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"""Test functions for the sparse.linalg.interface module
"""
from __future__ import division, print_function, absolute_import
from functools import partial
from itertools import product
import operator
import pytest
from pytest import raises as assert_raises
from numpy.testing import assert_, assert_equal
import numpy as np
import scipy.sparse as sparse
from scipy.sparse.linalg import interface
from scipy.sparse.sputils import matrix
# Only test matmul operator (A @ B) when available (Python 3.5+)
TEST_MATMUL = hasattr(operator, 'matmul')
class TestLinearOperator(object):
def setup_method(self):
self.A = np.array([[1,2,3],
[4,5,6]])
self.B = np.array([[1,2],
[3,4],
[5,6]])
self.C = np.array([[1,2],
[3,4]])
def test_matvec(self):
def get_matvecs(A):
return [{
'shape': A.shape,
'matvec': lambda x: np.dot(A, x).reshape(A.shape[0]),
'rmatvec': lambda x: np.dot(A.T.conj(),
x).reshape(A.shape[1])
},
{
'shape': A.shape,
'matvec': lambda x: np.dot(A, x),
'rmatvec': lambda x: np.dot(A.T.conj(), x),
'matmat': lambda x: np.dot(A, x)
}]
for matvecs in get_matvecs(self.A):
A = interface.LinearOperator(**matvecs)
assert_(A.args == ())
assert_equal(A.matvec(np.array([1,2,3])), [14,32])
assert_equal(A.matvec(np.array([[1],[2],[3]])), [[14],[32]])
assert_equal(A * np.array([1,2,3]), [14,32])
assert_equal(A * np.array([[1],[2],[3]]), [[14],[32]])
assert_equal(A.dot(np.array([1,2,3])), [14,32])
assert_equal(A.dot(np.array([[1],[2],[3]])), [[14],[32]])
assert_equal(A.matvec(matrix([[1],[2],[3]])), [[14],[32]])
assert_equal(A * matrix([[1],[2],[3]]), [[14],[32]])
assert_equal(A.dot(matrix([[1],[2],[3]])), [[14],[32]])
assert_equal((2*A)*[1,1,1], [12,30])
assert_equal((2*A).rmatvec([1,1]), [10, 14, 18])
assert_equal((2*A).H.matvec([1,1]), [10, 14, 18])
assert_equal((2*A)*[[1],[1],[1]], [[12],[30]])
assert_equal((2*A).matmat([[1],[1],[1]]), [[12],[30]])
assert_equal((A*2)*[1,1,1], [12,30])
assert_equal((A*2)*[[1],[1],[1]], [[12],[30]])
assert_equal((2j*A)*[1,1,1], [12j,30j])
assert_equal((A+A)*[1,1,1], [12, 30])
assert_equal((A+A).rmatvec([1,1]), [10, 14, 18])
assert_equal((A+A).H.matvec([1,1]), [10, 14, 18])
assert_equal((A+A)*[[1],[1],[1]], [[12], [30]])
assert_equal((A+A).matmat([[1],[1],[1]]), [[12], [30]])
assert_equal((-A)*[1,1,1], [-6,-15])
assert_equal((-A)*[[1],[1],[1]], [[-6],[-15]])
assert_equal((A-A)*[1,1,1], [0,0])
assert_equal((A-A)*[[1],[1],[1]], [[0],[0]])
z = A+A
assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is A)
z = 2*A
assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] == 2)
assert_(isinstance(A.matvec([1, 2, 3]), np.ndarray))
assert_(isinstance(A.matvec(np.array([[1],[2],[3]])), np.ndarray))
assert_(isinstance(A * np.array([1,2,3]), np.ndarray))
assert_(isinstance(A * np.array([[1],[2],[3]]), np.ndarray))
assert_(isinstance(A.dot(np.array([1,2,3])), np.ndarray))
assert_(isinstance(A.dot(np.array([[1],[2],[3]])), np.ndarray))
assert_(isinstance(A.matvec(matrix([[1],[2],[3]])), np.ndarray))
assert_(isinstance(A * matrix([[1],[2],[3]]), np.ndarray))
assert_(isinstance(A.dot(matrix([[1],[2],[3]])), np.ndarray))
assert_(isinstance(2*A, interface._ScaledLinearOperator))
assert_(isinstance(2j*A, interface._ScaledLinearOperator))
assert_(isinstance(A+A, interface._SumLinearOperator))
assert_(isinstance(-A, interface._ScaledLinearOperator))
