Replace Array.fill with a helper function, replace var with let…

…/`const`, return `.values` as Matrix too when input is a Matrix. See #1705

HISTORY.md

@@ -1,6 +1,11 @@
 # History
 
 
+# not yet published, version 6.6.0
+
+- Implemented function `eigs`, see #1705, #542 #1175. Thanks @arkajitmandal.
+
+
 # 2020-01-08, version 6.5.0
 
 - Implemented `baseName` option for `createUnit`, see #1707. 

package.json

@@ -8,6 +8,7 @@
  "Albert Emil (https://github.com/AlbertEmil)",
  "Alexander Beyn (https://github.com/AlexanderBeyn)",
  "Andy Pan (https://github.com/andy0130tw)",
+ "Arkajit Mandal (https://github.com/arkajitmandal)",
  "Arthur Guiot (https://github.com/arguiot)",
  "Bart Kiers (https://github.com/bkiers)",
  "Bartosz Leoniak (https://github.com/kmdrGroch)",

src/function/matrix/eigs.js

@@ -32,7 +32,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  * inv
  *
  * @param {Array | Matrix} x Matrix to be diagonalized
- * @return {{values: Array, vectors: Array} | {values: Array, vectors: Matrix}} Object containing eigenvalues (Array) and eigenvectors (2D Array/Matrix).
+ * @return {{values: Array, vectors: Array} | {values: Matrix, vectors: Matrix}} Object containing eigenvalues (Array or Matrix) and eigenvectors (2D Array/Matrix).
  */
  const eigs = typed('eigs', {
 
@@ -59,7 +59,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  '(size: ' + format(size) + ')')
  }
  const ans = checkAndSubmit(x, size[0])
- return { values: ans[0], vectors: matrix(ans[1]) }
+ return { values: matrix(ans[0]), vectors: matrix(ans[1]) }
  }
  })
 
@@ -118,10 +118,10 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const N = x.length
  const e0 = Math.abs(precision / N)
  let psi
- var Sij = new Array(N)
+ let Sij = new Array(N)
  // Sij is Identity Matrix
  for (let i = 0; i < N; i++) {
- Sij[i] = Array(N).fill(0)
+ Sij[i] = createArray(N, 0)
  Sij[i][i] = 1.0
  }
  // initial error
@@ -134,7 +134,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  Sij = Sij1(Sij, psi, i, j)
  Vab = getAij(x)
  }
- var Ei = Array(N).fill(0) // eigenvalues
+ const Ei = createArray(N, 0) // eigenvalues
  for (let i = 0; i < N; i++) {
  Ei[i] = x[i][i]
  }
@@ -146,10 +146,10 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const N = x.length
  const e0 = abs(precision / N)
  let psi
- var Sij = new Array(N)
+ let Sij = new Array(N)
  // Sij is Identity Matrix
  for (let i = 0; i < N; i++) {
- Sij[i] = Array(N).fill(0)
+ Sij[i] = createArray(N, 0)
  Sij[i][i] = 1.0
  }
  // initial error
@@ -162,7 +162,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  Sij = Sij1Big(Sij, psi, i, j)
  Vab = getAijBig(x)
  }
- var Ei = Array(N).fill(0) // eigenvalues
+ const Ei = createArray(N, 0) // eigenvalues
  for (let i = 0; i < N; i++) {
  Ei[i] = x[i][i]
  }
@@ -172,7 +172,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
 
  // get angle
  function getTheta (aii, ajj, aij) {
- let th = 0.0
+ let th = 0
  const denom = (ajj - aii)
  if (Math.abs(denom) <= 1E-14) {
  th = Math.PI / 4.0
@@ -184,7 +184,7 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
 
