Corected use of UPLO parameter in Eigh.grad.

Numpy's eigh(a, 'L') (eigh(a, 'U')) is a function of tril(a) (triu(a)) only. This means that partial derivative of eigh(a, 'L') (eigh(a, 'U')) with respect to a[i,j] is zero for i < j (i > j). At the same time, non-zero components of the gradient must account for the fact that variation of the opposite triangle contributes to variation of two elements of Hermitian (symmetric) matrix.

Corected use of UPLO parameter in Eigh.grad.
cd478ba2 · abalkin · Frederic · 1219334d · cd478ba2 · cd478ba2
--- a/theano/sandbox/linalg/ops.py
+++ b/theano/sandbox/linalg/ops.py
@@ -991,7 +991,13 @@ class EighGrad(Op):
    """
    def __init__(self, UPLO='L'):
        self.UPLO = UPLO
-
+        if UPLO == 'L':
+            self.tri0 = numpy.tril
+            self.tri1 = lambda a: numpy.triu(a, 1)
+        else:
+            self.tri0 = numpy.triu
+            self.tri1 = lambda a: numpy.tril(a, -1)
+            
    def props(self):
        return ()

@@ -1043,11 +1049,9 @@ class EighGrad(Op):

        G = lambda n: sum(v[:,m]*V.T[n].dot(v[:,m])/(w[n]-w[m])
                          for m in xrange(N) if m != n)
-        tri = numpy.tri(N)
-        if self.UPLO == 'U':
-            tri = tri.T
-        outputs[0][0] = sum(outer(v[:,n], v[:,n]*W[n] + G(n))
-                            for n in xrange(N))#*tri
+        g = sum(outer(v[:,n], v[:,n]*W[n] + G(n))
+                for n in xrange(N))
+        outputs[0][0] = self.tri0(g) + self.tri1(g).T

    def infer_shape(self, node, shapes):
        return [shapes[0]]

--- a/theano/sandbox/linalg/tests/test_linalg.py
+++ b/theano/sandbox/linalg/tests/test_linalg.py
@@ -511,5 +511,7 @@ class test_Eigh(test_Eig):
            
    def test_grad(self):
        S = self.S
-        utt.verify_grad(lambda x: self.op(x + x.T)[0], [S], rng=self.rng)
-        utt.verify_grad(lambda x: self.op(x + x.T)[1], [S], rng=self.rng)
+        utt.verify_grad(lambda x: self.op(x)[0], [S], rng=self.rng)
+        utt.verify_grad(lambda x: self.op(x)[1], [S], rng=self.rng)
+        utt.verify_grad(lambda x: self.op(x, 'U')[0], [S], rng=self.rng)
+        utt.verify_grad(lambda x: self.op(x, 'U')[1], [S], rng=self.rng)