def test_submatrix_specialcases(self):
mat = matrix.assemble(numpy.array([1,2,3,4]), numpy.array([[0,0,2,2],[0,2,0,2]]), (3,3))
self.assertAllEqual(mat.export('dense'), [[1,0,2],[0,0,0],[3,0,4]])
self.assertAllEqual(mat.submatrix([0,2],[0,1,2]).export('dense'), [[1,0,2],[3,0,4]])
self.assertAllEqual(mat.submatrix([0,1,2],[0,2]).export('dense'), [[1,2],[0,0],[3,4]])
self.assertAllEqual(mat.submatrix([0,2],[0,2]).export('dense'), [[1,2],[3,4]])
self.assertAllEqual(mat.submatrix([1],[1]).export('dense'), [[0]])
def test_transpose(self):
asym = matrix.assemble(numpy.array([1, 2, 3, 4], dtype=float),
numpy.array([[0, 0, 1, 1], [0, 1, 1, 2]]),
shape=(2, 3))
exact = numpy.array([[1, 2, 0], [0, 3, 4]], dtype=float)
transpose = asym.T
numpy.testing.assert_equal(actual=transpose.export('dense'),
desired=exact.T)
def test_singular(self):
singularmatrix = matrix.assemble(
numpy.arange(self.n) - self.n // 2,
numpy.arange(self.n)[numpy.newaxis].repeat(2, 0),
shape=(self.n, self.n))
rhs = numpy.ones(self.n)
with self.assertRaises(matrix.MatrixError):
lhs = singularmatrix.solve(rhs, **self.args)
print(lhs)
def test_singular(self):
singularmatrix = matrix.assemble(
numpy.arange(self.n) - self.n // 2,
numpy.arange(self.n)[numpy.newaxis].repeat(2, 0),
shape=(self.n, self.n))
rhs = numpy.ones(self.n)
for args in self.args:
with self.subTest(args.get('solver', 'direct')), self.assertRaises(
matrix.MatrixError):
lhs = singularmatrix.solve(rhs, **args)
def setUp(self):
super().setUp()
self._backend = matrix.backend(self.backend)
self._backend.__enter__()
r = numpy.arange(self.n)
index = numpy.concatenate([[r, r], [r[:-1], r[1:]], [r[1:], r[:-1]]], axis=1)
data = numpy.hstack([2.] * self.n + [-1.] * (2*self.n-2))
self.matrix = matrix.assemble(data, index, shape=(self.n, self.n))
self.exact = 2 * numpy.eye(self.n) - numpy.eye(self.n, self.n, -1) - numpy.eye(self.n, self.n, +1)
self.tol = self.args.get('atol', 1e-10)
def test_add(self):
j = self.n//2
v = 10.
other = matrix.assemble(numpy.array([v]*self.n), numpy.array([numpy.arange(self.n),[j]*self.n]), shape=(self.n, self.n))
add = self.matrix + other
numpy.testing.assert_equal(actual=add.export('dense'), desired=self.exact + numpy.eye(self.n)[j]*v)
with self.assertRaises(TypeError):
self.matrix + 'foo'
with self.assertRaises(matrix.MatrixError):
self.matrix + matrix.eye(self.n+1)
def test_sub(self):
j = self.n // 2
v = 10.
other = matrix.assemble(numpy.array([v] * self.n),
numpy.array(
[numpy.arange(self.n), [j] * self.n]),
shape=(self.n, self.n))
sub = self.matrix - other
numpy.testing.assert_equal(actual=sub.export('dense'),
desired=self.exact -
numpy.eye(self.n)[j] * v)
def setUp(self):
super().setUp()
self._backend = matrix.backend(self.backend)
self._backend.__enter__()
r = numpy.arange(self.n)
index = numpy.concatenate([[r, r], [r[:-1], r[1:]], [r[1:], r[:-1]]],
axis=1)
data = numpy.hstack([2.] * self.n + [-1.] * (2 * self.n - 2))
self.matrix = matrix.assemble(data, index, shape=(self.n, self.n))
self.exact = 2 * numpy.eye(self.n) - numpy.eye(
self.n, self.n, -1) - numpy.eye(self.n, self.n, +1)
self.tol = self.args.get('atol', 1e-10)
def setUpContext(self, stack):
super().setUpContext(stack)
if self.backend:
stack.enter_context(self.backend)
index = numpy.empty([2, (self.n - 1) * 4], dtype=int)
data = numpy.empty([(self.n - 1) * 4], dtype=float)
for i in range(self.n - 1):
index[:, i * 4:(i + 1) * 4] = [i, i, i + 1,
i + 1], [i, i + 1, i, i + 1]
data[i * 4:(i + 1) *
4] = 1 if i else 2, -1, -1, 1 if i < self.n - 2 else 2
self.matrix = matrix.assemble(data, index, shape=(self.n, self.n))
self.exact = 2 * numpy.eye(self.n) - numpy.eye(
self.n, self.n, -1) - numpy.eye(self.n, self.n, +1)
def test_scalar(self):
s = matrix.assemble(numpy.array([1., 2.]),
index=numpy.empty((0, 2), dtype=int),
shape=())
self.assertEqual(s, 3.)
def test_transpose(self):
asym = matrix.assemble(numpy.array([1,2,3,4], dtype=float), numpy.array([[0,0,1,1],[0,1,1,2]]), shape=(2,3))
exact = numpy.array([[1,2,0],[0,3,4]], dtype=float)
transpose = asym.T
numpy.testing.assert_equal(actual=transpose.export('dense'), desired=exact.T)
def test_sub(self):
j = self.n//2
v = 10.
other = matrix.assemble(numpy.array([v]*self.n), numpy.array([numpy.arange(self.n),[j]*self.n]), shape=(self.n, self.n))
sub = self.matrix - other
numpy.testing.assert_equal(actual=sub.export('dense'), desired=self.exact - numpy.eye(self.n)[j]*v)
def test_rowsupp(self): sparse = matrix.assemble(numpy.array([1e-10,0,1,1]), numpy.array([[0,0,2,2],[0,1,1,2]]), shape=(3,3)) self.assertEqual(tuple(sparse.rowsupp(tol=1e-5)), (False,False,True)) self.assertEqual(tuple(sparse.rowsupp(tol=0)), (True,False,True))
def test_vector(self): v = matrix.assemble(numpy.array([1.,2.,3.]), index=numpy.array([[0,2,0]]), shape=(3,)) self.assertEqual(tuple(v), (4.,0.,2.))
def test_scalar(self): s = matrix.assemble(numpy.array([1.,2.]), index=numpy.empty((0,2), dtype=int), shape=()) self.assertEqual(s, 3.)
def test_singular(self):
singularmatrix = matrix.assemble(numpy.arange(self.n)-self.n//2, numpy.arange(self.n)[numpy.newaxis].repeat(2,0), shape=(self.n, self.n))
rhs = numpy.ones(self.n)
with self.assertRaises(matrix.MatrixError):
lhs = singularmatrix.solve(rhs, **self.args)
print(lhs)
def test_rowsupp(self): sparse = matrix.assemble(numpy.array([1e-10,0,1,1]), numpy.array([[0,0,2,2],[0,1,1,2]]), shape=(3,3)) self.assertEqual(tuple(sparse.rowsupp(tol=1e-5)), (False,False,True)) self.assertEqual(tuple(sparse.rowsupp(tol=0)), (True,False,True))
def test_vector(self):
v = matrix.assemble(numpy.array([1., 2., 3.]),
index=numpy.array([[0, 2, 0]]),
shape=(3, ))
self.assertEqual(tuple(v), (4., 0., 2.))