def test_raise(self):
with self.assertRaises(ValueError):
array = np.ones(5)
util.array2image(array)
with self.assertRaises(ValueError):
array = np.ones((2, 2))
util.array2cube(array, 2, 2)
with self.assertRaises(ValueError):
x, y = np.ones(6), np.ones(6)
util.get_axes(x, y)
with self.assertRaises(ValueError):
util.selectBest(array=np.ones(6),
criteria=np.ones(5),
numSelect=1,
highest=True)
with self.assertRaises(ValueError):
util.select_best(array=np.ones(6),
criteria=np.ones(5),
num_select=1,
highest=True)
with self.assertRaises(ValueError):
util.convert_bool_list(n=2, k=[3, 7])
with self.assertRaises(ValueError):
util.convert_bool_list(n=3, k=[True, True])
with self.assertRaises(ValueError):
util.convert_bool_list(n=2, k=[0.1, True])
def test_raise(self):
with self.assertRaises(ValueError):
array = np.ones(5)
util.array2image(array)
with self.assertRaises(ValueError):
x, y = np.ones(6), np.ones(6)
util.get_axes(x, y)
with self.assertRaises(ValueError):
util.selectBest(array=np.ones(6), criteria=np.ones(5), numSelect=1, highest=True)
def test_get_axes():
numPix = 11
deltapix = 0.1
x_grid, y_grid = Util.make_grid(numPix, deltapix)
x_axes, y_axes = Util.get_axes(x_grid, y_grid)
assert x_axes[0] == -0.5
assert y_axes[0] == -0.5
assert x_axes[1] == -0.4
assert y_axes[1] == -0.4
x_grid += 1
x_axes, y_axes = Util.get_axes(x_grid, y_grid)
assert x_axes[0] == 0.5
assert y_axes[0] == -0.5
def test_get_axes():
numPix = 11
deltapix = 0.1
x_grid, y_grid = util.make_grid(numPix, deltapix)
x_axes, y_axes = util.get_axes(x_grid, y_grid)
npt.assert_almost_equal(x_axes[0], -0.5, decimal=12)
npt.assert_almost_equal(y_axes[0], -0.5, decimal=12)
npt.assert_almost_equal(x_axes[1], -0.4, decimal=12)
npt.assert_almost_equal(y_axes[1], -0.4, decimal=12)
x_grid += 1
x_axes, y_axes = util.get_axes(x_grid, y_grid)
npt.assert_almost_equal(x_axes[0], 0.5, decimal=12)
npt.assert_almost_equal(y_axes[0], -0.5, decimal=12)
def test_do_interpol(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
f_xx_sis, f_yy_sis, f_xy_sis = sis.hessian(x_grid_interp,
y_grid_interp, **kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
interp_func = Interpol_func()
interp_func_loop = Interpol_func(grid=False)
interp_func.do_interp(x_axes, y_axes, util.array2image(f_sis),
util.array2image(f_x_sis),
util.array2image(f_y_sis),
util.array2image(f_xx_sis),
util.array2image(f_yy_sis),
util.array2image(f_xy_sis))
interp_func_loop.do_interp(x_axes, y_axes, util.array2image(f_sis),
util.array2image(f_x_sis),
util.array2image(f_y_sis),
util.array2image(f_xx_sis),
util.array2image(f_yy_sis),
util.array2image(f_xy_sis))
# test derivatives
assert interp_func.derivatives(1, 0) == sis.derivatives(
1, 0, **kwargs_SIS)
assert interp_func.derivatives(1, 0) == interp_func_loop.derivatives(
1, 0)
alpha1_interp, alpha2_interp = interp_func.derivatives(
np.array([0, 1, 0, 1]), np.array([1, 1, 2, 2]))
alpha1_interp_loop, alpha2_interp_loop = interp_func_loop.derivatives(
np.array([0, 1, 0, 1]), np.array([1, 1, 2, 2]))
alpha1_true, alpha2_true = sis.derivatives(np.array([0, 1, 0, 1]),
np.array([1, 1, 2, 2]),
**kwargs_SIS)
assert alpha1_interp[0] == alpha1_true[0]
assert alpha1_interp[1] == alpha1_true[1]
assert alpha1_interp[0] == alpha1_interp_loop[0]
assert alpha1_interp[1] == alpha1_interp_loop[1]
# test hessian
assert interp_func.hessian(1, 0) == sis.hessian(1, 0, **kwargs_SIS)
f_xx_interp, f_yy_interp, f_xy_interp = interp_func.hessian(
np.array([0, 1, 0, 1]), np.array([1, 1, 2, 2]))
f_xx_interp_loop, f_yy_interp_loop, f_xy_interp_loop = interp_func_loop.hessian(
np.array([0, 1, 0, 1]), np.array([1, 1, 2, 2]))
f_xx_true, f_yy_true, f_xy_true = sis.hessian(np.array([0, 1, 0, 1]),
np.array([1, 1, 2, 2]),
**kwargs_SIS)
assert f_xx_interp[0] == f_xx_true[0]
assert f_xx_interp[1] == f_xx_true[1]
assert f_xy_interp[0] == f_xy_true[0]
assert f_xy_interp[1] == f_xy_true[1]
assert f_xx_interp[0] == f_xx_interp_loop[0]
assert f_xx_interp[1] == f_xx_interp_loop[1]
assert f_xy_interp[0] == f_xy_interp_loop[0]
assert f_xy_interp[1] == f_xy_interp_loop[1]
def function(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx,
f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_ = self.f_interp(y, x)
