{"version":3,"file":"ml-pcr.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/views/base.js","../node_modules/ml-matrix/src/views/transpose.js","../node_modules/ml-matrix/src/wrap/WrapperMatrix2D.js","../node_modules/ml-matrix/src/dc/util.js","../node_modules/ml-matrix/src/dc/svd.js","../node_modules/ml-matrix/src/pseudoInverse.js","../node_modules/ml-matrix/src/dc/evd.js","../node_modules/ml-matrix/src/dc/nipals.js","../node_modules/ml-pca/src/pca.js","../node_modules/ml-regression-multivariate-linear/src/index.js","../lib-esm/pcr.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 { maxRows = 15, maxColumns = 10, maxNumSize = 8 } = options;\n  return `${matrix.constructor.name} {\n${indent}[\n${indentData}${inspectData(matrix, maxRows, maxColumns, maxNumSize)}\n${indent}]\n${indent}rows: ${matrix.rows}\n${indent}columns: ${matrix.columns}\n}`;\n}\n\nfunction inspectData(matrix, maxRows, maxColumns, maxNumSize) {\n  const { rows, columns } = matrix;\n  const maxI = Math.min(rows, maxRows);\n  const maxJ = Math.min(columns, maxColumns);\n  const result = [];\n  for (let i = 0; i < maxI; i++) {\n    let line = [];\n    for (let j = 0; j < maxJ; j++) {\n      line.push(formatNumber(matrix.get(i, j), maxNumSize));\n    }\n    result.push(`${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) {\n  const numStr = String(num);\n  if (numStr.length <= maxNumSize) {\n    return numStr.padEnd(maxNumSize, ' ');\n  }\n  const precise = num.toPrecision(maxNumSize - 2);\n  if (precise.length <= maxNumSize) {\n    return precise;\n  }\n  const exponential = num.toExponential(maxNumSize - 2);\n  const eIndex = exponential.indexOf('e');\n  const e = exponential.slice(eIndex);\n  return exponential.slice(0, maxNumSize - e.length) + e;\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 BaseView extends AbstractMatrix {\n  constructor(matrix, rows, columns) {\n    super();\n    this.matrix = matrix;\n    this.rows = rows;\n    this.columns = columns;\n  }\n}\n","import BaseView from './base';\n\nexport default class MatrixTransposeView extends BaseView {\n  constructor(matrix) {\n    super(matrix, matrix.columns, matrix.rows);\n  }\n\n  set(rowIndex, columnIndex, value) {\n    this.matrix.set(columnIndex, rowIndex, value);\n    return this;\n  }\n\n  get(rowIndex, columnIndex) {\n    return this.matrix.get(columnIndex, rowIndex);\n  }\n}\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","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 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 SVD from './dc/svd';\nimport Matrix from './matrix';\n\nexport function pseudoInverse(matrix, threshold = Number.EPSILON) {\n  matrix = Matrix.checkMatrix(matrix);\n  if (matrix.isEmpty()) {\n    // with a zero dimension, the pseudo-inverse is the transpose, since all 0xn and nx0 matrices are singular\n    // (0xn)*(nx0)*(0xn) = 0xn\n    // (nx0)*(0xn)*(nx0) = nx0\n    return matrix.transpose();\n  }\n  let svdSolution = new SVD(matrix, { autoTranspose: true });\n\n  let U = svdSolution.leftSingularVectors;\n  let V = svdSolution.rightSingularVectors;\n  let s = svdSolution.diagonal;\n\n  for (let i = 0; i < s.length; i++) {\n    if (Math.abs(s[i]) > threshold) {\n      s[i] = 1.0 / s[i];\n    } else {\n      s[i] = 0.0;\n    }\n  }\n\n  return V.mmul(Matrix.diag(s).mmul(U.transpose()));\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nimport { hypotenuse } from './util';\n\nexport default class EigenvalueDecomposition {\n  constructor(matrix, options = {}) {\n    const { assumeSymmetric = false } = options;\n\n    matrix = WrapperMatrix2D.checkMatrix(matrix);\n    if (!matrix.isSquare()) {\n      throw new Error('Matrix is not a square matrix');\n    }\n\n    if (matrix.isEmpty()) {\n      throw new Error('Matrix must be non-empty');\n    }\n\n    let n = matrix.columns;\n    let V = new Matrix(n, n);\n    let d = new Float64Array(n);\n    let e = new Float64Array(n);\n    let value = matrix;\n    let i, j;\n\n    let isSymmetric = false;\n    if (assumeSymmetric) {\n      isSymmetric = true;\n    } else {\n      isSymmetric = matrix.isSymmetric();\n    }\n\n    if (isSymmetric) {\n      for (i = 0; i < n; i++) {\n        for (j = 0; j < n; j++) {\n          V.set(i, j, value.get(i, j));\n        }\n      }\n      tred2(n, e, d, V);\n      tql2(n, e, d, V);\n    } else {\n      let H = new Matrix(n, n);\n      let ort = new Float64Array(n);\n      for (j = 0; j < n; j++) {\n        for (i = 0; i < n; i++) {\n          H.set(i, j, value.get(i, j));\n        }\n      }\n      orthes(n, H, ort, V);\n      hqr2(n, e, d, V, H);\n    }\n\n    this.n = n;\n    this.e = e;\n    this.d = d;\n    this.V = V;\n  }\n\n  get realEigenvalues() {\n    return Array.from(this.d);\n  }\n\n  get imaginaryEigenvalues() {\n    return Array.from(this.e);\n  }\n\n  get eigenvectorMatrix() {\n    return this.V;\n  }\n\n  get diagonalMatrix() {\n    let n = this.n;\n    let e = this.e;\n    let d = this.d;\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        X.set(i, j, 0);\n      }\n      X.set(i, i, d[i]);\n      