Feat/rotate matrix (#1984)

* providing rotationMatrix(theta, v)

* increase coverage

* adding latex test as is

* fixing rounding issues with math.pi

* fixing lint

* Update rotationMatrix.js

remove non-sense doc

* Update rotationMatrix.js

Remove non-sense from docs

* removing nonsense from docs

* Renaming functions

Co-authored-by: Jos de Jong <wjosdejong@gmail.com>

src/expression/embeddedDocs/embeddedDocs.js

@@ -214,6 +214,7 @@ import { sinDocs } from './function/trigonometry/sin'
 import { numericDocs } from './function/utils/numeric'
 import { columnDocs } from './function/matrix/column'
 import { rowDocs } from './function/matrix/row'
+import { rotationMatrixDocs } from './function/matrix/rotationMatrix'
 
 export const embeddedDocs = {
 
@@ -426,6 +427,7 @@ export const embeddedDocs = {
   range: rangeDocs,
   resize: resizeDocs,
   reshape: reshapeDocs,
+  rotationMatrix: rotationMatrixDocs,
   row: rowDocs,
   size: sizeDocs,
   sort: sortDocs,

src/expression/embeddedDocs/function/matrix/rotationMatrix.js

@@ -0,0 +1,19 @@
+export const rotationMatrixDocs = {
+  name: 'rotationMatrix',
+  category: 'Matrix',
+  syntax: [
+    'rotationMatrix(theta)',
+    'rotationMatrix(theta, v)',
+    'rotationMatrix(theta, v, format)'
+  ],
+  description: 'Returns a 2-D rotation matrix (2x2) for a given angle (in radians). ' +
+    'Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.',
+  examples: [
+    'rotationMatrix(pi / 2)',
+    'rotationMatrix(unit("45deg"), [0, 0, 1])',
+    'rotationMatrix(1, matrix([0, 0, 1]), "sparse")'
+  ],
+  seealso: [
+    'cos', 'sin'
+  ]
+}

src/factoriesAny.js

@@ -78,6 +78,7 @@ export { createOnes } from './function/matrix/ones'
 export { createRange } from './function/matrix/range'
 export { createReshape } from './function/matrix/reshape'
 export { createResize } from './function/matrix/resize'
+export { createRotationMatrix } from './function/matrix/rotationMatrix'
 export { createRow } from './function/matrix/row'
 export { createSize } from './function/matrix/size'
 export { createSqueeze } from './function/matrix/squeeze'

