proj: Add Gauss Jordan

README.md

@@ -12,6 +12,7 @@ guiNumKnife is an attempt to ease the burden of undergraduate B.Tech coursework,
 - Add Max Iterations for secant
 - Hide and enable UI elements per method
 - Use Naive Gauss Elimination Again
+- Unbreak pivoting for Gauss Jordan
 - Show steps for everything
 - Plot 
 

gui.py

@@ -161,6 +161,15 @@ def calcLASGEP(self):
        self.outTextLA.append("\nThe vector b is \n" + str(b.reshape((-1, 1))))
        self.outTextLA.append("\nThe X vector is \n" + str(classAns.x.reshape((-1,1))))
 
+    def calcLASGJ(self):
+       A = np.matrix(np.loadtxt(StringIO(self.inpTextLA.toPlainText())))
+       b = np.fromstring(self.inpVecB.text(),sep=' ')
+       classAns = las.gaussJordan(A,b)
+       self.outTextLA.append("<b> Gauss Jordan Method </b><br>")
+       self.outTextLA.append("The matrix A is \n" + str(A))
+       self.outTextLA.append("\nThe vector b is \n" + str(b.reshape((-1, 1))))
+       self.outTextLA.append("\nThe X vector is \n" + str(classAns.reshape((-1,1))))
+
     def calcLASGS(self):
        A = np.matrix(np.loadtxt(StringIO(self.inpTextLA.toPlainText())))
        b = np.fromstring(self.inpVecB.text(),sep=' ')

modules/las.py

@@ -88,7 +88,6 @@ def _elimination(self):
 
     def _backsub(self):
         # Back Substitution
-
         self.x = np.zeros(self.n)
         for k in range(self.n - 1, -1, -1):
             self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k]
@@ -120,4 +119,36 @@ def gaussSeidel(A, b, itrMax = 1000):
 
         old_x = copy.deepcopy(x)
 
-    return x,k
+    return x,k
+
+
+def gaussJordan(A,b):
+    """
+    Returns the vector x such that Ax=b.
+    
+    A is assumed to be an n by n matrix and b an n-element vector.
+    """
+    n,m = A.shape
+    # should put in some checks of our assumptions, e.g. n == m
+    C = np.zeros((n,m+1),float)
+    C[:,0:n],C[:,n] = A, b
+
+    for j in range(n):
+        # First, do partial pivoting.
+        p = j # the current diagonal element is pivot by default
+        # look for alternate pivot by searching for largest element in column
+        for i in range(j+1,n):
+            if abs(C[i,j]) > abs(C[p,j]): p = i
+        if abs(C[p,j]) < 1.0e-16:
+            print("matrix is (likely) singular")
+            return b 
+        # swap rows to get largest magnitude element on the diagonal (BROKEN)
+        # C[p,:],C[j,:] = copy(C[j,:]),copy(C[p,:])
+        # Now, do scaling and elimination.
+        pivot = C[j,j]
+        C[j,:] = C[j,:] / pivot
+        for i in range(n):
+            if i == j: continue
+            C[i,:] = C[i,:] - C[i,j]*C[j,:]
+    I,x = C[:,0:n],C[:,n]
+    return x

testUI.ui

@@ -354,7 +354,7 @@
           <string>&lt;html&gt;&lt;head/&gt;&lt;body&gt;&lt;p&gt;Input a &lt;span style=&quot; text-decoration: underline;&quot;&gt;single variable&lt;/span&gt; function in terms of &lt;span style=&quot; font-weight:600;&quot;&gt;x&lt;/span&gt;.&lt;/p&gt;&lt;/body&gt;&lt;/html&gt;</string>
          </property>
          <property name="placeholderText">
-          <string>1000</string>
+          <string/>
          </property>
         </widget>
        </item>
@@ -416,6 +416,9 @@
          <property name="text">
           <string/>
          </property>
+         <property name="placeholderText">
+          <string>1000</string>
+         </property>
         </widget>
        </item>
       </layout>