return f_[0][0]
else:
if self._grid:
x_axes, y_axes = util.get_axes(x, y)
f_ = self.f_interp(y_axes, x_axes)
f_ = util.image2array(f_)
else:
n = len(x)
f_ = np.zeros(n)
for i in range(n):
f_[i] = self.f_interp(y[i], x[i])
return f_
def derivatives(self, x, y, grid_interp_x=None, grid_interp_y=None, f_=None, f_x=None, f_y=None, f_xx=None, f_yy=None, f_xy=None):
"""
returns df/dx and df/dy of the function
:param x: x-coordinate (angular position), float or numpy array
:param y: y-coordinate (angular position), float or numpy array
:param grid_interp_x: numpy array (ascending) to mark the x-direction of the interpolation grid
:param grid_interp_y: numpy array (ascending) to mark the y-direction of the interpolation grid
:param f_: 2d numpy array of lensing potential, matching the grids in grid_interp_x and grid_interp_y
:param f_x: 2d numpy array of deflection in x-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_y: 2d numpy array of deflection in y-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_xx: 2d numpy array of df/dxx, matching the grids in grid_interp_x and grid_interp_y
:param f_yy: 2d numpy array of df/dyy, matching the grids in grid_interp_x and grid_interp_y
:param f_xy: 2d numpy array of df/dxy, matching the grids in grid_interp_x and grid_interp_y
:return: f_x, f_y at interpolated positions (x, y)
"""
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_x_out = self.f_x_interp(x, y, grid_interp_x, grid_interp_y, f_x)
f_y_out = self.f_y_interp(x, y, grid_interp_x, grid_interp_y, f_y)
return f_x_out, f_y_out
else:
if self._grid and n >= self._min_grid_number:
x_, y_ = util.get_axes(x, y)
f_x_out = self.f_x_interp(x_, y_, grid_interp_x, grid_interp_y, f_x, grid=self._grid)
f_y_out = self.f_y_interp(x_, y_, grid_interp_x, grid_interp_y, f_y, grid=self._grid)
f_x_out = util.image2array(f_x_out)
f_y_out = util.image2array(f_y_out)
else:
#n = len(x)
f_x_out = self.f_x_interp(x, y, grid_interp_x, grid_interp_y, f_x)
f_y_out = self.f_y_interp(x, y, grid_interp_x, grid_interp_y, f_y)
return f_x_out, f_y_out
def function(self, x, y, grid_interp_x=None, grid_interp_y=None, f_=None, f_x=None, f_y=None, f_xx=None, f_yy=None,
f_xy=None):
"""
:param x: x-coordinate (angular position), float or numpy array
:param y: y-coordinate (angular position), float or numpy array
:param grid_interp_x: numpy array (ascending) to mark the x-direction of the interpolation grid
:param grid_interp_y: numpy array (ascending) to mark the y-direction of the interpolation grid
:param f_: 2d numpy array of lensing potential, matching the grids in grid_interp_x and grid_interp_y
:param f_x: 2d numpy array of deflection in x-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_y: 2d numpy array of deflection in y-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_xx: 2d numpy array of df/dxx, matching the grids in grid_interp_x and grid_interp_y
:param f_yy: 2d numpy array of df/dyy, matching the grids in grid_interp_x and grid_interp_y
:param f_xy: 2d numpy array of df/dxy, matching the grids in grid_interp_x and grid_interp_y
:return: potential at interpolated positions (x, y)
"""
#self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx, f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_out = self.f_interp(x, y, grid_interp_x, grid_interp_y, f_)
return f_out
else:
if self._grid and n >= self._min_grid_number:
x_axes, y_axes = util.get_axes(x, y)
f_out = self.f_interp(x_axes, y_axes, grid_interp_x, grid_interp_y, f_, grid=self._grid)
f_out = util.image2array(f_out)
else:
#n = len(x)
f_out = np.zeros(n)
for i in range(n):
f_out[i] = self.f_interp(x[i], y[i], grid_interp_x, grid_interp_y, f_)
return f_out
def test_kwargs_interpolation(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
f_xx_sis, f_yy_sis, f_xy_sis = sis.hessian(x_grid_interp,
y_grid_interp, **kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
interp_func = Interpol_func()
kwargs_interp = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_sis),
'f_x': util.array2image(f_x_sis),
'f_y': util.array2image(f_y_sis),
'f_xx': util.array2image(f_xx_sis),
'f_yy': util.array2image(f_yy_sis),
'f_xy': util.array2image(f_xy_sis)
}
x, y = 1., 1.
