Fix test_linalg.py for float32, also use it to compute log(det|A|) where A is positive-definite

theano/gpuarray/tests/test_linalg.py

@@ -599,8 +599,7 @@ class TestMagma(unittest.TestCase):
             for node in fn.maker.fgraph.toposort()
         ])
 
-# copied from theano/tensor/tests/test_slinalg.py
-
+# mostly copied from theano/tensor/tests/test_slinalg.py
 def test_cholesky_grad():
     rng = np.random.RandomState(utt.fetch_seed())
     r = rng.randn(5, 5).astype(config.floatX)
@@ -630,16 +629,28 @@ def test_cholesky_grad_indef():
     # assert np.all(np.isnan(chol_f(matrix)))
 
 def test_lower_triangular_and_cholesky_grad():
+    # Random lower triangular system is ill-conditioned.
+    #
+    # Reference
+    # -----------
+    # Viswanath, Divakar, and L. N. Trefethen. "Condition numbers of random triangular matrices."
+    # SIAM Journal on Matrix Analysis and Applications 19.2 (1998): 564-581.
+    #
+    # Use smaller number of N when using float32
+    if config.floatX == 'float64':
+        N = 100
+    else:
+        N = 5
     rng = np.random.RandomState(utt.fetch_seed())
-    r = rng.randn(10, 10).astype(config.floatX)
-    y = rng.rand(10, 1).astype(config.floatX)
+    r = rng.randn(N, N).astype(config.floatX)
+    y = rng.rand(N, 1).astype(config.floatX)
 
     def f(r,y):
         PD = r.dot(r.T)
         L = gpu_cholesky(PD)
         A = gpu_solve_lower_triangular(L,y)
         AAT = theano.tensor.dot(A,A.T)
-        B = AAT + theano.tensor.eye(10)
+        B = AAT + theano.tensor.eye(N)
         LB = gpu_cholesky(B)
-        return theano.tensor.sum(LB)
+        return theano.tensor.sum(theano.tensor.log(theano.tensor.diag(LB)))
     yield (lambda: utt.verify_grad(f, [r,y], 3, rng))