def test_copy(self):
d = 3
n = np.array([5, 7, 8])
l = np.array([[-2., 3.], [-4., 5.], [-6., 9.]])
GR1 = Grid(d=d, n=n, l=l)
GR2 = GR1.copy()
GR2.d = 1
GR2.n = np.array([5])
GR2.l = np.array([[-2., 3.]])
self.assertEqual(
GR1.d, 3
)
np.testing.assert_array_equal(
GR1.n, np.array([5, 7, 8])
)
np.testing.assert_almost_equal(
GR1.l, np.array([[-2., 3.], [-4., 5.], [-6., 9.]])
)
self.assertEqual(
GR2.d, 1
)
np.testing.assert_array_equal(
GR2.n, np.array([5])
)
np.testing.assert_almost_equal(
GR2.l, np.array([[-2., 3.]])
)
def test_indm(self):
GR = Grid(n=[5, 7, 8])
np.testing.assert_equal(GR.indm(0), np.array([0, 0, 0]))
np.testing.assert_equal(GR.indm(1), np.array([1, 0, 0]))
np.testing.assert_equal(GR.indm(5), np.array([0, 1, 0]))
np.testing.assert_equal(GR.indm(279), np.array([4, 6, 7]))
def test_indf(self):
GR = Grid(n=[5, 7, 8])
self.assertEqual(GR.indf([0, 0, 0]), 0)
self.assertEqual(GR.indf([1, 0, 0]), 1)
self.assertEqual(GR.indf([0, 1, 0]), 5)
self.assertEqual(GR.indf([4, 6, 7]), 279)
def test_comp_c(self):
GR = Grid(n=[5, 7], l=[
[-4., 3.],
[-1., 2.],
], k='c')
X = GR.comp([0, 0])
np.testing.assert_almost_equal(
X, np.array([[3.], [2.]])
)
X = GR.comp([4, 6])
np.testing.assert_almost_equal(
X, np.array([[-4.], [-1.]])
)
X = GR.comp([
[0, 4],
[0, 6],
])
np.testing.assert_almost_equal(
X, np.array([
[3., -4.],
[2., -1.],
])
)
def test_info(self):
GR = Grid(n=[5, 7], l=[[-4., 3.], [-1., 2.]])
s = GR.info(is_ret=True)
self.assertTrue('Kind : Chebyshev' in s)
self.assertTrue('Dimensions : 2' in s)
self.assertTrue('Poi 5 | Min -4.000 | Max 3.000 |' in s)
self.assertTrue('Poi 7 | Min -1.000 | Max 2.000 |' in s)
def test_copy_err(self):
d = 2
n1 = np.array([3, 4])
l1 = np.array([[-2, 4], [-5, 7]])
GR1 = Grid(d, n1, l1, 'u')
msg = 'Invalid dimension for number of points (n).'
with self.assertRaises(IndexError) as ctx:
GR2 = GR1.copy(d=1)
self.assertIn(msg, str(ctx.exception))
def test_init_kind(self):
d = 2
n = np.array([3, 4])
l = np.array([[-2, 4], [-5, 7]])
GR = Grid(d, n, l, 'u')
self.assertEqual(GR.k, 'u')
GR = Grid(d, n, l, 'c')
self.assertEqual(GR.k, 'c')
self.assertRaises(ValueError, lambda: Grid(d, n, l, 'xxx'))
def test_fpe_1d_oup(self):
MD = Model.select('fpe_1d_oup')
MD.init(s=1., D=0.5, A=1.)
SL = Solver(TG=Grid(d=1, n=1000, l=[+0., +8.], k='u'),
SG=Grid(d=1, n=101, l=[-6., +6.], k='c'),
MD=MD)
SL.init()
SL.prep()
SL.calc(dsbl_print=True)
self.assertTrue(SL.hst['err_real'][-1] < 9.29e-06)
self.assertTrue(SL.hst['err_stat'][-1] < 9.34e-06)
def test_fpe_3d_drift_zero_tt(self):
return # TODO: Remove.