  // get angle
  function getThetaBig (aii, ajj, aij) {
- let th = 0.0
+ let th = 0
  const denom = subtract(ajj, aii)
  if (abs(denom) <= 1E-14) {
  th = Math.PI / 4.0
@@ -199,8 +199,8 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const N = Sij.length
  const c = Math.cos(theta)
  const s = Math.sin(theta)
- var Ski = new Array(N).fill(0)
- var Skj = new Array(N).fill(0)
+ const Ski = createArray(N, 0)
+ const Skj = createArray(N, 0)
  for (let k = 0; k < N; k++) {
  Ski[k] = c * Sij[k][i] - s * Sij[k][j]
  Skj[k] = s * Sij[k][i] + c * Sij[k][j]
@@ -216,8 +216,8 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const N = Sij.length
  const c = cos(theta)
  const s = sin(theta)
- var Ski = new Array(N).fill(0)
- var Skj = new Array(N).fill(0)
+ const Ski = createArray(N, 0)
+ const Skj = createArray(N, 0)
  for (let k = 0; k < N; k++) {
  Ski[k] = subtract(multiplyScalar(c, Sij[k][i]), multiplyScalar(s, Sij[k][j]))
  Skj[k] = addScalar(multiplyScalar(s, Sij[k][i]), multiplyScalar(c, Sij[k][j]))
@@ -236,9 +236,8 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const s = bignumber(sin(theta))
  const c2 = multiplyScalar(c, c)
  const s2 = multiplyScalar(s, s)
- // var Ans = new Array(N).fill(Array(N).fill(0));
- var Aki = new Array(N).fill(0)
- var Akj = new Array(N).fill(0)
+ const Aki = createArray(N, 0)
+ const Akj = createArray(N, 0)
  // 2cs Hij
  const csHij = multiply(2, c, s, Hij[i][j])
  // Aii
@@ -273,9 +272,8 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
  const s = Math.sin(theta)
  const c2 = c * c
  const s2 = s * s
- // var Ans = new Array(N).fill(Array(N).fill(0));
- var Aki = new Array(N).fill(0)
- var Akj = new Array(N).fill(0)
+ const Aki = createArray(N, 0)
+ const Akj = createArray(N, 0)
  // Aii
  const Aii = c2 * Hij[i][i] - 2 * c * s * Hij[i][j] + s2 * Hij[j][j]
  const Ajj = s2 * Hij[i][i] + 2 * c * s * Hij[i][j] + c2 * Hij[j][j]
@@ -303,11 +301,11 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
 
  // get max off-diagonal value from Upper Diagonal
  function getAij (Mij) {
- var N = Mij.length
- var maxMij = 0.0
- var maxIJ = [0, 1]
- for (var i = 0; i < N; i++) {
- for (var j = i + 1; j < N; j++) {
+ const N = Mij.length
+ let maxMij = 0
+ let maxIJ = [0, 1]
+ for (let i = 0; i < N; i++) {
+ for (let j = i + 1; j < N; j++) {
  if (Math.abs(maxMij) < Math.abs(Mij[i][j])) {
  maxMij = Math.abs(Mij[i][j])
  maxIJ = [i, j]
@@ -319,11 +317,11 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
 
  // get max off-diagonal value from Upper Diagonal
  function getAijBig (Mij) {
- var N = Mij.length
- var maxMij = 0.0
- var maxIJ = [0, 1]
- for (var i = 0; i < N; i++) {
- for (var j = i + 1; j < N; j++) {
+ const N = Mij.length
+ let maxMij = 0
+ let maxIJ = [0, 1]
+ for (let i = 0; i < N; i++) {
+ for (let j = i + 1; j < N; j++) {
  if (abs(maxMij) < abs(Mij[i][j])) {
  maxMij = abs(Mij[i][j])
  maxIJ = [i, j]
@@ -335,29 +333,46 @@ export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ typed,
 
  // sort results
  function sorting (E, S) {
- var N = E.length
- var Ef = Array(N)
- var Sf = Array(N)
+ const N = E.length
+ const Ef = Array(N)
+ const Sf = Array(N)
  for (let k = 0; k < N; k++) {
  Sf[k] = Array(N)
  }
- for (var i = 0; i < N; i++) {
- var minID = 0
- var minE = E[0]
- for (var j = 0; j < E.length; j++) {
+ for (let i = 0; i < N; i++) {
+ let minID = 0
+ let minE = E[0]
+ for (let j = 0; j < E.length; j++) {
  if (E[j] < minE) {
  minID = j
  minE = E[minID]
  }
  }
  Ef[i] = E.splice(minID, 1)[0]
- for (var k = 0; k < N; k++) {
+ for (let k = 0; k < N; k++) {
  Sf[k][i] = S[k][minID]
  S[k].splice(minID, 1)
  }
  }
  return [clone(Ef), clone(Sf)]
  }
 
+ /**
+ * Create an array of a certain size and fill all items with an initial value
+ * @param {number} size
+ * @param {number} value
+ * @return {number[]}
+ */
+ function createArray (size, value) {
+ // TODO: as soon as all browsers support Array.fill, use that instead (IE doesn't support it)
+ const array = new Array(size)
+
+ for (let i = 0; i < size; i++) {
+ array[i] = value
+ }
+
+ return array
+ }
+
  return eigs
 })

test/unit-tests/function/matrix/eigs.test.js

@@ -33,7 +33,7 @@ describe('eigs', function () {
  [[1, 0.1], [0.1, 1]]).values, [0.9, 1.1]
  )
  approx.deepEqual(eigs(
- math.matrix([[1, 0.1], [0.1, 1]])).values, [0.9, 1.1]
+ math.matrix([[1, 0.1], [0.1, 1]])).values, math.matrix([0.9, 1.1])
  )
  approx.deepEqual(eigs(
  [[5, 2.3], [2.3, 1]]).values, [-0.04795013082563382, 6.047950130825635]