdivide input matrices.\n      let a11 = a.subMatrix(0, halfRows - 1, 0, halfCols - 1);\n      let b11 = b.subMatrix(0, halfRows - 1, 0, halfCols - 1);\n\n      let a12 = a.subMatrix(0, halfRows - 1, halfCols, a.columns - 1);\n      let b12 = b.subMatrix(0, halfRows - 1, halfCols, b.columns - 1);\n\n      let a21 = a.subMatrix(halfRows, a.rows - 1, 0, halfCols - 1);\n      let b21 = b.subMatrix(halfRows, b.rows - 1, 0, halfCols - 1);\n\n      let a22 = a.subMatrix(halfRows, a.rows - 1, halfCols, a.columns - 1);\n      let b22 = b.subMatrix(halfRows, b.rows - 1, halfCols, b.columns - 1);\n\n      // Compute intermediate values.\n      let m1 = blockMult(\n        AbstractMatrix.add(a11, a22),\n        AbstractMatrix.add(b11, b22),\n        halfRows,\n        halfCols,\n      );\n      let m2 = blockMult(AbstractMatrix.add(a21, a22), b11, halfRows, halfCols);\n      let m3 = blockMult(a11, AbstractMatrix.sub(b12, b22), halfRows, halfCols);\n      let m4 = blockMult(a22, AbstractMatrix.sub(b21, b11), halfRows, halfCols);\n      let m5 = blockMult(AbstractMatrix.add(a11, a12), b22, halfRows, halfCols);\n      let m6 = blockMult(\n        AbstractMatrix.sub(a21, a11),\n        AbstractMatrix.add(b11, b12),\n        halfRows,\n        halfCols,\n      );\n      let m7 = blockMult(\n        AbstractMatrix.sub(a12, a22),\n        AbstractMatrix.add(b21, b22),\n        halfRows,\n        halfCols,\n      );\n\n      // Combine intermediate values into the output.\n      let c11 = AbstractMatrix.add(m1, m4);\n      c11.sub(m5);\n      c11.add(m7);\n      let c12 = AbstractMatrix.add(m3, m5);\n      let c21 = AbstractMatrix.add(m2, m4);\n      let c22 = AbstractMatrix.sub(m1, m2);\n      c22.add(m3);\n      c22.add(m6);\n\n      // Crop output to the desired size (undo dynamic padding).\n      let resultat = AbstractMatrix.zeros(2 * c11.rows, 2 * c11.columns);\n      resultat = resultat.setSubMatrix(c11, 0, 0);\n      resultat = resultat.setSubMatrix(c12, c11.rows, 0);\n      resultat = resultat.setSubMatrix(c21, 0, c11.columns);\n      resultat = resultat.setSubMatrix(c22, c11.rows, c11.columns);\n      return resultat.subMatrix(0, rows - 1, 0, cols - 1);\n    }\n\n    return blockMult(x, y, r, c);\n  }\n\n  scaleRows(options = {}) {\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { min = 0, max = 1 } = options;\n    if (!Number.isFinite(min)) throw new TypeError('min must be a number');\n    if (!Number.isFinite(max)) throw new TypeError('max must be a number');\n    if (min >= max) throw new RangeError('min must be smaller than max');\n    let newMatrix = new Matrix(this.rows, this.columns);\n    for (let i = 0; i < this.rows; i++) {\n      const row = this.getRow(i);\n      if (row.length > 0) {\n        rescale(row, { min, max, output: row });\n      }\n      newMatrix.setRow(i, row);\n    }\n    return newMatrix;\n  }\n\n  scaleColumns(options = {}) {\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { min = 0, max = 1 } = options;\n    if (!Number.isFinite(min)) throw new TypeError('min must be a number');\n    if (!Number.isFinite(max)) throw new TypeError('max must be a number');\n    if (min >= max) throw new RangeError('min must be smaller than max');\n    let newMatrix = new Matrix(this.rows, this.columns);\n    for (let i = 0; i < this.columns; i++) {\n      const column = this.getColumn(i);\n      if (column.length) {\n        rescale(column, {\n          min: min,\n          max: max,\n          output: column,\n        });\n      }\n      newMatrix.setColumn(i, column);\n    }\n    return newMatrix;\n  }\n\n  flipRows() {\n    const middle = Math.ceil(this.columns / 2);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < middle; j++) {\n        let first = this.get(i, j);\n        let last = this.get(i, this.columns - 1 - j);\n        this.set(i, j, last);\n        this.set(i, this.columns - 1 - j, first);\n      }\n    }\n    return this;\n  }\n\n  flipColumns() {\n    const middle = Math.ceil(this.rows / 2);\n    for (let j = 0; j < this.columns; j++) {\n      for (let i = 0; i < middle; i++) {\n        let first = this.get(i, j);\n        let last = this.get(this.rows - 1 - i, j);\n        this.set(i, j, last);\n        this.set(this.rows - 1 - i, j, first);\n      }\n    }\n    return this;\n  }\n\n  kroneckerProduct(other) {\n    other = Matrix.checkMatrix(other);\n\n    let m = this.rows;\n    let n = this.columns;\n    let p = other.rows;\n    let q = other.columns;\n\n    let result = new Matrix(m * p, n * q);\n    for (let i = 0; i < m; i++) {\n      for (let j = 0; j < n; j++) {\n        for (let k = 0; k < p; k++) {\n          for (let l = 0; l < q; l++) {\n            result.set(p * i + k, q * j + l, this.get(i, j) * other.get(k, l));\n          }\n        }\n      }\n    }\n    return result;\n  }\n\n  kroneckerSum(other) {\n    other = Matrix.checkMatrix(other);\n    if (!this.isSquare() || !other.isSquare()) {\n      throw new Error('Kronecker Sum needs two Square Matrices');\n    }\n    let m = this.rows;\n    let n = other.rows;\n    let AxI = this.kroneckerProduct(Matrix.eye(n, n));\n    let IxB = Matrix.eye(m, m).kroneckerProduct(other);\n    return AxI.add(IxB);\n  }\n\n  transpose() {\n    let result = new Matrix(this.columns, this.rows);\n    for (let i = 0; i < this.rows; i++) {\n      for (let j = 0; j < this.columns; j++) {\n        result.set(j, i, this.get(i, j));\n      }\n    }\n    return result;\n  }\n\n  sortRows(compareFunction = compareNumbers) {\n    for (let i = 0; i < this.rows; i++) {\n      this.setRow(i, this.getRow(i).sort(compareFunction));\n    }\n    return this;\n  }\n\n  sortColumns(compareFunction = compareNumbers) {\n    for (let i = 0; i < this.columns; i++) {\n      this.setColumn(i, this.getColumn(i).sort(compareFunction));\n    }\n    return this;\n  }\n\n  subMatrix(startRow, endRow, startColumn, endColumn) {\n    checkRange(this, startRow, endRow, startColumn, endColumn);\n    let newMatrix = new Matrix(\n      endRow - startRow + 1,\n      endColumn - startColumn + 1,\n    );\n    for (let i = startRow; i <= endRow; i++) {\n      for (let j = startColumn; j <= endColumn; j++) {\n        newMatrix.set(i - startRow, j - startColumn, this.get(i, j));\n      }\n    }\n    return newMatrix;\n  }\n\n  subMatrixRow(indices, startColumn, endColumn) {\n    if (startColumn === undefined) startColumn = 0;\n    if (endColumn === undefined) endColumn = this.columns - 1;\n    if (\n      startColumn > endColumn ||\n      startColumn < 0 ||\n      startColumn >= this.columns ||\n      endColumn < 0 ||\n      endColumn >= this.columns\n    ) {\n      throw new RangeError('Argument out of range');\n    }\n\n    let newMatrix = new Matrix(indices.length, endColumn - startColumn + 1);\n    for (let i = 0; i < indices.length; i++) {\n      for (let j = startColumn; j <= endColumn; j++) {\n        if (indices[i] < 0 || indices[i] >= this.rows) {\n          throw new RangeError(`Row index out of range: ${indices[i]}`);\n        }\n        newMatrix.set(i, j - startColumn, this.get(indices[i], j));\n      }\n    }\n    return newMatrix;\n  }\n\n  subMatrixColumn(indices, startRow, endRow) {\n    if (startRow === undefined) startRow = 0;\n    if (endRow === undefined) endRow = this.rows - 1;\n    if (\n      startRow > endRow ||\n      startRow < 0 ||\n      startRow >= this.rows ||\n      endRow < 0 ||\n      endRow >= this.rows\n    ) {\n      throw new RangeError('Argument out of range');\n    }\n\n    let newMatrix = new Matrix(endRow - startRow + 1, indices.length);\n    for (let i = 0; i < indices.length; i++) {\n      for (let j = startRow; j <= endRow; j++) {\n        if (indices[i] < 0 || indices[i] >= this.columns) {\n          throw new RangeError(`Column index out of range: ${indices[i]}`);\n        }\n        newMatrix.set(j - startRow, i, this.get(j, indices[i]));\n      }\n    }\n    return newMatrix;\n  }\n\n  setSubMatrix(matrix, startRow, startColumn) {\n    matrix = Matrix.checkMatrix(matrix);\n    if (matrix.isEmpty()) {\n      return this;\n    }\n    let endRow = startRow + matrix.rows - 1;\n    let endColumn = startColumn + matrix.columns - 1;\n    checkRange(this, startRow, endRow, startColumn, endColumn);\n    for (let i = 0; i < matrix.rows; i++) {\n      for (let j = 0; j < matrix.columns; j++) {\n        this.set(startRow + i, startColumn + j, matrix.get(i, j));\n      }\n    }\n    return this;\n  }\n\n  selection(rowIndices, columnIndices) {\n    checkRowIndices(this, rowIndices);\n    checkColumnIndices(this, columnIndices);\n    let newMatrix = new Matrix(rowIndices.length, columnIndices.length);\n    for (let i = 0; i < rowIndices.length; i++) {\n      let rowIndex = rowIndices[i];\n      for (let j = 0; j < columnIndices.length; j++) {\n        let columnIndex = columnIndices[j];\n        newMatrix.set(i, j, this.get(rowIndex, columnIndex));\n      }\n    }\n    return newMatrix;\n  }\n\n  trace() {\n    let min = Math.min(this.rows, this.columns);\n    let trace = 0;\n    for (let i = 0; i < min; i++) {\n      trace += this.get(i, i);\n    }\n    return trace;\n  }\n\n  clone() {\n    let newMatrix = new Matrix(this.rows, this.columns);\n    for (let row = 0; row < this.rows; row++) {\n      for (let column = 0; column < this.columns; column++) {\n        newMatrix.set(row, column, this.get(row, column));\n      }\n    }\n    return newMatrix;\n  }\n\n  sum(by) {\n    switch (by) {\n      case 'row':\n        return sumByRow(this);\n      case 'column':\n        return sumByColumn(this);\n      case undefined:\n        return sumAll(this);\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  product(by) {\n    switch (by) {\n      case 'row':\n        return productByRow(this);\n      case 'column':\n        return productByColumn(this);\n      case undefined:\n        return productAll(this);\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  mean(by) {\n    const sum = this.sum(by);\n    switch (by) {\n      case 'row': {\n        for (let i = 0; i < this.rows; i++) {\n          sum[i] /= this.columns;\n        }\n        return sum;\n      }\n      case 'column': {\n        for (let i = 0; i < this.columns; i++) {\n          sum[i] /= this.rows;\n        }\n        return sum;\n      }\n      case undefined:\n        return sum / this.size;\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  variance(by, options = {}) {\n    if (typeof by === 'object') {\n      options = by;\n      by = undefined;\n    }\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { unbiased = true, mean = this.mean(by) } = options;\n    if (typeof unbiased !== 'boolean') {\n      throw new TypeError('unbiased must be a boolean');\n    }\n    switch (by) {\n      case 'row': {\n        if (!isAnyArray(mean)) {\n          throw new TypeError('mean must be an array');\n        }\n        return varianceByRow(this, unbiased, mean);\n      }\n      case 'column': {\n        if (!isAnyArray(mean)) {\n          throw new TypeError('mean must be an array');\n        }\n        return varianceByColumn(this, unbiased, mean);\n      }\n      case undefined: {\n        if (typeof mean !== 'number') {\n          throw new TypeError('mean must be a number');\n        }\n        return varianceAll(this, unbiased, mean);\n      }\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  standardDeviation(by, options) {\n    if (typeof by === 'object') {\n      options = by;\n      by = undefined;\n    }\n    const variance = this.variance(by, options);\n    if (by === undefined) {\n      return Math.sqrt(variance);\n    } else {\n      for (let i = 0; i < variance.length; i++) {\n        variance[i] = Math.sqrt(variance[i]);\n      }\n      return variance;\n    }\n  }\n\n  center(by, options = {}) {\n    if (typeof by === 'object') {\n      options = by;\n      by = undefined;\n    }\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    const { center = this.mean(by) } = options;\n    switch (by) {\n      case 'row': {\n        if (!isAnyArray(center)) {\n          throw new TypeError('center must be an array');\n        }\n        centerByRow(this, center);\n        return this;\n      }\n      case 'column': {\n        if (!isAnyArray(center)) {\n          throw new TypeError('center must be an array');\n        }\n        centerByColumn(this, center);\n        return this;\n      }\n      case undefined: {\n        if (typeof center !== 'number') {\n          throw new TypeError('center must be a number');\n        }\n        centerAll(this, center);\n        return this;\n      }\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  scale(by, options = {}) {\n    if (typeof by === 'object') {\n      options = by;\n      by = undefined;\n    }\n    if (typeof options !