ml-matrix/src/matrix.js

Matrix manipulation and computation library

import { isAnyArray } from 'is-any-array';
import rescale from 'ml-array-rescale';

import { inspectMatrix, inspectMatrixWithOptions } from './inspect';
import { installMathOperations } from './mathOperations';
import {
  sumByRow,
  sumByColumn,
  sumAll,
  productByRow,
  productByColumn,
  productAll,
  varianceByRow,
  varianceByColumn,
  varianceAll,
  centerByRow,
  centerByColumn,
  centerAll,
  scaleByRow,
  scaleByColumn,
  scaleAll,
  getScaleByRow,
  getScaleByColumn,
  getScaleAll,
} from './stat';
import {
  checkRowVector,
  checkRowIndex,
  checkColumnIndex,
  checkColumnVector,
  checkRange,
  checkNonEmpty,
  checkRowIndices,
  checkColumnIndices,
} from './util';

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    return true;
  }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  maxRow(row) {
    checkRowIndex(this, row);
    if (this.isEmpty()) {
      return NaN;
    }
    let v = this.get(row, 0);
    for (let i = 1; i < this.columns; i++) {
      if (this.get(row, i) > v) {
        v = this.get(row, i);
      }
    }
    return v;
  }

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

  minRow(row) {
    checkRowIndex(this, row);
    if (this.isEmpty()) {
      return NaN;
    }
    let v = this.get(row, 0);
    for (let i = 1; i < this.columns; i++) {
      if (this.get(row, i) < v) {
        v = this.get(row, i);
      }
    }
    return v;
  }

  minRowIndex(row) {
    checkRowIndex(this, row);
    checkNonEmpty(this);
    let v = this.get(row, 0);
    let idx = [row, 0];
    for (let i = 1; i < this.columns; i++) {
      if (this.get(row, i) < v) {
        v = this.get(row, i);
        idx[1] = i;
      }
    }
    return idx;
  }

  maxColumn(column) {
    checkColumnIndex(this, column);
    if (this.isEmpty()) {
      return NaN;
    }
    let v = this.get(0, column);
    for (let i = 1; i < this.rows; i++) {
      if (this.get(i, column) > v) {
        v = this.get(i, column);
      }
    }
    return v;
  }

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

  minColumn(column) {
    checkColumnIndex(this, column);
    if (this.isEmpty()) {
      return NaN;
    }
    let v = this.get(0, column);
    for (let i = 1; i < this.rows; i++) {
      if (this.get(i, column) < v) {
        v = this.get(i, column);
      }
    }
    return v;
  }

  minColumnIndex(column) {
    checkColumnIndex(this, column);
    checkNonEmpty(this);
    let v = this.get(0, column);
    let idx = [0, column];
    for (let i = 1; i < this.rows; i++) {
      if (this.get(i, column) < v) {
        v = this.get(i, column);
        idx[0] = i;
      }
    }
    return idx;
  }

  diag() {
    let min = Math.min(this.rows, this.columns);
    let diag = [];
    for (let i = 0; i < min; i++) {
      diag.push(this.get(i, i));
    }
    return diag;
  }

  norm(type = 'frobenius') {
    switch (type) {
      case 'max':
        return this.max();
      case 'frobenius':
        return Math.sqrt(this.dot(this));
      default:
        throw new RangeError(`unknown norm type: ${type}`);
    }
  }

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

  dot(vector2) {
    if (AbstractMatrix.isMatrix(vector2)) vector2 = vector2.to1DArray();
    let vector1 = this.to1DArray();
    if (vector1.length !== vector2.length) {
      throw new RangeError('vectors do not have the same size');
    }
    let dot = 0;
    for (let i = 0; i < vector1.length; i++) {
      dot += vector1[i] * vector2[i];
    }
    return dot;
  }

  mmul(other) {
    other = Matrix.checkMatrix(other);

    let m = this.rows;
    let n = this.columns;
    let p = other.columns;

    let result = new Matrix(m, p);

    let Bcolj = new Float64Array(n);
    for (let j = 0; j < p; j++) {
      for (let k = 0; k < n; k++) {
        Bcolj[k] = other.get(k, j);
      }

      for (let i = 0; i < m; i++) {
        let s = 0;
        for (let k = 0; k < n; k++) {
          s += this.get(i, k) * Bcolj[k];
        }