assert_(isinstance(A-A, interface._SumLinearOperator))
assert_((2j*A).dtype == np.complex_)
assert_raises(ValueError, A.matvec, np.array([1,2]))
assert_raises(ValueError, A.matvec, np.array([1,2,3,4]))
assert_raises(ValueError, A.matvec, np.array([[1],[2]]))
assert_raises(ValueError, A.matvec, np.array([[1],[2],[3],[4]]))
assert_raises(ValueError, lambda: A*A)
assert_raises(ValueError, lambda: A**2)
for matvecsA, matvecsB in product(get_matvecs(self.A),
get_matvecs(self.B)):
A = interface.LinearOperator(**matvecsA)
B = interface.LinearOperator(**matvecsB)
assert_equal((A*B)*[1,1], [50,113])
assert_equal((A*B)*[[1],[1]], [[50],[113]])
assert_equal((A*B).matmat([[1],[1]]), [[50],[113]])
assert_equal((A*B).rmatvec([1,1]), [71,92])
assert_equal((A*B).H.matvec([1,1]), [71,92])
assert_(isinstance(A*B, interface._ProductLinearOperator))
assert_raises(ValueError, lambda: A+B)
assert_raises(ValueError, lambda: A**2)
z = A*B
assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is B)
for matvecsC in get_matvecs(self.C):
C = interface.LinearOperator(**matvecsC)
assert_equal((C**2)*[1,1], [17,37])
assert_equal((C**2).rmatvec([1,1]), [22,32])
assert_equal((C**2).H.matvec([1,1]), [22,32])
assert_equal((C**2).matmat([[1],[1]]), [[17],[37]])
assert_(isinstance(C**2, interface._PowerLinearOperator))
def test_matmul(self):
if not TEST_MATMUL:
pytest.skip("matmul is only tested in Python 3.5+")
D = {'shape': self.A.shape,
'matvec': lambda x: np.dot(self.A, x).reshape(self.A.shape[0]),
'rmatvec': lambda x: np.dot(self.A.T.conj(),
x).reshape(self.A.shape[1]),
'matmat': lambda x: np.dot(self.A, x)}
A = interface.LinearOperator(**D)
B = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
b = B[0]
assert_equal(operator.matmul(A, b), A * b)
assert_equal(operator.matmul(A, B), A * B)
assert_raises(ValueError, operator.matmul, A, 2)
assert_raises(ValueError, operator.matmul, 2, A)
class TestAsLinearOperator(object):
def setup_method(self):
self.cases = []
def make_cases(dtype):
self.cases.append(matrix([[1,2,3],[4,5,6]], dtype=dtype))
self.cases.append(np.array([[1,2,3],[4,5,6]], dtype=dtype))
self.cases.append(sparse.csr_matrix([[1,2,3],[4,5,6]], dtype=dtype))
# Test default implementations of _adjoint and _rmatvec, which
# refer to each other.
def mv(x, dtype):
y = np.array([1 * x[0] + 2 * x[1] + 3 * x[2],
4 * x[0] + 5 * x[1] + 6 * x[2]], dtype=dtype)
if len(x.shape) == 2:
y = y.reshape(-1, 1)
return y
def rmv(x, dtype):
return np.array([1 * x[0] + 4 * x[1],
2 * x[0] + 5 * x[1],
3 * x[0] + 6 * x[1]], dtype=dtype)
class BaseMatlike(interface.LinearOperator):
def __init__(self, dtype):
self.dtype = np.dtype(dtype)
self.shape = (2,3)
def _matvec(self, x):
return mv(x, self.dtype)
class HasRmatvec(BaseMatlike):
def _rmatvec(self,x):
return rmv(x, self.dtype)
class HasAdjoint(BaseMatlike):
def _adjoint(self):
shape = self.shape[1], self.shape[0]
matvec = partial(rmv, dtype=self.dtype)
rmatvec = partial(mv, dtype=self.dtype)
return interface.LinearOperator(matvec=matvec,
rmatvec=rmatvec,
dtype=self.dtype,
shape=shape)
self.cases.append(HasRmatvec(dtype))
self.cases.append(HasAdjoint(dtype))
make_cases('int32')
make_cases('float32')
make_cases('float64')
def test_basic(self):
for M in self.cases:
A = interface.aslinearoperator(M)
M,N = A.shape
assert_equal(A.matvec(np.array([1,2,3])), [14,32])
