def test_transform(num_free_param=10,co_ran=.1):
#x1 = np.linspace(0,2000,num=1000) - 1000
#x1 = np.concatenate([x1, x1, x1, x1, x1, x1, x1, x1, x1, x1])
#y1 = np.zeros(x1.shape)
#for i in range(10):
# for j in range(1000):
# y1[i*1000 + j] = i*200.0-1000
#print y1
x1 = np.random.rand(10000)*4096 - 2048
y1 = np.random.rand(10000)*4096 - 2048
coeff_trans_x = np.random.randn(num_free_param)*co_ran
coeff_trans_y = np.random.randn(num_free_param)*co_ran
del_x = high_order.poly(np.array([x1,y1]), coeff_trans_x)
del_y = high_order.poly(np.array([x1,y1]), coeff_trans_y)
xref = x1 + del_x
yref = y1 + del_y
c_x, c_y = high_order.fit_poly(x1, y1, del_x, del_y , len(coeff_trans_x))
print 'Transform Coefficents (given)'
print coeff_trans_x
print coeff_trans_y
print 'Calculated Coefficients'
print c_x
print c_y
return x1, y1, xref, yref
def coeff_err(num_poly_param=10, size_rand_co=.1, trials=1000, num_points=100):
'''
calulates then plots the fracinoal error in polynomial coefficients copmared to known transform
'''
first_time = True
co_x_frac = []
co_y_frac = []
for i in range(trials):
x = (np.random.random(num_points) -.5 ) * 4096
y = (np.random.random(num_points) -.5 ) * 4096
co_x = np.random.random(num_poly_param) * size_rand_co
co_y = np.random.random(num_poly_param) * size_rand_co
xref = high_order.poly(np.array([x,y]) , co_x)
yref = high_order.poly(np.array([x,y]) , co_y)
c_x, c_y = high_order.fit_poly(x,y,xref,yref,num_poly_param)
for ii in range(num_poly_param):
if first_time:
co_x_frac.append([])
co_y_frac.append([])
co_x_frac[ii].append(np.abs((co_x[ii]-c_x[ii])/co_x[ii]))
co_y_frac[ii].append(np.abs((co_y[ii]-c_y[ii])/co_y[ii]))
first_time = False
co_x_frac = np.median(np.array(co_x_frac), axis=1)
co_y_frac = np.median(np.array(co_y_frac), axis=1)
plt.plot(co_x_frac[1:])
plt.plot(co_y_frac[1:])
plt.show()
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