- Added cholesky solve for symmetric matrices + tests

theano/gpuarray/linalg.py

@@ -6,6 +6,9 @@ import theano
 from theano import Op
 from theano.gpuarray import basic_ops, GpuArrayType
 
+import numpy
+from numpy.linalg.linalg import LinAlgError
+
 try:
     import pygpu
 except ImportError:
@@ -18,6 +21,34 @@ try:
 except (ImportError, OSError, RuntimeError, pkg_resources.DistributionNotFound):
     pass
 
+if cusolver_available:
+    # Add cusolver call as it is missing in skcuda
+    # SPOTRS
+    cusolver._libcusolver.cusolverDnSpotrs.restype = int
+    cusolver._libcusolver.cusolverDnSpotrs.argtypes = [cusolver.ctypes.c_void_p,
+                                                       cusolver.ctypes.c_int,
+                                                       cusolver.ctypes.c_int,
+                                                       cusolver.ctypes.c_int,
+                                                       cusolver.ctypes.c_void_p,
+                                                       cusolver.ctypes.c_int,
+                                                       cusolver.ctypes.c_void_p,
+                                                       cusolver.ctypes.c_int,
+                                                       cusolver.ctypes.c_void_p]
+
+    def cusolverDnSpotrs(handle, uplo, n, nrhs, A, lda,
+                         B, ldb, devInfo):
+        """
+        Solve real single precision linear system for hermitian matrices.
+        References
+        ----------
+        `cusolverDn<t>potrs <http://docs.nvidia.com/cuda/cusolver/index.html#cuds-lt-t-gt-potrs>`_
+        """
+
+        status = cusolver._libcusolver.cusolverDnSpotrs(handle, uplo, n, nrhs,
+                                                        int(A), lda, int(B),
+                                                        ldb, int(devInfo))
+        cusolver.cusolverCheckStatus(status)
+
 
 class GpuCusolverSolve(Op):
     """
@@ -30,11 +61,12 @@ class GpuCusolverSolve(Op):
 
     """
 
-    __props__ = ('trans', 'inplace')
+    __props__ = ('A_structure', 'trans', 'inplace')
 
-    def __init__(self, trans='N', inplace=False):
+    def __init__(self, A_structure='general', trans='N', inplace=False):
         self.trans = trans
         self.inplace = inplace
+        self.A_structure = A_structure
         if self.inplace:
             self.destroy_map = {0: [0, 1]}
         super(GpuCusolverSolve, self).__init__()
@@ -70,6 +102,11 @@ class GpuCusolverSolve(Op):
             with ctx:
                 ctx.cusolver_handle = cusolver.cusolverDnCreate()
 
+    def check_dev_info(self, dev_info):
+        val = numpy.asarray(dev_info)[0]
+        if val > 0:
+            raise LinAlgError('A is singular')
+
     def perform(self, node, inputs, outputs):
         context = inputs[0][0].context
 
@@ -116,32 +153,58 @@ class GpuCusolverSolve(Op):
         if A.flags['C_CONTIGUOUS']:
             trans = 1 - trans
 
-        with context:
-            workspace_size = cusolver.cusolverDnSgetrf_bufferSize(
-                context.cusolver_handle, n, n, A_ptr, lda)
+        if self.A_structure == 'symmetric':
+            with context:
+                workspace_size = cusolver.cusolverDnSpotrf_bufferSize(
+                    context.cusolver_handle, 0, n, A_ptr, lda)
+
+            workspace = pygpu.zeros(workspace_size, dtype='float32',
+                                    context=context)
+
+            dev_info = pygpu.zeros((1,), dtype='int32', context=context)
+
+            workspace_ptr = workspace.gpudata
+            dev_info_ptr = dev_info.gpudata
+
+            with context:
+                cusolver.cusolverDnSpotrf(
+                    context.cusolver_handle, 0, n, A_ptr, lda, workspace_ptr,
+                    workspace_size, dev_info_ptr)
+                self.check_dev_info(dev_info)
+
+                cusolverDnSpotrs(
+                    context.cusolver_handle, 0, n, m, A_ptr, lda,
+                    b_ptr, ldb, dev_info_ptr)
+
+        else:
+            # general case for A
+            with context:
+                workspace_size = cusolver.cusolverDnSgetrf_bufferSize(
+                    context.cusolver_handle, n, n, A_ptr, lda)
 
-        workspace = pygpu.zeros(workspace_size, dtype='float32',
-                                context=context)
+            workspace = pygpu.zeros(workspace_size, dtype='float32',
+                                    context=context)
 
-        pivots = pygpu.zeros(n, dtype='int32', context=context)
+            pivots = pygpu.zeros(n, dtype='int32', context=context)
 
-        dev_info = pygpu.zeros((1,), dtype='int32', context=context)
+            dev_info = pygpu.zeros((1,), dtype='int32', context=context)
 
-        workspace_ptr = workspace.gpudata
-        pivots_ptr = pivots.gpudata
-        dev_info_ptr = dev_info.gpudata
+            workspace_ptr = workspace.gpudata
+            pivots_ptr = pivots.gpudata
+            dev_info_ptr = dev_info.gpudata
 