MD = Model.select('fpe_3d_drift_zero')
MD.init(s=1., D=0.5)
SL = Solver(TG=Grid(d=1, n=10, l=[+0., +1.], k='u'),
SG=Grid(d=3, n=21, l=[-5., +5.], k='c'),
MD=MD,
eps=1.E-2,
with_tt=True)
SL.init()
SL.prep()
SL.calc(dsbl_print=True)
self.assertTrue(SL.hst['err_real'][-1] < 4.48e-03)
def test_copy(self):
d = 2
n1 = np.array([3, 4])
l1 = np.array([[-2, 4], [-5, 7]])
n2 = [4, 5]
l2 = np.array([[-3, 5], [-6, 8]])
GR1 = Grid(d, n1, l1, 'u')
GR2 = GR1.copy(n=n2, l=l2)
np.testing.assert_array_equal(GR1.n, n1)
np.testing.assert_array_equal(GR2.n, n2)
np.testing.assert_array_equal(GR1.l, l1)
np.testing.assert_array_equal(GR2.l, l2)
def test_int_3d_tt(self):
return # DRAFT
GR = Grid(n=[35, 35, 35], l=[-10., 10.])
FN = Func(GR, eps=1.E-6, with_tt=True)
FN.init(lambda X: func_for_int(X, 3)).prep().calc()
e = np.abs(1. - FN.comp_int()) / np.abs(1.)
self.assertTrue(e < 6.0E-7)
def test_init4(self):
n = np.array([3])
l = np.array([[-2, 4]])
GR = Grid(n=n, l=l)
self.assertEqual(GR.d, 1)
np.testing.assert_array_equal(GR.n, np.array([3]))
np.testing.assert_almost_equal(GR.l, np.array([[-2., 4.]]))
def test_2ord_elements(self):
N = 5
SG = Grid(d=1, n=N + 1, l=[-1., 1.])
D1, D2 = difs(SG, 2)
e = D1 @ D1 - D2
self.assertTrue(np.max(np.abs(e)) < 1.E-13)
def test_2d_tt(self):
GR = Grid(d=2, n=[28, 30], l=[
[-3., 4.],
[-2., 3.],
])
FN = Func(GR, with_tt=True).init(func_2d).prep().calc()
self.assertTrue(np.max(FN.test(1000, is_u=True)) < 8.0E-2)
def test_init3(self):
n = 3
l = np.array([[-2, 4], [-5, 7]])
GR = Grid(n=n, l=l)
self.assertEqual(GR.d, 2)
np.testing.assert_array_equal(GR.n, np.array([3, 3]))
np.testing.assert_almost_equal(GR.l, np.array([[-2., 4.], [-5., 7.]]))
def test_init2(self):
n = [3, 4]
l = np.array([-2, 4])
GR = Grid(n=n, l=l)
self.assertEqual(GR.d, 2)
np.testing.assert_array_equal(GR.n, np.array([3, 4]))
np.testing.assert_almost_equal(GR.l, np.array([[-2., 4.], [-2., 4.]]))
def test_1d_ivp(self):
TG = Grid(1, 2, [0., 0.0001], k='u')
r0 = -2.5 * np.arange(1000).reshape(1, -1) + 0.2
r_real = func_rt_1d(TG.l2, r0)
SL = OrdSolver(TG, 'ivp').init(func_f0_1d, with_y0=True)
e = np.mean(np.abs((r_real - SL.comp(r0)) / r_real))
self.assertTrue(e < 2.E-06)
def test_init1(self):
d = 2
n = 3
l = [-2, 4]
GR = Grid(d=d, n=n, l=l)
self.assertEqual(GR.d, 2)
np.testing.assert_array_equal(GR.n, np.array([3, 3]))
np.testing.assert_almost_equal(GR.l, np.array([[-2., 4.], [-2., 4.]]))
def test_3d_tt(self):
GR = Grid(d=3, n=[24, 26, 28], l=[
[-3., 4.],
[-2., 3.],
[-1., 1.],
])
FN = Func(GR, with_tt=True).init(func_3d).prep().calc()
self.assertTrue(np.max(FN.test(1000, is_u=True)) < 5.0E-2)
def test_1ord_elements(self):
N = 5
SG = Grid(d=1, n=N + 1, l=[-1., 1.])
X = SG.comp()[0, :]
D = dif1(SG)
e = D[0, 0] - (2. * N**2 + 1.) / 6.
self.assertTrue(np.max(np.abs(e)) < 1.E-14)
e = D[0, 2] - 2. / (1. - X[2])
self.assertTrue(np.max(np.abs(e)) < 1.E-14)
e = D[0, 3] + 2. / (1. - X[3])
self.assertTrue(np.max(np.abs(e)) < 1.E-14)
e = D[4, 4] + X[4] / (1. - X[4]**2) / 2.
self.assertTrue(np.max(np.abs(e)) < 1.E-14)
def test_init7(self):
d = 1
n = [3, 4]
l = np.array([[-2, 4]])
msg = 'Invalid dimension for number of points (n).'