alpha_x, alpha_y = interp_func.derivatives(x, y, **kwargs_interp)
assert alpha_x == 0.31622776601683794
f_ = interp_func.function(x, y, **kwargs_interp)
npt.assert_almost_equal(f_, 1.5811388300841898)
def hessian(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
"""
returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
:param x: x-coordinate (angular position), float or numpy array
:param y: y-coordinate (angular position), float or numpy array
:param grid_interp_x: numpy array (ascending) to mark the x-direction of the interpolation grid
:param grid_interp_y: numpy array (ascending) to mark the y-direction of the interpolation grid
:param f_: 2d numpy array of lensing potential, matching the grids in grid_interp_x and grid_interp_y
:param f_x: 2d numpy array of deflection in x-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_y: 2d numpy array of deflection in y-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_xx: 2d numpy array of df/dxx, matching the grids in grid_interp_x and grid_interp_y
:param f_yy: 2d numpy array of df/dyy, matching the grids in grid_interp_x and grid_interp_y
:param f_xy: 2d numpy array of df/dxy, matching the grids in grid_interp_x and grid_interp_y
:return: f_xx, f_yy, f_xy at interpolated positions (x, y)
"""
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_xx_out = self.f_xx_interp(x, y, grid_interp_x, grid_interp_y,
f_xx)
f_yy_out = self.f_yy_interp(x, y, grid_interp_x, grid_interp_y,
f_yy)
f_xy_out = self.f_xy_interp(x, y, grid_interp_x, grid_interp_y,
f_xy)
return f_xx_out[0][0], f_yy_out[0][0], f_xy_out[0][0]
else:
if self._grid and n >= self._min_grid_number:
x_, y_ = util.get_axes(x, y)
f_xx_out = self.f_xx_interp(x_, y_, grid_interp_x,
grid_interp_y, f_xx)
f_yy_out = self.f_yy_interp(x_, y_, grid_interp_x,
grid_interp_y, f_yy)
f_xy_out = self.f_xy_interp(x_, y_, grid_interp_x,
grid_interp_y, f_xy)
f_xx_out = util.image2array(f_xx_out)
f_yy_out = util.image2array(f_yy_out)
f_xy_out = util.image2array(f_xy_out)
else:
#n = len(x)
f_xx_out, f_yy_out, f_xy_out = np.zeros(n), np.zeros(
n), np.zeros(n)
for i in range(n):
f_xx_out[i] = self.f_xx_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_xx)
f_yy_out[i] = self.f_yy_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_yy)
f_xy_out[i] = self.f_xy_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_xy)
return f_xx_out, f_yy_out, f_xy_out
def test_hessian_finite_differential(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
interp_func = Interpol()
kwargs_interp = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_sis),
'f_x': util.array2image(f_x_sis),
'f_y': util.array2image(f_y_sis)
}
x, y = 1., 0.