-        with context:
-            cusolver.cusolverDnSgetrf(
-                context.cusolver_handle, n, n, A_ptr, lda, workspace_ptr,
-                pivots_ptr, dev_info_ptr)
+            with context:
+                cusolver.cusolverDnSgetrf(
+                    context.cusolver_handle, n, n, A_ptr, lda, workspace_ptr,
+                    pivots_ptr, dev_info_ptr)
+                self.check_dev_info(dev_info)
 
-            cusolver.cusolverDnSgetrs(
-                context.cusolver_handle, trans, n, m, A_ptr, lda,
-                pivots_ptr, b_ptr, ldb, dev_info_ptr)
+                cusolver.cusolverDnSgetrs(
+                    context.cusolver_handle, trans, n, m, A_ptr, lda,
+                    pivots_ptr, b_ptr, ldb, dev_info_ptr)
 
         z[0] = b
 
 
-def gpu_solve(A, b, trans='N'):
-    return GpuCusolverSolve(trans)(A, b)
+def gpu_solve(A, b, A_structure='general', trans='N'):
+    return GpuCusolverSolve(A_structure, trans)(A, b)

theano/gpuarray/tests/test_linalg.py

@@ -7,6 +7,8 @@ import theano
 from theano.tests import unittest_tools as utt
 from .config import mode_with_gpu
 
+from numpy.linalg.linalg import LinAlgError
+
 # Skip tests if cuda_ndarray is not available.
 from nose.plugins.skip import SkipTest
 from theano.gpuarray.linalg import (cusolver_available, gpu_solve)
@@ -16,7 +18,7 @@ if not cusolver_available:
 
 
 class TestCusolver(unittest.TestCase):
-    def run_gpu_solve(self, A_val, x_val):
+    def run_gpu_solve(self, A_val, x_val, A_struct=None):
         b_val = numpy.dot(A_val, x_val)
         b_val_trans = numpy.dot(A_val.T, x_val)
 
@@ -24,14 +26,19 @@ class TestCusolver(unittest.TestCase):
         b = theano.tensor.matrix("b", dtype="float32")
         b_trans = theano.tensor.matrix("b", dtype="float32")
 
-        solver = gpu_solve(A, b)
-        solver_trans = gpu_solve(A, b_trans, trans='T')
+        if A_struct is None:
+            solver = gpu_solve(A, b)
+            solver_trans = gpu_solve(A, b_trans, trans='T')
+        else:
+            solver = gpu_solve(A, b, A_struct)
+            solver_trans = gpu_solve(A, b_trans, A_struct, trans='T')
+
         fn = theano.function([A, b, b_trans], [solver, solver_trans], mode=mode_with_gpu)
         res = fn(A_val, b_val, b_val_trans)
         x_res = numpy.array(res[0])
         x_res_trans = numpy.array(res[1])
-        utt.assert_allclose(x_res, x_val)
-        utt.assert_allclose(x_res_trans, x_val)
+        utt.assert_allclose(x_val, x_res)
+        utt.assert_allclose(x_val, x_res_trans)
 
     def test_diag_solve(self):
         numpy.random.seed(1)
@@ -55,10 +62,10 @@ class TestCusolver(unittest.TestCase):
     def test_sym_solve(self):
         numpy.random.seed(1)
         A_val = numpy.random.uniform(-0.4, 0.4, (5, 5)).astype("float32")
-        A_sym = (A_val + A_val.T) / 2.0
+        A_sym = numpy.dot(A_val, A_val.T)
         x_val = numpy.random.uniform(-0.4, 0.4, (A_val.shape[1],
                                      1)).astype("float32")
-        self.run_gpu_solve(A_sym, x_val)
+        self.run_gpu_solve(A_sym, x_val, 'symmetric')
 
     def test_orth_solve(self):
         numpy.random.seed(1)
@@ -74,3 +81,34 @@ class TestCusolver(unittest.TestCase):
         x_val = numpy.random.uniform(-0.4, 0.4,
                                      (A_val.shape[1], 4)).astype("float32")
         self.run_gpu_solve(A_val, x_val)
+
+    def test_linalgerrsym_solve(self):
+        numpy.random.seed(1)
+        A_val = numpy.random.uniform(-0.4, 0.4, (5, 5)).astype("float32")
+        x_val = numpy.random.uniform(-0.4, 0.4,
+                                     (A_val.shape[1], 4)).astype("float32")
+        A_val = numpy.dot(A_val.T, A_val)
+        # make A singular
+        A_val[:, 2] = A_val[:, 1] + A_val[:, 3]
+
+        A = theano.tensor.matrix("A", dtype="float32")
+        b = theano.tensor.matrix("b", dtype="float32")
+        solver = gpu_solve(A, b, 'symmetric')
+
+        fn = theano.function([A, b], [solver], mode=mode_with_gpu)
+        self.assertRaises(LinAlgError, fn, A_val, x_val)
+
+    def test_linalgerr_solve(self):
+        numpy.random.seed(1)
+        A_val = numpy.random.uniform(-0.4, 0.4, (5, 5)).astype("float32")
+        x_val = numpy.random.uniform(-0.4, 0.4,
+                                     (A_val.shape[1], 4)).astype("float32")
+        # make A singular
+        A_val[:, 2] = 0
+
+        A = theano.tensor.matrix("A", dtype="float32")
+        b = theano.tensor.matrix("b", dtype="float32")
+        solver = gpu_solve(A, b, trans='T')
+
+        fn = theano.function([A, b], [solver], mode=mode_with_gpu)
+        self.assertRaises(LinAlgError, fn, A_val, x_val)