Adding eigs function (#1705)

* eigs test file initialize

* file for function for diagonalization of a real symmetrix matrix

* eigs typed function written according to mathjs requirements

* some linting issues addressed

* more linting issues in eigs

* linting passed for eigs (blank template function)

* making eigs fail

* eigs added to factory any

* initial check of input in eigs

* linting issues fix in eigs

* added rotation and theta matrix

* diagonalization loop added

* diagonalization result return

* diagonalization returns eigenvalue and eigenvectors

* function for updating Sij

* function for updating matrix

* a small bug fix

* some linting fixed in eigs

* lint and bug fix at eigs

* linting passed in eigs

* tests for input in eigs

* tests for trivial eigenvalue problem (sanity check)

* 2x2 check for non-diagonal matrix

* sorting added to eigs

* sorting function lint fix in eigs

* example for eigs updated

* 3x3 diagonalization by eigs passed

* bug in eigenvector

* eigenvalues seem to work

* cloning array so that original matrix do not get transformed in eigs

* eigenvector check

* eigenvector deep check and eigs description modified

* embedding dos for eigs

* doc for eigs fix

* slight change in example

* adding checkInput type

* type error for bad matrix elements

* type error for every element

* name change for typecheck function

* check matrix type of array input

* type error message update in eigs

* type error message grammer in eigs

* eigs bug fix

* eigs bug fix in check function

* eigs typecheck test

* some lint fix in eigs and corresponding tests

* before adding bingNumber implementation in eigs

* support for fractions

* obtain angle for bigNumber type

* theta for bignumbers

* update overlap for bigNumber

* jacobi rotation of input matrix for BigNumbers

* largest element for bigNumbers

* diagonalization for bigNumbers

* adding dependedncies

* diagonization for bigNumber

* diag for bigNumber is tested

* linting fix for eig and eigs test

* problem for bigNumber fix

* error message modification for eigs

* more coverage for eigs function

* eigs test bug fix

* simplify test

* is Symmetric function

* use matrix instead in eigs

* slight cleanup

* is symmetric bug fix

* no need to return in isSymmetrix

* small bug fix for fractions

* using scalar function when possible

* small lint correction

* return object in eigs

* bug fix in array eigs

* test object implementation

* description update

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

src/expression/embeddedDocs/embeddedDocs.js

@@ -154,6 +154,7 @@ import { floorDocs } from './function/arithmetic/floor'
 import { fixDocs } from './function/arithmetic/fix'
 import { expm1Docs } from './function/arithmetic/expm1'
 import { expmDocs } from './function/arithmetic/expm'
+import { eigsDocs } from './function/matrix/eigs'
 import { expDocs } from './function/arithmetic/exp'
 import { dotMultiplyDocs } from './function/arithmetic/dotMultiply'
 import { dotDivideDocs } from './function/arithmetic/dotDivide'
@@ -409,6 +410,7 @@ export const embeddedDocs = {
   flatten: flattenDocs,
   forEach: forEachDocs,
   inv: invDocs,
+  eigs: eigsDocs,
   kron: kronDocs,
   map: mapDocs,
   ones: onesDocs,

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

@@ -0,0 +1,14 @@
+export const eigsDocs = {
+  name: 'eigs',
+  category: 'Matrix',
+  syntax: [
+    'eigs(x)'
+  ],
+  description: 'Calculate the eigenvalues and eigenvectors of a real symmetric matrix',
+  examples: [
+    'eigs([[5, 2.3], [2.3, 1]])'
+  ],
+  seealso: [
+    'inv'
+  ]
+}

src/factoriesAny.js

@@ -203,6 +203,7 @@ export { createHelp } from './expression/function/help'
 export { createChain } from './type/chain/function/chain'
 export { createDet } from './function/matrix/det'
 export { createInv } from './function/matrix/inv'
+export { createEigs } from './function/matrix/eigs'
 export { createExpm } from './function/matrix/expm'
 export { createSqrtm } from './function/matrix/sqrtm'
 export { createDivide } from './function/arithmetic/divide'