with self.assertRaises(IndexError) as ctx:
GR = Grid(d=d, n=n, l=l)
self.assertIn(msg, str(ctx.exception))
def test_init6(self):
d = -2
n = np.array([3])
l = np.array([[-2, 4]])
msg = 'Invalid number of dimensions (d).'
with self.assertRaises(ValueError) as ctx:
GR = Grid(d=d, n=n, l=l)
self.assertIn(msg, str(ctx.exception))
def test_2d_eul(self):
TG = Grid(1, 2, [0., 0.001], k='u')
r0 = np.vstack([
np.arange(100) * 1.1 + 0.2,
np.arange(100) * 1.5 + 0.3,
])
r_real = func_rt_2d(TG.l2, r0)
SL = OrdSolver(TG, 'eul').init(func_f0_2d, with_y0=True)
e = np.mean(np.abs((r_real - SL.comp(r0)) / r_real))
self.assertTrue(e < 1.E-07)
def test_4d_tt(self):
GR = Grid(d=4,
n=[30, 31, 32, 33],
l=[
[-3., 4.],
[-2., 3.],
[-1., 1.],
[-1., 3.],
])
FN = Func(GR, with_tt=True).init(func_4d).prep().calc()
self.assertTrue(np.max(FN.test(1000, is_u=True)) < 9.0E-09)
def test_mean(self):
n = np.array([8, 10])
l = np.array([
[-4., 3.],
[-2., 5.],
])
GR = Grid(2, n, l)
np.testing.assert_equal(GR.n0, 9)
np.testing.assert_almost_equal(GR.l1, -3.)
np.testing.assert_almost_equal(GR.l2, +4.)
np.testing.assert_equal(GR.h0, 0.5 * (7./7. + 7./9.))
def test_init(self):
d = 3
n = np.array([5, 7, 8])
l = np.array([[-2., 3.], [-4., 5.], [-6., 9.]])
GR = Grid(d=d, n=n, l=l)
self.assertEqual(
GR.d, 3
)
np.testing.assert_array_equal(
GR.n, np.array([5, 7, 8])
)
np.testing.assert_almost_equal(
GR.l, np.array([[-2., 3.], [-4., 5.], [-6., 9.]])
)
def test_pars(self):
d = 1
n = [11]
l = [[-4., 6.]]
k = 'u'
e = 1.E-10
GR = Grid(d, n, l, k, e)
np.testing.assert_equal(GR.d, d)
np.testing.assert_array_equal(GR.n, np.array(n))
np.testing.assert_array_equal(GR.l, np.array(l))
self.assertEqual(GR.k, k)
self.assertEqual(GR.e, e)
np.testing.assert_array_equal(GR.h, [1.])
self.assertEqual(GR.n0, +11)
self.assertEqual(GR.l1, -4.)
self.assertEqual(GR.l2, +6.)
self.assertEqual(GR.h0, +1.)
def test_pars(self):
d = 2
n = [11, 5]
l = [[-4., 6.], [2., 4.]]
k = 'u'
e = 1.E-10
GR = Grid(d, n, l, k, e)
self.assertEqual(GR.d, d)
np.testing.assert_array_equal(GR.n, n)
np.testing.assert_array_equal(GR.l, np.array(l))
self.assertEqual(GR.k, k)
self.assertEqual(GR.e, e)
np.testing.assert_array_equal(GR.h, [1., 0.5])
np.testing.assert_array_equal(GR.n0, 8)
self.assertEqual(GR.l1, -1.)
self.assertEqual(GR.l2, +5.)
self.assertEqual(GR.h0, +0.75)
def test_pars(self):
d = 3
n = [8, 7, 11]
l = [[-4., 3.], [-1., 2.], [-5., 5.]]
k = 'u'
e = 1.E-10
GR = Grid(d, n, l, k, e)
self.assertEqual(GR.d, d)
np.testing.assert_array_equal(GR.n, n)
np.testing.assert_array_equal(GR.l, np.array(l))
self.assertEqual(GR.k, k)
self.assertEqual(GR.e, e)
np.testing.assert_array_equal(GR.h, [1., 0.5, 1. ])
self.assertEqual(GR.n0, 9)
self.assertEqual(GR.l1, -3.3333333333333335)
self.assertEqual(GR.l2, +3.3333333333333335)
self.assertEqual(GR.h0, +2.5 / 3)
def test_is_sym_zero(self):
self.assertTrue(Grid(n=5, l=[[-3., 3.]], k='u').is_sym_zero())
self.assertFalse(Grid(n=5, l=[[-4., 3.]], k='u').is_sym_zero())
self.assertFalse(Grid(n=5, l=[[1., 3.]], k='u').is_sym_zero())