== 'object') {\n      throw new TypeError('options must be an object');\n    }\n    let scale = options.scale;\n    switch (by) {\n      case 'row': {\n        if (scale === undefined) {\n          scale = getScaleByRow(this);\n        } else if (!isAnyArray(scale)) {\n          throw new TypeError('scale must be an array');\n        }\n        scaleByRow(this, scale);\n        return this;\n      }\n      case 'column': {\n        if (scale === undefined) {\n          scale = getScaleByColumn(this);\n        } else if (!isAnyArray(scale)) {\n          throw new TypeError('scale must be an array');\n        }\n        scaleByColumn(this, scale);\n        return this;\n      }\n      case undefined: {\n        if (scale === undefined) {\n          scale = getScaleAll(this);\n        } else if (typeof scale !== 'number') {\n          throw new TypeError('scale must be a number');\n        }\n        scaleAll(this, scale);\n        return this;\n      }\n      default:\n        throw new Error(`invalid option: ${by}`);\n    }\n  }\n\n  toString(options) {\n    return inspectMatrixWithOptions(this, options);\n  }\n}\n\nAbstractMatrix.prototype.klass = 'Matrix';\nif (typeof Symbol !== 'undefined') {\n  AbstractMatrix.prototype[Symbol.for('nodejs.util.inspect.custom')] =\n    inspectMatrix;\n}\n\nfunction compareNumbers(a, b) {\n  return a - b;\n}\n\nfunction isArrayOfNumbers(array) {\n  return array.every((element) => {\n    return typeof element === 'number';\n  });\n}\n\n// Synonyms\nAbstractMatrix.random = AbstractMatrix.rand;\nAbstractMatrix.randomInt = AbstractMatrix.randInt;\nAbstractMatrix.diagonal = AbstractMatrix.diag;\nAbstractMatrix.prototype.diagonal = AbstractMatrix.prototype.diag;\nAbstractMatrix.identity = AbstractMatrix.eye;\nAbstractMatrix.prototype.negate = AbstractMatrix.prototype.neg;\nAbstractMatrix.prototype.tensorProduct =\n  AbstractMatrix.prototype.kroneckerProduct;\n\nexport default class Matrix extends AbstractMatrix {\n  constructor(nRows, nColumns) {\n    super();\n    if (Matrix.isMatrix(nRows)) {\n      // eslint-disable-next-line no-constructor-return\n      return nRows.clone();\n    } else if (Number.isInteger(nRows) && nRows >= 0) {\n      // Create an empty matrix\n      this.data = [];\n      if (Number.isInteger(nColumns) && nColumns >= 0) {\n        for (let i = 0; i < nRows; i++) {\n          this.data.push(new Float64Array(nColumns));\n        }\n      } else {\n        throw new TypeError('nColumns must be a positive integer');\n      }\n    } else if (isAnyArray(nRows)) {\n      // Copy the values from the 2D array\n      const arrayData = nRows;\n      nRows = arrayData.length;\n      nColumns = nRows ? arrayData[0].length : 0;\n      if (typeof nColumns !== 'number') {\n        throw new TypeError(\n          'Data must be a 2D array with at least one element',\n        );\n      }\n      this.data = [];\n      for (let i = 0; i < nRows; i++) {\n        if (arrayData[i].length !== nColumns) {\n          throw new RangeError('Inconsistent array dimensions');\n        }\n        if (!isArrayOfNumbers(arrayData[i])) {\n          throw new TypeError('Input data contains non-numeric values');\n        }\n        this.data.push(Float64Array.from(arrayData[i]));\n      }\n    } else {\n      throw new TypeError(\n        'First argument must be a positive number or an array',\n      );\n    }\n    this.rows = nRows;\n    this.columns = nColumns;\n  }\n\n  set(rowIndex, columnIndex, value) {\n    this.data[rowIndex][columnIndex] = value;\n    return this;\n  }\n\n  get(rowIndex, columnIndex) {\n    return this.data[rowIndex][columnIndex];\n  }\n\n  removeRow(index) {\n    checkRowIndex(this, index);\n    this.data.splice(index, 1);\n    this.rows -= 1;\n    return this;\n  }\n\n  addRow(index, array) {\n    if (array === undefined) {\n      array = index;\n      index = this.rows;\n    }\n    checkRowIndex(this, index, true);\n    array = Float64Array.from(checkRowVector(this, array));\n    this.data.splice(index, 0, array);\n    this.rows += 1;\n    return this;\n  }\n\n  removeColumn(index) {\n    checkColumnIndex(this, index);\n    for (let i = 0; i < this.rows; i++) {\n      const newRow = new Float64Array(this.columns - 1);\n      for (let j = 0; j < index; j++) {\n        newRow[j] = this.data[i][j];\n      }\n      for (let j = index + 1; j < this.columns; j++) {\n        newRow[j - 1] = this.data[i][j];\n      }\n      this.data[i] = newRow;\n    }\n    this.columns -= 1;\n    return this;\n  }\n\n  addColumn(index, array) {\n    if (typeof array === 'undefined') {\n      array = index;\n      index = this.columns;\n    }\n    checkColumnIndex(this, index, true);\n    array = checkColumnVector(this, array);\n    for (let i = 0; i < this.rows; i++) {\n      const newRow = new Float64Array(this.columns + 1);\n      let j = 0;\n      for (; j < index; j++) {\n        newRow[j] = this.data[i][j];\n      }\n      newRow[j++] = array[i];\n      for (; j < this.columns + 1; j++) {\n        newRow[j] = this.data[i][j - 1];\n      }\n      this.data[i] = newRow;\n    }\n    this.columns += 1;\n    return this;\n  }\n}\n\ninstallMathOperations(AbstractMatrix, Matrix);\n","import { AbstractMatrix } from '../matrix';\n\nexport default class WrapperMatrix2D extends AbstractMatrix {\n  constructor(data) {\n    super();\n    this.data = data;\n    this.rows = data.length;\n    this.columns = data[0].length;\n  }\n\n  set(rowIndex, columnIndex, value) {\n    this.data[rowIndex][columnIndex] = value;\n    return this;\n  }\n\n  get(rowIndex, columnIndex) {\n    return this.data[rowIndex][columnIndex];\n  }\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nexport default class LuDecomposition {\n  constructor(matrix) {\n    matrix = WrapperMatrix2D.checkMatrix(matrix);\n\n    let lu = matrix.clone();\n    let rows = lu.rows;\n    let columns = lu.columns;\n    let pivotVector = new Float64Array(rows);\n    let pivotSign = 1;\n    let i, j, k, p, s, t, v;\n    let LUcolj, kmax;\n\n    for (i = 0; i < rows; i++) {\n      pivotVector[i] = i;\n    }\n\n    LUcolj = new Float64Array(rows);\n\n    for (j = 0; j < columns; j++) {\n      for (i = 0; i < rows; i++) {\n        LUcolj[i] = lu.get(i, j);\n      }\n\n      for (i = 0; i < rows; i++) {\n        kmax = Math.min(i, j);\n        s = 0;\n        for (k = 0; k < kmax; k++) {\n          s += lu.get(i, k) * LUcolj[k];\n        }\n        LUcolj[i] -= s;\n        lu.set(i, j, LUcolj[i]);\n      }\n\n      p = j;\n      for (i = j + 1; i < rows; i++) {\n        if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {\n          p = i;\n        }\n      }\n\n      if (p !== j) {\n        for (k = 0; k < columns; k++) {\n          t = lu.get(p, k);\n          lu.set(p, k, lu.get(j, k));\n          lu.set(j, k, t);\n        }\n\n        v = pivotVector[p];\n        pivotVector[p] = pivotVector[j];\n        pivotVector[j] = v;\n\n        pivotSign = -pivotSign;\n      }\n\n      if (j < rows && lu.get(j, j) !== 0) {\n        for (i = j + 1; i < rows; i++) {\n          lu.set(i, j, lu.get(i, j) / lu.get(j, j));\n        }\n      }\n    }\n\n    this.LU = lu;\n    this.pivotVector = pivotVector;\n    this.pivotSign = pivotSign;\n  }\n\n  isSingular() {\n    let data = this.LU;\n    let col = data.columns;\n    for (let j = 0; j < col; j++) {\n      if (data.get(j, j) === 0) {\n        return true;\n      }\n    }\n    return false;\n  }\n\n  solve(value) {\n    value = Matrix.checkMatrix(value);\n\n    let lu = this.LU;\n    let rows = lu.rows;\n\n    if (rows !== value.rows) {\n      throw new Error('Invalid matrix dimensions');\n    }\n    if (this.isSingular()) {\n      throw new Error('LU matrix is singular');\n    }\n\n    let count = value.columns;\n    let X = value.subMatrixRow(this.pivotVector, 0, count - 1);\n    let columns = lu.columns;\n    let i, j, k;\n\n    for (k = 0; k < columns; k++) {\n      for (i = k + 1; i < columns; i++) {\n        for (j = 0; j < count; j++) {\n          X.set(i, j, X.get(i, j) - X.get(k, j) * lu.get(i, k));\n        }\n      }\n    }\n    for (k = columns - 1; k >= 0; k--) {\n      for (j = 0; j < count; j++) {\n        X.set(k, j, X.get(k, j) / lu.get(k, k));\n      }\n      for (i = 0; i < k; i++) {\n        for (j = 0; j < count; j++) {\n          X.set(i, j, X.get(i, j) - X.get(k, j) * lu.get(i, k));\n        }\n      }\n    }\n    return X;\n  }\n\n  get determinant() {\n    let data = this.LU;\n    if (!data.isSquare()) {\n      throw new Error('Matrix must be square');\n    }\n    let determinant = this.pivotSign;\n    let col = data.columns;\n    for (let j = 0; j < col; j++) {\n      determinant *= data.get(j, j);\n    }\n    return determinant;\n  }\n\n  get lowerTriangularMatrix() {\n    let data = this.LU;\n    let rows = data.rows;\n    let columns = data.columns;\n    let X = new Matrix(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        if (i > j) {\n          X.set(i, j, data.get(i, j));\n        } else if (i === j) {\n          X.set(i, j, 1);\n        } else {\n          X.set(i, j, 0);\n        }\n      }\n    }\n    return X;\n  }\n\n  get upperTriangularMatrix() {\n    let data = this.LU;\n    let rows = data.rows;\n    let columns = data.columns;\n    let X = new Matrix(rows, columns);\n    for (let i = 0; i < rows; i++) {\n      for (let j = 0; j < columns; j++) {\n        if (i <= j) {\n          X.set(i, j, data.get(i, j));\n        } else {\n          X.set(i, j, 0);\n        }\n      }\n    }\n    return X;\n  }\n\n  get pivotPermutationVector() {\n    return Array.from(this.pivotVector);\n  }\n}\n","export function hypotenuse(a, b) {\n  let r = 0;\n  if (Math.abs(a) > Math.abs(b)) {\n    r = b / a;\n    return Math.abs(a) * Math.sqrt(1 + r * r);\n  }\n  if (b !== 0) {\n    r = a / b;\n    return Math.abs(b) * Math.sqrt(1 + r * r);\n  }\n  return 0;\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nimport { hypotenuse } from './util';\n\nexport default class QrDecomposition {\n  constructor(value) {\n    value = WrapperMatrix2D.checkMatrix(value);\n\n    let qr = value.clone();\n    let m = value.rows;\n    let n = value.columns;\n    let rdiag = new Float64Array(n);\n    let i, j, k, s;\n\n    for (k = 0; k < n; k++) {\n      let nrm = 0;\n      for (i = k; i < m; i++) {\n        nrm = hypotenuse(nrm, qr.get(i, k));\n      }\n      if (nrm !== 0) {\n        if (qr.get(k, k) < 0) {\n          nrm = -nrm;\n        }\n        for (i = k; i < m; i++) {\n          qr.set(i, k, qr.get(i, k) / nrm);\n        }\n        qr.set(k, k, qr.get(k, k) + 1);\n        for (j = k + 1; j < n; j++) {\n          s = 0;\n          for (i = k; i < m; i++) {\n            s += qr.get(i, k) * qr.get(i, j);\n          }\n          s = -s / qr.get(k, k);\n          for (i = k; i < m; i++) {\n            qr.set(i, j, qr.get(i, j) + s * qr.get(i, k));\n          }\n        }\n      }\n      rdiag[k] = -nrm;\n    }\n\n    this.QR = qr;\n    this.Rdiag = rdiag;\n  }\n\n  solve(value) {\n    value = Matrix.checkMatrix(value);\n\n    let qr = this.QR;\n    let m = qr.rows;\n\n    if (value.rows !== m) {\n      throw new Error('Matrix row dimensions must agree');\n    }\n    if (!this.isFullRank()) {\n      throw new Error('Matrix is rank deficient');\n    }\n\n    let count = value.columns;\n    let X = value.clone();\n    let n = qr.columns;\n    let i, j, k, s;\n\n    for (k = 0; k < n; k++) {\n      for (j = 0; j < count; j++) {\n        s = 0;\n        for (i = k; i < m; i++) {\n          s += qr.get(i, k) * X.get(i, j);\n        }\n        s = -s / qr.get(k, k);\n        for (i = k; i < m; i++) {\n          X.set(i, j, X.get(i, j) + s * qr.get(i, k));\n        }\n      }\n    }\n    for (k = n - 1; k >= 0; k--) {\n      for (j = 0; j < count; j++) {\n        X.set(k, j, X.get(k, j) / this.Rdiag[k]);\n      }\n      for (i = 0; i < k; i++) {\n        for (j = 0; j < count; j++) {\n          X.set(i, j, X.get(i, j) - X.get(k, j) * qr.get(i, k));\n        }\n      }\n    }\n\n    return X.subMatrix(0, n - 1, 0, count - 1);\n  }\n\n  isFullRank() {\n    let columns = this.QR.columns;\n    for (let i = 0; i < columns; i++) {\n      if (this.Rdiag[i] === 0) {\n        return false;\n      }\n    }\n    return true;\n  }\n\n  get upperTriangularMatrix() {\n    let qr = this.QR;\n    let n = qr.columns;\n    let X = new Matrix(n, n);\n    let i, j;\n    for (i = 0; i < n; i++) {\n      for (j = 0; j < n; j++) {\n        if (i < j) {\n          X.set(i, j, qr.get(i, j));\n        } else if (i === j) {\n          X.set(i, j, this.Rdiag[i]);\n        } else {\n          X.set(i, j, 0);\n        }\n      }\n    }\n    return X;\n  }\n\n  get orthogonalMatrix() {\n    let qr = this.QR;\n    let rows = qr.rows;\n    let columns = qr.columns;\n    let X = new Matrix(rows, columns);\n    let i, j, k, s;\n\n    for (k = columns - 1; k >= 0; k--) {\n      for (i = 0; i < rows; i++) {\n        X.set(i, k, 0);\n      }\n      X.set(k, k, 1);\n      for (j = k; j < columns; j++) {\n        if (qr.get(k, k) !