{"version":3,"file":"ml-spectra-fitting.min.js","sources":["../node_modules/is-any-array/src/index.js","../node_modules/ml-array-max/lib-es6/index.js","../node_modules/ml-levenberg-marquardt/src/errorCalculation.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/util.js","../node_modules/ml-matrix/src/matrix.js","../node_modules/ml-matrix/src/stat.js","../node_modules/ml-matrix/src/mathOperations.js","../node_modules/ml-matrix/src/wrap/WrapperMatrix2D.js","../node_modules/ml-matrix/src/dc/lu.js","../node_modules/ml-matrix/src/dc/util.js","../node_modules/ml-matrix/src/dc/qr.js","../node_modules/ml-matrix/src/dc/svd.js","../node_modules/ml-matrix/src/decompositions.js","../node_modules/ml-levenberg-marquardt/src/step.js","../node_modules/ml-levenberg-marquardt/src/gradientFunction.js","../node_modules/ml-levenberg-marquardt/src/index.js","../node_modules/ml-levenberg-marquardt/src/checkOptions.js","../src/selectMethod.js","../node_modules/ml-peak-shape-generator/src/util/constants.js","../node_modules/ml-peak-shape-generator/src/classes/Gaussian.js","../node_modules/ml-peak-shape-generator/src/util/erfinv.js","../node_modules/ml-peak-shape-generator/src/classes/Lorentzian.js","../node_modules/ml-peak-shape-generator/src/classes/PseudoVoigt.js","../src/shapes/sumOfGaussianLorentzians.js","../src/shapes/sumOfGaussians.js","../src/shapes/sumOfLorentzians.js","../src/index.js"],"sourcesContent":["const toString = Object.prototype.toString;\n\nexport default function isAnyArray(object) {\n return toString.call(object).endsWith('Array]');\n}\n","import isArray from 'is-any-array';\n\nfunction max(input) {\n var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n if (!isArray(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 default max;\n","/**\n * the sum of the weighted squares of the errors (or weighted residuals) between the data.y\n * and the curve-fit function.\n * @ignore\n * @param {{x:Array, y:Array}} data - Array of points to fit in the format [x1, x2, ... ], [y1, y2, ... ]\n * @param {Array} parameters - Array of current parameter values\n * @param {function} parameterizedFunction - The parameters and returns a function with the independent variable as a parameter\n * @param {Array} weightSquare - Square of weights\n * @return {number}\n */\nexport default function errorCalculation(\n data,\n parameters,\n parameterizedFunction,\n weightSquare,\n) {\n let error = 0;\n const func = parameterizedFunction(parameters);\n for (let i = 0; i < data.x.length; i++) {\n error += Math.pow(data.y[i] - func(data.x[i]), 2) / weightSquare[i];\n }\n\n return error;\n}\n","import isArray from 'is-any-array';\n\nfunction min(input) {\n var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n\n if (!isArray(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 default min;\n","import isArray 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 (!isArray(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 (!isArray(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 default rescale;\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","/**\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 checkIndices(matrix, rowIndices, columnIndices) {\n return {\n row: checkRowIndices(matrix, rowIndices),\n column: checkColumnIndices(matrix, columnIndices),\n };\n}\n\nexport function checkRowIndices(matrix, rowIndices) {\n if (typeof rowIndices !== 'object') {\n throw new TypeError('unexpected type for row indices');\n }\n\n let rowOut = rowIndices.some((r) => {\n return r < 0 || r >= matrix.rows;\n });\n\n if (rowOut) {\n throw new RangeError('row indices are out of range');\n }\n\n if (!Array.isArray(rowIndices)) rowIndices = Array.from(rowIndices);\n\n return rowIndices;\n}\n\nexport function checkColumnIndices(matrix, columnIndices) {\n if (typeof columnIndices !== 'object') {\n throw new TypeError('unexpected type for column indices');\n }\n\n let columnOut = columnIndices.some((c) => {\n return c < 0 || c >= matrix.columns;\n });\n\n if (columnOut) {\n throw new RangeError('column indices are out of range');\n }\n if (!Array.isArray(columnIndices)) columnIndices = Array.from(columnIndices);\n\n return columnIndices;\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 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 checkIndices,\n checkNonEmpty,\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() {\n if (this.isEmpty()) {\n return NaN;\n }\n let v = this.get(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 }\n }\n }\n return v;\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() {\n if (this.isEmpty()) {\n return NaN;\n }\n let v = this.get(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 }\n }\n }\n return v;\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 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 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 let indices = checkIndices(this, rowIndices, columnIndices);\n let newMatrix = new Matrix(rowIndices.length, columnIndices.length);\n for (let i = 0; i < indices.row.length; i++) {\n let rowIndex = indices.row[i];\n for (let j = 0; j < indices.column.length; j++) {\n let columnIndex = indices.column[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 (!Array.isArray(mean)) {\n throw new TypeError('mean must be an array');\n }\n return varianceByRow(this, unbiased, mean);\n }\n case 'column': {\n if (!Array.isArray(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 (!Array.isArray(center)) {\n throw new TypeError('center must be an array');\n }\n centerByRow(this, center);\n return this;\n }\n case 'column': {\n if (!Array.isArray(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 (!Array.isArray(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 (!Array.isArray(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[\n Symbol.for('nodejs.util.inspect.custom')\n ] = inspectMatrix;\n}\n\nfunction compareNumbers(a, b) {\n return a - b;\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 (Array.isArray(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 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 { 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","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 { AbstractMatrix } from '../matrix';\n\nexport default class WrapperMatrix2D extends AbstractMatrix {\n constructor(data) {\n super();\n this.data = data;\n this.rows = data.length;\n this.columns = data[0].length;\n }\n\n set(rowIndex, columnIndex, value) {\n this.data[rowIndex][columnIndex] = value;\n return this;\n }\n\n get(rowIndex, columnIndex) {\n return this.data[rowIndex][columnIndex];\n }\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nexport default class LuDecomposition {\n constructor(matrix) {\n matrix = WrapperMatrix2D.checkMatrix(matrix);\n\n let lu = matrix.clone();\n let rows = lu.rows;\n let columns = lu.columns;\n let pivotVector = new Float64Array(rows);\n let pivotSign = 1;\n let i, j, k, p, s, t, v;\n let LUcolj, kmax;\n\n for (i = 0; i < rows; i++) {\n pivotVector[i] = i;\n }\n\n LUcolj = new Float64Array(rows);\n\n for (j = 0; j < columns; j++) {\n for (i = 0; i < rows; i++) {\n LUcolj[i] = lu.get(i, j);\n }\n\n for (i = 0; i < rows; i++) {\n kmax = Math.min(i, j);\n s = 0;\n for (k = 0; k < kmax; k++) {\n s += lu.get(i, k) * LUcolj[k];\n }\n LUcolj[i] -= s;\n lu.set(i, j, LUcolj[i]);\n }\n\n p = j;\n for (i = j + 1; i < rows; i++) {\n if (Math.abs(LUcolj[i]) > Math.abs(LUcolj[p])) {\n p = i;\n }\n }\n\n if (p !== j) {\n for (k = 0; k < columns; k++) {\n t = lu.get(p, k);\n lu.set(p, k, lu.get(j, k));\n lu.set(j, k, t);\n }\n\n v = pivotVector[p];\n pivotVector[p] = pivotVector[j];\n pivotVector[j] = v;\n\n pivotSign = -pivotSign;\n }\n\n if (j < rows && lu.get(j, j) !