ai-content-maker/.venv/Lib/site-packages/scipy/sparse/linalg/tests/test_interface.py

482 lines
18 KiB
Python

"""Test functions for the sparse.linalg._interface module
"""
from functools import partial
from itertools import product
import operator
from pytest import raises as assert_raises, warns
from numpy.testing import assert_, assert_equal
import numpy as np
import scipy.sparse as sparse
import scipy.sparse.linalg._interface as interface
from scipy.sparse._sputils import matrix
class TestLinearOperator:
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),
'rmatmat': 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]])
X = np.array([[1, 2], [3, 4]])
# A_asarray = np.array([[1, 2, 3], [4, 5, 6]])
assert_equal((2 * A).rmatmat(X), np.dot((2 * self.A).T, X))
assert_equal((A * 2).rmatmat(X), np.dot((self.A * 2).T, X))
assert_equal((2j * A).rmatmat(X),
np.dot((2j * self.A).T.conj(), X))
assert_equal((A * 2j).rmatmat(X),
np.dot((self.A * 2j).T.conj(), X))
assert_equal((A + A).rmatmat(X),
np.dot((self.A + self.A).T, X))
assert_equal((A + 2j * A).rmatmat(X),
np.dot((self.A + 2j * self.A).T.conj(), X))
assert_equal((-A).rmatmat(X), np.dot((-self.A).T, X))
assert_equal((A - A).rmatmat(X),
np.dot((self.A - self.A).T, X))
assert_equal((2j * A).rmatmat(2j * X),
np.dot((2j * self.A).T.conj(), 2j * X))
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_(isinstance(A/2, interface._ScaledLinearOperator))
assert_(isinstance(A/2j, interface._ScaledLinearOperator))
assert_(((A * 3) / 3).args[0] is A) # check for simplification
# Test that prefactor is of _ScaledLinearOperator is not mutated
# when the operator is multiplied by a number
result = A @ np.array([1, 2, 3])
B = A * 3
C = A / 5
assert_equal(A @ np.array([1, 2, 3]), result)
assert_((2j*A).dtype == np.complex128)
# Test division by non-scalar
msg = "Can only divide a linear operator by a scalar."
with assert_raises(ValueError, match=msg):
A / np.array([1, 2])
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)
# AtimesB = np.array([[22, 28], [49, 64]])
AtimesB = self.A.dot(self.B)
X = np.array([[1, 2], [3, 4]])
assert_equal((A * B).rmatmat(X), np.dot((AtimesB).T, X))
assert_equal((2j * A * B).rmatmat(X),
np.dot((2j * AtimesB).T.conj(), X))
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)
X = np.array([[1, 2], [3, 4]])
assert_equal(C.rmatmat(X), np.dot((self.C).T, X))
assert_equal((C**2).rmatmat(X),
np.dot((np.dot(self.C, self.C)).T, X))
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):
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]),
'rmatmat': lambda x: np.dot(self.A.T.conj(), x),
'matmat': lambda x: np.dot(self.A, x)}
A = interface.LinearOperator(**D)
B = np.array([[1 + 1j, 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.reshape(-1, 1)), A * b.reshape(-1, 1))
assert_equal(operator.matmul(A, B), A * B)
assert_equal(operator.matmul(b, A.H), b * A.H)
assert_equal(operator.matmul(b.reshape(1, -1), A.H), b.reshape(1, -1) * A.H)
assert_equal(operator.matmul(B, A.H), B * A.H)
assert_raises(ValueError, operator.matmul, A, 2)
assert_raises(ValueError, operator.matmul, 2, A)
class TestAsLinearOperator:
def setup_method(self):
self.cases = []
def make_cases(original, dtype):
cases = []
cases.append((matrix(original, dtype=dtype), original))
cases.append((np.array(original, dtype=dtype), original))
cases.append((sparse.csr_matrix(original, dtype=dtype), original))
