def test_eval(self):
x = np.arange(1, 31) * (1.0 + 1.0j)
x.shape = (10, 3)
y = np.arange(1, 31) * (2.0 - 3.0j)
y.shape = (10, 3)
z = np.arange(1, 31) * (3.0 - 9.0j)
z.shape = (10, 3)
w = np.arange(1, 31) * (4.0 + 2.0j)
w.shape = (10, 3)
x_, y_, z_, w_ = list(map(np.conjugate, (x, y, z, w)))
expressions = [
'x*y+z*w', '2*x_*y_+z*w-1.0j*z*w', '2*x*w', '1.0j*x + y*z',
'-1*x*z+3*y*w*x+y', '2*w_', '2*x_ + 3*y - 4*z'
]
data = {}
for ex in expressions:
data[ex] = eval(ex)
currentSol = {'x': 1.1 * x, 'y': .9 * y, 'z': 1.1 * z, 'w': 1.2 * w}
for i in range(
5
): # reducing iters prevents printing a bunch of "The exact solution is x = 0"
testSolve = linsolve.LinProductSolver(data,
currentSol,
sparse=self.sparse)
currentSol = testSolve.solve()
for var in 'wxyz':
np.testing.assert_almost_equal(currentSol[var], eval(var), 4)
result = testSolve.eval(currentSol)
for eq in data:
np.testing.assert_almost_equal(data[eq], result[eq], 4)
def test_chisq(self):
x = 1.
d = {'x*y': 1, '.5*x*y+.5*x*y': 2, 'y': 1}
currentSol = {'x': 2.3, 'y': .9}
for i in range(
5
): # reducing iters prevents printing a bunch of "The exact solution is x = 0"
testSolve = linsolve.LinProductSolver(d,
currentSol,
sparse=self.sparse)
currentSol = testSolve.solve()
chisq = testSolve.chisq(currentSol)
np.testing.assert_almost_equal(chisq, .5)
def test_real_solve(self):
x, y, z = 1., 2., 3.
keys = ['x*y', 'x*z', 'y*z']
d, w = {}, {}
for k in keys:
d[k], w[k] = eval(k), 1.
sol0 = {}
for k in 'xyz':
sol0[k] = eval(k) + .01
ls = linsolve.LinProductSolver(d, sol0, w, sparse=self.sparse)
sol = ls.solve()
for k in sol:
np.testing.assert_almost_equal(sol[k], eval(k), 4)
def test_init(self):
x,y,z = 1.+1j, 2.+2j, 3.+3j
d,w = {'x*y_':x*y.conjugate(), 'x*z_':x*z.conjugate(), 'y*z_':y*z.conjugate()}, {}
for k in list(d.keys()): w[k] = 1.
sol0 = {}
for k in 'xyz': sol0[k] = eval(k)+.01
ls = linsolve.LinProductSolver(d,sol0,w,sparse=self.sparse)
x,y,z = 1.,1.,1.
x_,y_,z_ = 1.,1.,1.
dx = dy = dz = .001
dx_ = dy_ = dz_ = .001
for k in ls.ls.keys:
self.assertAlmostEqual(eval(k), 0.002)
self.assertEqual(len(ls.ls.prms), 3)
def test_complex_conj_solve(self):
x, y, z = 1. + 1j, 2. + 2j, 3. + 3j
d, w = {
'x*y_': x * y.conjugate(),
'x*z_': x * z.conjugate(),
'y*z_': y * z.conjugate()
}, {}
for k in list(d.keys()):
w[k] = 1.
sol0 = {}
for k in 'xyz':
sol0[k] = eval(k) + .01
ls = linsolve.LinProductSolver(d, sol0, w, sparse=self.sparse)
ls.prm_order = {'x': 0, 'y': 1, 'z': 2}
_, sol = ls.solve_iteratively(mode='lsqr') # XXX fails for pinv
x, y, z = sol['x'], sol['y'], sol['z']
np.testing.assert_almost_equal(x * y.conjugate(), d['x*y_'], 3)
np.testing.assert_almost_equal(x * z.conjugate(), d['x*z_'], 3)
np.testing.assert_almost_equal(y * z.conjugate(), d['y*z_'], 3)
def test_degen_sol(self):
# test how various solvers deal with degenerate solutions
x, y, z = 1. + 1j, 2. + 2j, 3. + 3j
d, w = {
'x*y_': x * y.conjugate(),
'x*z_': x * z.conjugate(),
'y*z_': y * z.conjugate()
}, {}
for k in list(d.keys()):
w[k] = 1.
sol0 = {}
for k in 'xyz':
sol0[k] = eval(k) + .01
ls = linsolve.LinProductSolver(d, sol0, w, sparse=self.sparse)
ls.prm_order = {'x': 0, 'y': 1, 'z': 2}
for mode in ('pinv', 'lsqr'):
_, sol = ls.solve_iteratively(mode=mode)
x, y, z = sol['x'], sol['y'], sol['z']
np.testing.assert_almost_equal(x * y.conjugate(), d['x*y_'], 3)
np.testing.assert_almost_equal(x * z.conjugate(), d['x*z_'], 3)
np.testing.assert_almost_equal(y * z.conjugate(), d['y*z_'], 3)
def test_solve_iteratively_dtype(self):
x = np.arange(1, 31) * (1.0 + 1.0j)
x.shape = (10, 3)
y = np.arange(1, 31) * (2.0 - 3.0j)
y.shape = (10, 3)
z = np.arange(1, 31) * (3.0 - 9.0j)
z.shape = (10, 3)
w = np.arange(1, 31) * (4.0 + 2.0j)
w.shape = (10, 3)
x_, y_, z_, w_ = list(map(np.conjugate, (x, y, z, w)))
expressions = [
'x*y+z*w', '2*x_*y_+z*w-1.0j*z*w', '2*x*w', '1.0j*x + y*z',
'-1*x*z+3*y*w*x+y', '2*w_', '2*x_ + 3*y - 4*z'
]
data = {}
for dtype in (np.complex128, np.complex64):
for ex in expressions:
data[ex] = eval(ex).astype(dtype)
currentSol = {
'x': 1.1 * x,
'y': .9 * y,
'z': 1.1 * z,
'w': 1.2 * w
}
currentSol = {k: v.astype(dtype) for k, v in currentSol.items()}
testSolve = linsolve.LinProductSolver(data,
currentSol,
sparse=self.sparse)
# some ridiculousness to avoid "The exact solution is x = 0" prints
save_stdout = sys.stdout
sys.stdout = io.StringIO()
meta, new_sol = testSolve.solve_iteratively(conv_crit=1e-7)
sys.stdout = save_stdout
for var in 'wxyz':
assert new_sol[var].dtype == dtype
np.testing.assert_almost_equal(new_sol[var], eval(var), 4)