src/function/matrix/rotationMatrix.js

@@ -0,0 +1,185 @@
+import { isBigNumber } from '../../utils/is'
+import { factory } from '../../utils/factory'
+
+const name = 'rotationMatrix'
+const dependencies = [
+  'typed',
+  'config',
+  'multiplyScalar',
+  'addScalar',
+  'unaryMinus',
+  'norm',
+  'matrix',
+  'BigNumber',
+  'DenseMatrix',
+  'SparseMatrix',
+  'cos',
+  'sin'
+]
+
+export const createRotationMatrix = /* #__PURE__ */ factory(name, dependencies, (
+  {
+    typed, config, multiplyScalar,
+    addScalar, unaryMinus, norm, BigNumber,
+    matrix, DenseMatrix, SparseMatrix, cos, sin
+  }) => {
+  /**
+   * Create a 2-dimensional counter-clockwise rotation matrix (2x2) for a given angle (expressed in radians).
+   * Create a 2-dimensional counter-clockwise rotation matrix (3x3) by a given angle (expressed in radians) around a given axis (1x3).
+   *
+   * Syntax:
+   *
+   *    math.rotationMatrix(theta)
+   *    math.rotationMatrix(theta, format)
+   *    math.rotationMatrix(theta, [v])
+   *    math.rotationMatrix(theta, [v], format)
+   *
+   * Examples:
+   *
+   *    math.rotationMatrix(math.pi / 2)                      // returns [[0, -1], [1, 0]]
+   *    math.rotationMatrix(math.bignumber(45))               // returns [[ bignumber(1 / sqrt(2)), - bignumber(1 / sqrt(2))], [ bignumber(1 / sqrt(2)),  bignumber(1 / sqrt(2))]]
+   *    math.rotationMatrix(math.complex(1 + i))              // returns [[cos(1 + i), -sin(1 + i)], [sin(1 + i), cos(1 + i)]]
+   *    math.rotationMatrix(math.unit('1rad'))                // returns [[cos(1), -sin(1)], [sin(1), cos(1)]]
+   *
+   *    math.rotationMatrix(math.pi / 2, [0, 1, 0])           // returns [[0, 0, 1], [0, 1, 0], [-1, 0, 0]]
+   *    math.rotationMatrix(math.pi / 2, matrix([0, 1, 0]))   // returns matrix([[0, 0, 1], [0, 1, 0], [-1, 0, 0]])
+   *
+   *
+   * See also:
+   *
+   *    matrix, cos, sin
+   *
+   *
+   * @param {number | BigNumber | Complex | Unit} theta    Rotation angle
+   * @param {Array | Matrix} [v]                           Rotation axis
+   * @param {string} [format]                              Result Matrix storage format
+   * @return {Array | Matrix}                              Rotation matrix
+   */
+
+  return typed(name, {
+    '': function () {
+      return (config.matrix === 'Matrix') ? matrix([]) : []
+    },
+
+    string: function (format) {
+      return matrix(format)
+    },
+
+    'number | BigNumber | Complex | Unit': function (theta) {
+      return _rotationMatrix2x2(theta, config.matrix === 'Matrix' ? 'dense' : undefined)
+    },
+
+    'number | BigNumber | Complex | Unit, string': function (theta, format) {
+      return _rotationMatrix2x2(theta, format)
+    },
+
+    'number | BigNumber | Complex | Unit, Array': function (theta, v) {
+      const matrixV = matrix(v)
+      _validateVector(matrixV)
+      return _rotationMatrix3x3(theta, matrixV, config.matrix === 'Matrix' ? 'dense' : undefined)
+    },
+
+    'number | BigNumber | Complex | Unit, Matrix': function (theta, v) {
+      _validateVector(v)
+      return _rotationMatrix3x3(theta, v, config.matrix === 'Matrix' ? 'dense' : undefined)
+    },
+
+    'number | BigNumber | Complex | Unit, Array, string': function (theta, v, format) {
+      const matrixV = matrix(v)
+      _validateVector(matrixV)
+      return _rotationMatrix3x3(theta, matrixV, format)
+    },
+
+    'number | BigNumber | Complex | Unit, Matrix, string': function (theta, v, format) {
+      _validateVector(v)
+      return _rotationMatrix3x3(theta, v, format)
+    }
+
+  })
+
+  /**
+   * Returns 2x2 matrix of 2D rotation of angle theta
+   *
+   * @param {number | BigNumber | Complex | Unit} theta  The rotation angle
+   * @param {string} format                              The result Matrix storage format
+   * @returns {Matrix}
+   * @private
+   */
+  function _rotationMatrix2x2 (theta, format) {
+    const Big = isBigNumber(theta)
+
+    const minusOne = Big ? new BigNumber(-1) : -1
+    const cosTheta = cos(theta)
+    const sinTheta = sin(theta)
+    const data = [[cosTheta, multiplyScalar(minusOne, sinTheta)], [sinTheta, cosTheta]]
+
+    return _convertToFormat(data, format)
+  }
+
+  function _validateVector (v) {
+    const size = v.size()
+    if (size.length < 1 || size[0] !== 3) {
+      throw new RangeError('Vector must be of dimensions 1x3')
+    }
+  }
+
+  function _mul (array) {
+    return array.reduce((p, curr) => multiplyScalar(p, curr))
+  }
+
+  function _convertToFormat (data, format) {
+    if (format) {
+      if (format === 'sparse') {
+        return new SparseMatrix(data)
+      }
+      if (format === 'dense') {
+        return new DenseMatrix(data)
+      }
+      throw new TypeError(`Unknown matrix type "${format}"`)
+    }
+    return data
+  }
+
+  /**
+   * Returns a 3x3 matrix of rotation of angle theta around vector v
+   *
+   * @param {number | BigNumber | Complex | Unit} theta The rotation angle
+   * @param {Matrix} v                                  The rotation axis vector
+   * @param {string} format                             The storage format of the resulting matrix
+   * @returns {Matrix}
+   * @private
+   */
+  function _rotationMatrix3x3 (theta, v, format) {
+    const normV = norm(v)
+    if (normV === 0) {
+      return _convertToFormat([], format)
+    }
+
+    const Big = isBigNumber(theta) ? BigNumber : null
+
+    const one = Big ? new Big(1) : 1
+    const minusOne = Big ? new Big(-1) : -1
+    const vx = Big ? new Big(v.get([0]) / normV) : v.get([0]) / normV
+    const vy = Big ? new Big(v.get([1]) / normV) : v.get([1]) / normV
+    const vz = Big ? new Big(v.get([2]) / normV) : v.get([2]) / normV
+    const c = cos(theta)
+    const oneMinusC = addScalar(one, unaryMinus(c))
+    const s = sin(theta)
+
+    const r11 = addScalar(c, _mul([vx, vx, oneMinusC]))
+    const r12 = addScalar(_mul([vx, vy, oneMinusC]), _mul([minusOne, vz, s]))
+    const r13 = addScalar(_mul([vx, vz, oneMinusC]), _mul([vy, s]))
+
+    const r21 = addScalar(_mul([vx, vy, oneMinusC]), _mul([vz, s]))
+    const r22 = addScalar(c, _mul([vy, vy, oneMinusC]))
+    const r23 = addScalar(_mul([vy, vz, oneMinusC]), _mul([minusOne, vx, s]))
+
+    const r31 = addScalar(_mul([vx, vz, oneMinusC]), _mul([minusOne, vy, s]))
+    const r32 = addScalar(_mul([vy, vz, oneMinusC]), _mul([vx, s]))
+    const r33 = addScalar(c, _mul([vz, vz, oneMinusC]))
+
+    const data = [[r11, r12, r13], [r21, r22, r23], [r31, r32, r33]]
+
+    return _convertToFormat(data, format)
+  }
+})