        result.set(i, j, s);
      }
    }
    return result;
  }

  mpow(scalar) {
    if (!this.isSquare()) {
      throw new RangeError('Matrix must be square');
    }
    if (!Number.isInteger(scalar) || scalar < 0) {
      throw new RangeError('Exponent must be a non-negative integer');
    }
    // Russian Peasant exponentiation, i.e. exponentiation by squaring
    let result = Matrix.eye(this.rows);
    let bb = this;
    // Note: Don't bit shift. In JS, that would truncate at 32 bits
    for (let e = scalar; e > 1; e /= 2) {
      if ((e & 1) !== 0) {
        result = result.mmul(bb);
      }
      bb = bb.mmul(bb);
    }
    return result;
  }

  strassen2x2(other) {
    other = Matrix.checkMatrix(other);
    let result = new Matrix(2, 2);
    const a11 = this.get(0, 0);
    const b11 = other.get(0, 0);
    const a12 = this.get(0, 1);
    const b12 = other.get(0, 1);
    const a21 = this.get(1, 0);
    const b21 = other.get(1, 0);
    const a22 = this.get(1, 1);
    const b22 = other.get(1, 1);

    // Compute intermediate values.
    const m1 = (a11 + a22) * (b11 + b22);
    const m2 = (a21 + a22) * b11;
    const m3 = a11 * (b12 - b22);
    const m4 = a22 * (b21 - b11);
    const m5 = (a11 + a12) * b22;
    const m6 = (a21 - a11) * (b11 + b12);
    const m7 = (a12 - a22) * (b21 + b22);

    // Combine intermediate values into the output.
    const c00 = m1 + m4 - m5 + m7;
    const c01 = m3 + m5;
    const c10 = m2 + m4;
    const c11 = m1 - m2 + m3 + m6;

    result.set(0, 0, c00);
    result.set(0, 1, c01);
    result.set(1, 0, c10);
    result.set(1, 1, c11);
    return result;
  }

  strassen3x3(other) {
    other = Matrix.checkMatrix(other);
    let result = new Matrix(3, 3);

    const a00 = this.get(0, 0);
    const a01 = this.get(0, 1);
    const a02 = this.get(0, 2);
    const a10 = this.get(1, 0);
    const a11 = this.get(1, 1);
    const a12 = this.get(1, 2);
    const a20 = this.get(2, 0);
    const a21 = this.get(2, 1);
    const a22 = this.get(2, 2);

    const b00 = other.get(0, 0);
    const b01 = other.get(0, 1);
    const b02 = other.get(0, 2);
    const b10 = other.get(1, 0);
    const b11 = other.get(1, 1);
    const b12 = other.get(1, 2);
    const b20 = other.get(2, 0);
    const b21 = other.get(2, 1);
    const b22 = other.get(2, 2);

    const m1 = (a00 + a01 + a02 - a10 - a11 - a21 - a22) * b11;
    const m2 = (a00 - a10) * (-b01 + b11);
    const m3 = a11 * (-b00 + b01 + b10 - b11 - b12 - b20 + b22);
    const m4 = (-a00 + a10 + a11) * (b00 - b01 + b11);
    const m5 = (a10 + a11) * (-b00 + b01);
    const m6 = a00 * b00;
    const m7 = (-a00 + a20 + a21) * (b00 - b02 + b12);
    const m8 = (-a00 + a20) * (b02 - b12);
    const m9 = (a20 + a21) * (-b00 + b02);
    const m10 = (a00 + a01 + a02 - a11 - a12 - a20 - a21) * b12;
    const m11 = a21 * (-b00 + b02 + b10 - b11 - b12 - b20 + b21);
    const m12 = (-a02 + a21 + a22) * (b11 + b20 - b21);
    const m13 = (a02 - a22) * (b11 - b21);
    const m14 = a02 * b20;
    const m15 = (a21 + a22) * (-b20 + b21);
    const m16 = (-a02 + a11 + a12) * (b12 + b20 - b22);
    const m17 = (a02 - a12) * (b12 - b22);
    const m18 = (a11 + a12) * (-b20 + b22);
    const m19 = a01 * b10;
    const m20 = a12 * b21;
    const m21 = a10 * b02;
    const m22 = a20 * b01;
    const m23 = a22 * b22;