if (e[i] > 0) {\n        X.set(i, i + 1, e[i]);\n      } else if (e[i] < 0) {\n        X.set(i, i - 1, e[i]);\n      }\n    }\n    return X;\n  }\n}\n\nfunction tred2(n, e, d, V) {\n  let f, g, h, i, j, k, hh, scale;\n\n  for (j = 0; j < n; j++) {\n    d[j] = V.get(n - 1, j);\n  }\n\n  for (i = n - 1; i > 0; i--) {\n    scale = 0;\n    h = 0;\n    for (k = 0; k < i; k++) {\n      scale = scale + Math.abs(d[k]);\n    }\n\n    if (scale === 0) {\n      e[i] = d[i - 1];\n      for (j = 0; j < i; j++) {\n        d[j] = V.get(i - 1, j);\n        V.set(i, j, 0);\n        V.set(j, i, 0);\n      }\n    } else {\n      for (k = 0; k < i; k++) {\n        d[k] /= scale;\n        h += d[k] * d[k];\n      }\n\n      f = d[i - 1];\n      g = Math.sqrt(h);\n      if (f > 0) {\n        g = -g;\n      }\n\n      e[i] = scale * g;\n      h = h - f * g;\n      d[i - 1] = f - g;\n      for (j = 0; j < i; j++) {\n        e[j] = 0;\n      }\n\n      for (j = 0; j < i; j++) {\n        f = d[j];\n        V.set(j, i, f);\n        g = e[j] + V.get(j, j) * f;\n        for (k = j + 1; k <= i - 1; k++) {\n          g += V.get(k, j) * d[k];\n          e[k] += V.get(k, j) * f;\n        }\n        e[j] = g;\n      }\n\n      f = 0;\n      for (j = 0; j < i; j++) {\n        e[j] /= h;\n        f += e[j] * d[j];\n      }\n\n      hh = f / (h + h);\n      for (j = 0; j < i; j++) {\n        e[j] -= hh * d[j];\n      }\n\n      for (j = 0; j < i; j++) {\n        f = d[j];\n        g = e[j];\n        for (k = j; k <= i - 1; k++) {\n          V.set(k, j, V.get(k, j) - (f * e[k] + g * d[k]));\n        }\n        d[j] = V.get(i - 1, j);\n        V.set(i, j, 0);\n      }\n    }\n    d[i] = h;\n  }\n\n  for (i = 0; i < n - 1; i++) {\n    V.set(n - 1, i, V.get(i, i));\n    V.set(i, i, 1);\n    h = d[i + 1];\n    if (h !== 0) {\n      for (k = 0; k <= i; k++) {\n        d[k] = V.get(k, i + 1) / h;\n      }\n\n      for (j = 0; j <= i; j++) {\n        g = 0;\n        for (k = 0; k <= i; k++) {\n          g += V.get(k, i + 1) * V.get(k, j);\n        }\n        for (k = 0; k <= i; k++) {\n          V.set(k, j, V.get(k, j) - g * d[k]);\n        }\n      }\n    }\n\n    for (k = 0; k <= i; k++) {\n      V.set(k, i + 1, 0);\n    }\n  }\n\n  for (j = 0; j < n; j++) {\n    d[j] = V.get(n - 1, j);\n    V.set(n - 1, j, 0);\n  }\n\n  V.set(n - 1, n - 1, 1);\n  e[0] = 0;\n}\n\nfunction tql2(n, e, d, V) {\n  let g, h, i, j, k, l, m, p, r, dl1, c, c2, c3, el1, s, s2, iter;\n\n  for (i = 1; i < n; i++) {\n    e[i - 1] = e[i];\n  }\n\n  e[n - 1] = 0;\n\n  let f = 0;\n  let tst1 = 0;\n  let eps = Number.EPSILON;\n\n  for (l = 0; l < n; l++) {\n    tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));\n    m = l;\n    while (m < n) {\n      if (Math.abs(e[m]) <= eps * tst1) {\n        break;\n      }\n      m++;\n    }\n\n    if (m > l) {\n      iter = 0;\n      do {\n        iter = iter + 1;\n\n        g = d[l];\n        p = (d[l + 1] - g) / (2 * e[l]);\n        r = hypotenuse(p, 1);\n        if (p < 0) {\n          r = -r;\n        }\n\n        d[l] = e[l] / (p + r);\n        d[l + 1] = e[l] * (p + r);\n        dl1 = d[l + 1];\n        h = g - d[l];\n        for (i = l + 2; i < n; i++) {\n          d[i] -= h;\n        }\n\n        f = f + h;\n\n        p = d[m];\n        c = 1;\n        c2 = c;\n        c3 = c;\n        el1 = e[l + 1];\n        s = 0;\n        s2 = 0;\n        for (i = m - 1; i >= l; i--) {\n          c3 = c2;\n          c2 = c;\n          s2 = s;\n          g = c * e[i];\n          h = c * p;\n          r = hypotenuse(p, e[i]);\n          e[i + 1] = s * r;\n          s = e[i] / r;\n          c = p / r;\n          p = c * d[i] - s * g;\n          d[i + 1] = h + s * (c * g + s * d[i]);\n\n          for (k = 0; k < n; k++) {\n            h = V.get(k, i + 1);\n            V.set(k, i + 1, s * V.get(k, i) + c * h);\n            V.set(k, i, c * V.get(k, i) - s * h);\n          }\n        }\n\n        p = (-s * s2 * c3 * el1 * e[l]) / dl1;\n        e[l] = s * p;\n        d[l] = c * p;\n      } while (Math.abs(e[l]) > eps * tst1);\n    }\n    d[l] = d[l] + f;\n    e[l] = 0;\n  }\n\n  for (i = 0; i < n - 1; i++) {\n    k = i;\n    p = d[i];\n    for (j = i + 1; j < n; j++) {\n      if (d[j] < p) {\n        k = j;\n        p = d[j];\n      }\n    }\n\n    if (k !== i) {\n      d[k] = d[i];\n      d[i] = p;\n      for (j = 0; j < n; j++) {\n        p = V.get(j, i);\n        V.set(j, i, V.get(j, k));\n        V.set(j, k, p);\n      }\n    }\n  }\n}\n\nfunction orthes(n, H, ort, V) {\n  let low = 0;\n  let high = n - 1;\n  let f, g, h, i, j, m;\n  let scale;\n\n  for (m = low + 1; m <= high - 1; m++) {\n    scale = 0;\n    for (i = m; i <= high; i++) {\n      scale = scale + Math.abs(H.get(i, m - 1));\n    }\n\n    if (scale !