== 0) {\n          s = 0;\n          for (i = k; i < rows; i++) {\n            s += qr.get(i, k) * X.get(i, j);\n          }\n\n          s = -s / qr.get(k, k);\n\n          for (i = k; i < rows; i++) {\n            X.set(i, j, X.get(i, j) + s * qr.get(i, k));\n          }\n        }\n      }\n    }\n    return X;\n  }\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nimport { hypotenuse } from './util';\n\nexport default class SingularValueDecomposition {\n  constructor(value, options = {}) {\n    value = WrapperMatrix2D.checkMatrix(value);\n\n    if (value.isEmpty()) {\n      throw new Error('Matrix must be non-empty');\n    }\n\n    let m = value.rows;\n    let n = value.columns;\n\n    const {\n      computeLeftSingularVectors = true,\n      computeRightSingularVectors = true,\n      autoTranspose = false,\n    } = options;\n\n    let wantu = Boolean(computeLeftSingularVectors);\n    let wantv = Boolean(computeRightSingularVectors);\n\n    let swapped = false;\n    let a;\n    if (m < n) {\n      if (!autoTranspose) {\n        a = value.clone();\n        // eslint-disable-next-line no-console\n        console.warn(\n          'Computing SVD on a matrix with more columns than rows. Consider enabling autoTranspose',\n        );\n      } else {\n        a = value.transpose();\n        m = a.rows;\n        n = a.columns;\n        swapped = true;\n        let aux = wantu;\n        wantu = wantv;\n        wantv = aux;\n      }\n    } else {\n      a = value.clone();\n    }\n\n    let nu = Math.min(m, n);\n    let ni = Math.min(m + 1, n);\n    let s = new Float64Array(ni);\n    let U = new Matrix(m, nu);\n    let V = new Matrix(n, n);\n\n    let e = new Float64Array(n);\n    let work = new Float64Array(m);\n\n    let si = new Float64Array(ni);\n    for (let i = 0; i < ni; i++) si[i] = i;\n\n    let nct = Math.min(m - 1, n);\n    let nrt = Math.max(0, Math.min(n - 2, m));\n    let mrc = Math.max(nct, nrt);\n\n    for (let k = 0; k < mrc; k++) {\n      if (k < nct) {\n        s[k] = 0;\n        for (let i = k; i < m; i++) {\n          s[k] = hypotenuse(s[k], a.get(i, k));\n        }\n        if (s[k] !== 0) {\n          if (a.get(k, k) < 0) {\n            s[k] = -s[k];\n          }\n          for (let i = k; i < m; i++) {\n            a.set(i, k, a.get(i, k) / s[k]);\n          }\n          a.set(k, k, a.get(k, k) + 1);\n        }\n        s[k] = -s[k];\n      }\n\n      for (let j = k + 1; j < n; j++) {\n        if (k < nct && s[k] !== 0) {\n          let t = 0;\n          for (let i = k; i < m; i++) {\n            t += a.get(i, k) * a.get(i, j);\n          }\n          t = -t / a.get(k, k);\n          for (let i = k; i < m; i++) {\n            a.set(i, j, a.get(i, j) + t * a.get(i, k));\n          }\n        }\n        e[j] = a.get(k, j);\n      }\n\n      if (wantu && k < nct) {\n        for (let i = k; i < m; i++) {\n          U.set(i, k, a.get(i, k));\n        }\n      }\n\n      if (k < nrt) {\n        e[k] = 0;\n        for (let i = k + 1; i < n; i++) {\n          e[k] = hypotenuse(e[k], e[i]);\n        }\n        if (e[k] !== 0) {\n          if (e[k + 1] < 0) {\n            e[k] = 0 - e[k];\n          }\n          for (let i = k + 1; i < n; i++) {\n            e[i] /= e[k];\n          }\n          e[k + 1] += 1;\n        }\n        e[k] = -e[k];\n        if (k + 1 < m && e[k] !== 0) {\n          for (let i = k + 1; i < m; i++) {\n            work[i] = 0;\n          }\n          for (let i = k + 1; i < m; i++) {\n            for (let j = k + 1; j < n; j++) {\n              work[i] += e[j] * a.get(i, j);\n            }\n          }\n          for (let j = k + 1; j < n; j++) {\n            let t = -e[j] / e[k + 1];\n            for (let i = k + 1; i < m; i++) {\n              a.set(i, j, a.get(i, j) + t * work[i]);\n            }\n          }\n        }\n        if (wantv) {\n          for (let i = k + 1; i < n; i++) {\n            V.set(i, k, e[i]);\n          }\n        }\n      }\n    }\n\n    let p = Math.min(n, m + 1);\n    if (nct < n) {\n      s[nct] = a.get(nct, nct);\n    }\n    if (m < p) {\n      s[p - 1] = 0;\n    }\n    if (nrt + 1 < p) {\n      e[nrt] = a.get(nrt, p - 1);\n    }\n    e[p - 1] = 0;\n\n    if (wantu) {\n      for (let j = nct; j < nu; j++) {\n        for (let i = 0; i < m; i++) {\n          U.set(i, j, 0);\n        }\n        U.set(j, j, 1);\n      }\n      for (let k = nct - 1; k >= 0; k--) {\n        if (s[k] !== 0) {\n          for (let j = k + 1; j < nu; j++) {\n            let t = 0;\n            for (let i = k; i < m; i++) {\n              t += U.get(i, k) * U.get(i, j);\n            }\n            t = -t / U.get(k, k);\n            for (let i = k; i < m; i++) {\n              U.set(i, j, U.get(i, j) + t * U.get(i, k));\n            }\n          }\n          for (let i = k; i < m; i++) {\n            U.set(i, k, -U.get(i, k));\n          }\n          U.set(k, k, 1 + U.get(k, k));\n          for (let i = 0; i < k - 1; i++) {\n            U.set(i, k, 0);\n          }\n        } else {\n          for (let i = 0; i < m; i++) {\n            U.set(i, k, 0);\n          }\n          U.set(k, k, 1);\n        }\n      }\n    }\n\n    if (wantv) {\n      for (let k = n - 1; k >= 0; k--) {\n        if (k < nrt && e[k] !== 0) {\n          for (let j = k + 1; j < n; j++) {\n            let t = 0;\n            for (let i = k + 1; i < n; i++) {\n              t += V.get(i, k) * V.get(i, j);\n            }\n            t = -t / V.get(k + 1, k);\n            for (let i = k + 1; i < n; i++) {\n              V.set(i, j, V.get(i, j) + t * V.get(i, k));\n            }\n          }\n        }\n        for (let i = 0; i < n; i++) {\n          V.set(i, k, 0);\n        }\n        V.set(k, k, 1);\n      }\n    }\n\n    let pp = p - 1;\n    let iter = 0;\n    let eps = Number.EPSILON;\n    while (p > 0) {\n      let k, kase;\n      for (k = p - 2; k >= -1; k--) {\n        if (k === -1) {\n          break;\n        }\n        const alpha =\n          Number.MIN_VALUE + eps * Math.abs(s[k] + Math.abs(s[k + 1]));\n        if (Math.abs(e[k]) <= alpha || Number.isNaN(e[k])) {\n          e[k] = 0;\n          break;\n        }\n      }\n      if (k === p - 2) {\n        kase = 4;\n      } else {\n        let ks;\n        for (ks = p - 1; ks >= k; ks--) {\n          if (ks === k) {\n            break;\n          }\n          let t =\n            (ks !== p ? Math.abs(e[ks]) : 0) +\n            (ks !== k + 1 ? Math.abs(e[ks - 1]) : 0);\n          if (Math.abs(s[ks]) <= eps * t) {\n            s[ks] = 0;\n            break;\n          }\n        }\n        if (ks === k) {\n          kase = 3;\n        } else if (ks === p - 1) {\n          kase = 1;\n        } else {\n          kase = 2;\n          k = ks;\n        }\n      }\n\n      k++;\n\n      switch (kase) {\n        case 1: {\n          let f = e[p - 2];\n          e[p - 2] = 0;\n          for (let j = p - 2; j >= k; j--) {\n            let t = hypotenuse(s[j], f);\n            let cs = s[j] / t;\n            let sn = f / t;\n            s[j] = t;\n            if (j !== k) {\n              f = -sn * e[j - 1];\n              e[j - 1] = cs * e[j - 1];\n            }\n            if (wantv) {\n              for (let i = 0; i < n; i++) {\n                t = cs * V.get(i, j) + sn * V.get(i, p - 1);\n                V.set(i, p - 1, -sn * V.get(i, j) + cs * V.get(i, p - 1));\n                V.set(i, j, t);\n              }\n            }\n          }\n          break;\n        }\n        case 2: {\n          let f = e[k - 1];\n          e[k - 1] = 0;\n          for (let j = k; j < p; j++) {\n            let t = hypotenuse(s[j], f);\n            let cs = s[j] / t;\n            let sn = f / t;\n            s[j] = t;\n            f = -sn * e[j];\n            e[j] = cs * e[j];\n            if (wantu) {\n              for (let i = 0; i < m; i++) {\n                t = cs * U.get(i, j) + sn * U.get(i, k - 1);\n                U.set(i, k - 1, -sn * U.get(i, j) + cs * U.get(i, k - 1));\n                U.set(i, j, t);\n              }\n            }\n          }\n          break;\n        }\n        case 3: {\n          const scale = Math.max(\n            Math.abs(s[p - 1]),\n            Math.abs(s[p - 2]),\n            Math.abs(e[p - 2]),\n            Math.abs(s[k]),\n            Math.abs(e[k]),\n          );\n          const sp = s[p - 1] / scale;\n          const spm1 = s[p - 2] / scale;\n          const epm1 = e[p - 2] / scale;\n          const sk = s[k] / scale;\n          const ek = e[k] / scale;\n          const b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;\n          const c = sp * epm1 * (sp * epm1);\n          let shift = 0;\n          if (b !== 0 || c !== 0) {\n            if (b < 0) {\n              shift = 0 - Math.sqrt(b * b + c);\n            } else {\n              shift = Math.sqrt(b * b + c);\n            }\n            shift = c / (b + shift);\n          }\n          let f = (sk + sp) * (sk - sp) + shift;\n          let g = sk * ek;\n          for (let j = k; j < p - 1; j++) {\n            let t = hypotenuse(f, g);\n            if (t === 0) t = Number.MIN_VALUE;\n            let cs = f / t;\n            let sn = g / t;\n            if (j !== k) {\n              e[j - 1] = t;\n            }\n            f = cs * s[j] + sn * e[j];\n            e[j] = cs * e[j] - sn * s[j];\n            g = sn * s[j + 1];\n            s[j + 1] = cs * s[j + 1];\n            if (wantv) {\n              for (let i = 0; i < n; i++) {\n                t = cs * V.get(i, j) + sn * V.get(i, j + 1);\n                V.set(i, j + 1, -sn * V.get(i, j) + cs * V.get(i, j + 1));\n                V.set(i, j, t);\n              }\n            }\n            t = hypotenuse(f, g);\n            if (t === 0) t = Number.MIN_VALUE;\n            cs = f / t;\n            sn = g / t;\n            s[j] = t;\n            f = cs * e[j] + sn * s[j + 1];\n            s[j + 1] = -sn * e[j] + cs * s[j + 1];\n            g = sn * e[j + 1];\n            e[j + 1] = cs * e[j + 1];\n            if (wantu && j < m - 1) {\n              for (let i = 0; i < m; i++) {\n                t = cs * U.get(i, j) + sn * U.get(i, j + 1);\n                U.set(i, j + 1, -sn * U.get(i, j) + cs * U.get(i, j + 1));\n                U.set(i, j, t);\n              }\n            }\n          }\n          e[p - 2] = f;\n          iter = iter + 1;\n          break;\n        }\n        case 4: {\n          if (s[k] <= 0) {\n            s[k] = s[k] < 0 ? -s[k] : 0;\n            if (wantv) {\n              for (let i = 0; i <= pp; i++) {\n                V.set(i, k, -V.get(i, k));\n              }\n            }\n          }\n          while (k < pp) {\n            if (s[k] >= s[k + 1]) {\n              break;\n            }\n            let t = s[k];\n            s[k] = s[k + 1];\n            s[k + 1] = t;\n            if (wantv && k < n - 1) {\n              for (let i = 0; i < n; i++) {\n                t = V.get(i, k + 1);\n                V.set(i, k + 1, V.get(i, k));\n                V.set(i, k, t);\n              }\n            }\n            if (wantu && k < m - 1) {\n              for (let i = 0; i < m; i++) {\n                t = U.get(i, k + 1);\n                U.set(i, k + 1, U.get(i, k));\n                U.set(i, k, t);\n              }\n            }\n            k++;\n          }\n          iter = 0;\n          p--;\n          break;\n        }\n        // no default\n      }\n    }\n\n    if (swapped) {\n      let tmp = V;\n      V = U;\n      U = tmp;\n    }\n\n    this.m = m;\n    this.n = n;\n    this.s = s;\n    this.U = U;\n    this.V = V;\n  }\n\n  solve(value) {\n    let Y = value;\n    let e = this.threshold;\n    let scols = this.s.length;\n    let Ls = Matrix.zeros(scols, scols);\n\n    for (let i = 0; i < scols; i++) {\n      if (Math.abs(this.s[i]) <= e) {\n        Ls.set(i, i, 0);\n      } else {\n        Ls.set(i, i, 1 / this.s[i]);\n      }\n    }\n\n    let U = this.U;\n    let V = this.rightSingularVectors;\n\n    let VL = V.mmul(Ls);\n    let vrows = V.rows;\n    let urows = U.rows;\n    let VLU = Matrix.zeros(vrows, urows);\n\n    for (let i = 0; i < vrows; i++) {\n      for (let j = 0; j < urows; j++) {\n        let sum = 0;\n        for (let k = 0; k < scols; k++) {\n          sum += VL.get(i, k) * U.get(j, k);\n        }\n        VLU.set(i, j, sum);\n      }\n    }\n\n    return VLU.mmul(Y);\n  }\n\n  solveForDiagonal(value) {\n    return this.solve(Matrix.diag(value));\n  }\n\n  inverse() {\n    let V = this.V;\n    let e = this.threshold;\n    let vrows = V.rows;\n    let vcols = V.columns;\n    let X = new Matrix(vrows, this.s.length);\n\n    for (let i = 0; i < vrows; i++) {\n      for (let j = 0; j < vcols; j++) {\n        if (Math.abs(this.s[j]) > e) {\n          X.set(i, j, V.get(i, j) / this.s[j]);\n        }\n      }\n    }\n\n    let U = this.U;\n\n    let urows = U.rows;\n    let ucols = U.columns;\n    let Y = new Matrix(vrows, urows);\n\n    for (let i = 0; i < vrows; i++) {\n      for (let j = 0; j < urows; j++) {\n        let sum = 0;\n        for (let k = 0; k < ucols; k++) {\n          sum += X.get(i, k) * U.get(j, k);\n        }\n        Y.set(i, j, sum);\n      }\n    }\n\n    return Y;\n  }\n\n  get condition() {\n    return this.s[0] / this.s[Math.min(this.m, this.n) - 1];\n  }\n\n  get norm2() {\n    return this.s[0];\n  }\n\n  get rank() {\n    let tol = Math.max(this.m, this.n) * this.s[0] * Number.EPSILON;\n    let r = 0;\n    let s = this.s;\n    for (let i = 0, ii = s.length; i < ii; i++) {\n      if (s[i] > tol) {\n        r++;\n      }\n    }\n    return r;\n  }\n\n  get diagonal() {\n    return Array.from(this.s);\n  }\n\n  get threshold() {\n    return (Number.EPSILON / 2) * Math.max(this.m, this.n) * this.s[0];\n  }\n\n  get leftSingularVectors() {\n    return this.U;\n  }\n\n  get rightSingularVectors() {\n    return this.V;\n  }\n\n  get diagonalMatrix() {\n    return Matrix.diag(this.s);\n  }\n}\n","import LuDecomposition from './dc/lu';\nimport QrDecomposition from './dc/qr';\nimport SingularValueDecomposition from './dc/svd';\nimport Matrix from './matrix';\nimport WrapperMatrix2D from './wrap/WrapperMatrix2D';\n\nexport function inverse(matrix, useSVD = false) {\n  matrix = WrapperMatrix2D.checkMatrix(matrix);\n  if (useSVD) {\n    return new SingularValueDecomposition(matrix).inverse();\n  } else {\n    return solve(matrix, Matrix.eye(matrix.rows));\n  }\n}\n\nexport function solve(leftHandSide, rightHandSide, useSVD = false) {\n  leftHandSide = WrapperMatrix2D.checkMatrix(leftHandSide);\n  rightHandSide = WrapperMatrix2D.checkMatrix(rightHandSide);\n  if (useSVD) {\n    return new SingularValueDecomposition(leftHandSide).solve(rightHandSide);\n  } else {\n    return leftHandSide.isSquare()\n      ? new LuDecomposition(leftHandSide).solve(rightHandSide)\n      : new QrDecomposition(leftHandSide).solve(rightHandSide);\n  }\n}\n","import { isAnyArray } from 'is-any-array';\n\nimport Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nexport default class nipals {\n  constructor(X, options = {}) {\n    X = WrapperMatrix2D.checkMatrix(X);\n    let { Y } = options;\n    const {\n      scaleScores = false,\n      maxIterations = 1000,\n      terminationCriteria = 1e-10,\n    } = options;\n\n    let u;\n    if (Y) {\n      if (isAnyArray(Y) && typeof Y[0] === 'number') {\n        Y = Matrix.columnVector(Y);\n      } else {\n        Y = WrapperMatrix2D.checkMatrix(Y);\n      }\n      if (Y.rows !== X.rows) {\n        throw new Error('Y should have the same number of rows as X');\n      }\n      u = Y.getColumnVector(0);\n    } else {\n      u = X.getColumnVector(0);\n    }\n\n    let diff = 1;\n    let t, q, w, tOld;\n\n    for (\n      let counter = 0;\n      counter < maxIterations && diff > terminationCriteria;\n      counter++\n    ) {\n      w = X.transpose().mmul(u).div(u.transpose().mmul(u).get(0, 0));\n      w = w.div(w.norm());\n\n      t = X.mmul(w).div(w.transpose().mmul(w).get(0, 0));\n\n      if (counter > 0) {\n        diff = t.clone().sub(tOld).pow(2).sum();\n      }\n      tOld = t.clone();\n\n      if (Y) {\n        q = Y.transpose().mmul(t).div(t.transpose().mmul(t).get(0, 0));\n        q = q.div(q.norm());\n\n        u = Y.mmul(q).div(q.transpose().mmul(q).get(0, 0));\n      } else {\n        u = t;\n      }\n    }\n\n    if (Y) {\n      let p = X.transpose().mmul(t).div(t.transpose().mmul(t).get(0, 0));\n      p = p.div(p.norm());\n      let xResidual = X.clone().sub(t.clone().mmul(p.transpose()));\n      let residual = u.transpose().mmul(t).div(t.transpose().mmul(t).get(0, 0));\n      let yResidual = Y.clone().sub(\n        t.clone().mulS(residual.get(0, 0)).mmul(q.transpose()),\n      );\n\n      this.t = t;\n      this.p = p.transpose();\n      this.w = w.transpose();\n      this.q = q;\n      this.u = u;\n      this.s = t.transpose().mmul(t);\n      this.xResidual = xResidual;\n      this.yResidual = yResidual;\n      this.betas = residual;\n    } else {\n      this.w = w.transpose();\n      this.s = t.transpose().mmul(t).sqrt();\n      if (scaleScores) {\n        this.t = t.clone().div(this.s.get(0, 0));\n      } else {\n        this.t = t;\n      }\n      this.xResidual = X.sub(t.mmul(w.transpose()));\n    }\n  }\n}\n","import { Matrix } from 'ml-matrix';\n\n/**\n * @private\n * Function that given vector, returns its norm\n * @param {Vector} X\n * @return {number} Norm of the vector\n */\nexport function norm(X) {\n  return Math.sqrt(X.clone().apply(pow2array).sum());\n}\n\n/**\n * @private\n * Function that pow 2 each element of a Matrix or a Vector,\n * used in the apply method of the Matrix object\n * @param {number} i - index i.\n * @param {number} j - index j.\n * @return {Matrix} The Matrix object modified at the index i, j.\n * */\nexport function pow2array(i, j) {\n  this.set(i, j, this.get(i, j) ** 2);\n}\n\n/**\n * @private\n * Function that normalize the dataset and return the means and\n * standard deviation of each feature.\n * @param {Matrix} dataset\n * @return {object} dataset normalized, means and standard deviations\n */\nexport function featureNormalize(dataset) {\n  let means = dataset.mean('column');\n  let std = dataset.standardDeviation('column', {\n    mean: means,\n    unbiased: true,\n  });\n  let result = Matrix.checkMatrix(dataset).subRowVector(means);\n  return { result: result.divRowVector(std), means, std };\n}\n\n/**\n * @private\n * Function that initialize an array of matrices.\n * @param {Array} array\n * @param {boolean} isMatrix\n * @return {Array} array with the matrices initialized.\n */\nexport function initializeMatrices(array, isMatrix) {\n  if (isMatrix) {\n    for (let i = 0; i < array.length; ++i) {\n      for (let j = 0; j < array[i].length; ++j) {\n        let elem = array[i][j];\n        array[i][j] = elem !== null ? new Matrix(array[i][j]) : undefined;\n      }\n    }\n  } else {\n    for (let i = 0; i < array.length; ++i) {\n      array[i] = new Matrix(array[i]);\n    }\n  }\n\n  return array;\n}\n","import { Matrix } from 'ml-matrix';\n\nimport * as Utils from './util/utils';\n\n/**\n * @class PLS\n */\nexport class PLS {\n  /**\n   * Constructor for Partial Least Squares (PLS)\n   * @param {object} options\n   * @param {number} [options.latentVectors] - Number of latent vector to get (if the algorithm doesn't find a good model below the tolerance)\n   * @param {number} [options.tolerance=1e-5]\n   * @param {boolean} [options.scale=true] - rescale dataset using mean.\n   * @param {object} model - for load purposes.\n   */\n  constructor(options, model) {\n    if (options === true) {\n      this.meanX = model.meanX;\n      this.stdDevX = model.stdDevX;\n      this.meanY = model.meanY;\n      this.stdDevY = model.stdDevY;\n      this.PBQ = Matrix.checkMatrix(model.PBQ);\n      this.R2X = model.R2X;\n      this.scale = model.scale;\n      this.scaleMethod = model.scaleMethod;\n      this.tolerance = model.tolerance;\n    } else {\n      let { tolerance = 1e-5, scale = true } = options;\n      this.tolerance = tolerance;\n      this.scale = scale;\n      this.latentVectors = options.latentVectors;\n    }\n  }\n\n  /**\n   * Fits the model with the given data and predictions, in this function is calculated the\n   * following outputs:\n   *\n   * T - Score matrix of X\n   * P - Loading matrix of X\n   * U - Score matrix of Y\n   * Q - Loading matrix of Y\n   * B - Matrix of regression coefficient\n   * W - Weight matrix of X\n   *\n   * @param {Matrix|Array} trainingSet\n   * @param {Matrix|Array} trainingValues\n   */\n  train(trainingSet, trainingValues) {\n    trainingSet = Matrix.checkMatrix(trainingSet);\n    trainingValues = Matrix.checkMatrix(trainingValues);\n\n    if (trainingSet.length !== trainingValues.length) {\n      throw new RangeError(\n        'The number of X rows must be equal to the number of Y rows',\n      );\n    }\n\n    this.meanX = trainingSet.mean('column');\n    this.stdDevX = trainingSet.standardDeviation('column', {\n      mean: this.meanX,\n      unbiased: true,\n    });\n    this.meanY = trainingValues.mean('column');\n    this.stdDevY = trainingValues.standardDeviation('column', {\n      mean: this.meanY,\n      unbiased: true,\n    });\n\n    if (this.scale) {\n      trainingSet = trainingSet\n        .clone()\n        .subRowVector(this.meanX)\n        .divRowVector(this.stdDevX);\n      trainingValues = trainingValues\n        .clone()\n        .subRowVector(this.meanY)\n        .divRowVector(this.stdDevY);\n    }\n\n    if (this.latentVectors === undefined) {\n      this.latentVectors = Math.min(trainingSet.rows - 1, trainingSet.columns);\n    }\n\n    let rx = trainingSet.rows;\n    let cx = trainingSet.columns;\n    let ry = trainingValues.rows;\n    let cy = trainingValues.columns;\n\n    let ssqXcal = trainingSet.clone().mul(trainingSet).sum(); // for the r²\n    let sumOfSquaresY = trainingValues.clone().mul(trainingValues).sum();\n\n    let tolerance = this.tolerance;\n    let n = this.latentVectors;\n    let T = Matrix.zeros(rx, n);\n    let P = Matrix.zeros(cx, n);\n    let U = Matrix.zeros(ry, n);\n    let Q = Matrix.zeros(cy, n);\n    let B = Matrix.zeros(n, n);\n    let W = P.clone();\n    let k = 0;\n    let t;\n    let w;\n    let q;\n    let p;\n\n    while (Utils.norm(trainingValues) > tolerance && k < n) {\n      let transposeX = trainingSet.transpose();\n      let transposeY = trainingValues.transpose();\n\n      let tIndex = maxSumColIndex(trainingSet.clone().mul(trainingSet));\n      let uIndex = maxSumColIndex(trainingValues.clone().mul(trainingValues));\n\n      let t1 = trainingSet.getColumnVector(tIndex);\n      let u = trainingValues.getColumnVector(uIndex);\n      t = Matrix.zeros(rx, 1);\n\n      while (Utils.norm(t1.clone().sub(t)) > tolerance) {\n        w = transposeX.mmul(u);\n        w.div(Utils.norm(w));\n        t = t1;\n        t1 = trainingSet.mmul(w);\n        q = transposeY.mmul(t1);\n        q.div(Utils.norm(q));\n        u = trainingValues.mmul(q);\n      }\n\n      t = t1;\n      let num = transposeX.mmul(t);\n      let den = t.transpose().mmul(t).get(0, 0);\n      p = num.div(den);\n      let pnorm = Utils.norm(p);\n      p.div(pnorm);\n      t.mul(pnorm);\n      w.mul(pnorm);\n\n      num = u.transpose().mmul(t);\n      den = t.transpose().mmul(t).get(0, 0);\n      let b = num.div(den).get(0, 0);\n      trainingSet.sub(t.mmul(p.transpose()));\n      trainingValues.sub(t.clone().mul(b).mmul(q.transpose()));\n\n      T.setColumn(k, t);\n      P.setColumn(k, p);\n      U.setColumn(k, u);\n      Q.setColumn(k, q);\n      W.setColumn(k, w);\n\n      B.set(k, k, b);\n      k++;\n    }\n\n    k--;\n    T = T.subMatrix(0, T.rows - 1, 0, k);\n    P = P.subMatrix(0, P.rows - 1, 0, k);\n    U = U.subMatrix(0, U.rows - 1, 0, k);\n    Q = Q.subMatrix(0, Q.rows - 1, 0, k);\n    W = W.subMatrix(0, W.rows - 1, 0, k);\n    B = B.subMatrix(0, k, 0, k);\n\n    this.ssqYcal = sumOfSquaresY;\n    this.E = trainingSet;\n    this.F = trainingValues;\n    this.T = T;\n    this.P = P;\n    this.U = U;\n    this.Q = Q;\n    this.W = W;\n    this.B = B;\n    this.PBQ = P.mmul(B).mmul(Q.transpose());\n    this.R2X = t\n      .transpose()\n      .mmul(t)\n      .mmul(p.transpose().mmul(p))\n      .div(ssqXcal)\n      .get(0, 0);\n  }\n\n  /**\n   * Predicts the behavior of the given dataset.\n   * @param {Matrix|Array} dataset - data to be predicted.\n   * @return {Matrix} - predictions of each element of the dataset.\n   */\n  predict(dataset) {\n    let X = Matrix.checkMatrix(dataset);\n    if (this.scale) {\n      X = X.subRowVector(this.meanX).divRowVector(this.stdDevX);\n    }\n    let Y = X.mmul(this.PBQ);\n    Y = Y.mulRowVector(this.stdDevY).addRowVector(this.meanY);\n    return Y;\n  }\n\n  /**\n   * Returns the explained variance on training of the PLS model\n   * @return {number}\n   */\n  getExplainedVariance() {\n    return this.R2X;\n  }\n\n  /**\n   * Export the current model to JSON.\n   * @return {object} - Current model.\n   */\n  toJSON() {\n    return {\n      name: 'PLS',\n      R2X: this.R2X,\n      meanX: this.meanX,\n      stdDevX: this.stdDevX,\n      meanY: this.meanY,\n      stdDevY: this.stdDevY,\n      PBQ: this.PBQ,\n      tolerance: this.tolerance,\n      scale: this.scale,\n    };\n  }\n\n  /**\n   * Load a PLS model from a JSON Object\n   * @param {object} model\n   * @return {PLS} - PLS object from the given model\n   */\n  static load(model) {\n    if (model.name !== 'PLS') {\n      throw new RangeError(`Invalid model: ${model.name}`);\n    }\n    return new PLS(true, model);\n  }\n}\n\n/**\n * @private\n * Function that returns the index where the sum of each\n * column vector is maximum.