f_xx, f_xy, f_yx, f_yy = interp_func.hessian(x, y, **kwargs_interp)
f_xx_true, f_xy_true, f_yx_true, f_yy_true = sis.hessian(
x, y, **kwargs_SIS)
npt.assert_almost_equal(f_xx, f_xx_true, decimal=1)
npt.assert_almost_equal(f_xy, f_xy_true, decimal=1)
npt.assert_almost_equal(f_yx, f_yx_true, decimal=1)
npt.assert_almost_equal(f_yy, f_yy_true, decimal=1)
def function(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
#self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx, f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_out = self.f_interp(x, y, grid_interp_x, grid_interp_y, f_)
return f_out[0][0]
else:
if self._grid and n >= self._min_grid_number:
x_axes, y_axes = util.get_axes(x, y)
f_out = self.f_interp(x_axes, y_axes, grid_interp_x,
grid_interp_y, f_)
f_out = util.image2array(f_out)
else:
#n = len(x)
f_out = np.zeros(n)
for i in range(n):
f_out[i] = self.f_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_)
return f_out
def hessian(self, x, y, grid_interp_x=None, grid_interp_y=None, f_=None, f_x=None, f_y=None, f_xx=None, f_yy=None, f_xy=None):
"""
returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2
:param x: x-coordinate (angular position), float or numpy array
:param y: y-coordinate (angular position), float or numpy array
:param grid_interp_x: numpy array (ascending) to mark the x-direction of the interpolation grid
:param grid_interp_y: numpy array (ascending) to mark the y-direction of the interpolation grid
:param f_: 2d numpy array of lensing potential, matching the grids in grid_interp_x and grid_interp_y
:param f_x: 2d numpy array of deflection in x-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_y: 2d numpy array of deflection in y-direction, matching the grids in grid_interp_x and grid_interp_y
:param f_xx: 2d numpy array of df/dxx, matching the grids in grid_interp_x and grid_interp_y
:param f_yy: 2d numpy array of df/dyy, matching the grids in grid_interp_x and grid_interp_y
:param f_xy: 2d numpy array of df/dxy, matching the grids in grid_interp_x and grid_interp_y
:return: f_xx, f_xy, f_yx, f_yy at interpolated positions (x, y)
"""
if not (hasattr(self, '_f_xx_interp')) and (f_xx is None or f_yy is None or f_xy is None):
diff = 0.000001
alpha_ra_pp, alpha_dec_pp = self.derivatives(x + diff / 2, y + diff / 2, grid_interp_x=grid_interp_x,
grid_interp_y=grid_interp_y, f_=f_, f_x=f_x, f_y=f_y)
alpha_ra_pn, alpha_dec_pn = self.derivatives(x + diff / 2, y - diff / 2, grid_interp_x=grid_interp_x,
grid_interp_y=grid_interp_y, f_=f_, f_x=f_x, f_y=f_y)
alpha_ra_np, alpha_dec_np = self.derivatives(x - diff / 2, y + diff / 2, grid_interp_x=grid_interp_x,
grid_interp_y=grid_interp_y, f_=f_, f_x=f_x, f_y=f_y)
alpha_ra_nn, alpha_dec_nn = self.derivatives(x - diff / 2, y - diff / 2, grid_interp_x=grid_interp_x,
grid_interp_y=grid_interp_y, f_=f_, f_x=f_x, f_y=f_y)
f_xx_out = (alpha_ra_pp - alpha_ra_np + alpha_ra_pn - alpha_ra_nn) / diff / 2
f_xy_out = (alpha_ra_pp - alpha_ra_pn + alpha_ra_np - alpha_ra_nn) / diff / 2
f_yx_out = (alpha_dec_pp - alpha_dec_np + alpha_dec_pn - alpha_dec_nn) / diff / 2
f_yy_out = (alpha_dec_pp - alpha_dec_pn + alpha_dec_np - alpha_dec_nn) / diff / 2
return f_xx_out, f_xy_out, f_yx_out, f_yy_out
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_xx_out = self.f_xx_interp(x, y, grid_interp_x, grid_interp_y, f_xx)
f_yy_out = self.f_yy_interp(x, y, grid_interp_x, grid_interp_y, f_yy)
f_xy_out = self.f_xy_interp(x, y, grid_interp_x, grid_interp_y, f_xy)
return f_xx_out, f_xy_out, f_xy_out, f_yy_out
else:
if self._grid and n >= self._min_grid_number:
x_, y_ = util.get_axes(x, y)
f_xx_out = self.f_xx_interp(x_, y_, grid_interp_x, grid_interp_y, f_xx, grid=self._grid)
f_yy_out = self.f_yy_interp(x_, y_, grid_interp_x, grid_interp_y, f_yy, grid=self._grid)
f_xy_out = self.f_xy_interp(x_, y_, grid_interp_x, grid_interp_y, f_xy, grid=self._grid)
f_xx_out = util.image2array(f_xx_out)
f_yy_out = util.image2array(f_yy_out)
f_xy_out = util.image2array(f_xy_out)
else:
#n = len(x)
f_xx_out, f_yy_out, f_xy_out = np.zeros(n), np.zeros(n), np.zeros(n)
for i in range(n):
f_xx_out[i] = self.f_xx_interp(x[i], y[i], grid_interp_x, grid_interp_y, f_xx)
f_yy_out[i] = self.f_yy_interp(x[i], y[i], grid_interp_x, grid_interp_y, f_yy)
f_xy_out[i] = self.f_xy_interp(x[i], y[i], grid_interp_x, grid_interp_y, f_xy)
return f_xx_out, f_xy_out, f_xy_out, f_yy_out
def test_effective_einstein_radius(self):
kwargs_lens = [{'theta_E': 1, 'center_x': 0, 'center_y': 0}]
lensModel = LensProfileAnalysis(LensModel(lens_model_list=['SIS']))
ret = lensModel.effective_einstein_radius(kwargs_lens,
get_precision=True)
assert len(ret) == 2
npt.assert_almost_equal(ret[0], 1., decimal=2)
kwargs_lens_bad = [{'theta_E': 100, 'center_x': 0, 'center_y': 0}]
ret_nan = lensModel.effective_einstein_radius(kwargs_lens_bad,
get_precision=True,
verbose=True)
assert np.isnan(ret_nan)
# test interpolated profile
numPix = 101
deltaPix = 0.02
from lenstronomy.Util import util
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
from lenstronomy.LensModel.Profiles.sis import SIS
sis = SIS()
center_x, center_y = 0., -0.
