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451 lines
16 KiB
Python
451 lines
16 KiB
Python
4 years ago
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"""Test functions for the sparse.linalg.interface module
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"""
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from functools import partial
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from itertools import product
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import operator
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import pytest
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from pytest import raises as assert_raises, warns
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from numpy.testing import assert_, assert_equal
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import numpy as np
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import scipy.sparse as sparse
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from scipy.sparse.linalg import interface
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from scipy.sparse.sputils import matrix
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class TestLinearOperator(object):
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def setup_method(self):
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self.A = np.array([[1,2,3],
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[4,5,6]])
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self.B = np.array([[1,2],
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[3,4],
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[5,6]])
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self.C = np.array([[1,2],
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[3,4]])
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def test_matvec(self):
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def get_matvecs(A):
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return [{
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'shape': A.shape,
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'matvec': lambda x: np.dot(A, x).reshape(A.shape[0]),
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'rmatvec': lambda x: np.dot(A.T.conj(),
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x).reshape(A.shape[1])
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},
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{
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'shape': A.shape,
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'matvec': lambda x: np.dot(A, x),
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'rmatvec': lambda x: np.dot(A.T.conj(), x),
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'rmatmat': lambda x: np.dot(A.T.conj(), x),
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'matmat': lambda x: np.dot(A, x)
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}]
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for matvecs in get_matvecs(self.A):
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A = interface.LinearOperator(**matvecs)
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assert_(A.args == ())
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assert_equal(A.matvec(np.array([1,2,3])), [14,32])
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assert_equal(A.matvec(np.array([[1],[2],[3]])), [[14],[32]])
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assert_equal(A * np.array([1,2,3]), [14,32])
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assert_equal(A * np.array([[1],[2],[3]]), [[14],[32]])
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assert_equal(A.dot(np.array([1,2,3])), [14,32])
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assert_equal(A.dot(np.array([[1],[2],[3]])), [[14],[32]])
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assert_equal(A.matvec(matrix([[1],[2],[3]])), [[14],[32]])
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assert_equal(A * matrix([[1],[2],[3]]), [[14],[32]])
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assert_equal(A.dot(matrix([[1],[2],[3]])), [[14],[32]])
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assert_equal((2*A)*[1,1,1], [12,30])
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assert_equal((2 * A).rmatvec([1, 1]), [10, 14, 18])
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assert_equal((2*A).H.matvec([1,1]), [10, 14, 18])
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assert_equal((2*A)*[[1],[1],[1]], [[12],[30]])
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assert_equal((2 * A).matmat([[1], [1], [1]]), [[12], [30]])
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assert_equal((A*2)*[1,1,1], [12,30])
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assert_equal((A*2)*[[1],[1],[1]], [[12],[30]])
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assert_equal((2j*A)*[1,1,1], [12j,30j])
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assert_equal((A+A)*[1,1,1], [12, 30])
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assert_equal((A + A).rmatvec([1, 1]), [10, 14, 18])
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assert_equal((A+A).H.matvec([1,1]), [10, 14, 18])
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assert_equal((A+A)*[[1],[1],[1]], [[12], [30]])
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assert_equal((A+A).matmat([[1],[1],[1]]), [[12], [30]])
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assert_equal((-A)*[1,1,1], [-6,-15])
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assert_equal((-A)*[[1],[1],[1]], [[-6],[-15]])
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assert_equal((A-A)*[1,1,1], [0,0])
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assert_equal((A - A) * [[1], [1], [1]], [[0], [0]])
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X = np.array([[1, 2], [3, 4]])
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# A_asarray = np.array([[1, 2, 3], [4, 5, 6]])
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assert_equal((2 * A).rmatmat(X), np.dot((2 * self.A).T, X))
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assert_equal((A * 2).rmatmat(X), np.dot((self.A * 2).T, X))
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assert_equal((2j * A).rmatmat(X),
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np.dot((2j * self.A).T.conj(), X))
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assert_equal((A * 2j).rmatmat(X),
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np.dot((self.A * 2j).T.conj(), X))
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assert_equal((A + A).rmatmat(X),
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np.dot((self.A + self.A).T, X))
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assert_equal((A + 2j * A).rmatmat(X),
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np.dot((self.A + 2j * self.A).T.conj(), X))
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assert_equal((-A).rmatmat(X), np.dot((-self.A).T, X))
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assert_equal((A - A).rmatmat(X),
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np.dot((self.A - self.A).T, X))
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assert_equal((2j * A).rmatmat(2j * X),
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np.dot((2j * self.A).T.conj(), 2j * X))
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z = A+A
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assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is A)
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z = 2*A