== 0) {\n for (i = j + 1; i < rows; i++) {\n lu.set(i, j, lu.get(i, j) / lu.get(j, j));\n }\n }\n }\n\n this.LU = lu;\n this.pivotVector = pivotVector;\n this.pivotSign = pivotSign;\n }\n\n isSingular() {\n let data = this.LU;\n let col = data.columns;\n for (let j = 0; j < col; j++) {\n if (data.get(j, j) === 0) {\n return true;\n }\n }\n return false;\n }\n\n solve(value) {\n value = Matrix.checkMatrix(value);\n\n let lu = this.LU;\n let rows = lu.rows;\n\n if (rows !== value.rows) {\n throw new Error('Invalid matrix dimensions');\n }\n if (this.isSingular()) {\n throw new Error('LU matrix is singular');\n }\n\n let count = value.columns;\n let X = value.subMatrixRow(this.pivotVector, 0, count - 1);\n let columns = lu.columns;\n let i, j, k;\n\n for (k = 0; k < columns; k++) {\n for (i = k + 1; i < columns; i++) {\n for (j = 0; j < count; j++) {\n X.set(i, j, X.get(i, j) - X.get(k, j) * lu.get(i, k));\n }\n }\n }\n for (k = columns - 1; k >= 0; k--) {\n for (j = 0; j < count; j++) {\n X.set(k, j, X.get(k, j) / lu.get(k, k));\n }\n for (i = 0; i < k; i++) {\n for (j = 0; j < count; j++) {\n X.set(i, j, X.get(i, j) - X.get(k, j) * lu.get(i, k));\n }\n }\n }\n return X;\n }\n\n get determinant() {\n let data = this.LU;\n if (!data.isSquare()) {\n throw new Error('Matrix must be square');\n }\n let determinant = this.pivotSign;\n let col = data.columns;\n for (let j = 0; j < col; j++) {\n determinant *= data.get(j, j);\n }\n return determinant;\n }\n\n get lowerTriangularMatrix() {\n let data = this.LU;\n let rows = data.rows;\n let columns = data.columns;\n let X = new Matrix(rows, columns);\n for (let i = 0; i < rows; i++) {\n for (let j = 0; j < columns; j++) {\n if (i > j) {\n X.set(i, j, data.get(i, j));\n } else if (i === j) {\n X.set(i, j, 1);\n } else {\n X.set(i, j, 0);\n }\n }\n }\n return X;\n }\n\n get upperTriangularMatrix() {\n let data = this.LU;\n let rows = data.rows;\n let columns = data.columns;\n let X = new Matrix(rows, columns);\n for (let i = 0; i < rows; i++) {\n for (let j = 0; j < columns; j++) {\n if (i <= j) {\n X.set(i, j, data.get(i, j));\n } else {\n X.set(i, j, 0);\n }\n }\n }\n return X;\n }\n\n get pivotPermutationVector() {\n return Array.from(this.pivotVector);\n }\n}\n","export function hypotenuse(a, b) {\n let r = 0;\n if (Math.abs(a) > Math.abs(b)) {\n r = b / a;\n return Math.abs(a) * Math.sqrt(1 + r * r);\n }\n if (b !== 0) {\n r = a / b;\n return Math.abs(b) * Math.sqrt(1 + r * r);\n }\n return 0;\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nimport { hypotenuse } from './util';\n\nexport default class QrDecomposition {\n constructor(value) {\n value = WrapperMatrix2D.checkMatrix(value);\n\n let qr = value.clone();\n let m = value.rows;\n let n = value.columns;\n let rdiag = new Float64Array(n);\n let i, j, k, s;\n\n for (k = 0; k < n; k++) {\n let nrm = 0;\n for (i = k; i < m; i++) {\n nrm = hypotenuse(nrm, qr.get(i, k));\n }\n if (nrm !== 0) {\n if (qr.get(k, k) < 0) {\n nrm = -nrm;\n }\n for (i = k; i < m; i++) {\n qr.set(i, k, qr.get(i, k) / nrm);\n }\n qr.set(k, k, qr.get(k, k) + 1);\n for (j = k + 1; j < n; j++) {\n s = 0;\n for (i = k; i < m; i++) {\n s += qr.get(i, k) * qr.get(i, j);\n }\n s = -s / qr.get(k, k);\n for (i = k; i < m; i++) {\n qr.set(i, j, qr.get(i, j) + s * qr.get(i, k));\n }\n }\n }\n rdiag[k] = -nrm;\n }\n\n this.QR = qr;\n this.Rdiag = rdiag;\n }\n\n solve(value) {\n value = Matrix.checkMatrix(value);\n\n let qr = this.QR;\n let m = qr.rows;\n\n if (value.rows !== m) {\n throw new Error('Matrix row dimensions must agree');\n }\n if (!this.isFullRank()) {\n throw new Error('Matrix is rank deficient');\n }\n\n let count = value.columns;\n let X = value.clone();\n let n = qr.columns;\n let i, j, k, s;\n\n for (k = 0; k < n; k++) {\n for (j = 0; j < count; j++) {\n s = 0;\n for (i = k; i < m; i++) {\n s += qr.get(i, k) * X.get(i, j);\n }\n s = -s / qr.get(k, k);\n for (i = k; i < m; i++) {\n X.set(i, j, X.get(i, j) + s * qr.get(i, k));\n }\n }\n }\n for (k = n - 1; k >= 0; k--) {\n for (j = 0; j < count; j++) {\n X.set(k, j, X.get(k, j) / this.Rdiag[k]);\n }\n for (i = 0; i < k; i++) {\n for (j = 0; j < count; j++) {\n X.set(i, j, X.get(i, j) - X.get(k, j) * qr.get(i, k));\n }\n }\n }\n\n return X.subMatrix(0, n - 1, 0, count - 1);\n }\n\n isFullRank() {\n let columns = this.QR.columns;\n for (let i = 0; i < columns; i++) {\n if (this.Rdiag[i] === 0) {\n return false;\n }\n }\n return true;\n }\n\n get upperTriangularMatrix() {\n let qr = this.QR;\n let n = qr.columns;\n let X = new Matrix(n, n);\n let i, j;\n for (i = 0; i < n; i++) {\n for (j = 0; j < n; j++) {\n if (i < j) {\n X.set(i, j, qr.get(i, j));\n } else if (i === j) {\n X.set(i, j, this.Rdiag[i]);\n } else {\n X.set(i, j, 0);\n }\n }\n }\n return X;\n }\n\n get orthogonalMatrix() {\n let qr = this.QR;\n let rows = qr.rows;\n let columns = qr.columns;\n let X = new Matrix(rows, columns);\n let i, j, k, s;\n\n for (k = columns - 1; k >= 0; k--) {\n for (i = 0; i < rows; i++) {\n X.set(i, k, 0);\n }\n X.set(k, k, 1);\n for (j = k; j < columns; j++) {\n if (qr.get(k, k) !== 0) {\n s = 0;\n for (i = k; i < rows; i++) {\n s += qr.get(i, k) * X.get(i, j);\n }\n\n s = -s / qr.get(k, k);\n\n for (i = k; i < rows; i++) {\n X.set(i, j, X.get(i, j) + s * qr.get(i, k));\n }\n }\n }\n }\n return X;\n }\n}\n","import Matrix from '../matrix';\nimport WrapperMatrix2D from '../wrap/WrapperMatrix2D';\n\nimport { hypotenuse } from './util';\n\nexport default class SingularValueDecomposition {\n constructor(value, options = {}) {\n value = WrapperMatrix2D.checkMatrix(value);\n\n if (value.isEmpty()) {\n throw new Error('Matrix must be non-empty');\n }\n\n let m = value.rows;\n let n = value.columns;\n\n const {\n computeLeftSingularVectors = true,\n computeRightSingularVectors = true,\n autoTranspose = false,\n } = options;\n\n let wantu = Boolean(computeLeftSingularVectors);\n let wantv = Boolean(computeRightSingularVectors);\n\n let swapped = false;\n let a;\n if (m < n) {\n if (!autoTranspose) {\n a = value.clone();\n // eslint-disable-next-line no-console\n console.warn(\n 'Computing SVD on a matrix with more columns than rows. Consider enabling autoTranspose',\n );\n } else {\n a = value.transpose();\n m = a.rows;\n n = a.columns;\n swapped = true;\n let aux = wantu;\n wantu = wantv;\n wantv = aux;\n }\n } else {\n a = value.clone();\n }\n\n let nu = Math.min(m, n);\n let ni = Math.min(m + 1, n);\n let s = new Float64Array(ni);\n let U = new Matrix(m, nu);\n let V = new Matrix(n, n);\n\n let e = new Float64Array(n);\n let work = new Float64Array(m);\n\n let si = new Float64Array(ni);\n for (let i = 0; i < ni; i++) si[i] = i;\n\n let nct = Math.min(m - 1, n);\n let nrt = Math.max(0, Math.min(n - 2, m));\n let mrc = Math.max(nct, nrt);\n\n for (let k = 0; k < mrc; k++) {\n if (k < nct) {\n s[k] = 0;\n for (let i = k; i < m; i++) {\n s[k] = hypotenuse(s[k], a.get(i, k));\n }\n if (s[k] !== 0) {\n if (a.get(k, k) < 0) {\n s[k] = -s[k];\n }\n for (let i = k; i < m; i++) {\n a.set(i, k, a.get(i, k) / s[k]);\n }\n a.set(k, k, a.get(k, k) + 1);\n }\n s[k] = -s[k];\n }\n\n for (let j = k + 1; j < n; j++) {\n if (k < nct && s[k] !== 0) {\n let t = 0;\n for (let i = k; i < m; i++) {\n t += a.get(i, k) * a.get(i, j);\n }\n t = -t / a.get(k, k);\n for (let i = k; i < m; i++) {\n a.set(i, j, a.get(i, j) + t * a.get(i, k));\n }\n }\n e[j] = a.get(k, j);\n }\n\n if (wantu && k < nct) {\n for (let i = k; i < m; i++) {\n U.set(i, k, a.get(i, k));\n }\n }\n\n if (k < nrt) {\n e[k] = 0;\n for (let i = k + 1; i < n; i++) {\n e[k] = hypotenuse(e[k], e[i]);\n }\n if (e[k] !