kwargs_SIS = {
'theta_E': 1.,
'center_x': center_x,
'center_y': center_y
}
f_ = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x, f_y = sis.derivatives(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_xx, f_yy, f_xy = sis.hessian(x_grid_interp, y_grid_interp,
**kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
kwargs_interpol = [{
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_),
'f_x': util.array2image(f_x),
'f_y': util.array2image(f_y),
'f_xx': util.array2image(f_xx),
'f_xy': util.array2image(f_xy),
'f_yy': util.array2image(f_yy)
}]
lensModel = LensProfileAnalysis(
LensModel(lens_model_list=['INTERPOL']))
theta_E_return = lensModel.effective_einstein_radius(
kwargs_interpol,
get_precision=False,
verbose=True,
center_x=center_x,
center_y=center_y)
npt.assert_almost_equal(theta_E_return, 1, decimal=2)
def hessian(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
"""
returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
"""
#self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx, f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_xx_out = self.f_xx_interp(x, y, grid_interp_x, grid_interp_y,
f_xx)
f_yy_out = self.f_yy_interp(x, y, grid_interp_x, grid_interp_y,
f_yy)
f_xy_out = self.f_xy_interp(x, y, grid_interp_x, grid_interp_y,
f_xy)
return f_xx_out[0][0], f_yy_out[0][0], f_xy_out[0][0]
else:
if self._grid and n >= self._min_grid_number:
x_, y_ = util.get_axes(x, y)
f_xx_out = self.f_xx_interp(x_, y_, grid_interp_x,
grid_interp_y, f_xx)
f_yy_out = self.f_yy_interp(x_, y_, grid_interp_x,
grid_interp_y, f_yy)
f_xy_out = self.f_xy_interp(x_, y_, grid_interp_x,
grid_interp_y, f_xy)
f_xx_out = util.image2array(f_xx_out)
f_yy_out = util.image2array(f_yy_out)
f_xy_out = util.image2array(f_xy_out)
else:
#n = len(x)
f_xx_out, f_yy_out, f_xy_out = np.zeros(n), np.zeros(
n), np.zeros(n)
for i in range(n):
f_xx_out[i] = self.f_xx_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_xx)
f_yy_out[i] = self.f_yy_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_yy)
f_xy_out[i] = self.f_xy_interp(x[i], y[i], grid_interp_x,
grid_interp_y, f_xy)
return f_xx_out, f_yy_out, f_xy_out
def test_interp_func_scaled(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
f_xx_sis, f_xy_sis, f_yx_sis, f_yy_sis = sis.hessian(
x_grid_interp, y_grid_interp, **kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
kwargs_interp = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_sis),
'f_x': util.array2image(f_x_sis),
'f_y': util.array2image(f_y_sis),
'f_xx': util.array2image(f_xx_sis),
'f_yy': util.array2image(f_yy_sis),
'f_xy': util.array2image(f_xy_sis)
}
interp_func = InterpolScaled(grid=False)
x, y = 1., 1.
