General eigenproblem algorithm (josdejong#1743)

* split the eigs function into multiple algorithms * moved checks and coersions to eigs.js, made them more robust * fix little bugs, make im and re more robust * Implemented matrix balancing algorithm * fix typos * a draft of reduction to Hessenberg matrix * finished implementation of reduction to Hessenberg * fix Hessenberg elimination for complex numbers * implemented non-shifted explicit QR algorithm for real matrices * implemented vector computation, won't work untill usolve is fixed * refactored to match yarn lint * some minor changes * solve merge conflicts * refactored and re-fixed josdejong#1789 * some old uncommited changes * fix small problems introduced by merging * done some polishing * improved jsdoc description of eigs * little changes in jsdoc Co-authored-by: Jos de Jong <[email protected]>
LearnSomethingTeam · Sep 16, 2021 · 6d6b89a · 6d6b89a
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diff --git a/src/function/arithmetic/norm.js b/src/function/arithmetic/norm.js
@@ -240,7 +240,7 @@ export const createNorm = /* #__PURE__ */ factory(
       const tx = ctranspose(x)
       const squaredX = multiply(tx, x)
       const eigenVals = eigs(squaredX).values
-      const rho = eigenVals.get([eigenVals.size()[0] - 1])
+      const rho = eigenVals[eigenVals.length - 1]
       return abs(sqrt(rho))
     }
 

diff --git a/src/function/complex/im.js b/src/function/complex/im.js
@@ -41,6 +41,10 @@ export const createIm = /* #__PURE__ */ factory(name, dependencies, ({ typed })
       return x.mul(0)
     },
 
+    Fraction: function (x) {
+      return x.mul(0)
+    },
+
     Complex: function (x) {
       return x.im
     },

diff --git a/src/function/complex/re.js b/src/function/complex/re.js
@@ -41,6 +41,10 @@ export const createRe = /* #__PURE__ */ factory(name, dependencies, ({ typed })
       return x
     },
 
+    Fraction: function (x) {
+      return x
+    },
+
     Complex: function (x) {
       return x.re
     },