== 0) {\n if (e[k + 1] < 0) {\n e[k] = 0 - e[k];\n }\n for (let i = k + 1; i < n; i++) {\n e[i] /= e[k];\n }\n e[k + 1] += 1;\n }\n e[k] = -e[k];\n if (k + 1 < m && e[k] !== 0) {\n for (let i = k + 1; i < m; i++) {\n work[i] = 0;\n }\n for (let i = k + 1; i < m; i++) {\n for (let j = k + 1; j < n; j++) {\n work[i] += e[j] * a.get(i, j);\n }\n }\n for (let j = k + 1; j < n; j++) {\n let t = -e[j] / e[k + 1];\n for (let i = k + 1; i < m; i++) {\n a.set(i, j, a.get(i, j) + t * work[i]);\n }\n }\n }\n if (wantv) {\n for (let i = k + 1; i < n; i++) {\n V.set(i, k, e[i]);\n }\n }\n }\n }\n\n let p = Math.min(n, m + 1);\n if (nct < n) {\n s[nct] = a.get(nct, nct);\n }\n if (m < p) {\n s[p - 1] = 0;\n }\n if (nrt + 1 < p) {\n e[nrt] = a.get(nrt, p - 1);\n }\n e[p - 1] = 0;\n\n if (wantu) {\n for (let j = nct; j < nu; j++) {\n for (let i = 0; i < m; i++) {\n U.set(i, j, 0);\n }\n U.set(j, j, 1);\n }\n for (let k = nct - 1; k >= 0; k--) {\n if (s[k] !== 0) {\n for (let j = k + 1; j < nu; j++) {\n let t = 0;\n for (let i = k; i < m; i++) {\n t += U.get(i, k) * U.get(i, j);\n }\n t = -t / U.get(k, k);\n for (let i = k; i < m; i++) {\n U.set(i, j, U.get(i, j) + t * U.get(i, k));\n }\n }\n for (let i = k; i < m; i++) {\n U.set(i, k, -U.get(i, k));\n }\n U.set(k, k, 1 + U.get(k, k));\n for (let i = 0; i < k - 1; i++) {\n U.set(i, k, 0);\n }\n } else {\n for (let i = 0; i < m; i++) {\n U.set(i, k, 0);\n }\n U.set(k, k, 1);\n }\n }\n }\n\n if (wantv) {\n for (let k = n - 1; k >= 0; k--) {\n if (k < nrt && e[k] !== 0) {\n for (let j = k + 1; j < n; j++) {\n let t = 0;\n for (let i = k + 1; i < n; i++) {\n t += V.get(i, k) * V.get(i, j);\n }\n t = -t / V.get(k + 1, k);\n for (let i = k + 1; i < n; i++) {\n V.set(i, j, V.get(i, j) + t * V.get(i, k));\n }\n }\n }\n for (let i = 0; i < n; i++) {\n V.set(i, k, 0);\n }\n V.set(k, k, 1);\n }\n }\n\n let pp = p - 1;\n let iter = 0;\n let eps = Number.EPSILON;\n while (p > 0) {\n let k, kase;\n for (k = p - 2; k >= -1; k--) {\n if (k === -1) {\n break;\n }\n const alpha =\n Number.MIN_VALUE + eps * Math.abs(s[k] + Math.abs(s[k + 1]));\n if (Math.abs(e[k]) <= alpha || Number.isNaN(e[k])) {\n e[k] = 0;\n break;\n }\n }\n if (k === p - 2) {\n kase = 4;\n } else {\n let ks;\n for (ks = p - 1; ks >= k; ks--) {\n if (ks === k) {\n break;\n }\n let t =\n (ks !== p ? Math.abs(e[ks]) : 0) +\n (ks !== k + 1 ? Math.abs(e[ks - 1]) : 0);\n if (Math.abs(s[ks]) <= eps * t) {\n s[ks] = 0;\n break;\n }\n }\n if (ks === k) {\n kase = 3;\n } else if (ks === p - 1) {\n kase = 1;\n } else {\n kase = 2;\n k = ks;\n }\n }\n\n k++;\n\n switch (kase) {\n case 1: {\n let f = e[p - 2];\n e[p - 2] = 0;\n for (let j = p - 2; j >= k; j--) {\n let t = hypotenuse(s[j], f);\n let cs = s[j] / t;\n let sn = f / t;\n s[j] = t;\n if (j !== k) {\n f = -sn * e[j - 1];\n e[j - 1] = cs * e[j - 1];\n }\n if (wantv) {\n for (let i = 0; i < n; i++) {\n t = cs * V.get(i, j) + sn * V.get(i, p - 1);\n V.set(i, p - 1, -sn * V.get(i, j) + cs * V.get(i, p - 1));\n V.set(i, j, t);\n }\n }\n }\n break;\n }\n case 2: {\n let f = e[k - 1];\n e[k - 1] = 0;\n for (let j = k; j < p; j++) {\n let t = hypotenuse(s[j], f);\n let cs = s[j] / t;\n let sn = f / t;\n s[j] = t;\n f = -sn * e[j];\n e[j] = cs * e[j];\n if (wantu) {\n for (let i = 0; i < m; i++) {\n t = cs * U.get(i, j) + sn * U.get(i, k - 1);\n U.set(i, k - 1, -sn * U.get(i, j) + cs * U.get(i, k - 1));\n U.set(i, j, t);\n }\n }\n }\n break;\n }\n case 3: {\n const scale = Math.max(\n Math.abs(s[p - 1]),\n Math.abs(s[p - 2]),\n Math.abs(e[p - 2]),\n Math.abs(s[k]),\n Math.abs(e[k]),\n );\n const sp = s[p - 1] / scale;\n const spm1 = s[p - 2] / scale;\n const epm1 = e[p - 2] / scale;\n const sk = s[k] / scale;\n const ek = e[k] / scale;\n const b = ((spm1 + sp) * (spm1 - sp) + epm1 * epm1) / 2;\n const c = sp * epm1 * (sp * epm1);\n let shift = 0;\n if (b !== 0 || c !== 0) {\n if (b < 0) {\n shift = 0 - Math.sqrt(b * b + c);\n } else {\n shift = Math.sqrt(b * b + c);\n }\n shift = c / (b + shift);\n }\n let f = (sk + sp) * (sk - sp) + shift;\n let g = sk * ek;\n for (let j = k; j < p - 1; j++) {\n let t = hypotenuse(f, g);\n if (t === 0) t = Number.MIN_VALUE;\n let cs = f / t;\n let sn = g / t;\n if (j !== k) {\n e[j - 1] = t;\n }\n f = cs * s[j] + sn * e[j];\n e[j] = cs * e[j] - sn * s[j];\n g = sn * s[j + 1];\n s[j + 1] = cs * s[j + 1];\n if (wantv) {\n for (let i = 0; i < n; i++) {\n t = cs * V.get(i, j) + sn * V.get(i, j + 1);\n V.set(i, j + 1, -sn * V.get(i, j) + cs * V.get(i, j + 1));\n V.set(i, j, t);\n }\n }\n t = hypotenuse(f, g);\n if (t === 0) t = Number.MIN_VALUE;\n cs = f / t;\n sn = g / t;\n s[j] = t;\n f = cs * e[j] + sn * s[j + 1];\n s[j + 1] = -sn * e[j] + cs * s[j + 1];\n g = sn * e[j + 1];\n e[j + 1] = cs * e[j + 1];\n if (wantu && j < m - 1) {\n for (let i = 0; i < m; i++) {\n t = cs * U.get(i, j) + sn * U.get(i, j + 1);\n U.set(i, j + 1, -sn * U.get(i, j) + cs * U.get(i, j + 1));\n U.set(i, j, t);\n }\n }\n }\n e[p - 2] = f;\n iter = iter + 1;\n break;\n }\n case 4: {\n if (s[k] <= 0) {\n s[k] = s[k] < 0 ? -s[k] : 0;\n if (wantv) {\n for (let i = 0; i <= pp; i++) {\n V.set(i, k, -V.get(i, k));\n }\n }\n }\n while (k < pp) {\n if (s[k] >= s[k + 1]) {\n break;\n }\n let t = s[k];\n s[k] = s[k + 1];\n s[k + 1] = t;\n if (wantv && k < n - 1) {\n for (let i = 0; i < n; i++) {\n t = V.get(i, k + 1);\n V.set(i, k + 1, V.get(i, k));\n V.set(i, k, t);\n }\n }\n if (wantu && k < m - 1) {\n for (let i = 0; i < m; i++) {\n t = U.get(i, k + 1);\n U.set(i, k + 1, U.get(i, k));\n U.set(i, k, t);\n }\n }\n k++;\n }\n iter = 0;\n p--;\n break;\n }\n // no default\n }\n }\n\n if (swapped) {\n let tmp = V;\n V = U;\n U = tmp;\n }\n\n this.m = m;\n this.n = n;\n this.s = s;\n this.U = U;\n this.V = V;\n }\n\n solve(value) {\n let Y = value;\n let e = this.threshold;\n let scols = this.s.length;\n let Ls = Matrix.zeros(scols, scols);\n\n for (let i = 0; i < scols; i++) {\n if (Math.abs(this.s[i]) <= e) {\n Ls.set(i, i, 0);\n } else {\n Ls.set(i, i, 1 / this.s[i]);\n }\n }\n\n let U = this.U;\n let V = this.rightSingularVectors;\n\n let VL = V.mmul(Ls);\n let vrows = V.rows;\n let urows = U.rows;\n let VLU = Matrix.zeros(vrows, urows);\n\n for (let i = 0; i < vrows; i++) {\n for (let j = 0; j < urows; j++) {\n let sum = 0;\n for (let k = 0; k < scols; k++) {\n sum += VL.get(i, k) * U.get(j, k);\n }\n VLU.set(i, j, sum);\n }\n }\n\n return VLU.mmul(Y);\n }\n\n solveForDiagonal(value) {\n return this.solve(Matrix.diag(value));\n }\n\n inverse() {\n let V = this.V;\n let e = this.threshold;\n let vrows = V.rows;\n let vcols = V.columns;\n let X = new Matrix(vrows, this.s.length);\n\n for (let i = 0; i < vrows; i++) {\n for (let j = 0; j < vcols; j++) {\n if (Math.abs(this.s[j]) > e) {\n X.set(i, j, V.get(i, j) / this.s[j]);\n }\n }\n }\n\n let U = this.U;\n\n let urows = U.rows;\n let ucols = U.columns;\n let Y = new Matrix(vrows, urows);\n\n for (let i = 0; i < vrows; i++) {\n for (let j = 0; j < urows; j++) {\n let sum = 0;\n for (let k = 0; k < ucols; k++) {\n sum += X.get(i, k) * U.get(j, k);\n }\n Y.set(i, j, sum);\n }\n }\n\n return Y;\n }\n\n get condition() {\n return this.s[0] / this.s[Math.min(this.m, this.n) - 1];\n }\n\n get norm2() {\n return this.s[0];\n }\n\n get rank() {\n let tol = Math.max(this.m, this.n) * this.s[0] * Number.EPSILON;\n let r = 0;\n let s = this.s;\n for (let i = 0, ii = s.length; i < ii; i++) {\n if (s[i] > tol) {\n r++;\n }\n }\n return r;\n }\n\n get diagonal() {\n return Array.from(this.s);\n }\n\n get threshold() {\n return (Number.EPSILON / 2) * Math.max(this.m, this.n) * this.s[0];\n }\n\n get leftSingularVectors() {\n return this.U;\n }\n\n get rightSingularVectors() {\n return this.V;\n }\n\n get diagonalMatrix() {\n return Matrix.diag(this.s);\n }\n}\n","import LuDecomposition from './dc/lu';\nimport QrDecomposition from './dc/qr';\nimport SingularValueDecomposition from './dc/svd';\nimport Matrix from './matrix';\nimport WrapperMatrix2D from './wrap/WrapperMatrix2D';\n\nexport function inverse(matrix, useSVD = false) {\n matrix = WrapperMatrix2D.checkMatrix(matrix);\n if (useSVD) {\n return new SingularValueDecomposition(matrix).inverse();\n } else {\n return solve(matrix, Matrix.eye(matrix.rows));\n }\n}\n\nexport function solve(leftHandSide, rightHandSide, useSVD = false) {\n leftHandSide = WrapperMatrix2D.checkMatrix(leftHandSide);\n rightHandSide = WrapperMatrix2D.checkMatrix(rightHandSide);\n if (useSVD) {\n return new SingularValueDecomposition(leftHandSide).solve(rightHandSide);\n } else {\n return leftHandSide.isSquare()\n ? new LuDecomposition(leftHandSide).solve(rightHandSide)\n : new QrDecomposition(leftHandSide).solve(rightHandSide);\n }\n}\n","import { inverse, Matrix } from 'ml-matrix';\n\nimport gradientFunction from './gradientFunction';\n\n/**\n * Matrix function over the samples\n * @ignore\n * @param {{x:Array, y:Array}} data - Array of points to fit in the format [x1, x2, ... ], [y1, y2, ... ]\n * @param {Array} evaluatedData - Array of previous evaluated function values\n * @return {Matrix}\n */\nfunction matrixFunction(data, evaluatedData) {\n const m = data.x.length;\n\n let ans = new Matrix(m, 1);\n\n for (let point = 0; point < m; point++) {\n ans.set(point, 0, data.y[point] - evaluatedData[point]);\n }\n return ans;\n}\n\n/**\n * Iteration for Levenberg-Marquardt\n * @ignore\n * @param {{x:Array, y:Array}} data - Array of points to fit in the format [x1, x2, ... ], [y1, y2, ... ]\n * @param {Array} params - Array of previous parameter values\n * @param {number} damping - Levenberg-Marquardt parameter\n * @param {number|array} gradientDifference - The step size to approximate the jacobian matrix\n * @param {boolean} centralDifference - If true the jacobian matrix is approximated by central differences otherwise by forward differences\n * @param {function} parameterizedFunction - The parameters and returns a function with the independent variable as a parameter\n * @return {Array}\n */\nexport default function step(\n data,\n params,\n damping,\n gradientDifference,\n parameterizedFunction,\n centralDifference,\n weights,\n) {\n let value = damping;\n let identity = Matrix.eye(params.length, params.length, value);\n\n const func = parameterizedFunction(params);\n\n let evaluatedData = new Float64Array(data.x.length);\n for (let i = 0; i < data.x.length; i++) {\n evaluatedData[i] = func(data.x[i]);\n }\n\n let gradientFunc = gradientFunction(\n data,\n evaluatedData,\n params,\n gradientDifference,\n parameterizedFunction,\n centralDifference,\n );\n let residualError = matrixFunction(data, evaluatedData);\n\n let inverseMatrix = inverse(\n identity.add(\n gradientFunc.mmul(\n gradientFunc.transpose().scale('row', { scale: weights }),\n ),\n ),\n );\n\n let jacobianWeigthResidualError = gradientFunc.mmul(\n residualError.scale('row', { scale: weights }),\n );\n\n let perturbations = inverseMatrix.mmul(jacobianWeigthResidualError);\n\n return {\n perturbations,\n jacobianWeigthResidualError,\n };\n}\n","import { Matrix } from 'ml-matrix';\n/**\n * Difference of the matrix function over the parameters\n * @ignore\n * @param {{x:Array, y:Array}} data - Array of points to fit in the format [x1, x2, ... ], [y1, y2, ... ]\n * @param {Array} evaluatedData - Array of previous evaluated function values\n * @param {Array} params - Array of previous parameter values\n * @param {number|array} gradientDifference - The step size to approximate the jacobian matrix\n * @param {boolean} centralDifference - If true the jacobian matrix is approximated by central differences otherwise by forward differences\n * @param {function} paramFunction - The parameters and returns a function with the independent variable as a parameter\n * @return {Matrix}\n */\n\nexport default function gradientFunction(\n data,\n evaluatedData,\n params,\n gradientDifference,\n paramFunction,\n centralDifference,\n) {\n const nbParams = params.length;\n const nbPoints = data.x.length;\n let ans = Matrix.zeros(nbParams, nbPoints);\n\n let rowIndex = 0;\n for (let param = 0; param < nbParams; param++) {\n if (gradientDifference[param] === 0) continue;\n let delta = gradientDifference[param];\n let auxParams = params.slice();\n auxParams[param] += delta;\n let funcParam = paramFunction(auxParams);\n if (!centralDifference) {\n for (let point = 0; point < nbPoints; point++) {\n ans.set(\n rowIndex,\n point,\n (evaluatedData[point] - funcParam(data.x[point])) / delta,\n );\n }\n } else {\n auxParams = params.slice();\n auxParams[param] -= delta;\n delta *= 2;\n let funcParam2 = paramFunction(auxParams);\n for (let point = 0; point < nbPoints; point++) {\n ans.set(\n rowIndex,\n point,\n (funcParam2(data.x[point]) - funcParam(data.x[point])) / delta,\n );\n }\n }\n rowIndex++;\n }\n\n return ans;\n}\n","import checkOptions from './checkOptions';\nimport errorCalculation from './errorCalculation';\nimport step from './step';\n\n/**\n * Curve fitting algorithm\n * @param {{x:Array, y:Array}} data - Array of points to fit in the format [x1, x2, ... ], [y1, y2, ... ]\n * @param {function} parameterizedFunction - The parameters and returns a function with the independent variable as a parameter\n * @param {object} [options] - Options object\n * @param {number|array} [options.weights = 1] - weighting vector, if the length does not match with the number of data points, the vector is reconstructed with first value.\n * @param {number} [options.damping = 1e-2] - Levenberg-Marquardt parameter, small values of the damping parameter λ result in a Gauss-Newton update and large\nvalues of λ result in a gradient descent update\n * @param {number} [options.dampingStepDown = 9] - factor to reduce the damping (Levenberg-Marquardt parameter) when there is not an improvement when updating parameters.\n * @param {number} [options.dampingStepUp = 11] - factor to increase the damping (Levenberg-Marquardt parameter) when there is an improvement when updating parameters.\n * @param {number} [options.improvementThreshold = 1e-3] - the threshold to define an improvement through an update of parameters\n * @param {number|array} [options.gradientDifference = 10e-2] - The step size to approximate the jacobian matrix\n * @param {boolean} [options.centralDifference = false] - If true the jacobian matrix is approximated by central differences otherwise by forward differences\n * @param {Array} [options.minValues] - Minimum allowed values for parameters\n * @param {Array} [options.maxValues] - Maximum allowed values for parameters\n * @param {Array} [options.initialValues] - Array of initial parameter values\n * @param {number} [options.maxIterations = 100] - Maximum of allowed iterations\n * @param {number} [options.errorTolerance = 10e-3] - Minimum uncertainty allowed for each point.\n * @param {number} [options.timeout] - maximum time running before throw in seconds.