alpha_x, alpha_y = interp_func.derivatives(x,
y,
scale_factor=1,
**kwargs_interp)
assert alpha_x == 0.31622776601683794
f_ = interp_func.function(x, y, scale_factor=1., **kwargs_interp)
npt.assert_almost_equal(f_, 1.5811388300841898)
f_xx, f_xy, f_yx, f_yy = interp_func.hessian(x,
y,
scale_factor=1.,
**kwargs_interp)
npt.assert_almost_equal(f_xx, 0.56920997883030822, decimal=8)
npt.assert_almost_equal(f_yy, 0.063245553203367583, decimal=8)
npt.assert_almost_equal(f_xy, -0.18973665961010275, decimal=8)
npt.assert_almost_equal(f_xy, f_yx, decimal=8)
x_grid, y_grid = util.make_grid(10, deltaPix)
f_xx, f_xy, f_yx, f_yy = interp_func.hessian(x_grid,
y_grid,
scale_factor=1.,
**kwargs_interp)
npt.assert_almost_equal(f_xx[0], 0, decimal=2)
def __init__(self, mass_map, grid_spacing, redshift):
"""
:param mass_map: 2d numpy array of mass map (in units physical Msol)
:param grid_spacing: grid spacing of the mass map (in units physical Mpc)
:param redshift: redshift
"""
nx, ny = np.shape(mass_map)
if nx != ny:
raise ValueError('Shape of mass map needs to be square!, set as %s %s' % (nx, ny))
self._mass_map = mass_map
self._grid_spacing = grid_spacing
self._redshift = redshift
self._f_x_mass, self._f_y_mass = convergence_integrals.deflection_from_kappa_grid(self._mass_map, self._grid_spacing)
self._f_mass = convergence_integrals.potential_from_kappa_grid(self._mass_map, self._grid_spacing)
x_grid, y_grid = util.make_grid(numPix=len(self._mass_map), deltapix=self._grid_spacing)
self._x_axes_mpc, self._y_axes_mpc = util.get_axes(x_grid, y_grid)
def test_shift(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
f_xx_sis, f_yy_sis, f_xy_sis = sis.hessian(x_grid_interp,
y_grid_interp, **kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
kwargs_interp = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_sis),
'f_x': util.array2image(f_x_sis),
'f_y': util.array2image(f_y_sis),
'f_xx': util.array2image(f_xx_sis),
'f_yy': util.array2image(f_yy_sis),
'f_xy': util.array2image(f_xy_sis)
}
interp_func = Interpol(grid=False)
x, y = 1., 1.
alpha_x, alpha_y = interp_func.derivatives(x, y, **kwargs_interp)
assert alpha_x == 0.31622776601683794
interp_func = Interpol(grid=False)
x_shift = 1.
kwargs_shift = {
'grid_interp_x': x_axes + x_shift,
'grid_interp_y': y_axes,
'f_': util.array2image(f_sis),
'f_x': util.array2image(f_x_sis),
'f_y': util.array2image(f_y_sis),
'f_xx': util.array2image(f_xx_sis),
'f_yy': util.array2image(f_yy_sis),
'f_xy': util.array2image(f_xy_sis)
}
alpha_x_shift, alpha_y_shift = interp_func.derivatives(
x + x_shift, y, **kwargs_shift)
npt.assert_almost_equal(alpha_x_shift, alpha_x, decimal=10)
def hessian(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
"""
returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy
"""
self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx,
f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_xx = self.f_xx_interp(y, x)
f_yy = self.f_yy_interp(y, x)
f_xy = self.f_xy_interp(y, x)
return f_xx[0][0], f_yy[0][0], f_xy[0][0]
else:
if self._grid:
x_, y_ = util.get_axes(x, y)
f_xx = self.f_xx_interp(y_, x_)
f_yy = self.f_yy_interp(y_, x_)
f_xy = self.f_xy_interp(y_, x_)
f_xx = util.image2array(f_xx)
f_yy = util.image2array(f_yy)
f_xy = util.image2array(f_xy)
else:
n = len(x)
f_xx, f_yy, f_xy = np.zeros(n), np.zeros(n), np.zeros(n)
for i in range(n):
f_xx[i] = self.f_xx_interp(y[i], x[i])
f_yy[i] = self.f_yy_interp(y[i], x[i])
f_xy[i] = self.f_xy_interp(y[i], x[i])
return f_xx, f_yy, f_xy
def test_call(self):
numPix = 101
deltaPix = 0.1
x_grid_interp, y_grid_interp = util.make_grid(numPix, deltaPix)
sis = SIS()
kwargs_SIS = {'theta_E': 1., 'center_x': 0.5, 'center_y': -0.5}
f_sis = sis.function(x_grid_interp, y_grid_interp, **kwargs_SIS)
f_x_sis, f_y_sis = sis.derivatives(x_grid_interp, y_grid_interp,
**kwargs_SIS)
f_xx_sis, f_yy_sis, f_xy_sis = sis.hessian(x_grid_interp,
y_grid_interp, **kwargs_SIS)
x_axes, y_axes = util.get_axes(x_grid_interp, y_grid_interp)
interp_func = Interpol(grid=True)
interp_func.do_interp(x_axes, y_axes, util.array2image(f_sis),
util.array2image(f_x_sis),
util.array2image(f_y_sis),
util.array2image(f_xx_sis),
util.array2image(f_yy_sis),
util.array2image(f_xy_sis))
x, y = 1., 1.