# Test default implementations of _adjoint and _rmatvec, which
# refer to each other.
def mv(x, dtype):
y = original.dot(x)
if len(x.shape) == 2:
y = y.reshape(-1, 1)
return y
def rmv(x, dtype):
return original.T.conj().dot(x)
class BaseMatlike(interface.LinearOperator):
args = ()
def __init__(self, dtype):
self.dtype = np.dtype(dtype)
self.shape = original.shape
def _matvec(self, x):
return mv(x, self.dtype)
class HasRmatvec(BaseMatlike):
args = ()
def _rmatvec(self,x):
return rmv(x, self.dtype)
class HasAdjoint(BaseMatlike):
args = ()
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)
class HasRmatmat(HasRmatvec):
def _matmat(self, x):
return original.dot(x)
def _rmatmat(self, x):
return original.T.conj().dot(x)
cases.append((HasRmatvec(dtype), original))
cases.append((HasAdjoint(dtype), original))
cases.append((HasRmatmat(dtype), original))
return cases
original = np.array([[1,2,3], [4,5,6]])
self.cases += make_cases(original, np.int32)
self.cases += make_cases(original, np.float32)
self.cases += make_cases(original, np.float64)
self.cases += [(interface.aslinearoperator(M).T, A.T)
for M, A in make_cases(original.T, np.float64)]
self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
for M, A in make_cases(original.T, np.float64)]
original = np.array([[1, 2j, 3j], [4j, 5j, 6]])
self.cases += make_cases(original, np.complex128)
self.cases += [(interface.aslinearoperator(M).T, A.T)
for M, A in make_cases(original.T, np.complex128)]
self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
for M, A in make_cases(original.T, np.complex128)]
def test_basic(self):
for M, A_array in self.cases:
A = interface.aslinearoperator(M)
M,N = A.shape
xs = [np.array([1, 2, 3]),
np.array([[1], [2], [3]])]
ys = [np.array([1, 2]), np.array([[1], [2]])]
if A.dtype == np.complex128:
xs += [np.array([1, 2j, 3j]),
np.array([[1], [2j], [3j]])]
ys += [np.array([1, 2j]), np.array([[1], [2j]])]
x2 = np.array([[1, 4], [2, 5], [3, 6]])
for x in xs:
assert_equal(A.matvec(x), A_array.dot(x))
assert_equal(A * x, A_array.dot(x))
assert_equal(A.matmat(x2), A_array.dot(x2))
assert_equal(A * x2, A_array.dot(x2))
for y in ys:
assert_equal(A.rmatvec(y), A_array.T.conj().dot(y))
assert_equal(A.T.matvec(y), A_array.T.dot(y))
assert_equal(A.H.matvec(y), A_array.T.conj().dot(y))
for y in ys:
if y.ndim < 2:
continue
assert_equal(A.rmatmat(y), A_array.T.conj().dot(y))
assert_equal(A.T.matmat(y), A_array.T.dot(y))
assert_equal(A.H.matmat(y), A_array.T.conj().dot(y))
if hasattr(M,'dtype'):
assert_equal(A.dtype, M.dtype)
assert_(hasattr(A, 'args'))
def test_dot(self):
for M, A_array in self.cases:
A = interface.aslinearoperator(M)
M,N = A.shape
x0 = np.array([1, 2, 3])
x1 = np.array([[1], [2], [3]])
x2 = np.array([[1, 4], [2, 5], [3, 6]])
assert_equal(A.dot(x0), A_array.dot(x0))
assert_equal(A.dot(x1), A_array.dot(x1))
assert_equal(A.dot(x2), A_array.dot(x2))
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
with warns(RuntimeWarning, match="should implement at least"):
assert_raises(TypeError, Empty)
class Identity(interface.LinearOperator):
def __init__(self, n):
super().__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().__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)
interface.LinearOperator((2, 2), matvec=matvec)
assert_equal(call_count[0], 1)
def test_adjoint_conjugate():
X = np.array([[1j]])
A = interface.aslinearoperator(X)
B = 1j * A
Y = 1j * X
v = np.array([1])
assert_equal(B.dot(v), Y.dot(v))
assert_equal(B.H.dot(v), Y.T.conj().dot(v))
def test_ndim():
X = np.array([[1]])
A = interface.aslinearoperator(X)
assert_equal(A.ndim, 2)
def test_transpose_noconjugate():
X = np.array([[1j]])
A = interface.aslinearoperator(X)
B = 1j * A
Y = 1j * X
v = np.array([1])
assert_equal(B.dot(v), Y.dot(v))
assert_equal(B.T.dot(v), Y.T.dot(v))
def test_sparse_matmat_exception():
A = interface.LinearOperator((2, 2), matvec=lambda x: x)
B = sparse.identity(2)
msg = "Unable to multiply a LinearOperator with a sparse matrix."
with assert_raises(TypeError, match=msg):
A @ B
with assert_raises(TypeError, match=msg):
B @ A
with assert_raises(ValueError):
A @ np.identity(4)
with assert_raises(ValueError):
np.identity(4) @ A