Implement eigen decomposition

packages/hedgehog-core/package.json

@@ -31,7 +31,7 @@
         "csv": "^5.5.0",
         "esbuild-loader": "^2.9.1",
         "gpu.js": "^2.9.5",
-        "mathjs": "^7.1.0",
+        "mathjs": "^9.3.0",
         "ml-hclust": "^3.0.0",
         "ml-matrix": "^6.8.0",
         "ml-pca": "^4.0.2",
@@ -43,7 +43,7 @@
     },
     "devDependencies": {
         "@babel/types": "^7.10.5",
-        "@types/mathjs": "^6.0.5",
+        "@types/mathjs": "^9.3.0",
         "@typescript-eslint/eslint-plugin": "^3.7.0",
         "@typescript-eslint/parser": "^3.7.0",
         "eslint": "^7.5.0",

packages/hedgehog-core/src/lib/algebra.ts

@@ -1,5 +1,5 @@
 import { Mat } from './matrix';
-import { lup, qr } from 'mathjs';
+import { lup, qr, eigs } from 'mathjs';
 
 // Cholesky
 export class Chol {
@@ -58,3 +58,16 @@ export class QR {
     this.R = new Mat(result.R as any);
   }
 }
+
+// Eigensystem: A*V = V*D or A = V*D*V.transpose()
+export class Eigensystem {
+  // V: the columns of V are eigenvectors
+  V: Mat;
+  // D: diagonal matrix of eigenvalues
+  D: Mat;
+  constructor(A: Mat) {
+    const result = eigs(A.val);
+    this.V = new Mat(result.vectors as any);
+    this.D = new Mat().diag(result.values as any);
+  }
+}

packages/hedgehog-core/src/runtime/prelude.ts

@@ -8,7 +8,7 @@ import { Tensor } from '../lib/tensor';
 import { Table } from '../lib/table';
 import _MathLib from '../lib/mathlib';
 import { Sym } from '../lib/symbolic';
-import { Chol, QR, LU } from '../lib/algebra';
+import { Chol, QR, LU, Eigensystem } from '../lib/algebra';
 import { OutputItem } from '../output/output-item';
 import { rawInputsToTex } from '../utilites/process-raw-inputs';
 
@@ -265,6 +265,10 @@ export function lu(A: Mat): LU {
   return new LU(A);
 }
 
+export function eig(A: Mat): Eigensystem {
+  return new Eigensystem(A);
+}
+
 //tic and toc
 let timestamp = 0;
 // eslint-disable-next-line @typescript-eslint/explicit-module-boundary-types

yarn.lock

@@ -1270,7 +1270,7 @@
   dependencies:
     regenerator-runtime "^0.13.4"
 
-"@babel/runtime@^7.1.2", "@babel/runtime@^7.13.10", "@babel/runtime@^7.15.4":
+"@babel/runtime@^7.1.2", "@babel/runtime@^7.13.10", "@babel/runtime@^7.14.6", "@babel/runtime@^7.15.4":
   version "7.15.4"
   resolved "https://registry.yarnpkg.com/@babel/runtime/-/runtime-7.15.4.tgz#fd17d16bfdf878e6dd02d19753a39fa8a8d9c84a"
   integrity sha512-99catp6bHCaxr4sJ/DbTGgHS4+Rs2RVd2g7iOap6SLGPDknRK9ztKNsE/Fg6QhSeh1FGE5f6gHGQmvvn3I3xhw==
@@ -3179,12 +3179,12 @@
   resolved "https://registry.yarnpkg.com/@types/json-schema/-/json-schema-7.0.6.tgz#f4c7ec43e81b319a9815115031709f26987891f0"
   integrity sha512-3c+yGKvVP5Y9TYBEibGNR+kLtijnj7mYrXRg+WpFb2X9xm04g/DXYkfg4hmzJQosc9snFNUPkbYIhu+KAm6jJw==
 