== 0) {\n      h = 0;\n      for (i = high; i >= m; i--) {\n        ort[i] = H.get(i, m - 1) / scale;\n        h += ort[i] * ort[i];\n      }\n\n      g = Math.sqrt(h);\n      if (ort[m] > 0) {\n        g = -g;\n      }\n\n      h = h - ort[m] * g;\n      ort[m] = ort[m] - g;\n\n      for (j = m; j < n; j++) {\n        f = 0;\n        for (i = high; i >= m; i--) {\n          f += ort[i] * H.get(i, j);\n        }\n\n        f = f / h;\n        for (i = m; i <= high; i++) {\n          H.set(i, j, H.get(i, j) - f * ort[i]);\n        }\n      }\n\n      for (i = 0; i <= high; i++) {\n        f = 0;\n        for (j = high; j >= m; j--) {\n          f += ort[j] * H.get(i, j);\n        }\n\n        f = f / h;\n        for (j = m; j <= high; j++) {\n          H.set(i, j, H.get(i, j) - f * ort[j]);\n        }\n      }\n\n      ort[m] = scale * ort[m];\n      H.set(m, m - 1, scale * g);\n    }\n  }\n\n  for (i = 0; i < n; i++) {\n    for (j = 0; j < n; j++) {\n      V.set(i, j, i === j ? 1 : 0);\n    }\n  }\n\n  for (m = high - 1; m >= low + 1; m--) {\n    if (H.get(m, m - 1) !== 0) {\n      for (i = m + 1; i <= high; i++) {\n        ort[i] = H.get(i, m - 1);\n      }\n\n      for (j = m; j <= high; j++) {\n        g = 0;\n        for (i = m; i <= high; i++) {\n          g += ort[i] * V.get(i, j);\n        }\n\n        g = g / ort[m] / H.get(m, m - 1);\n        for (i = m; i <= high; i++) {\n          V.set(i, j, V.get(i, j) + g * ort[i]);\n        }\n      }\n    }\n  }\n}\n\nfunction hqr2(nn, e, d, V, H) {\n  let n = nn - 1;\n  let low = 0;\n  let high = nn - 1;\n  let eps = Number.EPSILON;\n  let exshift = 0;\n  let norm = 0;\n  let p = 0;\n  let q = 0;\n  let r = 0;\n  let s = 0;\n  let z = 0;\n  let iter = 0;\n  let i, j, k, l, m, t, w, x, y;\n  let ra, sa, vr, vi;\n  let notlast, cdivres;\n\n  for (i = 0; i < nn; i++) {\n    if (i < low || i > high) {\n      d[i] = H.get(i, i);\n      e[i] = 0;\n    }\n\n    for (j = Math.max(i - 1, 0); j < nn; j++) {\n      norm = norm + Math.abs(H.get(i, j));\n    }\n  }\n\n  while (n >= low) {\n    l = n;\n    while (l > low) {\n      s = Math.abs(H.get(l - 1, l - 1)) + Math.abs(H.get(l, l));\n      if (s === 0) {\n        s = norm;\n      }\n      if (Math.abs(H.get(l, l - 1)) < eps * s) {\n        break;\n      }\n      l--;\n    }\n\n    if (l === n) {\n      H.set(n, n, H.get(n, n) + exshift);\n      d[n] = H.get(n, n);\n      e[n] = 0;\n      n--;\n      iter = 0;\n    } else if (l === n - 1) {\n      w = H.get(n, n - 1) * H.get(n - 1, n);\n      p = (H.get(n - 1, n - 1) - H.get(n, n)) / 2;\n      q = p * p + w;\n      z = Math.sqrt(Math.abs(q));\n      H.set(n, n, H.get(n, n) + exshift);\n      H.set(n - 1, n - 1, H.get(n - 1, n - 1) + exshift);\n      x = H.get(n, n);\n\n      if (q >= 0) {\n        z = p >= 0 ? p + z : p - z;\n        d[n - 1] = x + z;\n        d[n] = d[n - 1];\n        if (z !== 0) {\n          d[n] = x - w / z;\n        }\n        e[n - 1] = 0;\n        e[n] = 0;\n        x = H.get(n, n - 1);\n        s = Math.abs(x) + Math.abs(z);\n        p = x / s;\n        q = z / s;\n        r = Math.sqrt(p * p + q * q);\n        p = p / r;\n        q = q / r;\n\n        for (j = n - 1; j < nn; j++) {\n          z = H.get(n - 1, j);\n          H.set(n - 1, j, q * z + p * H.get(n, j));\n          H.set(n, j, q * H.get(n, j) - p * z);\n        }\n\n        for (i = 0; i <= n; i++) {\n          z = H.get(i, n - 1);\n          H.set(i, n - 1, q * z + p * H.get(i, n));\n          H.set(i, n, q * H.get(i, n) - p * z);\n        }\n\n        for (i = low; i <= high; i++) {\n          z = V.get(i, n - 1);\n          V.set(i, n - 1, q * z + p * V.get(i, n));\n          V.set(i, n, q * V.get(i, n) - p * z);\n        }\n      } else {\n        d[n - 1] = x + p;\n        d[n] = x + p;\n        e[n - 1] = z;\n        e[n] = -z;\n      }\n\n      n = n - 2;\n      iter = 0;\n    } else {\n      x = H.get(n, n);\n      y = 0;\n      w = 0;\n      if (l < n) {\n        y = H.get(n - 1, n - 1);\n        w = H.get(n, n - 1) * H.get(n - 1, n);\n      }\n\n      if (iter === 10) {\n        exshift += x;\n        for (i = low; i <= n; i++) {\n          H.set(i, i, H.get(i, i) - x);\n        }\n        s = Math.abs(H.get(n, n - 1)) + Math.abs(H.get(n - 1, n - 2));\n        x = y = 0.75 * s;\n        w = -0.4375 * s * s;\n      }\n\n      if (iter === 30) {\n        s = (y - x) / 2;\n        s = s * s + w;\n        if (s > 0) {\n          s = Math.sqrt(s);\n          if (y < x) {\n            s = -s;\n          }\n          s = x - w / ((y - x) / 2 + s);\n          for (i = low; i <= n; i++) {\n            H.set(i, i, H.get(i, i) - s);\n          }\n          exshift += s;\n          x = y = w = 0.964;\n        }\n      }\n\n      iter = iter + 1;\n\n      m = n - 2;\n      while (m >= l) {\n        z = H.get(m, m);\n        r = x - z;\n        s = y - z;\n        p = (r * s - w) / H.get(m + 1, m) + H.get(m, m + 1);\n        q = H.get(m + 1, m + 1) - z - r - s;\n        r = H.get(m + 2, m + 1);\n        s = Math.abs(p) + Math.abs(q) + Math.abs(r);\n        p = p / s;\n        q = q / s;\n        r = r / s;\n        if (m === l) {\n          break;\n        }\n        if (\n          Math.abs(H.get(m, m - 1)) * (Math.abs(q) + Math.abs(r)) <\n          eps *\n            (Math.abs(p) *\n              (Math.abs(H.get(m - 1, m - 1)) +\n                Math.abs(z) +\n                Math.abs(H.get(m + 1, m + 1))))\n        ) {\n          break;\n        }\n        m--;\n      }\n\n      for (i = m + 2; i <= n; i++) {\n        H.set(i, i - 2, 0);\n        if (i > m + 2) {\n          H.set(i, i - 3, 0);\n        }\n      }\n\n      for (k = m; k <= n - 1; k++) {\n        notlast = k !