\n * @return {{parameterValues: Array, parameterError: number, iterations: number}}\n */\nexport default function levenbergMarquardt(\n data,\n parameterizedFunction,\n options = {},\n) {\n let {\n checkTimeout,\n minValues,\n maxValues,\n parameters,\n weightSquare,\n damping,\n dampingStepUp,\n dampingStepDown,\n maxIterations,\n errorTolerance,\n centralDifference,\n gradientDifference,\n improvementThreshold,\n } = checkOptions(data, parameterizedFunction, options);\n\n let error = errorCalculation(\n data,\n parameters,\n parameterizedFunction,\n weightSquare,\n );\n\n let converged = error <= errorTolerance;\n\n let iteration = 0;\n for (; iteration < maxIterations && !converged; iteration++) {\n let previousError = error;\n\n let { perturbations, jacobianWeigthResidualError } = step(\n data,\n parameters,\n damping,\n gradientDifference,\n parameterizedFunction,\n centralDifference,\n weightSquare,\n );\n\n for (let k = 0; k < parameters.length; k++) {\n parameters[k] = Math.min(\n Math.max(minValues[k], parameters[k] - perturbations.get(k, 0)),\n maxValues[k],\n );\n }\n\n error = errorCalculation(\n data,\n parameters,\n parameterizedFunction,\n weightSquare,\n );\n\n if (isNaN(error)) break;\n\n let improvementMetric =\n (previousError - error) /\n perturbations\n .transpose()\n .mmul(perturbations.mulS(damping).add(jacobianWeigthResidualError))\n .get(0, 0);\n\n if (improvementMetric > improvementThreshold) {\n damping = Math.max(damping / dampingStepDown, 1e-7);\n } else {\n error = previousError;\n damping = Math.min(damping * dampingStepUp, 1e7);\n }\n\n if (checkTimeout()) {\n throw new Error(\n `The execution time is over to ${options.timeout} seconds`,\n );\n }\n\n converged = error <= errorTolerance;\n }\n\n return {\n parameterValues: parameters,\n parameterError: error,\n iterations: iteration,\n };\n}\n","import isArray from 'is-any-array';\n\nexport default function checkOptions(data, parameterizedFunction, options) {\n let {\n timeout,\n minValues,\n maxValues,\n initialValues,\n weights = 1,\n damping = 1e-2,\n dampingStepUp = 11,\n dampingStepDown = 9,\n maxIterations = 100,\n errorTolerance = 1e-7,\n centralDifference = false,\n gradientDifference = 10e-2,\n improvementThreshold = 1e-3,\n } = options;\n\n if (damping <= 0) {\n throw new Error('The damping option must be a positive number');\n } else if (!data.x || !data.y) {\n throw new Error('The data parameter must have x and y elements');\n } else if (\n !isArray(data.x) ||\n data.x.length < 2 ||\n !isArray(data.y) ||\n data.y.length < 2\n ) {\n throw new Error(\n 'The data parameter elements must be an array with more than 2 points',\n );\n } else if (data.x.length !== data.y.length) {\n throw new Error('The data parameter elements must have the same size');\n }\n\n let parameters =\n initialValues || new Array(parameterizedFunction.length).fill(1);\n\n let nbPoints = data.y.length;\n let parLen = parameters.length;\n maxValues = maxValues || new Array(parLen).fill(Number.MAX_SAFE_INTEGER);\n minValues = minValues || new Array(parLen).fill(Number.MIN_SAFE_INTEGER);\n\n if (maxValues.length !== minValues.length) {\n throw new Error('minValues and maxValues must be the same size');\n }\n\n if (!isArray(parameters)) {\n throw new Error('initialValues must be an array');\n }\n\n if (typeof gradientDifference === 'number') {\n gradientDifference = new Array(parameters.length).fill(gradientDifference);\n } else if (isArray(gradientDifference)) {\n if (gradientDifference.length !== parLen) {\n gradientDifference = new Array(parLen).fill(gradientDifference[0]);\n }\n } else {\n throw new Error(\n 'gradientDifference should be a number or array with length equal to the number of parameters',\n );\n }\n\n let filler;\n if (typeof weights === 'number') {\n let value = 1 / weights ** 2;\n filler = () => value;\n } else if (isArray(weights)) {\n if (weights.length < data.x.length) {\n let value = 1 / weights[0] ** 2;\n filler = () => value;\n } else {\n filler = (i) => 1 / weights[i] ** 2;\n }\n } else {\n throw new Error(\n 'weights should be a number or array with length equal to the number of data points',\n );\n }\n\n let checkTimeout;\n if (timeout !== undefined) {\n if (typeof timeout !== 'number') {\n throw new Error('timeout should be a number');\n }\n let endTime = Date.now() + timeout * 1000;\n checkTimeout = () => Date.now() > endTime;\n } else {\n checkTimeout = () => false;\n }\n\n let weightSquare = new Array(data.x.length);\n for (let i = 0; i < nbPoints; i++) {\n weightSquare[i] = filler(i);\n }\n\n return {\n checkTimeout,\n minValues,\n maxValues,\n parameters,\n weightSquare,\n damping,\n dampingStepUp,\n dampingStepDown,\n maxIterations,\n errorTolerance,\n centralDifference,\n gradientDifference,\n improvementThreshold,\n };\n}\n","import LM from 'ml-levenberg-marquardt';\n\nconst LEVENBERG_MARQUARDT = 1;\n\nexport function selectMethod(optimizationOptions = {}) {\n let { kind, options } = optimizationOptions;\n kind = getKind(kind);\n switch (kind) {\n case LEVENBERG_MARQUARDT:\n return {\n algorithm: LM,\n optimizationOptions: checkOptions(kind, options),\n };\n default:\n throw new Error(`Unknown kind algorithm`);\n }\n}\n\nfunction checkOptions(kind, options = {}) {\n // eslint-disable-next-line default-case\n switch (kind) {\n case LEVENBERG_MARQUARDT:\n return Object.assign({}, lmOptions, options);\n }\n}\n\nfunction getKind(kind) {\n if (typeof kind !== 'string') return kind;\n switch (kind.toLowerCase().replace(/[^a-z]/g, '')) {\n case 'lm':\n case 'levenbergmarquardt':\n return LEVENBERG_MARQUARDT;\n default:\n throw new Error(`Unknown kind algorithm`);\n }\n}\n\nconst lmOptions = {\n damping: 1.5,\n maxIterations: 100,\n errorTolerance: 1e-8,\n};\n","export const GAUSSIAN_EXP_FACTOR = -4 * Math.LN2;\nexport const ROOT_PI_OVER_LN2 = Math.sqrt(Math.PI / Math.LN2);\nexport const ROOT_THREE = Math.sqrt(3);\nexport const ROOT_2LN2 = Math.sqrt(2 * Math.LN2);\nexport const ROOT_2LN2_MINUS_ONE = Math.sqrt(2 * Math.LN2) - 1;\n","import {\n ROOT_2LN2,\n GAUSSIAN_EXP_FACTOR,\n ROOT_PI_OVER_LN2,\n} from '../util/constants';\nimport erfinv from '../util/erfinv';\n\nexport class Gaussian {\n /**\n * @param {object} [options = {}]\n * @param {number} [options.height=x] Define the height of the peak, by default area=1 (normalized)\n * @param {number} [options.fwhm = 500] - Full Width at Half Maximum in the number of points in FWHM.\n * @param {number} [options.sd] - Standard deviation, if it's defined options.fwhm will be ignored and the value will be computed sd * Math.sqrt(8 * Math.LN2);\n */\n constructor(options = {}) {\n this.fwhm = options.sd\n ? Gaussian.widthToFWHM(2 * options.sd)\n : options.fwhm\n ? options.fwhm\n : 500;\n this.height =\n options.height === undefined\n ? Math.sqrt(-GAUSSIAN_EXP_FACTOR / Math.PI) / this.fwhm\n : options.height;\n }\n /**\n * Calculate a gaussian shape\n * @param {object} [options = {}]\n * @param {number} [options.factor = 6] - Number of time to take fwhm to calculate length. Default covers 99.99 % of area.\n * @param {number} [options.length = fwhm * factor + 1] - total number of points to calculate\n * @return {Float64Array} y values\n */\n\n getData(options = {}) {\n let { length, factor = this.getFactor() } = options;\n\n if (!length) {\n length = Math.min(Math.ceil(this.fwhm * factor), Math.pow(2, 25) - 1);\n if (length % 2 === 0) length++;\n }\n\n const center = (length - 1) / 2;\n const data = new Float64Array(length);\n for (let i = 0; i <= center; i++) {\n data[i] = this.fct(i - center) * this.height;\n data[length - 1 - i] = data[i];\n }\n\n return data;\n }\n\n /**\n * Return a parameterized function of a gaussian shape (see README for equation).\n * @param {number} x - x value to calculate.\n * @returns {number} - the y value of gaussian with the current parameters.\n */\n fct(x) {\n return Gaussian.fct(x, this.fwhm);\n }\n\n /**\n * Calculate the number of times FWHM allows to reach a specific area coverage\n * @param {number} [area=0.9999]\n * @returns {number}\n */\n getFactor(area = 0.9999) {\n return Gaussian.getFactor(area);\n }\n\n /**\n * Calculate the area of the shape.