\n * @param {Matrix} data\n * @return {number} index of the maximum\n */\nfunction maxSumColIndex(data) {\n  return Matrix.rowVector(data.sum('column')).maxIndex()[0];\n}\n","import { Matrix, SingularValueDecomposition, inverse } from 'ml-matrix';\n\nimport { initializeMatrices } from './util/utils';\n\n/**\n * @class KOPLS\n */\nexport class KOPLS {\n  /**\n   * Constructor for Kernel-based Orthogonal Projections to Latent Structures (K-OPLS)\n   * @param {object} options\n   * @param {number} [options.predictiveComponents] - Number of predictive components to use.\n   * @param {number} [options.orthogonalComponents] - Number of Y-Orthogonal components.\n   * @param {Kernel} [options.kernel] - Kernel object to apply, see [ml-kernel](https://github.com/mljs/kernel).\n   * @param {object} model - for load purposes.\n   */\n  constructor(options, model) {\n    if (options === true) {\n      this.trainingSet = new Matrix(model.trainingSet);\n      this.YLoadingMat = new Matrix(model.YLoadingMat);\n      this.SigmaPow = new Matrix(model.SigmaPow);\n      this.YScoreMat = new Matrix(model.YScoreMat);\n      this.predScoreMat = initializeMatrices(model.predScoreMat, false);\n      this.YOrthLoadingVec = initializeMatrices(model.YOrthLoadingVec, false);\n      this.YOrthEigen = model.YOrthEigen;\n      this.YOrthScoreMat = initializeMatrices(model.YOrthScoreMat, false);\n      this.toNorm = initializeMatrices(model.toNorm, false);\n      this.TURegressionCoeff = initializeMatrices(\n        model.TURegressionCoeff,\n        false,\n      );\n      this.kernelX = initializeMatrices(model.kernelX, true);\n      this.kernel = model.kernel;\n      this.orthogonalComp = model.orthogonalComp;\n      this.predictiveComp = model.predictiveComp;\n    } else {\n      if (options.predictiveComponents === undefined) {\n        throw new RangeError('no predictive components found!');\n      }\n      if (options.orthogonalComponents === undefined) {\n        throw new RangeError('no orthogonal components found!');\n      }\n      if (options.kernel === undefined) {\n        throw new RangeError('no kernel found!');\n      }\n\n      this.orthogonalComp = options.orthogonalComponents;\n      this.predictiveComp = options.predictiveComponents;\n      this.kernel = options.kernel;\n    }\n  }\n\n  /**\n   * Train the K-OPLS model with the given training set and labels.\n   * @param {Matrix|Array} trainingSet\n   * @param {Matrix|Array} trainingValues\n   */\n  train(trainingSet, trainingValues) {\n    trainingSet = Matrix.checkMatrix(trainingSet);\n    trainingValues = Matrix.checkMatrix(trainingValues);\n\n    // to save and compute kernel with the prediction dataset.\n    this.trainingSet = trainingSet.clone();\n\n    let kernelX = this.kernel.compute(trainingSet);\n\n    let Identity = Matrix.eye(kernelX.rows, kernelX.rows, 1);\n    let temp = kernelX;\n    kernelX = new Array(this.orthogonalComp + 1);\n    for (let i = 0; i < this.orthogonalComp + 1; i++) {\n      kernelX[i] = new Array(this.orthogonalComp + 1);\n    }\n    kernelX[0][0] = temp;\n\n    let result = new SingularValueDecomposition(\n      trainingValues.transpose().mmul(kernelX[0][0]).mmul(trainingValues),\n      {\n        computeLeftSingularVectors: true,\n        computeRightSingularVectors: false,\n      },\n    );\n    let YLoadingMat = result.leftSingularVectors;\n    let Sigma = result.diagonalMatrix;\n\n    YLoadingMat = YLoadingMat.subMatrix(\n      0,\n      YLoadingMat.rows - 1,\n      0,\n      this.predictiveComp - 1,\n    );\n    Sigma = Sigma.subMatrix(\n      0,\n      this.predictiveComp - 1,\n      0,\n      this.predictiveComp - 1,\n    );\n\n    let YScoreMat = trainingValues.mmul(YLoadingMat);\n\n    let predScoreMat = new Array(this.orthogonalComp + 1);\n    let TURegressionCoeff = new Array(this.orthogonalComp + 1);\n    let YOrthScoreMat = new Array(this.orthogonalComp);\n    let YOrthLoadingVec = new Array(this.orthogonalComp);\n    let YOrthEigen = new Array(this.orthogonalComp);\n    let YOrthScoreNorm = new Array(this.orthogonalComp);\n\n    let SigmaPow = Matrix.pow(Sigma, -0.5);\n    // to avoid errors, check infinity\n\n    function removeInfinity(i, j) {\n      if (this.get(i, j) === Infinity) {\n        this.set(i, j, 0);\n      }\n    }\n\n    SigmaPow.apply(removeInfinity);\n\n    for (let i = 0; i < this.orthogonalComp; ++i) {\n      predScoreMat[i] = kernelX[0][i]\n        .transpose()\n        .mmul(YScoreMat)\n        .mmul(SigmaPow);\n\n      let TpiPrime = predScoreMat[i].transpose();\n      TURegressionCoeff[i] = inverse(TpiPrime.mmul(predScoreMat[i]))\n        .mmul(TpiPrime)\n        .mmul(YScoreMat);\n\n      result = new SingularValueDecomposition(\n        TpiPrime.mmul(\n          Matrix.sub(kernelX[i][i], predScoreMat[i].mmul(TpiPrime)),\n        ).mmul(predScoreMat[i]),\n        {\n          computeLeftSingularVectors: true,\n          computeRightSingularVectors: false,\n        },\n      );\n      let CoTemp = result.leftSingularVectors;\n      let SoTemp = result.diagonalMatrix;\n\n      YOrthLoadingVec[i] = CoTemp.subMatrix(0, CoTemp.rows - 1, 0, 0);\n      YOrthEigen[i] = SoTemp.get(0, 0);\n\n      YOrthScoreMat[i] = Matrix.sub(\n        kernelX[i][i],\n        predScoreMat[i].mmul(TpiPrime),\n      )\n        .mmul(predScoreMat[i])\n        .mmul(YOrthLoadingVec[i])\n        .mul(Math.pow(YOrthEigen[i], -0.5));\n\n      let toiPrime = YOrthScoreMat[i].transpose();\n      YOrthScoreNorm[i] = Matrix.sqrt(toiPrime.mmul(YOrthScoreMat[i]));\n\n      YOrthScoreMat[i] = YOrthScoreMat[i].divRowVector(YOrthScoreNorm[i]);\n\n      let ITo = Matrix.sub(\n        Identity,\n        YOrthScoreMat[i].mmul(YOrthScoreMat[i].transpose()),\n      );\n\n      kernelX[0][i + 1] = kernelX[0][i].mmul(ITo);\n      kernelX[i + 1][i + 1] = ITo.mmul(kernelX[i][i]).mmul(ITo);\n    }\n\n    let lastScoreMat = kernelX[0][this.orthogonalComp]\n      .transpose()\n      .mmul(YScoreMat)\n      .mmul(SigmaPow);\n    predScoreMat[this.orthogonalComp] = lastScoreMat.clone();\n    let lastTpPrime = lastScoreMat.transpose();\n    TURegressionCoeff[this.orthogonalComp] = inverse(\n      lastTpPrime.mmul(lastScoreMat),\n    )\n      .mmul(lastTpPrime)\n      .mmul(YScoreMat);\n\n    this.YLoadingMat = YLoadingMat;\n    this.SigmaPow = SigmaPow;\n    this.YScoreMat = YScoreMat;\n    this.predScoreMat = predScoreMat;\n    this.YOrthLoadingVec = YOrthLoadingVec;\n    this.YOrthEigen = YOrthEigen;\n    this.YOrthScoreMat = YOrthScoreMat;\n    this.toNorm = YOrthScoreNorm;\n    this.TURegressionCoeff = TURegressionCoeff;\n    this.kernelX = kernelX;\n  }\n\n  /**\n   * Predicts the output given the matrix to predict.\n   * @param {Matrix|Array} toPredict\n   * @return {{y: Matrix, predScoreMat: Array<Matrix>, predYOrthVectors: Array<Matrix>}} predictions\n   */\n  predict(toPredict) {\n    let KTestTrain = this.kernel.compute(toPredict, this.trainingSet);\n\n    let temp = KTestTrain;\n    KTestTrain = new Array(this.orthogonalComp + 1);\n    for (let i = 0; i < this.orthogonalComp + 1; i++) {\n      KTestTrain[i] = new Array(this.orthogonalComp + 1);\n    }\n    KTestTrain[0][0] = temp;\n\n    let YOrthScoreVector = new Array(this.orthogonalComp);\n    let predScoreMat = new Array(this.orthogonalComp);\n\n    let i;\n    for (i = 0; i < this.orthogonalComp; ++i) {\n      predScoreMat[i] = KTestTrain[i][0]\n        .mmul(this.YScoreMat)\n        .mmul(this.SigmaPow);\n\n      YOrthScoreVector[i] = Matrix.sub(\n        KTestTrain[i][i],\n        predScoreMat[i].mmul(this.predScoreMat[i].transpose()),\n      )\n        .mmul(this.predScoreMat[i])\n        .mmul(this.YOrthLoadingVec[i])\n        .mul(Math.pow(this.YOrthEigen[i], -0.5));\n\n      YOrthScoreVector[i] = YOrthScoreVector[i].divRowVector(this.toNorm[i]);\n\n      let scoreMatPrime = this.YOrthScoreMat[i].transpose();\n      KTestTrain[i + 1][0] = Matrix.sub(\n        KTestTrain[i][0],\n        YOrthScoreVector[i]\n          .mmul(scoreMatPrime)\n          .mmul(this.kernelX[0][i].transpose()),\n      );\n\n      let p1 = Matrix.sub(\n        KTestTrain[i][0],\n        KTestTrain[i][i].mmul(this.YOrthScoreMat[i]).mmul(scoreMatPrime),\n      );\n      let p2 = YOrthScoreVector[i].mmul(scoreMatPrime).mmul(this.kernelX[i][i]);\n      let p3 = p2.mmul(this.YOrthScoreMat[i]).mmul(scoreMatPrime);\n\n      KTestTrain[i + 1][i + 1] = p1.sub(p2).add(p3);\n    }\n\n    predScoreMat[i] = KTestTrain[i][0].mmul(this.YScoreMat).mmul(this.SigmaPow);\n    let prediction = predScoreMat[i]\n      .mmul(this.TURegressionCoeff[i])\n      .mmul(this.YLoadingMat.transpose());\n\n    return {\n      prediction,\n      predScoreMat,\n      predYOrthVectors: YOrthScoreVector,\n    };\n  }\n\n  /**\n   * Export the current model to JSON.\n   * @return {object} - Current model.\n   */\n  toJSON() {\n    return {\n      name: 'K-OPLS',\n      YLoadingMat: this.YLoadingMat,\n      SigmaPow: this.SigmaPow,\n      YScoreMat: this.YScoreMat,\n      predScoreMat: this.predScoreMat,\n      YOrthLoadingVec: this.YOrthLoadingVec,\n      YOrthEigen: this.YOrthEigen,\n      YOrthScoreMat: this.YOrthScoreMat,\n      toNorm: this.toNorm,\n      TURegressionCoeff: this.TURegressionCoeff,\n      kernelX: this.kernelX,\n      trainingSet: this.trainingSet,\n      orthogonalComp: this.orthogonalComp,\n      predictiveComp: this.predictiveComp,\n    };\n  }\n\n  /**\n   * Load a K-OPLS with the given model.\n   * @param {object} model\n   * @param {Kernel} kernel - kernel used on the model, see [ml-kernel](https://github.com/mljs/kernel).\n   * @return {KOPLS}\n   */\n  static load(model, kernel) {\n    if (model.name !== 'K-OPLS') {\n      throw new RangeError(`Invalid model: ${model.name}`);\n    }\n\n    if (!kernel) {\n      throw new RangeError('You must provide a kernel for the model!');\n    }\n\n    model.kernel = kernel;\n    return new KOPLS(true, model);\n  }\n}\n","/**\n *  Constructs a confusion matrix\n * @class ConfusionMatrix\n * @example\n * const CM = new ConfusionMatrix([[13, 2], [10, 5]], ['cat', 'dog'])\n * @param {Array<Array<number>>} matrix - The confusion matrix, a 2D Array. Rows represent the actual label and columns\n *     the predicted label.\n * @param {Array<any>} labels - Labels of the confusion matrix, a 1D Array\n */\nexport default class ConfusionMatrix {\n  constructor(matrix, labels) {\n    if (matrix.length !== matrix[0].length) {\n      throw new Error('Confusion matrix must be square');\n    }\n    if (labels.length !== matrix.length) {\n      throw new Error(\n        'Confusion matrix and labels should have the same length',\n      );\n    }\n    this.labels = labels;\n    this.matrix = matrix;\n  }\n\n  /**\n   * Construct confusion matrix from the predicted and actual labels (classes). Be sure to provide the arguments in\n   * the correct order!\n   * @param {Array<any>} actual  - The predicted labels of the classification\n   * @param {Array<any>} predicted     - The actual labels of the classification. Has to be of same length as\n   *     predicted.\n   * @param {object} [options] - Additional options\n   * @param {Array<any>} [options.labels] - The list of labels that should be used. If not provided the distinct set\n   *     of labels present in predicted and actual is used. Labels are compared using the strict equality operator\n   *     '==='\n   * @return {ConfusionMatrix} - Confusion matrix\n   */\n  static fromLabels(actual, predicted, options = {}) {\n    if (predicted.length !== actual.length) {\n      throw new Error('predicted and actual must have the same length');\n    }\n    let distinctLabels;\n    if (options.labels) {\n      distinctLabels = new Set(options.labels);\n    } else {\n      distinctLabels = new Set([...actual, ...predicted]);\n    }\n    distinctLabels = Array.from(distinctLabels);\n    if (options.sort) {\n      distinctLabels.sort(options.sort);\n    }\n\n    // Create confusion matrix and fill with 0's\n    const matrix = Array.from({ length: distinctLabels.length });\n    for (let i = 0; i < matrix.length; i++) {\n      matrix[i] = new Array(matrix.length);\n      matrix[i].fill(0);\n    }\n\n    for (let i = 0; i < predicted.length; i++) {\n      const actualIdx = distinctLabels.indexOf(actual[i]);\n      const predictedIdx = distinctLabels.indexOf(predicted[i]);\n      if (actualIdx >= 0 && predictedIdx >= 0) {\n        matrix[actualIdx][predictedIdx]++;\n      }\n    }\n\n    return new ConfusionMatrix(matrix, distinctLabels);\n  }\n\n  /**\n   * Get the confusion matrix\n   * @return {Array<Array<number> >}\n   */\n  getMatrix() {\n    return this.matrix;\n  }\n\n  getLabels() {\n    return this.labels;\n  }\n\n  /**\n   * Get the total number of samples\n   * @return {number}\n   */\n  getTotalCount() {\n    let predicted = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      for (let j = 0; j < this.matrix.length; j++) {\n        predicted += this.matrix[i][j];\n      }\n    }\n    return predicted;\n  }\n\n  /**\n   * Get the total number of true predictions\n   * @return {number}\n   */\n  getTrueCount() {\n    let count = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      count += this.matrix[i][i];\n    }\n    return count;\n  }\n\n  /**\n   * Get the total number of false predictions.