def test_integral(self):
x = [1,1,1,2,2,2,4,4,4]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
with suppress_warnings() as sup:
# This seems to fail (ier=1, see ticket 1642).
sup.filter(UserWarning, "\nThe required storage space")
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
tx = [1,2,4]
ty = [1,2,3]
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_integral(self):
x = [1,1,1,2,2,2,4,4,4]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
warn_ctx = WarningManager()
warn_ctx.__enter__()
try:
# This seems to fail (ier=1, see ticket 1642).
warnings.simplefilter('ignore', UserWarning)
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
finally:
warn_ctx.__exit__()
tx = [1,2,4]
ty = [1,2,3]
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_integral(self):
x = [1, 1, 1, 2, 2, 2, 4, 4, 4]
y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
z = array([0, 7, 8, 3, 4, 7, 1, 3, 4])
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
tx = [1, 2, 4]
ty = [1, 2, 3]
tz = lut(tx, ty)
trpz = (
0.25
* (diff(tx)[:, None] * diff(ty)[None, :] * (tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])).sum()
)
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(
lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz, decimal=0
) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = (
0.25
* (
diff(tx[:-1])[:, None]
* diff(ty[:-1])[None, :]
* (tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])
).sum()
)
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_linear_1d(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [0,0,0,2,2,2,4,4,4]
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]])
def test_linear_1d(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [0,0,0,2,2,2,4,4,4]
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]])
def test_array_like_input(self):
x = np.array([1, 1, 1, 2, 2, 2, 3, 3, 3])
y = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3])
z = np.array([3, 3, 3, 3, 3, 3, 3, 3, 3])
w = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1])
bbox = np.array([1.0, 3.0, 1.0, 3.0])
# np.array input
spl1 = SmoothBivariateSpline(x, y, z, w=w, bbox=bbox, kx=1, ky=1)
# list input
spl2 = SmoothBivariateSpline(x.tolist(), y.tolist(), z.tolist(),
bbox=bbox.tolist(), w=w.tolist(),
kx=1, ky=1)
assert_allclose(spl1(0.1, 0.5), spl2(0.1, 0.5))
def test_integral(self):
x = [1, 1, 1, 2, 2, 2, 4, 4, 4]
y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
z = array([0, 7, 8, 3, 4, 7, 1, 3, 4])
with suppress_warnings() as sup:
# This seems to fail (ier=1, see ticket 1642).
sup.filter(UserWarning, "\nThe required storage space")
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
tx = [1, 2, 4]
ty = [1, 2, 3]
tz = lut(tx, ty)
trpz = .25 * (
diff(tx)[:, None] * diff(ty)[None, :] *
(tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]),
trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25 * (
diff(tx[:-1])[:, None] * diff(ty[:-1])[None, :] *
(tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_integral(self):
x = [1,1,1,2,2,2,4,4,4]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
warn_ctx = WarningManager()
warn_ctx.__enter__()
try:
# This seems to fail (ier=1, see ticket 1642).
warnings.simplefilter('ignore', UserWarning)
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
finally:
warn_ctx.__exit__()
tx = [1,2,4]
ty = [1,2,3]
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_integral(self):
x = [1, 1, 1, 2, 2, 2, 4, 4, 4]
y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
z = array([0, 7, 8, 3, 4, 7, 1, 3, 4])
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
tx = [1, 2, 4]
ty = [1, 2, 3]
tz = lut(tx, ty)
trpz = .25 * (
diff(tx)[:, None] * diff(ty)[None, :] *
(tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]),
trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25 * (
diff(tx[:-1])[:, None] * diff(ty[:-1])[None, :] *
(tz[:-1, :-1] + tz[1:, :-1] + tz[:-1, 1:] + tz[1:, 1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
def test_rerun_lwrk2_too_small(self):
# in this setting, lwrk2 is too small in the default run. Here we
# check for equality with the bisplrep/bisplev output because there,
# an automatic re-run of the spline representation is done if ier>10.
x = np.linspace(-2, 2, 80)
y = np.linspace(-2, 2, 80)
z = x + y
xi = np.linspace(-1, 1, 100)
yi = np.linspace(-2, 2, 100)
tck = bisplrep(x, y, z)
res1 = bisplev(xi, yi, tck)
interp_ = SmoothBivariateSpline(x, y, z)
res2 = interp_(xi, yi)
assert_almost_equal(res1, res2)
def test_invalid_input(self):
with assert_raises(ValueError) as info:
x = np.linspace(1.0, 10.0)
y = np.linspace(1.0, 10.0)
z = np.linspace(1.0, 10.0, num=10)
SmoothBivariateSpline(x, y, z)
assert "x, y, and z should have a same length" in str(info.value)
with assert_raises(ValueError) as info:
x = np.linspace(1.0, 10.0)
y = np.linspace(1.0, 10.0)
z = np.linspace(1.0, 10.0)
w = np.linspace(1.0, 10.0, num=20)
SmoothBivariateSpline(x, y, z, w=w)
assert "x, y, z, and w should have a same length" in str(info.value)
with assert_raises(ValueError) as info:
w = np.linspace(-1.0, 10.0)
SmoothBivariateSpline(x, y, z, w=w)
assert "w should be positive" in str(info.value)
with assert_raises(ValueError) as info:
bbox = (-100, 100, -100)
SmoothBivariateSpline(x, y, z, bbox=bbox)
assert "bbox shape should be (4,)" in str(info.value)
with assert_raises(ValueError) as info:
SmoothBivariateSpline(x, y, z, kx=10, ky=10)
assert "The length of x, y and z should be at least (kx+1) * (ky+1)" in\
str(info.value)
with assert_raises(ValueError) as info:
SmoothBivariateSpline(x, y, z, s=-1.0)
assert "s should be s >= 0.0" in str(info.value)
with assert_raises(ValueError) as exc_info:
SmoothBivariateSpline(x, y, z, eps=0.0)
assert "eps should be between (0, 1)" in str(exc_info.value)
with assert_raises(ValueError) as exc_info:
SmoothBivariateSpline(x, y, z, eps=1.0)
assert "eps should be between (0, 1)" in str(exc_info.value)