-"@types/mathjs@^6.0.5":
-  version "6.0.7"
-  resolved "https://registry.yarnpkg.com/@types/mathjs/-/mathjs-6.0.7.tgz#89299b8e0dd369c970ee8f477ba2cd2527c56cd0"
-  integrity sha512-UPpG34wVjlr8uSijJ747q0SmC459t294xm/3Ed8GAnqM/I2K786WgCLQ4BO4lIsM07Gj1UhO7x0n0TSfqO0DNQ==
+"@types/mathjs@^9.3.0":
+  version "9.4.2"
+  resolved "https://registry.yarnpkg.com/@types/mathjs/-/mathjs-9.4.2.tgz#beec20340d768171fed8331b08fb321d218ec6e1"
+  integrity sha512-GF5g1vJmvKdWIWsE53XX7EDAyCaZ9p6gaYm1xhlXn5JjrY/NJrOfJN3fBxS3wyZpVh3QqKoMkS2WjFwxWMHOTw==
   dependencies:
-    decimal.js "^10.0.0"
+    mathjs "*"
 
 "@types/minimatch@*":
   version "3.0.3"
@@ -5656,10 +5656,10 @@ compare-versions@^3.6.0:
   resolved "https://registry.yarnpkg.com/compare-versions/-/compare-versions-3.6.0.tgz#1a5689913685e5a87637b8d3ffca75514ec41d62"
   integrity sha512-W6Af2Iw1z4CB7q4uU4hv646dW9GQuBM+YpC0UvUCWSD8w90SJjp+ujJuXaEMtAXBtSqGfMPuFOVn4/+FlaqfBA==
 
-complex.js@^2.0.11:
-  version "2.0.11"
-  resolved "https://registry.yarnpkg.com/complex.js/-/complex.js-2.0.11.tgz#09a873fbf15ffd8c18c9c2201ccef425c32b8bf1"
-  integrity sha512-6IArJLApNtdg1P1dFtn3dnyzoZBEF0MwMnrfF1exSBRpZYoy4yieMkpZhQDC0uwctw48vii0CFVyHfpgZ/DfGw==
+complex.js@^2.0.15:
+  version "2.0.15"
+  resolved "https://registry.yarnpkg.com/complex.js/-/complex.js-2.0.15.tgz#7add6848b4c1d12aa9262f7df925ebe7a51a7406"
+  integrity sha512-gDBvQU8IG139ZBQTSo2qvDFP+lANMGluM779csXOr6ny1NUtA3wkUnCFjlDNH/moAVfXtvClYt6G0zarFbtz5w==
 
 component-emitter@^1.2.1:
   version "1.3.0"
@@ -6630,10 +6630,10 @@ decamelize@^1.1.0, decamelize@^1.1.2, decamelize@^1.2.0:
   resolved "https://registry.yarnpkg.com/decamelize/-/decamelize-1.2.0.tgz#f6534d15148269b20352e7bee26f501f9a191290"
   integrity sha1-9lNNFRSCabIDUue+4m9QH5oZEpA=
 
-decimal.js@^10.0.0, decimal.js@^10.2.1:
-  version "10.2.1"
-  resolved "https://registry.yarnpkg.com/decimal.js/-/decimal.js-10.2.1.tgz#238ae7b0f0c793d3e3cea410108b35a2c01426a3"
-  integrity sha512-KaL7+6Fw6i5A2XSnsbhm/6B+NuEA7TZ4vqxnd5tXz9sbKtrN9Srj8ab4vKVdK8YAqZO9P1kg45Y6YLoduPf+kw==
+decimal.js@^10.3.1:
+  version "10.3.1"
+  resolved "https://registry.yarnpkg.com/decimal.js/-/decimal.js-10.3.1.tgz#d8c3a444a9c6774ba60ca6ad7261c3a94fd5e783"
+  integrity sha512-V0pfhfr8suzyPGOx3nmq4aHqabehUZn6Ch9kyFpV79TGDTWFmHqUqXdabR7QHqxzrYolF4+tVmJhUG4OURg5dQ==
 
 decode-uri-component@^0.2.0:
   version "0.2.0"
@@ -8263,10 +8263,10 @@ forwarded@~0.1.2:
   resolved "https://registry.yarnpkg.com/forwarded/-/forwarded-0.1.2.tgz#98c23dab1175657b8c0573e8ceccd91b0ff18c84"
   integrity sha1-mMI9qxF1ZXuMBXPozszZGw/xjIQ=
 
