def periodic(pix_sig=3, num_poly_param=10, num_knots=5, ret_diff=False, smooth=False, amp=.5):
x1 = (np.random.rand(10000) -.5 ) * 2048.0
y1 = (np.random.rand(10000) -.5) * 2048.0
knots_x = np.linspace(np.min(x1),np.max(x1),num=num_knots)
knots_y = np.linspace(np.min(y1),np.max(y1),num=num_knots)
'''
Now give random errors to xref, yref to see if spline fitter gets same measured error
Also use Egg Carton A**2 * sin(2pi X/L1) cos(2pi Y/L2)
'''
tot_dat_ran = np.max(x1) - np.min(x1)
L1 = tot_dat_ran / 2.0
L2 = tot_dat_ran / 2.0
Zx = amp**2 * np.cos(2 * np.pi * x1 / L1) * np.cos(2 * np.pi * y1 / L2)
L1 = tot_dat_ran / 2.0
L2 = tot_dat_ran / 3.0
Zy = amp**2 * np.cos(2 * np.pi * x1 / L1) * np.cos(2 * np.pi * y1 / L2)
xref = x1 + pix_sig * np.random.randn(len(x1)) + Zx
yref = y1 + pix_sig * np.random.randn(len(x1)) + Zy
#x_prime, y_prime, spline_x, spline_y, co_x, co_y = high_order.find_fit(x1, y1, xref, yref, num_knots=num_knots, num_poly_param=num_poly_param)
dx_sp, dx_spline = high_order.fit_spline(x1, y1, xref-x1, num_knots=num_knots, smooth=smooth)
dy_sp, dy_spline = high_order.fit_spline(x1, y1, yref-y1, num_knots=num_knots, smooth=smooth)
x_prime = x1 + dx_sp
y_prime = y1 + dy_sp
d_x_true = xref - x1
d_y_true = yref - y1
d_x_m = dx_sp
d_y_m = dy_sp
if ret_diff:
return x_prime, y_prime, x1, y1, xref, yref, d_x_true, d_y_true, d_x_m, d_y_m
return x_prime, y_prime, x1, y1, xref, yref
def test_spline(pix_sig=3, order=3, num_knots=5, ret_diff=False, amp=1, ret_u=False):
x1 = (np.random.rand(1000) -.5) * 4096
y1 = (np.random.rand(1000) -.5) * 4096
x_u = (np.random.rand(500)-.5)*4096
y_u = (np.random.rand(500)-.5)*4096
knots_x = np.linspace(-2048,2048,num=num_knots)
knots_y = np.linspace(-2048,2048,num=num_knots)
'''
Now give random errors to xref, yref to see if spline fitter gets same measured error
Also use Egg Carton A**2 * sin(2pi X/L1) cos(2pi Y/L2)
'''
A = amp
L1 = 40
L2 = 17
Zx = A**2 * np.cos(2 * np.pi * x1 / L1) * np.cos(2 * np.pi * y1 / L2)
Zx_u = A**2 * np.cos(2 * np.pi * x_u / L1) * np.cos(2 * np.pi * y_u / L2)
L1 = 5
L2 = 70
Zy = A**2 * np.cos(2 * np.pi * x1 / L1) * np.cos(2 * np.pi * y1 / L2)
Zy_u = A**2 * np.cos(2 * np.pi * x_u / L1) * np.cos(2 * np.pi * y_u / L2)
xref = x1 + pix_sig * np.random.randn(len(x1)) + Zx
yref = y1 + pix_sig * np.random.randn(len(x1)) + Zy
x_prime, spline_x = high_order.fit_spline(x1,y1,xref,order=order, num_knots=num_knots )
y_prime, spline_y = high_order.fit_spline(y1,x1,yref, order=order, num_knots=num_knots)
d_x = xref - x1
d_y = yref - y1
d_x_m = x_prime - x1
d_y_m = y_prime - y1
if ret_diff:
return x_prime, y_prime, x1, y1, xref, yref, d_x, d_y, d_x_m, d_y_m
elif ret_u:
return spline_x.ev(x_u, y_u), spline_y.ev(x_u, y_u), x_u, y_u, x_u +Zx_u, y_u +Zy_u, 0 ,0 ,0, 0
return x_prime, y_prime, x1, y1, xref, yref