    const c00 = m6 + m14 + m19;
    const c01 = m1 + m4 + m5 + m6 + m12 + m14 + m15;
    const c02 = m6 + m7 + m9 + m10 + m14 + m16 + m18;
    const c10 = m2 + m3 + m4 + m6 + m14 + m16 + m17;
    const c11 = m2 + m4 + m5 + m6 + m20;
    const c12 = m14 + m16 + m17 + m18 + m21;
    const c20 = m6 + m7 + m8 + m11 + m12 + m13 + m14;
    const c21 = m12 + m13 + m14 + m15 + m22;
    const c22 = m6 + m7 + m8 + m9 + m23;

    result.set(0, 0, c00);
    result.set(0, 1, c01);
    result.set(0, 2, c02);
    result.set(1, 0, c10);
    result.set(1, 1, c11);
    result.set(1, 2, c12);
    result.set(2, 0, c20);
    result.set(2, 1, c21);
    result.set(2, 2, c22);
    return result;
  }

  mmulStrassen(y) {
    y = Matrix.checkMatrix(y);
    let x = this.clone();
    let r1 = x.rows;
    let c1 = x.columns;
    let r2 = y.rows;
    let c2 = y.columns;
    if (c1 !== r2) {
      // eslint-disable-next-line no-console
      console.warn(
        `Multiplying ${r1} x ${c1} and ${r2} x ${c2} matrix: dimensions do not match.`,
      );
    }

    // Put a matrix into the top left of a matrix of zeros.
    // `rows` and `cols` are the dimensions of the output matrix.
    function embed(mat, rows, cols) {
      let r = mat.rows;
      let c = mat.columns;
      if (r === rows && c === cols) {
        return mat;
      } else {
        let resultat = AbstractMatrix.zeros(rows, cols);
        resultat = resultat.setSubMatrix(mat, 0, 0);
        return resultat;
      }
    }

    // Make sure both matrices are the same size.
    // This is exclusively for simplicity:
    // this algorithm can be implemented with matrices of different sizes.

    let r = Math.max(r1, r2);
    let c = Math.max(c1, c2);
    x = embed(x, r, c);
    y = embed(y, r, c);

    // Our recursive multiplication function.
    function blockMult(a, b, rows, cols) {
      // For small matrices, resort to naive multiplication.
      if (rows <= 512 || cols <= 512) {
        return a.mmul(b); // a is equivalent to this
      }

      // Apply dynamic padding.
      if (rows % 2 === 1 && cols % 2 === 1) {
        a = embed(a, rows + 1, cols + 1);
        b = embed(b, rows + 1, cols + 1);
      } else if (rows % 2 === 1) {
        a = embed(a, rows + 1, cols);
        b = embed(b, rows + 1, cols);
      } else if (cols % 2 === 1) {
        a = embed(a, rows, cols + 1);
        b = embed(b, rows, cols + 1);
      }

      let halfRows = parseInt(a.rows / 2, 10);
      let halfCols = parseInt(a.columns / 2, 10);
      // Subdivide input matrices.
      let a11 = a.subMatrix(0, halfRows - 1, 0, halfCols - 1);
      let b11 = b.subMatrix(0, halfRows - 1, 0, halfCols - 1);

      let a12 = a.subMatrix(0, halfRows - 1, halfCols, a.columns - 1);
      let b12 = b.subMatrix(0, halfRows - 1, halfCols, b.columns - 1);

      let a21 = a.subMatrix(halfRows, a.rows - 1, 0, halfCols - 1);
      let b21 = b.subMatrix(halfRows, b.rows - 1, 0, halfCols - 1);

      let a22 = a.subMatrix(halfRows, a.rows - 1, halfCols, a.columns - 1);
      let b22 = b.subMatrix(halfRows, b.rows - 1, halfCols, b.columns - 1);

      // Compute intermediate values.
      let m1 = blockMult(
        AbstractMatrix.add(a11, a22),
        AbstractMatrix.add(b11, b22),
        halfRows,
        halfCols,
      );
      let m2 = blockMult(AbstractMatrix.add(a21, a22), b11, halfRows, halfCols);
      let m3 = blockMult(a11, AbstractMatrix.sub(b12, b22), halfRows, halfCols);
      let m4 = blockMult(a22, AbstractMatrix.sub(b21, b11), halfRows, halfCols);
      let m5 = blockMult(AbstractMatrix.add(a11, a12), b22, halfRows, halfCols);
      let m6 = blockMult(
        AbstractMatrix.sub(a21, a11),
        AbstractMatrix.add(b11, b12),
        halfRows,
        halfCols,
      );
      let m7 = blockMult(
        AbstractMatrix.sub(a12, a22),
        AbstractMatrix.add(b21, b22),
        halfRows,
        halfCols,
      );