== n - 1;\n        if (k !== m) {\n          p = H.get(k, k - 1);\n          q = H.get(k + 1, k - 1);\n          r = notlast ? H.get(k + 2, k - 1) : 0;\n          x = Math.abs(p) + Math.abs(q) + Math.abs(r);\n          if (x !== 0) {\n            p = p / x;\n            q = q / x;\n            r = r / x;\n          }\n        }\n\n        if (x === 0) {\n          break;\n        }\n\n        s = Math.sqrt(p * p + q * q + r * r);\n        if (p < 0) {\n          s = -s;\n        }\n\n        if (s !== 0) {\n          if (k !== m) {\n            H.set(k, k - 1, -s * x);\n          } else if (l !== m) {\n            H.set(k, k - 1, -H.get(k, k - 1));\n          }\n\n          p = p + s;\n          x = p / s;\n          y = q / s;\n          z = r / s;\n          q = q / p;\n          r = r / p;\n\n          for (j = k; j < nn; j++) {\n            p = H.get(k, j) + q * H.get(k + 1, j);\n            if (notlast) {\n              p = p + r * H.get(k + 2, j);\n              H.set(k + 2, j, H.get(k + 2, j) - p * z);\n            }\n\n            H.set(k, j, H.get(k, j) - p * x);\n            H.set(k + 1, j, H.get(k + 1, j) - p * y);\n          }\n\n          for (i = 0; i <= Math.min(n, k + 3); i++) {\n            p = x * H.get(i, k) + y * H.get(i, k + 1);\n            if (notlast) {\n              p = p + z * H.get(i, k + 2);\n              H.set(i, k + 2, H.get(i, k + 2) - p * r);\n            }\n\n            H.set(i, k, H.get(i, k) - p);\n            H.set(i, k + 1, H.get(i, k + 1) - p * q);\n          }\n\n          for (i = low; i <= high; i++) {\n            p = x * V.get(i, k) + y * V.get(i, k + 1);\n            if (notlast) {\n              p = p + z * V.get(i, k + 2);\n              V.set(i, k + 2, V.get(i, k + 2) - p * r);\n            }\n\n            V.set(i, k, V.get(i, k) - p);\n            V.set(i, k + 1, V.get(i, k + 1) - p * q);\n          }\n        }\n      }\n    }\n  }\n\n  if (norm === 0) {\n    return;\n  }\n\n  for (n = nn - 1; n >= 0; n--) {\n    p = d[n];\n    q = e[n];\n\n    if (q === 0) {\n      l = n;\n      H.set(n, n, 1);\n      for (i = n - 1; i >= 0; i--) {\n        w = H.get(i, i) - p;\n        r = 0;\n        for (j = l; j <= n; j++) {\n          r = r + H.get(i, j) * H.get(j, n);\n        }\n\n        if (e[i] < 0) {\n          z = w;\n          s = r;\n        } else {\n          l = i;\n          if (e[i] === 0) {\n            H.set(i, n, w !== 0 ? -r / w : -r / (eps * norm));\n          } else {\n            x = H.get(i, i + 1);\n            y = H.get(i + 1, i);\n            q = (d[i] - p) * (d[i] - p) + e[i] * e[i];\n            t = (x * s - z * r) / q;\n            H.set(i, n, t);\n            H.set(\n              i + 1,\n              n,\n              Math.abs(x) > Math.abs(z) ? (-r - w * t) / x : (-s - y * t) / z,\n            );\n          }\n\n          t = Math.abs(H.get(i, n));\n          if (eps * t * t > 1) {\n            for (j = i; j <= n; j++) {\n              H.set(j, n, H.get(j, n) / t);\n            }\n          }\n        }\n      }\n    } else if (q < 0) {\n      l = n - 1;\n\n      if (Math.abs(H.get(n, n - 1)) > Math.abs(H.get(n - 1, n))) {\n        H.set(n - 1, n - 1, q / H.get(n, n - 1));\n        H.set(n - 1, n, -(H.get(n, n) - p) / H.get(n, n - 1));\n      } else {\n        cdivres = cdiv(0, -H.get(n - 1, n), H.get(n - 1, n - 1) - p, q);\n        H.set(n - 1, n - 1, cdivres[0]);\n        H.set(n - 1, n, cdivres[1]);\n      }\n\n      H.set(n, n - 1, 0);\n      H.set(n, n, 1);\n      for (i = n - 2; i >= 0; i--) {\n        ra = 0;\n        sa = 0;\n        for (j = l; j <= n; j++) {\n          ra = ra + H.get(i, j) * H.get(j, n - 1);\n          sa = sa + H.get(i, j) * H.get(j, n);\n        }\n\n        w = H.get(i, i) - p;\n\n        if (e[i] < 0) {\n          z = w;\n          r = ra;\n          s = sa;\n        } else {\n          l = i;\n          if (e[i] === 0) {\n            cdivres = cdiv(-ra, -sa, w, q);\n            H.set(i, n - 1, cdivres[0]);\n            H.set(i, n, cdivres[1]);\n          } else {\n            x = H.get(i, i + 1);\n            y = H.get(i + 1, i);\n            vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;\n            vi = (d[i] - p) * 2 * q;\n            if (vr === 0 && vi === 0) {\n              vr =\n                eps *\n                norm *\n                (Math.abs(w) +\n                  Math.abs(q) +\n                  Math.abs(x) +\n                  Math.abs(y) +\n                  Math.abs(z));\n            }\n            cdivres = cdiv(\n              x * r - z * ra + q * sa,\n              x * s - z * sa - q * ra,\n              vr,\n              vi,\n            );\n            H.set(i, n - 1, cdivres[0]);\n            H.set(i, n, cdivres[1]);\n            if (Math.abs(x) > Math.abs(z) + Math.abs(q)) {\n              H.set(\n                i + 1,\n                n - 1,\n                (-ra - w * H.get(i, n - 1) + q * H.get(i, n)) / x,\n              );\n              H.set(\n                i + 1,\n                n,\n                (-sa - w * H.get(i, n) - q * H.get(i, n - 1)) / x,\n              );\n            } else {\n              cdivres = cdiv(\n                -r - y * H.get(i, n - 1),\n                -s - y * H.get(i, n),\n                z,\n                q,\n              );\n              H.set(i + 1, n - 1, cdivres[0]);\n              H.set(i + 1, n, cdivres[1]);\n            }\n          }\n\n          t = Math.max(Math.abs(H.get(i, n - 1)), Math.abs(H.get(i, n)));\n          if (eps * t * t > 1) {\n            for (j = i; j <= n; j++) {\n              H.set(j, n - 1, H.get(j, n - 1) / t);\n              H.set(j, n, H.get(j, n) / t);\n            }\n          }\n        }\n      }\n    }\n  }\n\n  for (i = 0; i < nn; i++) {\n    if (i < low || i > high) {\n      for (j = i; j < nn; j++) {\n        V.set(i, j, H.get(i, j));\n      }\n    }\n  }\n\n  for (j = nn - 1; j >= low; j--) {\n    for (i = low; i <= high; i++) {\n      z = 0;\n      for (k = low; k <= Math.min(j, high); k++) {\n        z = z + V.get(i, k) * H.get(k, j);\n      }\n      V.set(i, j, z);\n    }\n  }\n}\n\nfunction cdiv(xr, xi, yr, yi) {\n  let r, d;\n  if (Math.abs(yr) > Math.abs(yi)) {\n    r = yi / yr;\n    d = yr + r * yi;\n    return [(xr + r * xi) / d, (xi - r * xr) / d];\n  } else {\n    r = yr / yi;\n    d = yi + r * yr;\n    return [(r * xr + xi) / d, (r * xi - xr) / d];\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, MatrixTransposeView, EVD, SVD, NIPALS } from 'ml-matrix';\r\n\r\n/**\r\n * Creates new PCA (Principal Component Analysis) from the dataset\r\n * @param {Matrix} dataset - dataset or covariance matrix.\r\n * @param {Object} [options]\r\n * @param {boolean} [options.isCovarianceMatrix=false] - true if the dataset is a covariance matrix.\r\n * @param {string} [options.method='SVD'] - select which method to use: SVD (default), covarianceMatrirx or NIPALS.\r\n * @param {number} [options.nCompNIPALS=2] - number of components to be computed with NIPALS.\r\n * @param {boolean} [options.center=true] - should the data be centered (subtract the mean).\r\n * @param {boolean} [options.scale=false] - should the data be scaled (divide by the standard deviation).\r\n * @param {boolean} [options.ignoreZeroVariance=false] - ignore columns with zero variance if `scale` is `true`.\r\n * */\r\nexport class PCA {\r\n  constructor(dataset, options = {}) {\r\n    if (dataset === true) {\r\n      const model = options;\r\n      this.center = model.center;\r\n      this.scale = model.scale;\r\n      this.means = model.means;\r\n      this.stdevs = model.stdevs;\r\n      this.U = Matrix.checkMatrix(model.U);\r\n      this.S = model.S;\r\n      this.R = model.R;\r\n      this.excludedFeatures = model.excludedFeatures || [];\r\n      return;\r\n    }\r\n\r\n    dataset = new Matrix(dataset);\r\n\r\n    const {\r\n      isCovarianceMatrix = false,\r\n      method = 'SVD',\r\n      nCompNIPALS = 2,\r\n      center = true,\r\n      scale = false,\r\n      ignoreZeroVariance = false,\r\n    } = options;\r\n\r\n    this.center = center;\r\n    this.scale = scale;\r\n    this.means = null;\r\n    this.stdevs = null;\r\n    this.excludedFeatures = [];\r\n\r\n    if (isCovarianceMatrix) {\r\n      // User provided a covariance matrix instead of dataset.\r\n      this._computeFromCovarianceMatrix(dataset);\r\n      return;\r\n    }\r\n\r\n    this._adjust(dataset, ignoreZeroVariance);\r\n    switch (method) {\r\n      case 'covarianceMatrix': {\r\n        // User provided a dataset but wants us to compute and use the covariance matrix.\r\n        const covarianceMatrix = new MatrixTransposeView(dataset)\r\n          .mmul(dataset)\r\n          .div(dataset.rows - 1);\r\n        this._computeFromCovarianceMatrix(covarianceMatrix);\r\n        break;\r\n      }\r\n      case 'NIPALS': {\r\n        this._computeWithNIPALS(dataset, nCompNIPALS);\r\n        break;\r\n      }\r\n      case 'SVD': {\r\n        const svd = new SVD(dataset, {\r\n          computeLeftSingularVectors: false,\r\n          computeRightSingularVectors: true,\r\n          autoTranspose: true,\r\n        });\r\n\r\n        this.U = svd.rightSingularVectors;\r\n\r\n        const singularValues = svd.diagonal;\r\n        const eigenvalues = [];\r\n        for (const singularValue of singularValues) {\r\n          eigenvalues.push(\r\n            (singularValue * singularValue) / (dataset.rows - 1),\r\n          );\r\n        }\r\n        this.S = eigenvalues;\r\n        break;\r\n      }\r\n      default: {\r\n        throw new Error(`unknown method: ${method}`);\r\n      }\r\n    }\r\n  }\r\n\r\n  /**\r\n   * Load a PCA model from JSON\r\n   * @param {Object} model\r\n   * @return {PCA}\r\n   */\r\n  static load(model) {\r\n    if (typeof model.name !