gauss_jordan_elimination can swap rows

fixes #1125
numbas · Oct 17, 2024 · 0ffaa76 · 0ffaa76
1 parent 4a6464a
commit 0ffaa76
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Showing 4 changed files with 52 additions and 6 deletions.
diff --git a/runtime/scripts/math.js b/runtime/scripts/math.js
@@ -3396,9 +3396,23 @@ var matrixmath = Numbas.matrixmath = {
         m = m.map(row => row.slice());
         for(let i=0; i<rows; i++) {
             // divide row i by m[i][i]
-            const f = m[i][i];
+            let f = m[i][i];
             if(f==0) {
-                throw(new Numbas.Error("matrixmath.not invertible"));
+                let j = i+1;
+                for(;j<rows;j++) {
+                    if(m[j][i] != 0) {
+                        // swap rows j and i
+                        let ri = m[i];
+                        let rj = m[j];
+                        m[i] = rj;
+                        m[j] = ri;
+                        f = m[i][i];
+                        break;
+                    }
+                }
+                if(j >= rows) {
+                    throw(new Numbas.Error("matrixmath.not invertible"));
+                }
             }
             for(let x=0; x<columns; x++) {
                 m[i][x] /= f;

diff --git a/tests/jme-runtime.js b/tests/jme-runtime.js
@@ -5633,9 +5633,23 @@ var matrixmath = Numbas.matrixmath = {
         m = m.map(row => row.slice());
         for(let i=0; i<rows; i++) {
             // divide row i by m[i][i]
-            const f = m[i][i];
+            let f = m[i][i];
             if(f==0) {
-                throw(new Numbas.Error("matrixmath.not invertible"));
+                let j = i+1;
+                for(;j<rows;j++) {
+                    if(m[j][i] != 0) {
+                        // swap rows j and i
+                        let ri = m[i];
+                        let rj = m[j];
+                        m[i] = rj;
+                        m[j] = ri;
+                        f = m[i][i];
+                        break;
+                    }
+                }
+                if(j >= rows) {
+                    throw(new Numbas.Error("matrixmath.not invertible"));
+                }
             }
             for(let x=0; x<columns; x++) {
                 m[i][x] /= f;

diff --git a/tests/jme/doc-tests.mjs b/tests/jme/doc-tests.mjs
@@ -2549,6 +2549,10 @@ export default
                     {
                         "in": "gauss_jordan_elimination(matrix([1,2,3,5],[5,6,9,11],[6,9,12,15]))",
                         "out": "matrix([1,0,0,-2],[0,1,0,-1],[0,0,1,3])"
+                    },
+                    {
+                        "in": "gauss_jordan_elimination(matrix([0,1],[1,0]))",
+                        "out": "matrix([1,0],[0,1])"
                     }
                 ]
             },

diff --git a/tests/numbas-runtime.js b/tests/numbas-runtime.js
@@ -5634,9 +5634,23 @@ var matrixmath = Numbas.matrixmath = {
         m = m.map(row => row.slice());
         for(let i=0; i<rows; i++) {
             // divide row i by m[i][i]
-            const f = m[i][i];
+            let f = m[i][i];
             if(f==0) {
-                throw(new Numbas.Error("matrixmath.not invertible"));
+                let j = i+1;
+                for(;j<rows;j++) {
+                    if(m[j][i] != 0) {
+                        // swap rows j and i
+                        let ri = m[i];
+                        let rj = m[j];
+                        m[i] = rj;
+                        m[j] = ri;
+                        f = m[i][i];
+                        break;
+                    }
+                }
+                if(j >= rows) {
+                    throw(new Numbas.Error("matrixmath.not invertible"));
+                }
             }
             for(let x=0; x<columns; x++) {
                 m[i][x] /= f;