\n   * @return {number}\n   */\n  getFalseCount() {\n    return this.getTotalCount() - this.getTrueCount();\n  }\n\n  /**\n   * Get the number of true positive predictions.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getTruePositiveCount(label) {\n    const index = this.getIndex(label);\n    return this.matrix[index][index];\n  }\n\n  /**\n   * Get the number of true negative predictions\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getTrueNegativeCount(label) {\n    const index = this.getIndex(label);\n    let count = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      for (let j = 0; j < this.matrix.length; j++) {\n        if (i !== index && j !== index) {\n          count += this.matrix[i][j];\n        }\n      }\n    }\n    return count;\n  }\n\n  /**\n   * Get the number of false positive predictions.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalsePositiveCount(label) {\n    const index = this.getIndex(label);\n    let count = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      if (i !== index) {\n        count += this.matrix[i][index];\n      }\n    }\n    return count;\n  }\n\n  /**\n   * Get the number of false negative predictions.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalseNegativeCount(label) {\n    const index = this.getIndex(label);\n    let count = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      if (i !== index) {\n        count += this.matrix[index][i];\n      }\n    }\n    return count;\n  }\n\n  /**\n   * Get the number of real positive samples.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getPositiveCount(label) {\n    return this.getTruePositiveCount(label) + this.getFalseNegativeCount(label);\n  }\n\n  /**\n   * Get the number of real negative samples.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getNegativeCount(label) {\n    return this.getTrueNegativeCount(label) + this.getFalsePositiveCount(label);\n  }\n\n  /**\n   * Get the index in the confusion matrix that corresponds to the given label\n   * @param {any} label - The label to search for\n   * @throws if the label is not found\n   * @return {number}\n   */\n  getIndex(label) {\n    const index = this.labels.indexOf(label);\n    if (index === -1) throw new Error('The label does not exist');\n    return index;\n  }\n\n  /**\n   * Get the true positive rate a.k.a. sensitivity. Computes the ratio between the number of true positive predictions and the total number of positive samples.\n   * {@link https://en.wikipedia.org/wiki/Sensitivity_and_specificity}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number} - The true positive rate [0-1]\n   */\n  getTruePositiveRate(label) {\n    return this.getTruePositiveCount(label) / this.getPositiveCount(label);\n  }\n\n  /**\n   * Get the true negative rate a.k.a. specificity. Computes the ration between the number of true negative predictions and the total number of negative samples.\n   * {@link https://en.wikipedia.org/wiki/Sensitivity_and_specificity}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getTrueNegativeRate(label) {\n    return this.getTrueNegativeCount(label) / this.getNegativeCount(label);\n  }\n\n  /**\n   * Get the positive predictive value a.k.a. precision. Computes TP / (TP + FP)\n   * {@link https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getPositivePredictiveValue(label) {\n    const TP = this.getTruePositiveCount(label);\n    return TP / (TP + this.getFalsePositiveCount(label));\n  }\n\n  /**\n   * Negative predictive value\n   * {@link https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getNegativePredictiveValue(label) {\n    const TN = this.getTrueNegativeCount(label);\n    return TN / (TN + this.getFalseNegativeCount(label));\n  }\n\n  /**\n   * False negative rate a.k.a. miss rate.\n   * {@link https://en.wikipedia.org/wiki/Type_I_and_type_II_errors#False_positive_and_false_negative_rates}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalseNegativeRate(label) {\n    return 1 - this.getTruePositiveRate(label);\n  }\n\n  /**\n   * False positive rate a.k.a. fall-out rate.\n   * {@link https://en.wikipedia.org/wiki/Type_I_and_type_II_errors#False_positive_and_false_negative_rates}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalsePositiveRate(label) {\n    return 1 - this.getTrueNegativeRate(label);\n  }\n\n  /**\n   * False discovery rate (FDR)\n   * {@link https://en.wikipedia.org/wiki/False_discovery_rate}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalseDiscoveryRate(label) {\n    const FP = this.getFalsePositiveCount(label);\n    return FP / (FP + this.getTruePositiveCount(label));\n  }\n\n  /**\n   * False omission rate (FOR)\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getFalseOmissionRate(label) {\n    const FN = this.getFalseNegativeCount(label);\n    return FN / (FN + this.getTruePositiveCount(label));\n  }\n\n  /**\n   * F1 score\n   * {@link https://en.wikipedia.org/wiki/F1_score}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getF1Score(label) {\n    const TP = this.getTruePositiveCount(label);\n    return (\n      (2 * TP) /\n      (2 * TP +\n        this.getFalsePositiveCount(label) +\n        this.getFalseNegativeCount(label))\n    );\n  }\n\n  /**\n   * Matthews correlation coefficient (MCC)\n   * {@link https://en.wikipedia.org/wiki/Matthews_correlation_coefficient}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getMatthewsCorrelationCoefficient(label) {\n    const TP = this.getTruePositiveCount(label);\n    const TN = this.getTrueNegativeCount(label);\n    const FP = this.getFalsePositiveCount(label);\n    const FN = this.getFalseNegativeCount(label);\n    return (\n      (TP * TN - FP * FN) /\n      Math.sqrt((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN))\n    );\n  }\n\n  /**\n   * Informedness\n   * {@link https://en.wikipedia.org/wiki/Youden%27s_J_statistic}\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getInformedness(label) {\n    return (\n      this.getTruePositiveRate(label) + this.getTrueNegativeRate(label) - 1\n    );\n  }\n\n  /**\n   * Markedness\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {number}\n   */\n  getMarkedness(label) {\n    return (\n      this.getPositivePredictiveValue(label) +\n      this.getNegativePredictiveValue(label) -\n      1\n    );\n  }\n\n  /**\n   * Get the confusion table.\n   * @param {any} label - The label that should be considered \"positive\"\n   * @return {Array<Array<number> >} - The 2x2 confusion table. [[TP, FN], [FP, TN]]\n   */\n  getConfusionTable(label) {\n    return [\n      [this.getTruePositiveCount(label), this.getFalseNegativeCount(label)],\n      [this.getFalsePositiveCount(label), this.getTrueNegativeCount(label)],\n    ];\n  }\n\n  /**\n   * Get total accuracy.\n   * @return {number} - The ratio between the number of true predictions and total number of classifications ([0-1])\n   */\n  getAccuracy() {\n    let correct = 0;\n    let incorrect = 0;\n    for (let i = 0; i < this.matrix.length; i++) {\n      for (let j = 0; j < this.matrix.length; j++) {\n        if (i === j) correct += this.matrix[i][j];\n        else incorrect += this.matrix[i][j];\n      }\n    }\n    return correct / (correct + incorrect);\n  }\n\n  /**\n   * Returns the element in the confusion matrix that corresponds to the given actual and predicted labels.\n   * @param {any} actual - The true label\n   * @param {any} predicted - The predicted label\n   * @return {number} - The element in the confusion matrix\n   */\n  getCount(actual, predicted) {\n    const actualIndex = this.getIndex(actual);\n    const predictedIndex = this.getIndex(predicted);\n    return this.matrix[actualIndex][predictedIndex];\n  }\n\n  /**\n   * Compute the general prediction accuracy\n   * @deprecated Use getAccuracy\n   * @return {number} - The prediction accuracy ([0-1]\n   */\n  get accuracy() {\n    return this.getAccuracy();\n  }\n\n  /**\n   * Compute the number of predicted observations\n   * @deprecated Use getTotalCount\n   * @return {number}\n   */\n  get total() {\n    return this.getTotalCount();\n  }\n}\n","/**\n * get folds indexes\n * @param {Array} features\n * @param {Number} k - number of folds, a\n */\nexport function getFolds(features, k = 5) {\n  let N = features.length;\n  let allIdx = new Array(N);\n  for (let i = 0; i < N; i++) {\n    allIdx[i] = i;\n  }\n\n  let l = Math.floor(N / k);\n  // create random k-folds\n  let current = [];\n  let folds = [];\n  while (allIdx.length) {\n    let randi = Math.floor(Math.random() * allIdx.length);\n    current.push(allIdx[randi]);\n    allIdx.splice(randi, 1);\n    if (current.length === l) {\n      folds.push(current);\n      current = [];\n    }\n  }\n  // we push the remaining to the last fold so that the total length is\n  // preserved. Otherwise the Q2 will fail.\n  if (current.length) current.forEach((e) => folds[k - 1].push(e));\n  folds = folds.slice(0, k);\n\n  let foldsIndex = folds.map((x, idx) => ({\n    testIndex: x,\n    trainIndex: [].concat(...folds.filter((el, idx2) => idx2 !== idx)),\n  }));\n  return foldsIndex;\n}\n","import { isAnyArray } from 'is-any-array';\n\nfunction sum(input) {\n  if (!isAnyArray(input)) {\n    throw new TypeError('input must be an array');\n  }\n\n  if (input.length === 0) {\n    throw new TypeError('input must not be empty');\n  }\n\n  var sumValue = 0;\n\n  for (var i = 0; i < input.length; i++) {\n    sumValue += input[i];\n  }\n\n  return sumValue;\n}\n\nexport { sum as default };\n","import sum from 'ml-array-sum';\n\nfunction mean(input) {\n  return sum(input) / input.length;\n}\n\nexport { mean as default };\n","import mean from 'ml-array-mean';\n/**\n * Returns the Area under the curve.\n * @param curves Object containing the true positivie and false positive rate vectors.\n * @return Area under the curve.\n */\nexport function getAuc(curves) {\n    const auc = [];\n    for (const curve of curves) {\n        let area = 0;\n        const x = curve.specificities;\n        const y = curve.sensitivities;\n        for (let i = 1; i < x.length; i++) {\n            area += 0.5 * (x[i] - x[i - 1]) * (y[i] + y[i - 1]);\n        }\n        area = area > 0.5 ? area : 1 - area;\n        auc.push(area);\n    }\n    return mean(auc);\n}\n//# sourceMappingURL=getAuc.js.map","/**\n * Returns an array of thresholds to build the curve.\n * @param predictions Array of predictions.\n * @return An array of thresholds.\n */\nexport function getThresholds(predictions) {\n    const uniques = [...new Set(predictions)].sort((a, b) => a - b);\n    const thresholds = [Number.NEGATIVE_INFINITY];\n    for (let i = 0; i < uniques.length - 1; i++) {\n        const half = (uniques[i + 1] - uniques[i]) / 2;\n        thresholds.push(uniques[i] + half);\n    }\n    thresholds.push(Number.POSITIVE_INFINITY);\n    return thresholds;\n}\n//# sourceMappingURL=getThresholds.js.map","import { getThresholds } from './utilities/getThresholds';\n/**\n * Returns a ROC (Receiver Operating Characteristic) curve for a given response and prediction vectors.\n * @param responses Array containing category metadata.\n * @param predictions Array containing the results of regression.\n * @return sensitivities and specificities as a object.\n */\nexport function getBinaryClassifiers(responses, predictions) {\n    const limits = getThresholds(predictions);\n    const truePositives = [];\n    const falsePositives = [];\n    const trueNegatives = [];\n    const falseNegatives = [];\n    for (const limit of limits) {\n        let truePositive = 0;\n        let falsePositive = 0;\n        let trueNegative = 0;\n        let falseNegative = 0;\n        const category = responses[0];\n        for (let j = 0; j < responses.length; j++) {\n            if (responses[j] !== category && predictions[j] > limit)\n                truePositive++;\n            if (responses[j] === category && predictions[j] > limit)\n                falsePositive++;\n            if (responses[j] === category && predictions[j] < limit)\n                trueNegative++;\n            if (responses[j] !== category && predictions[j] < limit)\n                falseNegative++;\n        }\n        truePositives.push(truePositive);\n        falsePositives.push(falsePositive);\n        trueNegatives.push(trueNegative);\n        falseNegatives.push(falseNegative);\n    }\n    return {\n        truePositives,\n        falsePositives,\n        trueNegatives,\n        falseNegatives,\n    };\n}\n//# sourceMappingURL=getBinaryClassifiers.js.map","/**\n * @param array Array containing category metadata\n * @return Class object.