\n * @returns {number} - returns the area.\n */\n\n getArea() {\n return Gaussian.getArea(this.fwhm, { height: this.height });\n }\n\n /**\n * Compute the value of Full Width at Half Maximum (FWHM) from the width between the inflection points.\n * //https://mathworld.wolfram.com/GaussianFunction.html\n * @param {number} width - Width between the inflection points\n * @returns {number} fwhm\n */\n widthToFWHM(width) {\n //https://mathworld.wolfram.com/GaussianFunction.html\n return Gaussian.widthToFWHM(width);\n }\n\n /**\n * Compute the value of width between the inflection points from Full Width at Half Maximum (FWHM).\n * //https://mathworld.wolfram.com/GaussianFunction.html\n * @param {number} fwhm - Full Width at Half Maximum.\n * @returns {number} width\n */\n fwhmToWidth(fwhm = this.fwhm) {\n return Gaussian.fwhmToWidth(fwhm);\n }\n\n /**\n * set a new full width at half maximum\n * @param {number} fwhm - full width at half maximum\n */\n setFWHM(fwhm) {\n this.fwhm = fwhm;\n }\n\n /**\n * set a new height\n * @param {number} height - The maximal intensity of the shape.\n */\n setHeight(height) {\n this.height = height;\n }\n}\n\n/**\n * Return a parameterized function of a gaussian shape (see README for equation).\n * @param {number} x - x value to calculate.\n * @param {number} fwhm - full width half maximum\n * @returns {number} - the y value of gaussian with the current parameters.\n */\nGaussian.fct = function fct(x, fwhm = 500) {\n return Math.exp(GAUSSIAN_EXP_FACTOR * Math.pow(x / fwhm, 2));\n};\n\n/**\n * Compute the value of Full Width at Half Maximum (FWHM) from the width between the inflection points.\n * //https://mathworld.wolfram.com/GaussianFunction.html\n * @param {number} width - Width between the inflection points\n * @returns {number} fwhm\n */\nGaussian.widthToFWHM = function widthToFWHM(width) {\n return width * ROOT_2LN2;\n};\n\n/**\n * Compute the value of width between the inflection points from Full Width at Half Maximum (FWHM).\n * //https://mathworld.wolfram.com/GaussianFunction.html\n * @param {number} fwhm - Full Width at Half Maximum.\n * @returns {number} width\n */\nGaussian.fwhmToWidth = function fwhmToWidth(fwhm) {\n return fwhm / ROOT_2LN2;\n};\n\n/**\n * Calculate the area of a specific shape.\n * @param {number} fwhm - Full width at half maximum.\n * @param {object} [options = {}] - options.\n * @param {number} [options.height = 1] - Maximum y value of the shape.\n * @returns {number} - returns the area of the specific shape and parameters.\n */\n\nGaussian.getArea = function getArea(fwhm, options = {}) {\n let { height = 1 } = options;\n return (height * ROOT_PI_OVER_LN2 * fwhm) / 2;\n};\n\n/**\n * Calculate the number of times FWHM allows to reach a specific area coverage.\n * @param {number} [area=0.9999]\n * @returns {number}\n */\nGaussian.getFactor = function getFactor(area = 0.9999) {\n return Math.sqrt(2) * erfinv(area);\n};\n","// https://en.wikipedia.org/wiki/Error_function#Inverse_functions\n// This code yields to a good approximation\n\n// If needed a better implementation using polynomial can be found on https://en.wikipedia.org/wiki/Error_function#Inverse_functions\n\nexport default function erfinv(x) {\n let a = 0.147;\n if (x === 0) return 0;\n let ln1MinusXSqrd = Math.log(1 - x * x);\n let lnEtcBy2Plus2 = ln1MinusXSqrd / 2 + 2 / (Math.PI * a);\n let firstSqrt = Math.sqrt(lnEtcBy2Plus2 ** 2 - ln1MinusXSqrd / a);\n let secondSqrt = Math.sqrt(firstSqrt - lnEtcBy2Plus2);\n return secondSqrt * (x > 0 ? 1 : -1);\n}\n","import { ROOT_THREE } from '../util/constants';\n\nexport class Lorentzian {\n /**\n * @param {object} [options = {}]\n * @param {number} [options.height=x] Define the height of the peak, by default area=1 (normalized)\n * @param {number} [options.fwhm = 500] - Full Width at Half Maximum in the number of points in FWHM.\n * @param {number} [options.sd] - Standard deviation, if it's defined options.fwhm will be ignored and the value will be computed sd * Math.sqrt(8 * Math.LN2);\n */\n constructor(options = {}) {\n this.fwhm = options.fwhm === undefined ? 500 : options.fwhm;\n this.height =\n options.height === undefined ? 2 / Math.PI / this.fwhm : options.height;\n }\n /**\n * Calculate a lorentzian shape\n * @param {object} [options = {}]\n * @param {number} [options.factor = Math.tan(Math.PI * (0.9999 - 0.5))] - Number of time to take fwhm to calculate length. Default covers 99.99 % of area.\n * @param {number} [options.length = fwhm * factor + 1] - total number of points to calculate\n * @return {Float64Array} y values\n */\n getData(options = {}) {\n let { length, factor = this.getFactor() } = options;\n\n if (!length) {\n length = Math.min(Math.ceil(this.fwhm * factor), Math.pow(2, 25) - 1);\n if (length % 2 === 0) length++;\n }\n\n const center = (length - 1) / 2;\n const data = new Float64Array(length);\n for (let i = 0; i <= center; i++) {\n data[i] = this.fct(i - center) * this.height;\n data[length - 1 - i] = data[i];\n }\n return data;\n }\n\n /**\n * Return a parameterized function of a lorentzian shape (see README for equation).\n * @param {number} x - x value to calculate.\n * @returns {number} - the y value of lorentzian with the current parameters.\n */\n fct(x) {\n return Lorentzian.fct(x, this.fwhm);\n }\n\n /**\n * Calculate the number of times FWHM allows to reach a specific area coverage\n * @param {number} [area=0.9999]\n * @returns {number}\n */\n getFactor(area = 0.9999) {\n return Lorentzian.getFactor(area);\n }\n\n /**\n * Calculate the area of the shape.\n * @returns {number} - returns the area.\n */\n\n getArea() {\n return Lorentzian.getArea(this.fwhm, { height: this.height });\n }\n\n /**\n * Compute the value of width between the inflection points of a specific shape from Full Width at Half Maximum (FWHM).\n * //https://mathworld.wolfram.com/LorentzianFunction.html\n * @param {number} [fwhm] - Full Width at Half Maximum.\n * @returns {number} width between the inflection points\n */\n fwhmToWidth(fwhm = this.fwhm) {\n return Lorentzian.fwhmToWidth(fwhm);\n }\n\n /**\n * Compute the value of Full Width at Half Maximum (FWHM) of a specific shape from the width between the inflection points.\n * //https://mathworld.wolfram.com/LorentzianFunction.html\n * @param {number} [width] Width between the inflection points\n * @returns {number} fwhm\n */\n widthToFWHM(width) {\n return Lorentzian.widthToFWHM(width);\n }\n /**\n * set a new full width at half maximum\n * @param {number} fwhm - full width at half maximum\n */\n setFWHM(fwhm) {\n this.fwhm = fwhm;\n }\n\n /**\n * set a new height\n * @param {number} height - The maximal intensity of the shape.\n */\n setHeight(height) {\n this.height = height;\n }\n}\n\n/**\n * Return a parameterized function of a gaussian shape (see README for equation).\n * @param {number} x - x value to calculate.\n * @param {number} fwhm - full width half maximum\n * @returns {number} - the y value of gaussian with the current parameters.\n */\nLorentzian.fct = function fct(x, fwhm) {\n const squareFWHM = fwhm * fwhm;\n return squareFWHM / (4 * Math.pow(x, 2) + squareFWHM);\n};\n\n/**\n * Compute the value of width between the inflection points of a specific shape from Full Width at Half Maximum (FWHM).\n * //https://mathworld.wolfram.com/LorentzianFunction.html\n * @param {number} [fwhm] - Full Width at Half Maximum.