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assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] == 2)
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assert_(isinstance(A.matvec([1, 2, 3]), np.ndarray))
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assert_(isinstance(A.matvec(np.array([[1],[2],[3]])), np.ndarray))
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assert_(isinstance(A * np.array([1,2,3]), np.ndarray))
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assert_(isinstance(A * np.array([[1],[2],[3]]), np.ndarray))
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assert_(isinstance(A.dot(np.array([1,2,3])), np.ndarray))
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assert_(isinstance(A.dot(np.array([[1],[2],[3]])), np.ndarray))
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assert_(isinstance(A.matvec(matrix([[1],[2],[3]])), np.ndarray))
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assert_(isinstance(A * matrix([[1],[2],[3]]), np.ndarray))
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assert_(isinstance(A.dot(matrix([[1],[2],[3]])), np.ndarray))
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assert_(isinstance(2*A, interface._ScaledLinearOperator))
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assert_(isinstance(2j*A, interface._ScaledLinearOperator))
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assert_(isinstance(A+A, interface._SumLinearOperator))
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assert_(isinstance(-A, interface._ScaledLinearOperator))
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assert_(isinstance(A-A, interface._SumLinearOperator))
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assert_((2j*A).dtype == np.complex_)
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assert_raises(ValueError, A.matvec, np.array([1,2]))
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assert_raises(ValueError, A.matvec, np.array([1,2,3,4]))
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assert_raises(ValueError, A.matvec, np.array([[1],[2]]))
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assert_raises(ValueError, A.matvec, np.array([[1],[2],[3],[4]]))
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assert_raises(ValueError, lambda: A*A)
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assert_raises(ValueError, lambda: A**2)
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for matvecsA, matvecsB in product(get_matvecs(self.A),
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get_matvecs(self.B)):
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A = interface.LinearOperator(**matvecsA)
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B = interface.LinearOperator(**matvecsB)
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# AtimesB = np.array([[22, 28], [49, 64]])
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AtimesB = self.A.dot(self.B)
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X = np.array([[1, 2], [3, 4]])
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assert_equal((A * B).rmatmat(X), np.dot((AtimesB).T, X))
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assert_equal((2j * A * B).rmatmat(X),
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np.dot((2j * AtimesB).T.conj(), X))
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assert_equal((A*B)*[1,1], [50,113])
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assert_equal((A*B)*[[1],[1]], [[50],[113]])
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assert_equal((A*B).matmat([[1],[1]]), [[50],[113]])
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assert_equal((A * B).rmatvec([1, 1]), [71, 92])
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assert_equal((A * B).H.matvec([1, 1]), [71, 92])
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assert_(isinstance(A*B, interface._ProductLinearOperator))
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assert_raises(ValueError, lambda: A+B)
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assert_raises(ValueError, lambda: A**2)
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z = A*B
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assert_(len(z.args) == 2 and z.args[0] is A and z.args[1] is B)
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for matvecsC in get_matvecs(self.C):
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C = interface.LinearOperator(**matvecsC)
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X = np.array([[1, 2], [3, 4]])
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assert_equal(C.rmatmat(X), np.dot((self.C).T, X))
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assert_equal((C**2).rmatmat(X),
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np.dot((np.dot(self.C, self.C)).T, X))
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assert_equal((C**2)*[1,1], [17,37])
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assert_equal((C**2).rmatvec([1, 1]), [22, 32])
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assert_equal((C**2).H.matvec([1, 1]), [22, 32])
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assert_equal((C**2).matmat([[1],[1]]), [[17],[37]])
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assert_(isinstance(C**2, interface._PowerLinearOperator))
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def test_matmul(self):
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D = {'shape': self.A.shape,
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'matvec': lambda x: np.dot(self.A, x).reshape(self.A.shape[0]),
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'rmatvec': lambda x: np.dot(self.A.T.conj(),
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x).reshape(self.A.shape[1]),
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'rmatmat': lambda x: np.dot(self.A.T.conj(), x),
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'matmat': lambda x: np.dot(self.A, x)}
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A = interface.LinearOperator(**D)
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B = np.array([[1, 2, 3],
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[4, 5, 6],
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[7, 8, 9]])
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b = B[0]
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assert_equal(operator.matmul(A, b), A * b)
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assert_equal(operator.matmul(A, B), A * B)
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assert_raises(ValueError, operator.matmul, A, 2)
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assert_raises(ValueError, operator.matmul, 2, A)
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class TestAsLinearOperator(object):
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def setup_method(self):
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self.cases = []
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def make_cases(original, dtype):
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cases = []
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cases.append((matrix(original, dtype=dtype), original))
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cases.append((np.array(original, dtype=dtype), original))
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cases.append((sparse.csr_matrix(original, dtype=dtype), original))
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# Test default implementations of _adjoint and _rmatvec, which
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# refer to each other.