== 'string') {\r\n      throw new TypeError('model must have a name property');\r\n    }\r\n    if (model.name !== 'PCA') {\r\n      throw new RangeError(`invalid model: ${model.name}`);\r\n    }\r\n    return new PCA(true, model);\r\n  }\r\n\r\n  /**\r\n   * Project the dataset into the PCA space\r\n   * @param {Matrix} dataset\r\n   * @param {Object} options\r\n   * @return {Matrix} dataset projected in the PCA space\r\n   */\r\n  predict(dataset, options = {}) {\r\n    const { nComponents = this.U.columns } = options;\r\n    dataset = new Matrix(dataset);\r\n    if (this.center) {\r\n      dataset.subRowVector(this.means);\r\n      if (this.scale) {\r\n        for (let i of this.excludedFeatures) {\r\n          dataset.removeColumn(i);\r\n        }\r\n        dataset.divRowVector(this.stdevs);\r\n      }\r\n    }\r\n    let predictions = dataset.mmul(this.U);\r\n    return predictions.subMatrix(0, predictions.rows - 1, 0, nComponents - 1);\r\n  }\r\n\r\n  /**\r\n   * Calculates the inverse PCA transform\r\n   * @param {Matrix} dataset\r\n   * @return {Matrix} dataset projected in the PCA space\r\n   */\r\n  invert(dataset) {\r\n    dataset = Matrix.checkMatrix(dataset);\r\n\r\n    let inverse = dataset.mmul(this.U.transpose());\r\n\r\n    if (this.center) {\r\n      if (this.scale) {\r\n        inverse.mulRowVector(this.stdevs);\r\n      }\r\n      inverse.addRowVector(this.means);\r\n    }\r\n\r\n    return inverse;\r\n  }\r\n\r\n  /**\r\n   * Returns the proportion of variance for each component\r\n   * @return {[number]}\r\n   */\r\n  getExplainedVariance() {\r\n    let sum = 0;\r\n    for (const s of this.S) {\r\n      sum += s;\r\n    }\r\n    return this.S.map((value) => value / sum);\r\n  }\r\n\r\n  /**\r\n   * Returns the cumulative proportion of variance\r\n   * @return {[number]}\r\n   */\r\n  getCumulativeVariance() {\r\n    let explained = this.getExplainedVariance();\r\n    for (let i = 1; i < explained.length; i++) {\r\n      explained[i] += explained[i - 1];\r\n    }\r\n    return explained;\r\n  }\r\n\r\n  /**\r\n   * Returns the Eigenvectors of the covariance matrix\r\n   * @returns {Matrix}\r\n   */\r\n  getEigenvectors() {\r\n    return this.U;\r\n  }\r\n\r\n  /**\r\n   * Returns the Eigenvalues (on the diagonal)\r\n   * @returns {[number]}\r\n   */\r\n  getEigenvalues() {\r\n    return this.S;\r\n  }\r\n\r\n  /**\r\n   * Returns the standard deviations of the principal components\r\n   * @returns {[number]}\r\n   */\r\n  getStandardDeviations() {\r\n    return this.S.map((x) => Math.sqrt(x));\r\n  }\r\n\r\n  /**\r\n   * Returns the loadings matrix\r\n   * @return {Matrix}\r\n   */\r\n  getLoadings() {\r\n    return this.U.transpose();\r\n  }\r\n\r\n  /**\r\n   * Export the current model to a JSON object\r\n   * @return {Object} model\r\n   */\r\n  toJSON() {\r\n    return {\r\n      name: 'PCA',\r\n      center: this.center,\r\n      scale: this.scale,\r\n      means: this.means,\r\n      stdevs: this.stdevs,\r\n      U: this.U,\r\n      S: this.S,\r\n      excludedFeatures: this.excludedFeatures,\r\n    };\r\n  }\r\n\r\n  _adjust(dataset, ignoreZeroVariance) {\r\n    if (this.center) {\r\n      const mean = dataset.mean('column');\r\n      const stdevs = this.scale\r\n        ? dataset.standardDeviation('column', { mean })\r\n        : null;\r\n      this.means = mean;\r\n      dataset.subRowVector(mean);\r\n      if (this.scale) {\r\n        for (let i = 0; i < stdevs.length; i++) {\r\n          if (stdevs[i] === 0) {\r\n            if (ignoreZeroVariance) {\r\n              dataset.removeColumn(i);\r\n              stdevs.splice(i, 1);\r\n              this.excludedFeatures.push(i);\r\n              i--;\r\n            } else {\r\n              throw new RangeError(\r\n                `Cannot scale the dataset (standard deviation is zero at index ${i}`,\r\n              );\r\n            }\r\n          }\r\n        }\r\n        this.stdevs = stdevs;\r\n        dataset.divRowVector(stdevs);\r\n      }\r\n    }\r\n  }\r\n\r\n  _computeFromCovarianceMatrix(dataset) {\r\n    const evd = new EVD(dataset, { assumeSymmetric: true });\r\n    this.U = evd.eigenvectorMatrix;\r\n    this.U.flipRows();\r\n    this.S = evd.realEigenvalues;\r\n    this.S.reverse();\r\n  }\r\n\r\n  _computeWithNIPALS(dataset, nCompNIPALS) {\r\n    this.U = new Matrix(nCompNIPALS, dataset.columns);\r\n    this.S = [];\r\n\r\n    let x = dataset;\r\n    for (let i = 0; i < nCompNIPALS; i++) {\r\n      let dc = new NIPALS(x);\r\n\r\n      this.U.setRow(i, dc.w.transpose());\r\n      this.S.push(Math.pow(dc.s.get(0, 0), 2));\r\n\r\n      x = dc.xResidual;\r\n    }\r\n    this.U = this.U.transpose(); // to be compatible with API\r\n  }\r\n}\r\n","import { Matrix, SVD, pseudoInverse } from 'ml-matrix';\n\nexport default class MultivariateLinearRegression {\n  constructor(x, y, options = {}) {\n    const { intercept = true, statistics = true } = options;\n    this.statistics = statistics;\n    if (x === true) {\n      this.weights = y.weights;\n      this.inputs = y.inputs;\n      this.outputs = y.outputs;\n      this.intercept = y.intercept;\n    } else {\n      x = new Matrix(x);\n      y = new Matrix(y);\n      if (intercept) {\n        x.addColumn(new Array(x.rows).fill(1));\n      }\n      let xt = x.transpose();\n      const xx = xt.mmul(x);\n      const xy = xt.mmul(y);\n      const invxx = new SVD(xx).inverse();\n      const beta = xy.transpose().mmul(invxx).transpose();\n      this.weights = beta.to2DArray();\n      this.inputs = x.columns;\n      this.outputs = y.columns;\n      if (intercept) this.inputs--;\n      this.intercept = intercept;\n      if (statistics) {\n        /*\n         * Let's add some basic statistics about the beta's to be able to interpret them.