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Replace Array.fill with a helper function, replace var with let…
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…/`const`, return `.values` as Matrix too when input is a Matrix. See #1705
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@josdejong
josdejong committed Jan 20, 2020
1 parent 0b188e3 commit b9246d9
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5 changes: 5 additions & 0 deletions HISTORY.md
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@@ -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.
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1 change: 1 addition & 0 deletions package.json
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Expand Up @@ -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)",
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91 changes: 53 additions & 38 deletions src/function/matrix/eigs.js
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Expand Up @@ -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', {

Expand All @@ -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]) }
}
})

Expand Down Expand Up @@ -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
Expand All @@ -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]
}
Expand All @@ -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
Expand All @@ -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]
}
Expand All @@ -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
Expand All @@ -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
Expand All @@ -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]
Expand All @@ -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]))
Expand All @@ -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
Expand Down Expand Up @@ -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]
Expand Down Expand Up @@ -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]
Expand All @@ -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]
Expand All @@ -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
})
2 changes: 1 addition & 1 deletion test/unit-tests/function/matrix/eigs.test.js
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Expand Up @@ -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]
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