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def mv(x, dtype):
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y = original.dot(x)
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if len(x.shape) == 2:
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y = y.reshape(-1, 1)
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return y
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def rmv(x, dtype):
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return original.T.conj().dot(x)
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class BaseMatlike(interface.LinearOperator):
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args = ()
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def __init__(self, dtype):
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self.dtype = np.dtype(dtype)
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self.shape = original.shape
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def _matvec(self, x):
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return mv(x, self.dtype)
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class HasRmatvec(BaseMatlike):
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args = ()
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def _rmatvec(self,x):
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return rmv(x, self.dtype)
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class HasAdjoint(BaseMatlike):
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args = ()
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def _adjoint(self):
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shape = self.shape[1], self.shape[0]
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matvec = partial(rmv, dtype=self.dtype)
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rmatvec = partial(mv, dtype=self.dtype)
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return interface.LinearOperator(matvec=matvec,
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rmatvec=rmatvec,
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dtype=self.dtype,
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shape=shape)
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class HasRmatmat(HasRmatvec):
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def _matmat(self, x):
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return original.dot(x)
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def _rmatmat(self, x):
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return original.T.conj().dot(x)
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cases.append((HasRmatvec(dtype), original))
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cases.append((HasAdjoint(dtype), original))
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cases.append((HasRmatmat(dtype), original))
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return cases
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original = np.array([[1,2,3], [4,5,6]])
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self.cases += make_cases(original, np.int32)
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self.cases += make_cases(original, np.float32)
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self.cases += make_cases(original, np.float64)
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self.cases += [(interface.aslinearoperator(M).T, A.T)
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for M, A in make_cases(original.T, np.float64)]
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self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
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for M, A in make_cases(original.T, np.float64)]
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original = np.array([[1, 2j, 3j], [4j, 5j, 6]])
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self.cases += make_cases(original, np.complex_)
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self.cases += [(interface.aslinearoperator(M).T, A.T)
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for M, A in make_cases(original.T, np.complex_)]
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self.cases += [(interface.aslinearoperator(M).H, A.T.conj())
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for M, A in make_cases(original.T, np.complex_)]
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def test_basic(self):
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for M, A_array in self.cases:
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A = interface.aslinearoperator(M)
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M,N = A.shape
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xs = [np.array([1, 2, 3]),
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np.array([[1], [2], [3]])]
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ys = [np.array([1, 2]), np.array([[1], [2]])]
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if A.dtype == np.complex_:
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xs += [np.array([1, 2j, 3j]),
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np.array([[1], [2j], [3j]])]
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ys += [np.array([1, 2j]), np.array([[1], [2j]])]
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x2 = np.array([[1, 4], [2, 5], [3, 6]])
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for x in xs:
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assert_equal(A.matvec(x), A_array.dot(x))
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assert_equal(A * x, A_array.dot(x))
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assert_equal(A.matmat(x2), A_array.dot(x2))
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assert_equal(A * x2, A_array.dot(x2))
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for y in ys:
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assert_equal(A.rmatvec(y), A_array.T.conj().dot(y))
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assert_equal(A.T.matvec(y), A_array.T.dot(y))
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assert_equal(A.H.matvec(y), A_array.T.conj().dot(y))
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for y in ys:
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if y.ndim < 2:
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continue
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assert_equal(A.rmatmat(y), A_array.T.conj().dot(y))
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assert_equal(A.T.matmat(y), A_array.T.dot(y))
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assert_equal(A.H.matmat(y), A_array.T.conj().dot(y))
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if hasattr(M,'dtype'):
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assert_equal(A.dtype, M.dtype)
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assert_(hasattr(A, 'args'))
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def test_dot(self):
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for M, A_array in self.cases:
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A = interface.aslinearoperator(M)
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M,N = A.shape
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x0 = np.array([1, 2, 3])
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x1 = np.array([[1], [2], [3]])
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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(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)
|
||
|
|
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))
|