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tdajs · Jul 24, 2021 · 2529980 · 2529980
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Showing 6 changed files with 60 additions and 29 deletions.
diff --git a/package.json b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "@tdajs/normal-form",
-  "version": "1.1.8",
+  "version": "1.2.0",
   "description": "Smith Normal Form and utility",
   "main": "dist/index.js",
   "types": "dist/index.d.ts",

diff --git a/src/elementary-ops.ts b/src/elementary-ops.ts
@@ -78,7 +78,7 @@ export function replaceRow(i: number, k: number, q: number, mat: number[][], opt
     const result = opts.copy ? copyMat(mat) : mat;
 
     for(let j = opts.offset || 0; j < result[0].length; j++)
-    result[i][j] += q * result[k][j];
+        result[i][j] += q * result[k][j];
 
     const baseChangeMat: number[][] = opts.changeBase ? replaceRow(i, k, - q, idMat(result.length), {
         copy: false, 
@@ -105,7 +105,7 @@ export function multiplyRow(i: number, q: number, mat: number[][], options?: Opt
     const result = opts.copy ? copyMat(mat) : mat;
     result[i] = result[i].map(val => q * val );
 
-    const baseChangeMat: number[][] = opts.changeBase ? multiplyRow(i, - q, idMat(result.length), {
+    const baseChangeMat: number[][] = opts.changeBase ? multiplyRow(i, q, idMat(result.length), {
         copy: false,
         changeBase: false
     })[0] : [];

diff --git a/src/index.ts b/src/index.ts
@@ -1,3 +1,3 @@
-export { changeBasis, mat2Tex, vec2Tex, isZero, findPivot, findAntiPivot, idMat, improvePivot } from './utils';
+export { changeBasis, mat2Tex, vec2Tex, isZero, findPivot, findAntiPivot, idMat, improvePivot, multiplyMat } from './utils';
 export { NormalForm, NFOpts } from './normal-form';
 export { exchangeRows, exchangeCols, multiplyCol, multiplyRow, replaceRow, replaceCol, Options } from './elementary-ops';
diff --git a/src/normal-form.ts b/src/normal-form.ts
@@ -1,4 +1,4 @@
-import { copyMat, idMat, multiplyMat } from './utils';
+import { copyMat, equalMatrix, idMat, multiplyMat } from './utils';
 import { exchangeCols, exchangeRows, replaceCol, replaceRow, multiplyRow, multiplyCol } from './elementary-ops';
 import { findAntiPivot, isZero, findPivot } from './utils' 
 
@@ -96,6 +96,10 @@ class NormalForm {
      * Optional arguments
      */
     opts: NFOpts;
+    /**
+     * 
+     */
+    Qinv: number[][];
 
     constructor(mat: number[][], options?: NFOpts)
     {
@@ -117,27 +121,32 @@ class NormalForm {
         this.m = this.A[0].length;
 
         this.D = this.opts.copy ? copyMat(mat) : mat;
-        [this.P, this.Q] = this.opts.changeBases ? [idMat(this.m), idMat(this.n)] : [[[]],[[]]];
+        [this.P, this.Q, this.Qinv] = this.opts.changeBases ? 
+            [idMat(this.m), idMat(this.n), idMat(this.n)] : [[], [], []];
+
         this.diag = new Array<number>();
         this.reduce(0, Math.min(this.m, this.n));
+        // Check sum
+        if(! equalMatrix( multiplyMat(this.A, this.P), multiplyMat(this.Q, this.D) ) )
+            throw new Error('Reduction failed.');
     }
 
     private reduce(startOffset: number, endOffset: number) {
         if( startOffset >= endOffset || isZero(this.D, startOffset) )
             return;
-
-        let [i,j] = this.improvePivot(startOffset);
-        this.addStep({ name: "improvedPivot", pivot: [i,j], antiPivot: [], offset: startOffset });
-        this.movePivot([i,j], startOffset);        
-        this.diagonalizePivot(startOffset);
-        this.addStep({ name: "offset", offset: startOffset });
-        this.diag.push(this.D[startOffset][startOffset]);
-        this.reduce(startOffset + 1, endOffset);
-    }
 
+            let [i,j] = this.improvePivot(startOffset);
+            this.addStep({ name: "improvedPivot", pivot: [i,j], antiPivot: [], offset: startOffset });
+            this.movePivot([i,j], startOffset);        
+            this.diagonalizePivot(startOffset);
+            this.addStep({ name: "offset", offset: startOffset });
+            this.diag.push(this.D[startOffset][startOffset]);
+            this.reduce(startOffset + 1, endOffset);
+        }
+
     private improvePivot(offset: number) {
         let i,j: number; // Pivot position
-
+        
         while(true) {
             [i,j]  = findPivot(this.D, offset);
 