alpha_x, alpha_y = interp_func.derivatives(x, y, **{})
assert alpha_x == 0.31622776601683794
def derivatives(self,
x,
y,
grid_interp_x=None,
grid_interp_y=None,
f_=None,
f_x=None,
f_y=None,
f_xx=None,
f_yy=None,
f_xy=None):
"""
returns df/dx and df/dy of the function
"""
self._check_interp(grid_interp_x, grid_interp_y, f_, f_x, f_y, f_xx,
f_yy, f_xy)
n = len(np.atleast_1d(x))
if n <= 1 and np.shape(x) == ():
#if type(x) == float or type(x) == int or type(x) == type(np.float64(1)) or len(x) <= 1:
f_x = self.f_x_interp(y, x)
f_y = self.f_y_interp(y, x)
return f_x[0][0], f_y[0][0]
else:
if self._grid:
x_, y_ = util.get_axes(x, y)
f_x = self.f_x_interp(y_, x_)
f_y = self.f_y_interp(y_, x_)
f_x = util.image2array(f_x)
f_y = util.image2array(f_y)
else:
n = len(x)
f_x, f_y = np.zeros(n), np.zeros(n)
for i in range(n):
f_x[i] = self.f_x_interp(y[i], x[i])
f_y[i] = self.f_y_interp(y[i], x[i])
return f_x, f_y
def light2mass_interpol(lens_light_model_list,
kwargs_lens_light,
numPix=100,
deltaPix=0.05,
subgrid_res=5,
center_x=0,
center_y=0):
"""
takes a lens light model and turns it numerically in a lens model
(with all lensmodel quantities computed on a grid). Then provides an interpolated grid for the quantities.
:param kwargs_lens_light: lens light keyword argument list
:param numPix: number of pixels per axis for the return interpolation
:param deltaPix: interpolation/pixel size
:param center_x: center of the grid
:param center_y: center of the grid
:param subgrid_res: subgrid for the numerical integrals
:return:
"""
# make super-sampled grid
x_grid_sub, y_grid_sub = util.make_grid(numPix=numPix * 5,
deltapix=deltaPix,
subgrid_res=subgrid_res)
import lenstronomy.Util.mask_util as mask_util
mask = mask_util.mask_sphere(x_grid_sub,
y_grid_sub,
center_x,
center_y,
r=1)
x_grid, y_grid = util.make_grid(numPix=numPix, deltapix=deltaPix)
# compute light on the subgrid
lightModel = LightModel(light_model_list=lens_light_model_list)
flux = lightModel.surface_brightness(x_grid_sub, y_grid_sub,
kwargs_lens_light)
flux_norm = np.sum(flux[mask == 1]) / np.sum(mask)
flux /= flux_norm
from lenstronomy.LensModel import convergence_integrals as integral
# compute lensing quantities with subgrid
convergence_sub = util.array2image(flux)
f_x_sub, f_y_sub = integral.deflection_from_kappa_grid(
convergence_sub, grid_spacing=deltaPix / float(subgrid_res))
f_sub = integral.potential_from_kappa_grid(convergence_sub,
grid_spacing=deltaPix /
float(subgrid_res))
# interpolation function on lensing quantities
x_axes_sub, y_axes_sub = util.get_axes(x_grid_sub, y_grid_sub)
from lenstronomy.LensModel.Profiles.interpol import Interpol
interp_func = Interpol()
interp_func.do_interp(x_axes_sub, y_axes_sub, f_sub, f_x_sub, f_y_sub)
# compute lensing quantities on sparser grid
x_axes, y_axes = util.get_axes(x_grid, y_grid)
f_ = interp_func.function(x_grid, y_grid)
f_x, f_y = interp_func.derivatives(x_grid, y_grid)
# numerical differentials for second order differentials
from lenstronomy.LensModel.lens_model import LensModel
lens_model = LensModel(lens_model_list=['INTERPOL'])
kwargs = [{
'grid_interp_x': x_axes_sub,
'grid_interp_y': y_axes_sub,
'f_': f_sub,
'f_x': f_x_sub,
'f_y': f_y_sub
}]
f_xx, f_xy, f_yx, f_yy = lens_model.hessian(x_grid,
y_grid,
kwargs,
diff=0.00001)
kwargs_interpol = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': util.array2image(f_),
'f_x': util.array2image(f_x),
'f_y': util.array2image(f_y),
'f_xx': util.array2image(f_xx),
'f_xy': util.array2image(f_xy),