-fraction.js@^4.0.12:
-  version "4.0.12"
-  resolved "https://registry.yarnpkg.com/fraction.js/-/fraction.js-4.0.12.tgz#0526d47c65a5fb4854df78bc77f7bec708d7b8c3"
-  integrity sha512-8Z1K0VTG4hzYY7kA/1sj4/r1/RWLBD3xwReT/RCrUCbzPszjNQCCsy3ktkU/eaEqX3MYa4pY37a52eiBlPMlhA==
+fraction.js@^4.1.1:
+  version "4.1.1"
+  resolved "https://registry.yarnpkg.com/fraction.js/-/fraction.js-4.1.1.tgz#ac4e520473dae67012d618aab91eda09bcb400ff"
+  integrity sha512-MHOhvvxHTfRFpF1geTK9czMIZ6xclsEor2wkIGYYq+PxcQqT7vStJqjhe6S1TenZrMZzo+wlqOufBDVepUEgPg==
 
 fragment-cache@^0.2.1:
   version "0.2.1"
@@ -11759,17 +11759,18 @@ math-log2@^1.0.1:
   resolved "https://registry.yarnpkg.com/math-log2/-/math-log2-1.0.1.tgz#fb8941be5f5ebe8979e718e6273b178e58694565"
   integrity sha1-+4lBvl9evol55xjmJzsXjlhpRWU=
 
-mathjs@^7.1.0:
-  version "7.6.0"
-  resolved "https://registry.yarnpkg.com/mathjs/-/mathjs-7.6.0.tgz#f0b7579e0756b13422995d0c4f29bd17d65d4dcc"
-  integrity sha512-abywR28hUpKF4at5jE8Ys+Kigk40eKMT5mcBLD0/dtsqjfOLbtzd3WjlRqIopNo7oQ6FME51qph6lb8h/bhpUg==
+mathjs@*, mathjs@^9.3.0:
+  version "9.4.4"
+  resolved "https://registry.yarnpkg.com/mathjs/-/mathjs-9.4.4.tgz#29acd67563c1e720910213062824c3faf61bc858"
+  integrity sha512-5EEJXnWOzLDgMHSFyw623nH+MTBZxquWwXtrzTsingOouJJ6UZG2VNO1lwH31IMt9aMno1axO6TYleIP4YSDaQ==
   dependencies:
-    complex.js "^2.0.11"
-    decimal.js "^10.2.1"
+    "@babel/runtime" "^7.14.6"
+    complex.js "^2.0.15"
+    decimal.js "^10.3.1"
     escape-latex "^1.2.0"
-    fraction.js "^4.0.12"
+    fraction.js "^4.1.1"
     javascript-natural-sort "^0.7.1"
-    seed-random "^2.2.0"
+    seedrandom "^3.0.5"
     tiny-emitter "^2.1.0"
     typed-function "^2.0.0"
 
@@ -15987,16 +15988,16 @@ screenfull@^5.1.0:
   resolved "https://registry.yarnpkg.com/screenfull/-/screenfull-5.1.0.tgz#85c13c70f4ead4c1b8a935c70010dfdcd2c0e5c8"
   integrity sha512-dYaNuOdzr+kc6J6CFcBrzkLCfyGcMg+gWkJ8us93IQ7y1cevhQAugFsaCdMHb6lw8KV3xPzSxzH7zM1dQap9mA==
 
-seed-random@^2.2.0:
-  version "2.2.0"
-  resolved "https://registry.yarnpkg.com/seed-random/-/seed-random-2.2.0.tgz#2a9b19e250a817099231a5b99a4daf80b7fbed54"
-  integrity sha1-KpsZ4lCoFwmSMaW5mk2vgLf77VQ=
-
 [email protected]:
   version "2.4.3"
   resolved "https://registry.yarnpkg.com/seedrandom/-/seedrandom-2.4.3.tgz#2438504dad33917314bff18ac4d794f16d6aaecc"
   integrity sha1-JDhQTa0zkXMUv/GKxNeU8W1qrsw=
 
+seedrandom@^3.0.5:
+  version "3.0.5"
+  resolved "https://registry.yarnpkg.com/seedrandom/-/seedrandom-3.0.5.tgz#54edc85c95222525b0c7a6f6b3543d8e0b3aa0a7"
+  integrity sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg==
+
 select-hose@^2.0.0:
   version "2.0.0"
   resolved "https://registry.yarnpkg.com/select-hose/-/select-hose-2.0.0.tgz#625d8658f865af43ec962bfc376a37359a4994ca"