\n */\nexport function getClasses(array) {\n    let nbClasses = 0;\n    const classes = [{ name: array[0], value: 0, ids: [] }];\n    for (const element of array) {\n        const currentClass = classes.some((item) => item.name === element);\n        if (!currentClass) {\n            nbClasses++;\n            classes.push({ name: element, value: nbClasses, ids: [] });\n        }\n    }\n    for (const category of classes) {\n        const label = category.name;\n        const indexes = [];\n        for (let j = 0; j < array.length; j++) {\n            if (array[j] === label)\n                indexes.push(j);\n        }\n        category.ids = indexes;\n    }\n    return classes;\n}\n//# sourceMappingURL=getClasses.js.map","/**\n * Returns an array of pairs of classes.\n * @param list Array containing a list of classes.\n * @return Array with pairs of classes.\n */\nexport function getClassesPairs(list) {\n    const pairs = [];\n    for (let i = 0; i < list.length - 1; i++) {\n        for (let j = i + 1; j < list.length; j++) {\n            pairs.push([list[i], list[j]]);\n        }\n    }\n    return pairs;\n}\n//# sourceMappingURL=getClassesPairs.js.map","/**\n * Returns the array of metadata numerically categorized.\n * @param array Array containing the categories.\n * @param pair Object containing information about the two classes to deal with.\n * @return Array containing the prediction values arranged for the corresponding classes.\n */\n// eslint-disable-next-line @typescript-eslint/no-explicit-any\nexport function getSelectedResults(array, pair) {\n    const results = [];\n    for (const item of pair) {\n        for (const id of item.ids) {\n            const result = array[id];\n            results.push(result);\n        }\n    }\n    return results;\n}\n//# sourceMappingURL=getSelectedResults.js.map","import { getBinaryClassifiers } from './getBinaryClassifiers';\nimport { getClasses } from './utilities/getClasses';\nimport { getClassesPairs } from './utilities/getClassesPairs';\nimport { getSelectedResults } from './utilities/getSelectedResults';\n/**\n * Returns a ROC (Receiver Operating Characteristic) curve for a given response and prediction vectors.\n * @param responses Array containing category metadata.\n * @param predictions Array containing the results of regression.\n * @return sensitivities and specificities as a object.\n */\nexport function getRocCurve(responses, predictions) {\n    const classes = getClasses(responses);\n    const pairsOfClasses = getClassesPairs(classes);\n    const curves = [];\n    for (const pairs of pairsOfClasses) {\n        const tests = getSelectedResults(predictions, pairs);\n        const targets = getSelectedResults(responses, pairs);\n        const { truePositives, falsePositives, trueNegatives, falseNegatives } = getBinaryClassifiers(targets, tests);\n        const curve = { sensitivities: [], specificities: [] };\n        for (let i = 0; i < truePositives.length; i++) {\n            curve.sensitivities.push(truePositives[i] / (truePositives[i] + falseNegatives[i]));\n            curve.specificities.push(trueNegatives[i] / (falsePositives[i] + trueNegatives[i]));\n        }\n        curves.push(curve);\n    }\n    return curves;\n}\n//# sourceMappingURL=getRocCurve.js.map","import { Matrix, NIPALS } from 'ml-matrix';\n\n/**\n * OPLS loop\n * @param {Array|Matrix} data matrix with features\n * @param {Array|Matrix} labels an array of labels (dependent variable)\n * @param {Object} [options={}] an object with options\n * @return {Object} an object with model (filteredX: err,\n    loadingsXOrtho: pOrtho,\n    scoresXOrtho: tOrtho,\n    weightsXOrtho: wOrtho,\n    weightsPred: w,\n    loadingsXpred: p,\n    scoresXpred: t,\n    loadingsY:)\n */\nexport function oplsNipals(data, labels, options = {}) {\n  const { numberOSC = 1000, limit = 1e-10 } = options;\n  data = Matrix.checkMatrix(data);\n  labels = Matrix.checkMatrix(labels);\n  let tW = [];\n  if (labels.columns > 1) {\n    const wh = getWh(data, labels);\n    const ssWh = wh.norm() ** 2;\n    let ssT = ssWh;\n    let pcaW;\n    let count = 0;\n    do {\n      if (count === 0) {\n        pcaW = new NIPALS(wh.clone());\n        tW.push(pcaW.t);\n      } else {\n        const data = pcaW.xResidual;\n        pcaW = new NIPALS(data);\n        tW.push(pcaW.t);\n      }\n      ssT = pcaW.t.norm() ** 2;\n      count++;\n    } while (ssT / ssWh > limit);\n  }\n  let u = labels.getColumnVector(0);\n  let diff = 1;\n  let t, c, w, uNew;\n  for (let i = 0; i < numberOSC && diff > limit; i++) {\n    w = u\n      .transpose()\n      .mmul(data)\n      .div(u.norm() ** 2);\n    w = w.transpose().div(w.norm());\n    t = data.mmul(w).div(w.norm() ** 2); // t_h paso 3\n\n    // calc loading\n    c = t\n      .transpose()\n      .mmul(labels)\n      .div(t.norm() ** 2);\n\n    // calc new u and compare with one in previus iteration (stop criterion)\n    uNew = labels.mmul(c.transpose()).div(c.norm() ** 2);\n    if (i > 0) {\n      diff = uNew.clone().sub(u).pow(2).sum() / uNew.clone().pow(2).sum();\n    }\n    u = uNew.clone();\n  }\n  // calc loadings\n  let wOrtho;\n  let p = t\n    .transpose()\n    .mmul(data)\n    .div(t.norm() ** 2);\n  if (labels.columns > 1) {\n    for (let i = 0; i < tW.length - 1; i++) {\n      let tw = tW[i].transpose();\n      p = p.sub(\n        tw\n          .mmul(p.transpose())\n          .div(tw.norm() ** 2)\n          .mmul(tw),\n      );\n    }\n    wOrtho = p.clone();\n  } else {\n    wOrtho = p.clone().sub(\n      w\n        .transpose()\n        .mmul(p.transpose())\n        .div(w.norm() ** 2)\n        .mmul(w.transpose()),\n    );\n  }\n  wOrtho.div(wOrtho.norm());\n  let tOrtho = data.mmul(wOrtho.transpose()).div(wOrtho.norm() ** 2);\n\n  // orthogonal loadings\n  let pOrtho = tOrtho\n    .transpose()\n    .mmul(data)\n    .div(tOrtho.norm() ** 2);\n\n  // filtered data\n  let err = data.clone().sub(tOrtho.mmul(pOrtho));\n  return {\n    filteredX: err,\n    weightsXOrtho: wOrtho,\n    loadingsXOrtho: pOrtho,\n    scoresXOrtho: tOrtho,\n    weightsXPred: w,\n    loadingsXpred: p,\n    scoresXpred: t,\n    loadingsY: c,\n  };\n}\n\nfunction getWh(xValue, yValue) {\n  let result = new Matrix(xValue.columns, yValue.columns);\n  for (let i = 0; i < yValue.columns; i++) {\n    let yN = yValue.getColumnVector(i).transpose();\n    let component = yN.mmul(xValue).div(yN.norm() ** 2);\n    result.setColumn(i, component.getRow(0));\n  }\n  return result;\n}\n","import { Matrix } from 'ml-matrix';\n\n/**\n * Get total sum of square\n * @param {Array} x an array\n * @return {Number} - the sum of the squares\n */\nexport function tss(x) {\n  return Matrix.mul(x, x).sum();\n}\n","import { isAnyArray } from 'is-any-array';\nimport ConfusionMatrix from 'ml-confusion-matrix';\nimport { getFolds } from 'ml-cross-validation';\nimport { Matrix, NIPALS } from 'ml-matrix';\nimport { getRocCurve, getAuc, getClasses } from 'ml-roc-multiclass';\n\nimport { oplsNipals } from './oplsNipals.js';\nimport { tss } from './util/tss.js';\n\n/**\n * Creates new OPLS (orthogonal partial latent structures) from features and labels.\n * @param {Array} data - matrix containing data (X).\n * @param {Array} labels - 1D Array containing metadata (Y).\n * @param {Object} [options={}]\n * @param {boolean} [options.center = true] - should the data be centered (subtract the mean).\n * @param {boolean} [options.scale = true] - should the data be scaled (divide by the standard deviation).\n * @param {Array} [options.cvFolds = []] - Allows to provide folds as array of objects with the arrays trainIndex and testIndex as properties.\n * @param {number} [options.nbFolds = 7] - Allows to generate the defined number of folds with the training and test set choosen randomly from the data set.\n * */\n\nexport class OPLS {\n  constructor(data, labels, options = {}) {\n    if (data === true) {\n      const opls = options;\n      this.center = opls.center;\n      this.scale = opls.scale;\n      this.means = opls.means;\n      this.meansY = opls.meansY;\n      this.stdevs = opls.stdevs;\n      this.stdevsY = opls.stdevsY;\n      this.model = opls.model;\n      this.predictiveScoresCV = opls.predictiveScoresCV;\n      this.orthogonalScoresCV = opls.orthogonalScoresCV;\n      this.yHatScoresCV = opls.yHatScoresCV;\n      this.mode = opls.mode;\n      return;\n    }\n\n    const features = new Matrix(data);\n    // set default values\n    // cvFolds allows to define folds for testing purpose\n    const { center = true, scale = true, cvFolds = [], nbFolds = 7 } = options;\n\n    this.labels = labels;\n    let group;\n    if (typeof labels[0] === 'number') {\n      // numeric labels: OPLS regression is used\n      this.mode = 'regression';\n      group = Matrix.from1DArray(labels.length, 1, labels);\n    } else if (typeof labels[0] === 'string') {\n      // non-numeric labels: OPLS-DA is used\n      this.mode = 'discriminantAnalysis';\n      group = Matrix.checkMatrix(createDummyY(labels)).transpose();\n    }\n\n    // getting center and scale the features (all)\n    this.center = center;\n    if (this.center) {\n      this.means = features.mean('column');\n      this.meansY = group.mean('column');\n    } else {\n      this.stdevs = null;\n    }\n    this.scale = scale;\n    if (this.scale) {\n      this.stdevs = features.standardDeviation('column');\n      this.stdevsY = group.standardDeviation('column');\n    } else {\n      this.means = null;\n    }\n\n    // check and remove for features with sd = 0 TODO here\n    // check opls.R line 70\n\n    const folds = cvFolds.length > 0 ? cvFolds : getFolds(labels, nbFolds);\n    const Q2 = [];\n    const aucResult = [];\n    this.model = [];\n    this.predictiveScoresCV = [];\n    this.orthogonalScoresCV = [];\n    this.yHatScoresCV = [];\n    const oplsCV = [];\n\n    let modelNC = [];\n\n    // this code could be made more efficient by reverting the order of the loops\n    // this is a legacy loop to be consistent with R code from MetaboMate package\n    // this allows for having statistic (R2) from CV to decide wether to continue\n    // with more latent structures\n    let overfitted = false;\n    let nc = 0;\n    let value;\n\n    do {\n      const yHatk = new Matrix(group.rows, 1);\n      const predictiveScoresK = new Matrix(group.rows, 1);\n      const orthogonalScoresK = new Matrix(group.rows, 1);\n      oplsCV[nc] = [];\n      for (let f = 0; f < folds.length; f++) {\n        const trainTest = this._getTrainTest(features, group, folds[f]);\n        const testFeatures = trainTest.testFeatures;\n        const trainFeatures = trainTest.trainFeatures;\n        const trainLabels = trainTest.trainLabels;\n        // determine center and scale of training set\n        const dataCenter = trainFeatures.mean('column');\n        const dataSD = trainFeatures.standardDeviation('column');\n\n        // center and scale training set\n        if (center) {\n          trainFeatures.center('column');\n          trainLabels.center('column');\n        }\n\n        if (scale) {\n          trainFeatures.scale('column');\n          trainLabels.scale('column');\n        }\n        // perform opls\n        let oplsk;\n        if (nc === 0) {\n          oplsk = oplsNipals(trainFeatures, trainLabels);\n        } else {\n          oplsk = oplsNipals(oplsCV[nc - 1][f].filteredX, trainLabels);\n        }\n\n        // store model for next component\n        oplsCV[nc][f] = oplsk;\n        const plsCV = new NIPALS(oplsk.filteredX, { Y: trainLabels });\n\n        // scaling the test dataset with respect to the train\n        testFeatures.center('column', { center: dataCenter });\n        testFeatures.scale('column', { scale: dataSD });\n\n        const Eh = testFeatures;\n        // removing the orthogonal components from PLS\n        let scores;\n        for (let idx = 0; idx < nc + 1; idx++) {\n          scores = Eh.mmul(oplsCV[idx][f].weightsXOrtho.transpose()); // ok\n          Eh.sub(scores.mmul(oplsCV[idx][f].loadingsXOrtho));\n        }\n        // prediction\n        const predictiveComponents = Eh.mmul(plsCV.w.transpose());\n        const yHatComponents = predictiveComponents\n          .mmul(plsCV.betas)\n          .mmul(plsCV.q.transpose()); // ok\n\n        const yHat = new Matrix(yHatComponents.rows, 1);\n        for (let i = 0; i < yHatComponents.rows; i++) {\n          yHat.setRow(i, [yHatComponents.getRowVector(i).sum()]);\n        }\n        // adding all prediction from all folds\n        for (let i = 0; i < folds[f].testIndex.length; i++) {\n          yHatk.setRow(folds[f].testIndex[i], [yHat.get(i, 0)]);\n          predictiveScoresK.setRow(folds[f].testIndex[i], [\n            predictiveComponents.get(i, 0),\n          ]);\n          orthogonalScoresK.setRow(folds[f].testIndex[i], [scores.get(i, 0)]);\n        }\n      } // end of loop over folds\n      this.predictiveScoresCV.push(predictiveScoresK);\n      this.orthogonalScoresCV.push(orthogonalScoresK);\n      this.yHatScoresCV.push(yHatk);\n\n      // calculate Q2y for all the prediction (all folds)\n      // ROC for