      // Combine intermediate values into the output.
      let c11 = AbstractMatrix.add(m1, m4);
      c11.sub(m5);
      c11.add(m7);
      let c12 = AbstractMatrix.add(m3, m5);
      let c21 = AbstractMatrix.add(m2, m4);
      let c22 = AbstractMatrix.sub(m1, m2);
      c22.add(m3);
      c22.add(m6);

      // Crop output to the desired size (undo dynamic padding).
      let result = AbstractMatrix.zeros(2 * c11.rows, 2 * c11.columns);
      result = result.setSubMatrix(c11, 0, 0);
      result = result.setSubMatrix(c12, c11.rows, 0);
      result = result.setSubMatrix(c21, 0, c11.columns);
      result = result.setSubMatrix(c22, c11.rows, c11.columns);
      return result.subMatrix(0, rows - 1, 0, cols - 1);
    }

    return blockMult(x, y, r, c);
  }

  scaleRows(options = {}) {
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { min = 0, max = 1 } = options;
    if (!Number.isFinite(min)) throw new TypeError('min must be a number');
    if (!Number.isFinite(max)) throw new TypeError('max must be a number');
    if (min >= max) throw new RangeError('min must be smaller than max');
    let newMatrix = new Matrix(this.rows, this.columns);
    for (let i = 0; i < this.rows; i++) {
      const row = this.getRow(i);
      if (row.length > 0) {
        rescale(row, { min, max, output: row });
      }
      newMatrix.setRow(i, row);
    }
    return newMatrix;
  }

  scaleColumns(options = {}) {
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { min = 0, max = 1 } = options;
    if (!Number.isFinite(min)) throw new TypeError('min must be a number');
    if (!Number.isFinite(max)) throw new TypeError('max must be a number');
    if (min >= max) throw new RangeError('min must be smaller than max');
    let newMatrix = new Matrix(this.rows, this.columns);
    for (let i = 0; i < this.columns; i++) {
      const column = this.getColumn(i);
      if (column.length) {
        rescale(column, {
          min,
          max,
          output: column,
        });
      }
      newMatrix.setColumn(i, column);
    }
    return newMatrix;
  }

  flipRows() {
    const middle = Math.ceil(this.columns / 2);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < middle; j++) {
        let first = this.get(i, j);
        let last = this.get(i, this.columns - 1 - j);
        this.set(i, j, last);
        this.set(i, this.columns - 1 - j, first);
      }
    }
    return this;
  }

  flipColumns() {
    const middle = Math.ceil(this.rows / 2);
    for (let j = 0; j < this.columns; j++) {
      for (let i = 0; i < middle; i++) {
        let first = this.get(i, j);
        let last = this.get(this.rows - 1 - i, j);
        this.set(i, j, last);
        this.set(this.rows - 1 - i, j, first);
      }
    }
    return this;
  }

  kroneckerProduct(other) {
    other = Matrix.checkMatrix(other);

    let m = this.rows;
    let n = this.columns;
    let p = other.rows;
    let q = other.columns;

    let result = new Matrix(m * p, n * q);
    for (let i = 0; i < m; i++) {
      for (let j = 0; j < n; j++) {
        for (let k = 0; k < p; k++) {
          for (let l = 0; l < q; l++) {
            result.set(p * i + k, q * j + l, this.get(i, j) * other.get(k, l));
          }
        }
      }
    }
    return result;
  }

  kroneckerSum(other) {
    other = Matrix.checkMatrix(other);
    if (!this.isSquare() || !other.isSquare()) {
      throw new Error('Kronecker Sum needs two Square Matrices');
    }
    let m = this.rows;
    let n = other.rows;
    let AxI = this.kroneckerProduct(Matrix.eye(n, n));
    let IxB = Matrix.eye(m, m).kroneckerProduct(other);
    return AxI.add(IxB);
  }

  transpose() {
    let result = new Matrix(this.columns, this.rows);
    for (let i = 0; i < this.rows; i++) {
      for (let j = 0; j < this.columns; j++) {
        result.set(j, i, this.get(i, j));
      }
    }
    return result;
  }

  sortRows(compareFunction = compareNumbers) {
    for (let i = 0; i < this.rows; i++) {
      this.setRow(i, this.getRow(i).sort(compareFunction));
    }
    return this;
  }