assert_equal(A.matvec(np.array([[1],[2],[3]])), [[14],[32]])
assert_equal(A * np.array([1,2,3]), [14,32])
assert_equal(A * np.array([[1],[2],[3]]), [[14],[32]])
assert_equal(A.rmatvec(np.array([1,2])), [9,12,15])
assert_equal(A.rmatvec(np.array([[1],[2]])), [[9],[12],[15]])
assert_equal(A.H.matvec(np.array([1,2])), [9,12,15])
assert_equal(A.H.matvec(np.array([[1],[2]])), [[9],[12],[15]])
assert_equal(
A.matmat(np.array([[1,4],[2,5],[3,6]])),
[[14,32],[32,77]])
assert_equal(A * np.array([[1,4],[2,5],[3,6]]), [[14,32],[32,77]])
if hasattr(M,'dtype'):
assert_equal(A.dtype, M.dtype)
def test_dot(self):
for M in self.cases:
A = interface.aslinearoperator(M)
M,N = A.shape
assert_equal(A.dot(np.array([1,2,3])), [14,32])
assert_equal(A.dot(np.array([[1],[2],[3]])), [[14],[32]])
assert_equal(
A.dot(np.array([[1,4],[2,5],[3,6]])),
[[14,32],[32,77]])
def test_repr():
A = interface.LinearOperator(shape=(1, 1), matvec=lambda x: 1)
repr_A = repr(A)
assert_('unspecified dtype' not in repr_A, repr_A)
def test_identity():
ident = interface.IdentityOperator((3, 3))
assert_equal(ident * [1, 2, 3], [1, 2, 3])
assert_equal(ident.dot(np.arange(9).reshape(3, 3)).ravel(), np.arange(9))
assert_raises(ValueError, ident.matvec, [1, 2, 3, 4])
def test_attributes():
A = interface.aslinearoperator(np.arange(16).reshape(4, 4))
def always_four_ones(x):
x = np.asarray(x)
assert_(x.shape == (3,) or x.shape == (3, 1))
return np.ones(4)
B = interface.LinearOperator(shape=(4, 3), matvec=always_four_ones)
for op in [A, B, A * B, A.H, A + A, B + B, A ** 4]:
assert_(hasattr(op, "dtype"))
assert_(hasattr(op, "shape"))
assert_(hasattr(op, "_matvec"))
def matvec(x):
""" Needed for test_pickle as local functions are not pickleable """
return np.zeros(3)
def test_pickle():
import pickle
for protocol in range(pickle.HIGHEST_PROTOCOL + 1):
A = interface.LinearOperator((3, 3), matvec)
s = pickle.dumps(A, protocol=protocol)
B = pickle.loads(s)
for k in A.__dict__:
assert_equal(getattr(A, k), getattr(B, k))
def test_inheritance():
class Empty(interface.LinearOperator):
pass
assert_raises(TypeError, Empty)
class Identity(interface.LinearOperator):
def __init__(self, n):
super(Identity, self).__init__(dtype=None, shape=(n, n))
def _matvec(self, x):
return x
id3 = Identity(3)
assert_equal(id3.matvec([1, 2, 3]), [1, 2, 3])
assert_raises(NotImplementedError, id3.rmatvec, [4, 5, 6])
class MatmatOnly(interface.LinearOperator):
def __init__(self, A):
super(MatmatOnly, self).__init__(A.dtype, A.shape)
self.A = A
def _matmat(self, x):
return self.A.dot(x)
mm = MatmatOnly(np.random.randn(5, 3))
assert_equal(mm.matvec(np.random.randn(3)).shape, (5,))
def test_dtypes_of_operator_sum():
# gh-6078
mat_complex = np.random.rand(2,2) + 1j * np.random.rand(2,2)
mat_real = np.random.rand(2,2)
complex_operator = interface.aslinearoperator(mat_complex)
real_operator = interface.aslinearoperator(mat_real)
sum_complex = complex_operator + complex_operator
sum_real = real_operator + real_operator
assert_equal(sum_real.dtype, np.float64)
assert_equal(sum_complex.dtype, np.complex128)
def test_no_double_init():
call_count = [0]
def matvec(v):
call_count[0] += 1
return v
# It should call matvec exactly once (in order to determine the
# operator dtype)
A = interface.LinearOperator((2, 2), matvec=matvec)
assert_equal(call_count[0], 1)
|