def test_total(num_poly=10, num_knots=4, noise=0.1, smooth=False):
'''
Function that performs transformation between x, y and xref yref then fits that difference using polynomial fit followed by spline
num_poly is the number of polynomial terms used, 10 gets all quadratic terms
num_knots is th enumber of knots in the slpine along each axis, that is 4 means there is a total of 16 knots
noise is the sigma (in pixels) used to
'''
xref = np.random.rand(10000) * 4096 - 2048
yref = np.random.rand(10000) * 4096 - 2048
'''
these star lists will be put through both the known tranformation (rotation and translation) and also put through the derived polynomial and spline fits as a check
'''
x_dim_ref = np.random.rand(1000) * 4096 - 2048
y_dim_ref = np.random.rand(1000) * 4096 - 2048
trans = transforms.Affine2D()
trans.rotate_deg(75.0)
trans.translate(184, -45)
cooref = np.array([xref, yref]).T
coo1 = trans.transform(cooref)
coo_dim = trans.transform(np.array([x_dim_ref,y_dim_ref]).T)
x_dim1 = coo_dim[:,0] + noise*np.random.randn(len(x_dim_ref))
y_dim1 = coo_dim[:,1] + noise*np.random.randn(len(y_dim_ref))
x1 = coo1[:,0] + noise*np.random.randn(len(xref))
y1 = coo1[:,1] + noise*np.random.randn(len(yref))
c_x, c_y = high_order.fit_poly(x1, y1, xref, yref, num_poly)
x_poly = high_order.poly(np.array([x1,y1]), c_x)
y_poly = high_order.poly(np.array([x1,y1]), c_y)
#if np.sum(np.abs(x_poly-xref)) < 1 and np.sum(np.abs(y_poly-yref)) < len(xref):
# print 'Polynomial Fit was sufficient'
# return c_x, c_y
'''
Now do spline fit between the polynomial fit and reference, to get rid of residual
'''
dx_sp, spline_dx = high_order.fit_spline(x_poly, y_poly, xref-x_poly, num_knots=num_knots, smooth=smooth)
dy_sp, spline_dy = high_order.fit_spline(x_poly, y_poly, yref-y_poly, num_knots=num_knots, smooth=smooth)
x_sp, spline_x = high_order.fit_spline(x_poly, y_poly, xref, num_knots=num_knots, smooth=smooth)
y_sp, spline_y = high_order.fit_spline(x_poly, y_poly, yref, num_knots=num_knots, smooth=smooth)
assert np.sum(np.abs(x_sp-(x_poly+dx_sp)))/len(x_poly) < noise
assert np.sum(np.abs(y_sp-(y_poly+dy_sp)))/len(y_poly) < noise
assert np.sum(np.abs(x_sp - xref))/len(x_sp) < noise
assert np.sum(np.abs(y_sp - yref))/len(y_sp) < noise
x_dim_poly = high_order.poly(np.array([x_dim1,y_dim1]), c_x)
y_dim_poly = high_order.poly(np.array([x_dim1,y_dim1]), c_y)
assert np.sum(np.abs(x_dim_poly - x_dim_ref)) / len(x_dim_ref) < noise
assert np.sum(np.abs(y_dim_poly - y_dim_ref)) / len(y_dim_ref) < noise
x_dim_sp = spline_x.ev(x_dim_poly, y_dim_poly)
y_dim_sp = spline_y.ev(x_dim_poly,y_dim_poly)
assert np.sum(np.abs(x_dim_sp - x_dim_ref)) / len(x_dim_ref) < noise
assert np.sum(np.abs(y_dim_sp - y_dim_ref)) / len(y_dim_ref) < noise
return x_sp, y_sp, xref, yref, spline_x, spline_y , c_x, c_y, x1, y1