  sortColumns(compareFunction = compareNumbers) {
    for (let i = 0; i < this.columns; i++) {
      this.setColumn(i, this.getColumn(i).sort(compareFunction));
    }
    return this;
  }

  subMatrix(startRow, endRow, startColumn, endColumn) {
    checkRange(this, startRow, endRow, startColumn, endColumn);
    let newMatrix = new Matrix(
      endRow - startRow + 1,
      endColumn - startColumn + 1,
    );
    for (let i = startRow; i <= endRow; i++) {
      for (let j = startColumn; j <= endColumn; j++) {
        newMatrix.set(i - startRow, j - startColumn, this.get(i, j));
      }
    }
    return newMatrix;
  }

  subMatrixRow(indices, startColumn, endColumn) {
    if (startColumn === undefined) startColumn = 0;
    if (endColumn === undefined) endColumn = this.columns - 1;
    if (
      startColumn > endColumn ||
      startColumn < 0 ||
      startColumn >= this.columns ||
      endColumn < 0 ||
      endColumn >= this.columns
    ) {
      throw new RangeError('Argument out of range');
    }

    let newMatrix = new Matrix(indices.length, endColumn - startColumn + 1);
    for (let i = 0; i < indices.length; i++) {
      for (let j = startColumn; j <= endColumn; j++) {
        if (indices[i] < 0 || indices[i] >= this.rows) {
          throw new RangeError(`Row index out of range: ${indices[i]}`);
        }
        newMatrix.set(i, j - startColumn, this.get(indices[i], j));
      }
    }
    return newMatrix;
  }

  subMatrixColumn(indices, startRow, endRow) {
    if (startRow === undefined) startRow = 0;
    if (endRow === undefined) endRow = this.rows - 1;
    if (
      startRow > endRow ||
      startRow < 0 ||
      startRow >= this.rows ||
      endRow < 0 ||
      endRow >= this.rows
    ) {
      throw new RangeError('Argument out of range');
    }

    let newMatrix = new Matrix(endRow - startRow + 1, indices.length);
    for (let i = 0; i < indices.length; i++) {
      for (let j = startRow; j <= endRow; j++) {
        if (indices[i] < 0 || indices[i] >= this.columns) {
          throw new RangeError(`Column index out of range: ${indices[i]}`);
        }
        newMatrix.set(j - startRow, i, this.get(j, indices[i]));
      }
    }
    return newMatrix;
  }

  setSubMatrix(matrix, startRow, startColumn) {
    matrix = Matrix.checkMatrix(matrix);
    if (matrix.isEmpty()) {
      return this;
    }
    let endRow = startRow + matrix.rows - 1;
    let endColumn = startColumn + matrix.columns - 1;
    checkRange(this, startRow, endRow, startColumn, endColumn);
    for (let i = 0; i < matrix.rows; i++) {
      for (let j = 0; j < matrix.columns; j++) {
        this.set(startRow + i, startColumn + j, matrix.get(i, j));
      }
    }
    return this;
  }

  selection(rowIndices, columnIndices) {
    checkRowIndices(this, rowIndices);
    checkColumnIndices(this, columnIndices);
    let newMatrix = new Matrix(rowIndices.length, columnIndices.length);
    for (let i = 0; i < rowIndices.length; i++) {
      let rowIndex = rowIndices[i];
      for (let j = 0; j < columnIndices.length; j++) {
        let columnIndex = columnIndices[j];
        newMatrix.set(i, j, this.get(rowIndex, columnIndex));
      }
    }
    return newMatrix;
  }

  trace() {
    let min = Math.min(this.rows, this.columns);
    let trace = 0;
    for (let i = 0; i < min; i++) {
      trace += this.get(i, i);
    }
    return trace;
  }

  clone() {
    return this.constructor.copy(this, new Matrix(this.rows, this.columns));
  }