\n * @returns {number} width between the inflection points\n */\nLorentzian.fwhmToWidth = function fwhmToWidth(fwhm) {\n return fwhm / ROOT_THREE;\n};\n\n/**\n * Compute the value of Full Width at Half Maximum (FWHM) of a specific shape from the width between the inflection points.\n * //https://mathworld.wolfram.com/LorentzianFunction.html\n * @param {number} [width] Width between the inflection points\n * @returns {number} fwhm\n */\nLorentzian.widthToFWHM = function widthToFWHM(width) {\n return width * ROOT_THREE;\n};\n\n/**\n * Calculate the area of a specific shape.\n * @param {number} fwhm - Full width at half maximum.\n * @param {*} [options = {}] - options.\n * @param {number} [options.height = 1] - Maximum y value of the shape.\n * @returns {number} - returns the area of the specific shape and parameters.\n */\nLorentzian.getArea = function getArea(fwhm, options = {}) {\n let { height = 1 } = options;\n\n return (height * Math.PI * fwhm) / 2;\n};\n\n/**\n * Calculate the number of times FWHM allows to reach a specific area coverage\n * @param {number} [area=0.9999]\n * @returns {number}\n */\nLorentzian.getFactor = function getFactor(area = 0.9999) {\n return 2 * Math.tan(Math.PI * (area - 0.5));\n};\n","import {\n GAUSSIAN_EXP_FACTOR,\n ROOT_2LN2_MINUS_ONE,\n ROOT_PI_OVER_LN2,\n} from '../util/constants';\n\nimport { Gaussian } from './Gaussian';\nimport { Lorentzian } from './Lorentzian';\n\nexport class PseudoVoigt {\n /**\n * @param {object} [options={}]\n * @param {number} [options.height=x] Define the height of the peak, by default area=1 (normalized)\n * @param {number} [options.fwhm=500] - Full Width at Half Maximum in the number of points in FWHM.\n * @param {number} [options.mu=0.5] - ratio of gaussian contribution.\n */\n\n constructor(options = {}) {\n this.mu = options.mu === undefined ? 0.5 : options.mu;\n this.fwhm = options.fwhm === undefined ? 500 : options.fwhm;\n this.height =\n options.height === undefined\n ? 1 /\n ((this.mu / Math.sqrt(-GAUSSIAN_EXP_FACTOR / Math.PI)) * this.fwhm +\n ((1 - this.mu) * this.fwhm * Math.PI) / 2)\n : options.height;\n }\n\n /**\n * Calculate a linear combination of gaussian and lorentzian function width an same full width at half maximum\n * @param { object } [options = {}]\n * @param { number } [options.factor = 2 * Math.tan(Math.PI * (0.9999 - 0.5))] - Number of time to take fwhm in the calculation of the length.Default covers 99.99 % of area.\n * @param { number } [options.length = fwhm * factor + 1] - total number of points to calculate\n * @return { object } - { fwhm, data} - An with the number of points at half maximum and the array of y values covering the 99.99 % of the area.\n */\n\n getData(options = {}) {\n let { length, factor = this.getFactor() } = options;\n if (!length) {\n length = Math.ceil(this.fwhm * factor);\n if (length % 2 === 0) length++;\n }\n\n const center = (length - 1) / 2;\n\n let data = new Float64Array(length);\n for (let i = 0; i <= center; i++) {\n data[i] = this.fct(i - center) * this.height;\n data[length - 1 - i] = data[i];\n }\n\n return data;\n }\n\n /**\n * Return a parameterized function of a linear combination of Gaussian and Lorentzian shapes where the full width at half maximum are the same for both kind of shapes (see README for equation).\n * @param {number} [x] x value to calculate.\n * @returns {number} - the y value of a pseudo voigt with the current parameters.\n */\n\n fct(x) {\n return PseudoVoigt.fct(x, this.fwhm, this.mu);\n }\n\n /**\n * Calculate the number of times FWHM allows to reach a specific area coverage\n * @param {number} [area=0.9999] - required area to be coverage\n * @param {number} [mu=this.mu] - ratio of gaussian contribution.\n * @returns {number}\n */\n getFactor(area = 0.9999, mu = this.mu) {\n return PseudoVoigt.getFactor(area, mu);\n }\n\n /**\n * Calculate the area of the shape.\n * @returns {number} - returns the area.\n */\n getArea() {\n return PseudoVoigt.getArea(this.fwhm, { height: this.height, mu: this.mu });\n }\n\n /**\n * Compute the value of Full Width at Half Maximum (FMHM) from width between the inflection points.\n * @param {number} width - width between the inflection points\n * @param {number} [mu = 0.5] - ratio of gaussian contribution.\n * @returns {number} Full Width at Half Maximum (FMHM).\n */\n widthToFWHM(width, mu) {\n return PseudoVoigt.widthToFWHM(width, mu);\n }\n /**\n * Compute the value of width between the inflection points from Full Width at Half Maximum (FWHM).\n * @param {number} fwhm - Full Width at Half Maximum.\n * @param {number} [mu] - ratio of gaussian contribution.\n * @returns {number} width between the inflection points.\n */\n fwhmToWidth(fwhm = this.fwhm, mu = this.mu) {\n return PseudoVoigt.fwhmToWidth(fwhm, mu);\n }\n\n /**\n * set a new full width at half maximum\n * @param {number} fwhm - full width at half maximum\n */\n setFWHM(fwhm) {\n this.fwhm = fwhm;\n }\n\n /**\n * set a new height\n * @param {number} height - The maximal intensity of the shape.\n */\n setHeight(height) {\n this.height = height;\n }\n\n /**\n * set a new mu\n * @param {number} mu - ratio of gaussian contribution.\n */\n setMu(mu) {\n this.mu = mu;\n }\n}\n\n/**\n * Return a parameterized function of a gaussian shape (see README for equation).\n * @param {number} x - x value to calculate.\n * @param {number} fwhm - full width half maximum\n * @param {number} [mu=0.5] - ratio of gaussian contribution.\n * @returns {number} - the y value of gaussian with the current parameters.\n */\nPseudoVoigt.fct = function fct(x, fwhm, mu = 0.5) {\n return (1 - mu) * Lorentzian.fct(x, fwhm) + mu * Gaussian.fct(x, fwhm);\n};\n\n/**\n * Compute the value of Full Width at Half Maximum (FMHM) from width between the inflection points.\n * @param {number} width - width between the inflection points\n * @param {number} [mu = 0.5] - ratio of gaussian contribution.\n * @returns {number} Full Width at Half Maximum (FMHM).\n */\nPseudoVoigt.widthToFWHM = function widthToFWHM(width, mu = 0.5) {\n return width * (mu * ROOT_2LN2_MINUS_ONE + 1);\n};\n/**\n * Compute the value of width between the inflection points from Full Width at Half Maximum (FWHM).\n * @param {number} fwhm - Full Width at Half Maximum.\n * @param {number} [mu = 0.5] - ratio of gaussian contribution.\n * @returns {number} width between the inflection points.\n */\nPseudoVoigt.fwhmToWidth = function fwhmToWidth(fwhm, mu = 0.5) {\n return fwhm / (mu * ROOT_2LN2_MINUS_ONE + 1);\n};\n\n/**\n * Calculate the area of a specific shape.\n * @param {number} fwhm - Full width at half maximum.\n * @param {*} [options = {}] - options.\n * @param {number} [options.height = 1] - Maximum y value of the shape.\n * @param {number} [options.mu = 0.5] - ratio of gaussian contribution.\n * @returns {number} - returns the area of the specific shape and parameters.\n */\nPseudoVoigt.getArea = function getArea(fwhm, options = {}) {\n let { height = 1, mu = 0.5 } = options;\n return (fwhm * height * (mu * ROOT_PI_OVER_LN2 + (1 - mu) * Math.PI)) / 2;\n};\n\n/**\n * Calculate the number of times FWHM allows to reach a specific area coverage\n * @param {number} [area=0.9999] - required area to be coverage\n * @param {number} [mu=this.mu] - ratio of gaussian contribution.\n * @returns {number}\n */\nPseudoVoigt.getFactor = function getFactor(area = 0.9999, mu = 0.5) {\n return mu < 1 ? Lorentzian.getFactor(area) : Gaussian.getFactor(area);\n};\n","import { PseudoVoigt } from 'ml-peak-shape-generator';\n\n/**\n * This function calculates the spectrum as a sum of linear combination of gaussian and lorentzian functions. The pseudo voigt\n * parameters are divided in 4 batches. 