\n         * source: http://dept.stat.lsa.umich.edu/~kshedden/Courses/Stat401/Notes/401-multreg.pdf\n         * validated against Excel Regression AddIn\n         * test: \"datamining statistics test\"\n         */\n        const fittedValues = x.mmul(beta);\n        const residuals = y.clone().addM(fittedValues.neg());\n        const variance =\n          residuals\n            .to2DArray()\n            .map((ri) => Math.pow(ri[0], 2))\n            .reduce((a, b) => a + b) /\n          (y.rows - x.columns);\n        this.stdError = Math.sqrt(variance);\n        this.stdErrorMatrix = pseudoInverse(xx).mul(variance);\n        this.stdErrors = this.stdErrorMatrix\n          .diagonal()\n          .map((d) => Math.sqrt(d));\n        this.tStats = this.weights.map((d, i) =>\n          this.stdErrors[i] === 0 ? 0 : d[0] / this.stdErrors[i],\n        );\n      }\n    }\n  }\n\n  predict(x) {\n    if (Array.isArray(x)) {\n      if (typeof x[0] === 'number') {\n        return this._predict(x);\n      } else if (Array.isArray(x[0])) {\n        const y = new Array(x.length);\n        for (let i = 0; i < x.length; i++) {\n          y[i] = this._predict(x[i]);\n        }\n        return y;\n      }\n    } else if (Matrix.isMatrix(x)) {\n      const y = new Matrix(x.rows, this.outputs);\n      for (let i = 0; i < x.rows; i++) {\n        y.setRow(i, this._predict(x.getRow(i)));\n      }\n      return y;\n    }\n    throw new TypeError('x must be a matrix or array of numbers');\n  }\n\n  _predict(x) {\n    const result = new Array(this.outputs);\n    if (this.intercept) {\n      for (let i = 0; i < this.outputs; i++) {\n        result[i] = this.weights[this.inputs][i];\n      }\n    } else {\n      result.fill(0);\n    }\n    for (let i = 0; i < this.inputs; i++) {\n      for (let j = 0; j < this.outputs; j++) {\n        result[j] += this.weights[i][j] * x[i];\n      }\n    }\n    return result;\n  }\n\n  score() {\n    throw new Error('score method is not implemented yet');\n  }\n\n  toJSON() {\n    return {\n      name: 'multivariateLinearRegression',\n      weights: this.weights,\n      inputs: this.inputs,\n      outputs: this.outputs,\n      intercept: this.intercept,\n      summary: this.statistics\n        ? {\n            regressionStatistics: {\n              standardError: this.stdError,\n              observations: this.outputs,\n            },\n            variables: this.weights.map((d, i) => {\n              return {\n                label:\n                  i === this.weights.length - 1\n                    ? 'Intercept'\n                    : `X Variable ${i + 1}`,\n                coefficients: d,\n                standardError: this.stdErrors[i],\n                tStat: this.tStats[i],\n              };\n            }),\n          }\n        : undefined,\n    };\n  }\n\n  static load(model) {\n    if (model.name !== 'multivariateLinearRegression') {\n      throw new Error('not a MLR model');\n    }\n    return new MultivariateLinearRegression(true, model);\n  }\n}\n","import { Matrix } from 'ml-matrix';\nimport { PCA } from 'ml-pca';\nimport MLR from 'ml-regression-multivariate-linear';\n/**\n * Creates new PCR (Principal component regression)\n * @param {Array} predictor - matrix with predictor variables. (Each column is an array)\n * @param {Array} response - matrix with response variables. (Each column is an array)\n * @param {number} pcaWeight - Weight to choose the principal components. It refers to the weight that components must sum with each other (in percent) to perform the regression.\n * @param {boolean} intercept - Intercept\n * */\nexport class PCR {\n    constructor(predictor, response, options = {}) {\n        const { intercept = true, pcaWeight = 1, nComp = 0, scale = false, center = true, } = options;\n        this.intercept = intercept;\n        this.pcaWeight = pcaWeight;\n        let pca;\n        if (nComp) {\n            pca = new PCA(predictor, {\n                scale,\n                center,\n                method: 'NIPALS',\n                nCompNIPALS: nComp,\n            });\n        }\n        else {\n            pca = new PCA(predictor, { scale, center });\n        }\n        let evalues = pca.getEigenvalues();\n        const sum = evalues.reduce((accumulator, currentValue) => accumulator + currentValue);\n        const weight = evalues.map((value, index) => ({\n            weight: value / sum,\n            evalues: evalues[index],\n            componentNumber: index + 1,\n        }));\n        weight.sort((first, second) => first.weight + second.weight);\n        let n = 0;\n        let z = 0;\n        let l = 0;\n        while (z < this.pcaWeight) {\n            l = weight[n].weight;\n            z += l;\n            n++;\n        }\n        let predictorsMatrix = Matrix.checkMatrix(predictor);\n        let responseMatrix = Matrix.checkMatrix(response);\n        const loadings = pca.getLoadings();\n        const selectedLoadings = loadings.subMatrixRow(new Array(n).fill(0).map((_, index) => index));\n        this.loadingsData = new Array(selectedLoadings.rows)\n            .fill(0)\n            .map((_, index) => ({\n            weight: (evalues[index] / sum) * 100,\n            evalues: evalues[index],\n            componentNumber: index + 1,\n            component: loadings.getRow(index),\n        }));\n        let scores = predictorsMatrix.mmul(loadings.transpose());\n        this.scores = scores;\n        const regressionScores = new MLR(scores, responseMatrix, {\n            intercept: this.intercept,\n        });\n        const coefficientsMatrix = new Matrix(regressionScores.weights).transpose();\n        const coefficients = coefficientsMatrix\n            .subMatrixColumn(new Array(coefficientsMatrix.columns - 1)\n            .fill(0)\n            .map((_, index) => index))\n            .mmul(loadings.transpose())\n            .transpose();\n        if (this.intercept) {\n            coefficients.addRow(0, coefficientsMatrix.getColumn(coefficientsMatrix.rows - 1));\n            predictorsMatrix.addColumn(0, new Array(predictorsMatrix.rows).fill(1));\n        }\n        this.coefficients = coefficients;\n        let yFittedValues = predictorsMatrix.mmul(coefficients);\n        this.yFittedValues = yFittedValues;\n        let residual = responseMatrix.sub(yFittedValues).to2DArray();\n        let xMedia = predictorsMatrix.mean('row');\n        let yMedia = responseMatrix.mean('row');\n        let sst = [];\n        for (let i = 0; i < responseMatrix.rows; i++) {\n            sst[i] = responseMatrix\n                .getRow(i)\n                .map((x) => Math.pow(x - yMedia[i], 2))\n                .reduce((a, b) => a + b);\n        }\n        let ssr = [];\n        let yVariance = [];\n        let stdDeviationY = [];\n        for (let i = 0; i < responseMatrix.rows; i++) {\n            ssr.push(yFittedValues\n                .getRow(i)\n                .map((x) => Math.pow(x - yMedia[i], 2))\n                .reduce((a, b) => a + b));\n            yVariance.push(ssr[i] / (responseMatrix.columns - 1));\n            stdDeviationY.push(Math.sqrt(yVariance[i]));\n        }\n        let sse = [];\n        sse = residual.map((a) => a.map((x) => Math.pow(x, 2)).reduce((a, b) => a + b));\n        let r2 = [];\n        for (let i = 0; i < ssr.length; i++) {\n            r2.push(ssr[i] / sst[i]);\n        }\n        let xVariance = [];\n        let stdDeviationX = [];\n        for (let i = 0; i < predictorsMatrix.rows; i++) {\n            xVariance.push(predictorsMatrix\n                .getRow(i)\n                .map((x) => Math.pow(x - xMedia[i], 2))\n                .reduce((a, b) => a + b) /\n                (predictorsMatrix.columns - 1));\n            stdDeviationX[i] = Math.sqrt(xVariance[i]);\n        }\n        let Statistic = {\n            residual,\n            yMedia,\n            xMedia,\n            SST: sst,\n            SSR: ssr,\n            SSE: sse,\n            R2: r2,\n            yVariance,\n            xVariance,\n            stdDeviationY,\n            stdDeviationX,\n        };\n        this.statistics = Statistic;\n    }\n    /**\n     * Predict y-values for a given x\n     * @returns {[Array]}\n     */\n    predict(x) {\n        const result = [];\n        let g = [];\n        if (this.intercept) {\n            x.unshift(1);\n        }\n        for (let i = 0; i < this.coefficients.columns; i++) {\n            for (let j = 0; j < this.coefficients.rows; j++) {\n                g.push(this.coefficients.get(j, i) * x[j]);\n            }\n            result[i] = g.reduce((a, b) => a + b);\n            g = [];\n        }\n        return result;\n    }\n    /**\n     * Returns some basic statistics of the regression\n     * @returns {[Array]}\n     */\n    getStatistic() {\n        return this.statistics;\n    }\n    /**\n     * Returns fitted values of Y\n     * @returns {[Array]}\n     */\n    getFittedValuesY() {\n        return this.yFittedValues;\n    }\n    /**\n     * Returns the regression coefficients\n     * @returns {[Array]}\n     */\n    getCoefficients() {\n        return this.coefficients;\n    }\n    /**\n     * Returns the scores for principal components\n     * @returns {[Object]}\n     */\n    getLoadingsdata() {\n        return this.loadingsData;\n    }\n    /**\n     * Returns the number of principal components used\n     * @returns {[Array]}\n     */\n    getScores() {\n        return this.scores;\n    }\n}\n//# 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