Added instance method rref for Reduced Row Echelon Form transformation

site/src/pages/api/matrix.haml

@@ -55,6 +55,7 @@
   <a href="#trace"><code>trace</code></a>,
   <a href="#transpose"><code>transpose</code></a>,
   <a href="#x"><code>x</code></a>
+  <a href="#rref"><code>rref</code></a>
   </p>
 
   <p>Instance variables:</p>
@@ -484,3 +485,8 @@
   <h3 class="method">x(<span class="arg">k</span>) <span class="version">0.1.0</span></h3>
 
   <p>Alias for <a href="#multiply"><code>multiply(k)</code></a>.</p>
+
+  <a name="rref"></a>
+  <h3 class="method">rref() <span class="version">0.2.0</span></h3>
+
+  <p>Returns the matrix in reduced row echelon form.</p>

src/matrix.js

@@ -436,6 +436,48 @@ Sylvester.Matrix.prototype = {
       this.elements.push([elements[i]]);
     }
     return this;
+  },
+
+  rref : function() {
+    var lead = 0;
+    var numRows = this.rows();
+    var numCols = this.cols();
+
+    for (var r = 0; r < numRows; r++) {
+      if (numCols <= lead) {
+        return;
+      }
+      var i = r;
+      while (this.elements[i][lead] == 0) {
+        i++;
+        if (numRows == i) {
+          i = r;
+          lead++;
+          if (numCols == lead) {
+            return;
+          }
+        }
+      }
+
+      var tmp = this.elements[i];
+      this.elements[i] = this.elements[r];
+      this.elements[r] = tmp;
+
+      var val = this.elements[r][lead];
+      for (var j = 0; j < numCols; j++) {
+        this.elements[r][j] /= val;
+      }
+
+      for (var i = 0; i < numRows; i++) {
+        if (i == r) continue;
+        val = this.elements[i][lead];
+        for (var j = 0; j < numCols; j++) {
+          this.elements[i][j] -= val * this.elements[r][j];
+        }
+      }
+      lead++;
+    }
+    return this;
   }
 };
 

test/specs/matrix_spec.js

@@ -334,4 +334,13 @@ JS.ENV.MatrixSpec = JS.Test.describe("Matrix", function() { with(this) {
       [0,0,0,7]
     ]))
   }})
+
+  test("rref - Reduced Row Echelon Form", function() { with(this) {
+    var testMatrix = Matrix.create([[5,0,0,1],[0,5,0,2],[0,0,5,3]]);
+    assert(testMatrix.rref().eql([
+      [1,0,0,0.2],
+      [0,1,0,0.4],
+      [0,0,1,0.6]
+    ]))
+  }})
 }})