1st: centers; 2nd: heights; 3th: widths; 4th: mu's ;\n * @param t Ordinate value\n * @param p Lorentzian parameters\n * @returns {*}\n */\n\nexport function sumOfGaussianLorentzians(p) {\n return function (t) {\n let nL = p.length / 4;\n let result = 0;\n for (let i = 0; i < nL; i++) {\n result +=\n p[i + nL] * PseudoVoigt.fct(t - p[i], p[i + nL * 2], p[i + nL * 3]);\n }\n return result;\n };\n}\n","import { Gaussian } from 'ml-peak-shape-generator';\n/**\n * This function calculates the spectrum as a sum of gaussian functions. The Gaussian\n * parameters are divided in 3 batches. 1st: centers; 2nd: height; 3th: widths;\n * @param t Ordinate values\n * @param p Gaussian parameters\n * @returns {*}\n */\n\nexport function sumOfGaussians(p) {\n return function (t) {\n let nL = p.length / 3;\n let result = 0;\n for (let i = 0; i < nL; i++) {\n result += p[i + nL] * Gaussian.fct(t - p[i], p[i + nL * 2]);\n }\n return result;\n };\n}\n","import { Lorentzian } from 'ml-peak-shape-generator';\n\n/**\n * This function calculates the spectrum as a sum of lorentzian functions. The Lorentzian\n * parameters are divided in 3 batches. 1st: centers; 2nd: heights; 3th: widths;\n * @param t Ordinate values\n * @param p Lorentzian parameters\n * @returns {*}\n */\n\nexport function sumOfLorentzians(p) {\n return function (t) {\n let nL = p.length / 3;\n let result = 0;\n for (let i = 0; i < nL; i++) {\n result += p[i + nL] * Lorentzian.fct(t - p[i], p[i + nL * 2]);\n }\n return result;\n };\n}\n","import getMaxValue from 'ml-array-max';\n\nimport { selectMethod } from './selectMethod';\nimport { sumOfGaussianLorentzians } from './shapes/sumOfGaussianLorentzians';\nimport { sumOfGaussians } from './shapes/sumOfGaussians';\nimport { sumOfLorentzians } from './shapes/sumOfLorentzians';\n\nconst STATE_INIT = 0;\nconst STATE_MIN = 1;\nconst STATE_MAX = 2;\nconst STATE_GRADIENT_DIFFERENCE = 3;\n\nconst X = 0;\nconst Y = 1;\nconst WIDTH = 2;\nconst MU = 3;\n\nconst keys = ['x', 'y', 'width', 'mu'];\n/**\n * Fits a set of points to the sum of a set of bell functions.\n * @param {object} data - An object containing the x and y data to be fitted.\n * @param {array} peaks - A list of initial parameters to be optimized. e.g. coming from a peak picking [{x, y, width}].\n * @param {object} [options = {}]\n * @param {object} [options.shape={}] - it's specify the kind of shape used to fitting.\n * @param {string} [options.shape.kind = 'gaussian'] - kind of shape; lorentzian, gaussian and pseudovoigt are supported.\n * @param {object} [options.optimization = {}] - it's specify the kind and options of the algorithm use to optimize parameters.\n * @param {object} [options.optimization.kind = 'lm'] - kind of algorithm. By default it's levenberg-marquardt.\n * @param {object} [options.optimization.options = {}] - options for the specific kind of algorithm.\n * @param {number} [options.optimization.options.timeout] - maximum time running before break in seconds.\n * @param {number} [options.optimization.options.damping=1.5]\n * @param {number} [options.optimization.options.maxIterations=100]\n * @param {number} [options.optimization.options.errorTolerance=1e-8]\n * @returns {object} - A object with fitting error and the list of optimized parameters { parameters: [ {x, y, width} ], error } if the kind of shape is pseudoVoigt mu parameter is optimized.\n */\nexport function optimize(data, peaks, options = {}) {\n let {\n shape = { kind: 'gaussian' },\n optimization = {\n kind: 'lm',\n },\n } = options;\n\n let {\n minFactorWidth = 0.25,\n maxFactorWidth = 4,\n minFactorX = 2,\n maxFactorX = 2,\n minFactorY = 0,\n maxFactorY = 1.5,\n minMuValue = 0,\n maxMuValue = 1,\n xGradientDifference,\n yGradientDifference = 1e-3,\n widthGradientDifference,\n muGradientDifference = 0.01,\n } = optimization;\n\n peaks = JSON.parse(JSON.stringify(peaks));\n\n if (typeof shape.kind !== 'string') {\n throw new Error('kind should be a string');\n }\n\n let kind = shape.kind.toLowerCase().replace(/[^a-z]/g, '');\n\n let x = data.x;\n let maxY = getMaxValue(data.y);\n let y = new Array(x.length);\n for (let i = 0; i < x.length; i++) {\n y[i] = data.y[i] / maxY;\n }\n\n let nbParams;\n let paramsFunc;\n switch (kind) {\n case 'gaussian':\n nbParams = 3;\n paramsFunc = sumOfGaussians;\n break;\n case 'lorentzian':\n nbParams = 3;\n paramsFunc = sumOfLorentzians;\n break;\n case 'pseudovoigt':\n nbParams = 4;\n paramsFunc = sumOfGaussianLorentzians;\n break;\n default:\n throw new Error('kind of shape is not supported');\n }\n\n const getValueOptions = {\n maxY,\n minFactorX,\n maxFactorX,\n minFactorY,\n maxFactorY,\n minMuValue,\n maxMuValue,\n minFactorWidth,\n maxFactorWidth,\n xGradientDifference,\n yGradientDifference,\n widthGradientDifference,\n muGradientDifference,\n };\n let nbShapes = peaks.length;\n let pMin = new Float64Array(nbShapes * nbParams);\n let pMax = new Float64Array(nbShapes * nbParams);\n let pInit = new Float64Array(nbShapes * nbParams);\n let gradientDifference = new Float64Array(nbShapes * nbParams);\n for (let i = 0; i < nbShapes; i++) {\n let peak = peaks[i];\n for (let s = 0; s < nbParams; s++) {\n pInit[i + s * nbShapes] = getValue(s, peak, STATE_INIT, getValueOptions);\n pMin[i + s * nbShapes] = getValue(s, peak, STATE_MIN, getValueOptions);\n pMax[i + s * nbShapes] = getValue(s, peak, STATE_MAX, getValueOptions);\n gradientDifference[i + s * nbShapes] = getValue(\n s,\n peak,\n STATE_GRADIENT_DIFFERENCE,\n getValueOptions,\n );\n }\n }\n\n let { algorithm, optimizationOptions } = selectMethod(optimization);\n\n optimizationOptions.minValues = pMin;\n optimizationOptions.maxValues = pMax;\n optimizationOptions.initialValues = pInit;\n optimizationOptions.gradientDifference = gradientDifference;\n\n let pFit = algorithm({ x, y }, paramsFunc, optimizationOptions);\n\n let { parameterError: error, iterations } = pFit;\n let result = { error, iterations, peaks };\n for (let i = 0; i < peaks.length; i++) {\n pFit.parameterValues[i + peaks.length] *= maxY;\n for (let s = 0; s < nbParams; s++) {\n // we modify the optimized parameters\n peaks[i][keys[s]] = pFit.parameterValues[i + s * peaks.length];\n }\n }\n\n return result;\n}\n\nfunction getValue(parameterIndex, peak, state, options) {\n let maxY = options.maxY;\n switch (state) {\n case STATE_INIT:\n switch (parameterIndex) {\n case X:\n return peak.x;\n case Y:\n return peak.y / maxY;\n case WIDTH:\n return peak.width;\n case MU:\n return peak.mu || 0.5;\n default:\n throw new Error('The parameter is not supported');\n }\n case STATE_GRADIENT_DIFFERENCE:\n switch (parameterIndex) {\n case X:\n return peak.xGradientDifference !== undefined\n ? peak.xGradientDifference\n : options.xGradientDifference !== undefined\n ? options.xGradientDifference\n : peak.width / 2e3;\n case Y:\n return peak.yGradientDifference !== undefined\n ? peak.yGradientDifference\n : options.yGradientDifference;\n case WIDTH:\n return peak.widthGradientDifference !== undefined\n ? peak.widthGradientDifference\n : options.widthGradientDifference !== undefined\n ? options.widthGradientDifference\n : peak.width / 2e3;\n case MU:\n return peak.muGradientDifference !== undefined\n ? peak.muGradientDifference\n : options.muGradientDifference;\n default:\n throw new Error('The parameter is not supported');\n }\n case STATE_MIN:\n switch (parameterIndex) {\n case X:\n return peak.x - peak.width * options.minFactorX;\n case Y:\n return (peak.y / maxY) * options.minFactorY;\n case WIDTH:\n return peak.width * options.minFactorWidth;\n case MU:\n return options.minMuValue;\n default:\n throw new Error('The parameter is not supported');\n }\n case STATE_MAX:\n 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