  /**
   * @template {AbstractMatrix} M
   * @param {AbstractMatrix} from
   * @param {M} to
   * @return {M}
   */
  static copy(from, to) {
    for (const [row, column, value] of from.entries()) {
      to.set(row, column, value);
    }

    return to;
  }

  sum(by) {
    switch (by) {
      case 'row':
        return sumByRow(this);
      case 'column':
        return sumByColumn(this);
      case undefined:
        return sumAll(this);
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  product(by) {
    switch (by) {
      case 'row':
        return productByRow(this);
      case 'column':
        return productByColumn(this);
      case undefined:
        return productAll(this);
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  mean(by) {
    const sum = this.sum(by);
    switch (by) {
      case 'row': {
        for (let i = 0; i < this.rows; i++) {
          sum[i] /= this.columns;
        }
        return sum;
      }
      case 'column': {
        for (let i = 0; i < this.columns; i++) {
          sum[i] /= this.rows;
        }
        return sum;
      }
      case undefined:
        return sum / this.size;
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  variance(by, options = {}) {
    if (typeof by === 'object') {
      options = by;
      by = undefined;
    }
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { unbiased = true, mean = this.mean(by) } = options;
    if (typeof unbiased !== 'boolean') {
      throw new TypeError('unbiased must be a boolean');
    }
    switch (by) {
      case 'row': {
        if (!isAnyArray(mean)) {
          throw new TypeError('mean must be an array');
        }
        return varianceByRow(this, unbiased, mean);
      }
      case 'column': {
        if (!isAnyArray(mean)) {
          throw new TypeError('mean must be an array');
        }
        return varianceByColumn(this, unbiased, mean);
      }
      case undefined: {
        if (typeof mean !== 'number') {
          throw new TypeError('mean must be a number');
        }
        return varianceAll(this, unbiased, mean);
      }
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  standardDeviation(by, options) {
    if (typeof by === 'object') {
      options = by;
      by = undefined;
    }
    const variance = this.variance(by, options);
    if (by === undefined) {
      return Math.sqrt(variance);
    } else {
      for (let i = 0; i < variance.length; i++) {
        variance[i] = Math.sqrt(variance[i]);
      }
      return variance;
    }
  }

  center(by, options = {}) {
    if (typeof by === 'object') {
      options = by;
      by = undefined;
    }
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    const { center = this.mean(by) } = options;
    switch (by) {
      case 'row': {
        if (!isAnyArray(center)) {
          throw new TypeError('center must be an array');
        }
        centerByRow(this, center);
        return this;
      }
      case 'column': {
        if (!isAnyArray(center)) {
          throw new TypeError('center must be an array');
        }
        centerByColumn(this, center);
        return this;
      }
      case undefined: {
        if (typeof center !== 'number') {
          throw new TypeError('center must be a number');
        }
        centerAll(this, center);
        return this;
      }
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  scale(by, options = {}) {
    if (typeof by === 'object') {
      options = by;
      by = undefined;
    }
    if (typeof options !== 'object') {
      throw new TypeError('options must be an object');
    }
    let scale = options.scale;
    switch (by) {
      case 'row': {
        if (scale === undefined) {
          scale = getScaleByRow(this);
        } else if (!isAnyArray(scale)) {
          throw new TypeError('scale must be an array');
        }
        scaleByRow(this, scale);
        return this;
      }
      case 'column': {
        if (scale === undefined) {
          scale = getScaleByColumn(this);
        } else if (!isAnyArray(scale)) {
          throw new TypeError('scale must be an array');
        }
        scaleByColumn(this, scale);
        return this;
      }
      case undefined: {
        if (scale === undefined) {
          scale = getScaleAll(this);
        } else if (typeof scale !== 'number') {
          throw new TypeError('scale must be a number');
        }
        scaleAll(this, scale);
        return this;
      }
      default:
        throw new Error(`invalid option: ${by}`);
    }
  }

  toString(options) {
    return inspectMatrixWithOptions(this, options);
  }

  [Symbol.iterator]() {
    return this.entries();
  }

  /**
   * iterator from left to right, from top to bottom
   * yield [row, column, value]
   * @returns {Generator<[number, number, number], void, void>}
   */
  *entries() {
    for (let row = 0; row < this.rows; row++) {
      for (let col = 0; col < this.columns; col++) {
        yield [row, col, this.get(row, col)];
      }
    }
  }

  /**
   * iterator from left to right, from top to bottom
   * yield value
   * @returns {Generator<number, void, void>}
   */
  *values() {
    for (let row = 0; row < this.rows; row++) {
      for (let col = 0; col < this.columns; col++) {
        yield this.get(row, col);
      }
    }
  }
}