DA is not implemented (check opls.R line 183) TODO\n      const tssy = tss(group.center('column').scale('column'));\n      let press = 0;\n      for (let i = 0; i < group.columns; i++) {\n        press += tss(group.getColumnVector(i).sub(yHatk));\n      }\n      const Q2y = 1 - press / group.columns / tssy;\n      Q2.push(Q2y);\n      if (this.mode === 'regression') {\n        value = Q2y;\n      } else if (this.mode === 'discriminantAnalysis') {\n        const rocCurve = getRocCurve(labels, yHatk.to1DArray());\n        const areaUnderCurve = getAuc(rocCurve);\n        aucResult.push(areaUnderCurve);\n        value = areaUnderCurve;\n      }\n\n      // calculate the R2y for the complete data\n      if (nc === 0) {\n        modelNC = this._predictAll(features, group);\n      } else {\n        modelNC = this._predictAll(modelNC.xRes, group, {\n          scale: false,\n          center: false,\n        });\n      }\n\n      // adding the predictive statistics from CV\n      let listOfValues;\n      modelNC.Q2y = Q2;\n      if (this.mode === 'regression') {\n        listOfValues = Q2;\n      } else {\n        listOfValues = aucResult;\n        modelNC.auc = aucResult;\n      }\n      modelNC.value = value;\n\n      if (nc > 0) {\n        overfitted = value - listOfValues[nc - 1] < 0.05;\n      }\n      this.model.push(modelNC);\n      // store the model for each component\n      nc++;\n      // console.warn(`OPLS iteration over # of Components: ${nc + 1}`);\n    } while (!overfitted); // end of loop over nc\n    // store scores from CV\n    const predictiveScoresCV = this.predictiveScoresCV;\n    const orthogonalScoresCV = this.orthogonalScoresCV;\n    const yHatScoresCV = this.yHatScoresCV;\n    const m = this.model[nc - 1];\n    const orthogonalData = new Matrix(features.rows, features.columns);\n    const orthogonalScores = new Matrix(features.rows, nc - 1);\n    const orthogonalLoadings = new Matrix(nc - 1, features.columns);\n    const orthogonalWeights = new Matrix(nc - 1, features.columns);\n    for (let i = 0; i < this.model.length - 1; i++) {\n      orthogonalData.add(this.model[i].XOrth);\n      orthogonalScores.setSubMatrix(this.model[i].orthogonalScores, 0, i);\n      orthogonalLoadings.setSubMatrix(this.model[i].orthogonalLoadings, i, 0);\n      orthogonalWeights.setSubMatrix(this.model[i].orthogonalWeights, i, 0);\n    }\n\n    const FeaturesCS = features.center('column').scale('column');\n    let labelsCS;\n    if (this.mode === 'regression') {\n      labelsCS = group.clone().center('column').scale('column');\n    } else {\n      labelsCS = group;\n    }\n\n    const orthogonalizedData = FeaturesCS.clone().sub(orthogonalData);\n    const plsCall = new NIPALS(orthogonalizedData, { Y: labelsCS });\n    const residualData = orthogonalizedData\n      .clone()\n      .sub(plsCall.t.mmul(plsCall.p));\n    const R2x = this.model.map((x) => x.R2x);\n    const R2y = this.model.map((x) => x.R2y);\n\n    this.output = {\n      Q2y: Q2,\n      auc: aucResult,\n      R2x,\n      R2y,\n      predictiveComponents: plsCall.t,\n      predictiveLoadings: plsCall.p,\n      predictiveWeights: plsCall.w,\n      betas: plsCall.betas,\n      Qpc: plsCall.q,\n      predictiveScoresCV,\n      orthogonalScoresCV,\n      yHatScoresCV,\n      oplsCV,\n      orthogonalScores,\n      orthogonalLoadings,\n      orthogonalWeights,\n      Xorth: orthogonalData,\n      yHat: m.totalPred,\n      Yres: m.plsC.yResidual,\n      residualData,\n      folds,\n    };\n  }\n\n  /**\n   * get access to all the computed elements\n   * Mainly for debug and testing\n   * @return {Object} output object\n   */\n  getLogs() {\n    return this.output;\n  }\n\n  getScores() {\n    const scoresX = this.predictiveScoresCV.map((x) => x.to1DArray());\n    const scoresY = this.orthogonalScoresCV.map((x) => x.to1DArray());\n    return { scoresX, scoresY };\n  }\n\n  /**\n   * Load an OPLS model from JSON\n   * @param {Object} model\n   * @return {OPLS}\n   */\n  static load(model) {\n    if (typeof model.name !== 'string') {\n      throw new TypeError('model must have a name property');\n    }\n    if (model.name !== 'OPLS') {\n      throw new RangeError(`invalid model: ${model.name}`);\n    }\n    return new OPLS(true, [], model);\n  }\n\n  /**\n   * Export the current model to a JSON object\n   * @return {Object} model\n   */\n  toJSON() {\n    return {\n      name: 'OPLS',\n      center: this.center,\n      scale: this.scale,\n      means: this.means,\n      stdevs: this.stdevs,\n      model: this.model,\n      predictiveScoresCV: this.predictiveScoresCV,\n      orthogonalScoresCV: this.orthogonalScoresCV,\n      yHatScoresCV: this.yHatScoresCV,\n    };\n  }\n\n  /**\n   * Predict scores for new data\n   * @param {Matrix} features - a matrix containing new data\n   * @param {Object} [options={}]\n   * @param {Array} [options.trueLabel] - an array with true values to compute confusion matrix\n   * @param {Number} [options.nc] - the number of components to be used\n   * @return {Object} - predictions\n   */\n  predictCategory(features, options = {}) {\n    const {\n      trueLabels = [],\n      center = this.center,\n      scale = this.scale,\n    } = options;\n    if (isAnyArray(features)) {\n      if (features[0].length === undefined) {\n        features = Matrix.from1DArray(1, features.length, features);\n      } else {\n        features = Matrix.checkMatrix(features);\n      }\n    }\n    const prediction = this.predict(features, { trueLabels, center, scale });\n    const predictiveComponents = this.output.predictiveComponents.to1DArray();\n    const newTPred = prediction.predictiveComponents.to1DArray();\n    const categories = getClasses(this.labels);\n    const classes = this.labels.slice();\n    const result = [];\n\n    for (const pred of newTPred) {\n      let item;\n      let auc = 0;\n      for (const category of categories) {\n        const testTPred = predictiveComponents.slice();\n        testTPred.push(pred);\n        const testClasses = classes.slice();\n        testClasses.push(category.name);\n        const rocCurve = getRocCurve(testClasses, testTPred);\n        const areaUnderCurve = getAuc(rocCurve);\n        if (auc < areaUnderCurve) {\n          item = category.name;\n          auc = areaUnderCurve;\n        }\n      }\n      result.push(item);\n    }\n    return result;\n  }\n\n  /**\n   * Predict scores for new data\n   * @param {Matrix} features - a matrix containing new data\n   * @param {Object} [options={}]\n   * @param {Array} [options.trueLabel] - an array with true values to compute confusion matrix\n   * @param {Number} [options.nc] - the number of components to be used\n   * @return {Object} - predictions\n   */\n  predict(features, options = {}) {\n    const {\n      trueLabels = [],\n      center = this.center,\n      scale = this.scale,\n    } = options;\n\n    let labels;\n    if (typeof trueLabels[0] === 'number') {\n      labels = Matrix.from1DArray(trueLabels.length, 1, trueLabels);\n    } else if (typeof trueLabels[0] === 'string') {\n      labels = Matrix.checkMatrix(createDummyY(trueLabels)).transpose();\n    }\n\n    features = new Matrix(features);\n\n    // scaling the test dataset with respect to the train\n    if (center) {\n      features.center('column', { center: this.means });\n      if (labels?.rows > 0) {\n        labels.center('column', { center: this.meansY });\n      }\n    }\n    if (scale) {\n      features.scale('column', { scale: this.stdevs });\n      if (labels?.rows > 0) {\n        labels.scale('column', { scale: this.stdevsY });\n      }\n    }\n\n    const nc =\n      this.mode === 'regression'\n        ? this.model[0].Q2y.length\n        : this.model[0].auc.length - 1;\n\n    const Eh = features.clone();\n    // removing the orthogonal components from PLS\n    let orthogonalScores;\n    let orthogonalWeights;\n    let orthogonalLoadings;\n    let totalPred;\n    let predictiveComponents;\n    for (let idx = 0; idx < nc; idx++) {\n      const model = this.model[idx];\n      orthogonalWeights = model.orthogonalWeights.transpose();\n      orthogonalLoadings = model.orthogonalLoadings;\n      orthogonalScores = Eh.mmul(orthogonalWeights);\n      Eh.sub(orthogonalScores.mmul(orthogonalLoadings));\n      // prediction\n      predictiveComponents = Eh.mmul(model.plsC.w.transpose());\n      const components = predictiveComponents\n        .mmul(model.plsC.betas)\n        .mmul(model.plsC.q.transpose());\n      totalPred = new Matrix(components.rows, 1);\n      for (let i = 0; i < components.rows; i++) {\n        totalPred.setRow(i, [components.getRowVector(i).sum()]);\n      }\n    }\n\n    if (labels?.rows > 0) {\n      if (this.mode === 'regression') {\n        const tssy = tss(labels);\n        const press = tss(labels.clone().sub(totalPred));\n        const Q2y = 1 - press / tssy;\n\n        return { predictiveComponents, orthogonalScores, yHat: totalPred, Q2y };\n      } else if (this.mode === 'discriminantAnalysis') {\n        const confusionMatrix = ConfusionMatrix.fromLabels(\n          trueLabels,\n          totalPred.to1DArray(),\n        );\n        const rocCurve = getRocCurve(trueLabels, totalPred.to1DArray());\n        const auc = getAuc(rocCurve);\n        return {\n          predictiveComponents,\n          orthogonalScores,\n          yHat: totalPred,\n          confusionMatrix,\n          auc,\n        };\n      }\n    } else {\n      return { predictiveComponents, orthogonalScores, yHat: totalPred };\n    }\n  }\n\n  _predictAll(data, categories, options = {}) {\n    // cannot use the global this.center here\n    // since it is used in the NC loop and\n    // centering and scaling should only be\n    // performed once\n    const { center = true, scale = true } = options;\n    const features = data.clone();\n    const labels = categories.clone();\n\n    if (center) {\n      const means = features.mean('column');\n      features.center('column', { center: means });\n      labels.center('column');\n    }\n    if (scale) {\n      const stdevs = features.standardDeviation('column');\n      features.scale('column', { scale: stdevs });\n      labels.scale('column');\n      // reevaluate tssy and tssx after scaling\n      // must be global because re-used for next nc iteration\n      // tssx is only evaluate the first time\n      this.tssy = tss(labels);\n      this.tssx = tss(features);\n    }\n    const oplsC = oplsNipals(features, labels);\n    const plsC = new NIPALS(oplsC.filteredX, { Y: labels });\n    const predictiveComponents = plsC.t.clone();\n    // const yHat = tPred.mmul(plsC.betas).mmul(plsC.q.transpose()); // ok\n    const yHatComponents = predictiveComponents\n      .mmul(plsC.betas)\n      .mmul(plsC.q.transpose()); // ok\n    const yHat = new Matrix(yHatComponents.rows, 1);\n    for (let i = 0; i < yHatComponents.rows; i++) {\n      yHat.setRow(i, [yHatComponents.getRowVector(i).sum()]);\n    }\n    let rss = 0;\n    for (let i = 0; i < labels.columns; i++) {\n      rss += tss(labels.getColumnVector(i).sub(yHat));\n    }\n    const R2y = 1 - rss / labels.columns / this.tssy;\n    const xEx = plsC.t.mmul(plsC.p);\n    const rssx = tss(xEx);\n    const R2x = rssx / this.tssx;\n\n    return {\n      R2y,\n      R2x,\n      xRes: oplsC.filteredX,\n      orthogonalScores: oplsC.scoresXOrtho,\n      orthogonalLoadings: oplsC.loadingsXOrtho,\n      orthogonalWeights: oplsC.weightsXOrtho,\n      predictiveComponents,\n      totalPred: yHat,\n      XOrth: oplsC.scoresXOrtho.mmul(oplsC.loadingsXOrtho),\n      oplsC,\n      plsC,\n    };\n  }\n  /**\n   *\n   * @param {*} X - dataset matrix object\n   * @param {*} group - labels matrix object\n   * @param {*} index - train and test index (output from getFold())\n   */\n  _getTrainTest(X, group, index) {\n    const testFeatures = new Matrix(index.testIndex.length, X.columns);\n    const testLabels = new Matrix(index.testIndex.length, group.columns);\n    index.testIndex.forEach((el, idx) => {\n      testFeatures.setRow(idx, X.getRow(el));\n      testLabels.setRow(idx, group.getRow(el));\n    });\n\n    const trainFeatures = new Matrix(index.trainIndex.length, X.columns);\n    const trainLabels = new Matrix(index.trainIndex.length, group.columns);\n    index.trainIndex.forEach((el, idx) => {\n      trainFeatures.setRow(idx, X.getRow(el));\n      trainLabels.setRow(idx, group.getRow(el));\n    });\n\n    return {\n      trainFeatures,\n      testFeatures,\n      trainLabels,\n      testLabels,\n    };\n  }\n}\n\nfunction createDummyY(array) {\n  const features = [...new Set(array)];\n  const result = [];\n  if (features.length > 2) {\n    for (let i = 0; i < features.length; i++) {\n      const feature = [];\n      for (let j = 0; j < array.length; j++) {\n        const point = features[i] === array[j] ? 1 : -1;\n        feature.push(point);\n      }\n      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