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"""Test functions for the sparse.linalg.interface module
"""
from __future__ import division, print_function, absolute_import
from numpy.testing import TestCase, assert_, assert_equal, \
assert_raises
import numpy as np
import scipy.sparse as sparse
from itertools import product
from scipy.sparse.linalg import interface
class TestLinearOperator(TestCase):
def setUp(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(np.matrix([[1],[2],[3]])), [[14],[32]])
assert_equal(A * np.matrix([[1],[2],[3]]), [[14],[32]])
assert_equal(A.dot(np.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)*[[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)*[[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(np.array([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(np.matrix([[1],[2],[3]])), np.ndarray))
assert_(isinstance(A * np.matrix([[1],[2],[3]]), np.ndarray))
assert_(isinstance(A.dot(np.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_(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).matmat([[1],[1]]), [[17],[37]])
assert_(isinstance(C**2, interface._PowerLinearOperator))
class TestAsLinearOperator(TestCase):
def setUp(self):
self.cases = []
def make_cases(dtype):
self.cases.append(np.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))
class matlike:
def __init__(self, dtype):
self.dtype = np.dtype(dtype)
self.shape = (2,3)
def matvec(self,x):
y = np.array([1*x[0] + 2*x[1] + 3*x[2],
4*x[0] + 5*x[1] + 6*x[2]], dtype=self.dtype)
if len(x.shape) == 2:
y = y.reshape(-1,1)
return y
def rmatvec(self,x):
return np.array([1*x[0] + 4*x[1],
2*x[0] + 5*x[1],
3*x[0] + 6*x[1]], dtype=self.dtype)
self.cases.append(matlike('int'))
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.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]])
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