AbstractMatrix.prototype.klass = 'Matrix';
if (typeof Symbol !== 'undefined') {
  AbstractMatrix.prototype[Symbol.for('nodejs.util.inspect.custom')] =
    inspectMatrix;
}

function compareNumbers(a, b) {
  return a - b;
}

function isArrayOfNumbers(array) {
  return array.every((element) => {
    return typeof element === 'number';
  });
}

// Synonyms
AbstractMatrix.random = AbstractMatrix.rand;
AbstractMatrix.randomInt = AbstractMatrix.randInt;
AbstractMatrix.diagonal = AbstractMatrix.diag;
AbstractMatrix.prototype.diagonal = AbstractMatrix.prototype.diag;
AbstractMatrix.identity = AbstractMatrix.eye;
AbstractMatrix.prototype.negate = AbstractMatrix.prototype.neg;
AbstractMatrix.prototype.tensorProduct =
  AbstractMatrix.prototype.kroneckerProduct;

export default class Matrix extends AbstractMatrix {
  /**
   * @type {Float64Array[]}
   */
  data;

  /**
   * Init an empty matrix
   * @param {number} nRows
   * @param {number} nColumns
   */
  #initData(nRows, nColumns) {
    this.data = [];

    if (Number.isInteger(nColumns) && nColumns >= 0) {
      for (let i = 0; i < nRows; i++) {
        this.data.push(new Float64Array(nColumns));
      }
    } else {
      throw new TypeError('nColumns must be a positive integer');
    }

    this.rows = nRows;
    this.columns = nColumns;
  }

  constructor(nRows, nColumns) {
    super();
    if (Matrix.isMatrix(nRows)) {
      this.#initData(nRows.rows, nRows.columns);
      Matrix.copy(nRows, this);
    } else if (Number.isInteger(nRows) && nRows >= 0) {
      this.#initData(nRows, nColumns);
    } else if (isAnyArray(nRows)) {
      // Copy the values from the 2D array
      const arrayData = nRows;
      nRows = arrayData.length;
      nColumns = nRows ? arrayData[0].length : 0;
      if (typeof nColumns !== 'number') {
        throw new TypeError(
          'Data must be a 2D array with at least one element',
        );
      }
      this.data = [];

      for (let i = 0; i < nRows; i++) {
        if (arrayData[i].length !== nColumns) {
          throw new RangeError('Inconsistent array dimensions');
        }
        if (!isArrayOfNumbers(arrayData[i])) {
          throw new TypeError('Input data contains non-numeric values');
        }
        this.data.push(Float64Array.from(arrayData[i]));
      }

      this.rows = nRows;
      this.columns = nColumns;
    } else {
      throw new TypeError(
        'First argument must be a positive number or an array',
      );
    }
  }

  set(rowIndex, columnIndex, value) {
    this.data[rowIndex][columnIndex] = value;
    return this;
  }

  get(rowIndex, columnIndex) {
    return this.data[rowIndex][columnIndex];
  }

  removeRow(index) {
    checkRowIndex(this, index);
    this.data.splice(index, 1);
    this.rows -= 1;
    return this;
  }

  addRow(index, array) {
    if (array === undefined) {
      array = index;
      index = this.rows;
    }
    checkRowIndex(this, index, true);
    array = Float64Array.from(checkRowVector(this, array));
    this.data.splice(index, 0, array);
    this.rows += 1;
    return this;
  }

  removeColumn(index) {
    checkColumnIndex(this, index);
    for (let i = 0; i < this.rows; i++) {
      const newRow = new Float64Array(this.columns - 1);
      for (let j = 0; j < index; j++) {
        newRow[j] = this.data[i][j];
      }
      for (let j = index + 1; j < this.columns; j++) {
        newRow[j - 1] = this.data[i][j];
      }
      this.data[i] = newRow;
    }
    this.columns -= 1;
    return this;
  }

  addColumn(index, array) {
    if (typeof array === 'undefined') {
      array = index;
      index = this.columns;
    }
    checkColumnIndex(this, index, true);
    array = checkColumnVector(this, array);
    for (let i = 0; i < this.rows; i++) {
      const newRow = new Float64Array(this.columns + 1);
      let j = 0;
      for (; j < index; j++) {
        newRow[j] = this.data[i][j];
      }
      newRow[j++] = array[i];
      for (; j < this.columns + 1; j++) {
        newRow[j] = this.data[i][j - 1];
      }
      this.data[i] = newRow;
    }
    this.columns += 1;
    return this;
  }
}

installMathOperations(AbstractMatrix, Matrix);