Eliminated pinv from grad eigh calculations.

theano/sandbox/linalg/ops.py

@@ -1026,21 +1026,20 @@ class EighGrad(Op):
         """
         x, w, v, W, V = inputs
         N = x.shape[0]
-        if imported_scipy:
-            pinv = scipy.linalg.pinv
-        else:
-            pinv = numpy.linalg.pinv
         diag = numpy.diag
         outer = numpy.outer
-        I = numpy.eye(x.shape[0])
+        I = numpy.eye(N)
 
         def Wterm(n):
-            return numpy.outer(v[:,n],v[:,n])*W[n]
+            return outer(v[:,n], v[:,n])*W[n]
     
         def Vterm(n):
-            return numpy.outer(v[:,n],numpy.linalg.pinv(w[n]*I-x).dot(V[:,n]))
-    
-        outputs[0][0] = numpy.sum(Wterm(n) + Vterm(n)for n in range(v.shape[1]))
+            G = sum(v[:,m]*V.T[n].dot(v[:,m])/(w[n]-w[m])
+                    for m in xrange(N) if m != n)
+            return outer(v[:,n], G)
+
+        outputs[0][0] = sum(Wterm(n) + Vterm(n)
+                            for n in range(N))
 
 
     def infer_shape(self, node, shapes):