@@ -152,7 +161,10 @@ class NormalForm {
             if(j === t) {
                 let q = - Math.floor(this.D[s][j] / this.D[i][j]);
                 let Q = replaceRow(s, i, q, this.D, { offset: offset, changeBase: this.opts.changeBases })[1];
-                if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+                if(this.opts.changeBases) {
+                    this.Q = multiplyMat(this.Q, Q);
+                    this.Qinv = multiplyMat(replaceRow(s, i, q, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+                }
                 this.addStep({ name: "replaceRow", args: [s, i, q], offset: offset });
             }
             else if(i === s) {
@@ -165,12 +177,18 @@ class NormalForm {
                 if(this.D[s][j] !== 0) {
                     let q = - Math.floor(this.D[s][j] / this.D[i][j]);
                     let Q = replaceRow(s, i, q, this.D, { offset: offset, changeBase: this.opts.changeBases })[1];
-                    if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+                    if(this.opts.changeBases) {
+                        this.Q = multiplyMat(this.Q, Q);
+                        this.Qinv = multiplyMat(replaceRow(s, i, q, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+                    }
                     this.addStep({ name: "replaceRow", args: [s, i, q], offset: offset });
                 }
-                
+
                 let Q = replaceRow(i, s, 1, this.D, { offset: offset, changeBase: this.opts.changeBases })[1];
-                if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+                if(this.opts.changeBases) {
+                    this.Q = multiplyMat(this.Q, Q);
+                    this.Qinv = multiplyMat(replaceRow(i, s, 1, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+                }
                 this.addStep({ name: "replaceRow", args: [i, s, 1], offset: offset });
 
                 let q = - Math.floor(this.D[i][t] / this.D[i][j]);
@@ -182,11 +200,13 @@ class NormalForm {
         return [i,j];
     }
 
-    private movePivot([i,j]: [number,number], offset: number) {
-
+    private movePivot([i,j]: [number,number], offset: number) { 
         if(i !== offset) {
             let Q = exchangeRows(offset, i, this.D, { changeBase: this.opts.changeBases })[1];
-            if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+            if(this.opts.changeBases) {
+                this.Q = multiplyMat(this.Q, Q);
+                this.Qinv = multiplyMat(exchangeRows(offset, i, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+            }
             this.addStep({ name: "exchangeRows", args: [offset, i], offset: offset });
         }
         if(j !== offset) {
@@ -196,7 +216,11 @@ class NormalForm {
         }
         if(this.D[offset][offset] < 0 ) {
             let Q = multiplyRow(offset, -1, this.D, { changeBase: this.opts.changeBases })[1];
-            if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+
+            if(this.opts.changeBases) {
+                this.Q = multiplyMat(this.Q, Q);
+                this.Qinv = multiplyMat(multiplyRow(offset, -1, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+            }
             this.addStep({ name: "multiplyRow", args: [offset, -1], offset: offset });
         }
     }
@@ -208,7 +232,10 @@ class NormalForm {
                 continue;
             let q = - Math.floor(this.D[i][offset] / this.D[offset][offset]);
             let Q = replaceRow(i, offset, q, this.D, { offset: offset, changeBase: this.opts.changeBases })[1];
-            if(this.opts.changeBases) this.Q = multiplyMat(this.Q, Q);
+            if(this.opts.changeBases) {
+                this.Q = multiplyMat(this.Q, Q);
+                this .Qinv = multiplyMat(replaceRow(i, offset, q, idMat(this.n), { offset: offset, changeBase: this.opts.changeBases })[0], this.Qinv);
+            }
             this.addStep({ name: "replaceRow", args: [i, offset], offset: offset })
         }
 

diff --git a/src/utils.ts b/src/utils.ts
@@ -119,8 +119,11 @@ export function multiplyMat(A: number[][], B: number[][]) {
     for(let i = 0; i < A.length; i++)
         for(let j = 0; j < B[0].length; j++) {
             let sum = 0;  
-            for(let k = 0; k < A[0].length; k++)
+            for(let k = 0; k < A[0].length; k++) {
                 sum += A[i][k] * B[k][j];
+                if(!Number.isSafeInteger(sum))    
+                    throw new Error('Integers too big.');
+            }
             prod[i][j] = sum;    
         }
     return prod;    
@@ -141,7 +144,6 @@ export function equalMatrix(A: number[][], B: number[][]) {
     for(let i = 0; i < A.length; i++)
         for(let j = 0; j < A[0].length; j++)
             if(A[i][j] !== B[i][j]) {
-                console.log(A[i][j] + ':' + B[i][j]);
                 return false;
             }
     return true;                
@@ -150,8 +152,10 @@ export function equalMatrix(A: number[][], B: number[][]) {
 export function isZero(mat: number[][], offset: number = 0) {
     for(let i = offset; i <  mat.length; i++)
         for(let j = offset; j < mat[0].length; j++) {
+            if(!Number.isSafeInteger(mat[i][j]))
+                throw new Error('Integers too big.');
             if(mat[i][j] !== 0)
-            return false;
+                return false;
     }
     return true;    
 }

diff --git a/tsconfig.json b/tsconfig.json
@@ -1,6 +1,6 @@
 {
     "compilerOptions": {
-      "target": "es2017",
+      "target": "esnext",
       "module": "commonjs",
       "removeComments": true,
       "declaration": true,