'f_yy': util.array2image(f_yy)
}
return kwargs_interpol
def setup(self):
# define a cosmology
cosmo = FlatLambdaCDM(H0=70, Om0=0.3, Ob0=0.05)
self._cosmo = cosmo
redshift_list = [0.1, 0.3, 0.8] # list of redshift of the deflectors
z_source = 2 # source redshift
self._z_source = z_source
# analytic profile class in multi plane
self._lensmodel = LensModel(lens_model_list=['NFW', 'NFW', 'NFW'],
lens_redshift_list=redshift_list,
multi_plane=True,
z_source_convention=z_source,
cosmo=cosmo,
z_source=z_source)
# a single plane class from which the convergence/mass maps are computeded
single_plane = LensModel(lens_model_list=['NFW'], multi_plane=False)
# multi-plane class with three interpolation grids
self._lens_model_interp = LensModel(
lens_model_list=['INTERPOL', 'INTERPOL', 'INTERPOL'],
lens_redshift_list=redshift_list,
multi_plane=True,
z_source_convention=z_source,
cosmo=cosmo,
z_source=z_source)
# deflector parameterisation in units of reduced deflection angles to the source convention redshift
logM_200_list = [8, 9,
10] # log 10 halo masses of the three deflectors
c_list = [20, 10, 8] # concentrations of the three halos
kwargs_lens = []
kwargs_lens_interp = []
grid_spacing = 0.01 # spacing of the convergence grid in units arc seconds
x_grid, y_grid = util.make_grid(
numPix=500, deltapix=grid_spacing
) # we create the grid coordinates centered at zero
x_axes, y_axes = util.get_axes(
x_grid, y_grid) # we need the axes only for the interpolation
mass_map_list = []
grid_spacing_list_mpc = []
for i, z in enumerate(
redshift_list): # loop through the three deflectors
lens_cosmo = LensCosmo(
z_lens=z, z_source=z_source, cosmo=cosmo
) # instance of LensCosmo, a class that manages cosmology relevant quantities of a lens
alpha_Rs, Rs = lens_cosmo.nfw_physical2angle(
M=10**(logM_200_list[i]), c=c_list[i]
) # we turn the halo mass and concentration in reduced deflection angles and angles on the sky
kwargs_nfw = {
'Rs': Rs,
'alpha_Rs': alpha_Rs,
'center_x': 0,
'center_y': 0
} # lensing parameters of the NFW profile in lenstronomy conventions
kwargs_lens.append(kwargs_nfw)
kappa_map = single_plane.kappa(
x_grid, y_grid,
[kwargs_nfw]) # convergence map of a single NFW profile
kappa_map = util.array2image(kappa_map)
mass_map = lens_cosmo.epsilon_crit_angle * kappa_map * grid_spacing**2 # projected mass per pixel on the gird
mass_map_list.append(mass_map)
npt.assert_almost_equal(
np.log10(np.sum(mass_map)), logM_200_list[i], decimal=0
) # check whether the sum of mass roughtly correspoonds the mass definition
grid_spacing_mpc = lens_cosmo.arcsec2phys_lens(
grid_spacing) # turn grid spacing from arcseconds into Mpc
grid_spacing_list_mpc.append(grid_spacing_mpc)
f_x, f_y = convergence_integrals.deflection_from_kappa_grid(
kappa_map, grid_spacing
) # perform the deflection calculation from the convergence map
f_ = convergence_integrals.potential_from_kappa_grid(
kappa_map, grid_spacing
) # perform the lensing potential calculation from the convergence map (attention: arbitrary normalization)
kwargs_interp = {
'grid_interp_x': x_axes,
'grid_interp_y': y_axes,
'f_': f_,
'f_x': f_x,
'f_y': f_y
} # keyword arguments of the interpolation model
kwargs_lens_interp.append(kwargs_interp)
self.kwargs_lens = kwargs_lens
self.kwargs_lens_interp = kwargs_lens_interp
self.lightCone = LightCone(
mass_map_list, grid_spacing_list_mpc, redshift_list
) # here we make the instance of the LightCone class based on the mass map, physical grid spacing and redshifts.