def spoly_centroid(data, A, f, sigma):
size = data.shape[0]
zero = size / 2 + .5
kernel = profile.makeGaussian(7, f, 0, np.array([3.5, 3.5]))
image = signal.convolve2d(data, kernel, mode="same")
bp = np.where(image == image.max()) #brightest pixel in the smoothed image
cen = [bp[1][0], bp[0][0]]
k = image[cen[1] - 1:cen[1] + 2, cen[0] - 1:cen[0] + 2]
if (k.shape != (3, 3)):
center = np.array([0., 0.])
X = np.arange(6) * 0.
else:
C = cov(f, sigma)
X = regression(A, C, k.flatten())
a, b, c, d, e, f = X
matrix = np.array([[2. * d, e], [e, 2. * f]])
#matrix = matrix + (np.max(np.abs(matrix))/9.)*np.array([[1,0],[0,1]])
matrix = matrix + (sigma / np.sqrt(4. * np.pi * f**2.)) * np.array(
[[1, 0], [0, 1]]) #add maximum per pixel variance
#of the smoothed image to the
# diagonal elements of the curvature
#matrix
vector = np.array([-1. * b, -1. * c])
center = np.dot(np.linalg.inv(matrix), vector)
#center = (c*e - b*f)/(2.*d*f - 2.*e**2.) , (b*e - c*d)/(2.*d*f - 2.*e**2.)
return np.array(cen) + np.array([.5, .5]) + center
def sdss_centroid(data , f , sigma):
"""
Inputs: image = postage_stamp of star
f = FWHM of smoothing kernel
sigma = variance of the background Gaussian noise
------------------------------------------------------------
Output:
x & y coordinate of centroid
"""
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(17 , f , 0 , np.array([zero,zero]))
smoothed_image = signal.convolve2d(data , kernel , mode = "same")
image = smoothed_image/np.sum(smoothed_image)
bp = np.where((image==image.max())) #brightest pixel in the smoothed image
cen = [bp[0][0] , bp[1][0]]
kk = image[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2]
if (kk.shape!= 3):
cen = [size/2 , size/2]
kk = image[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2]
xs = lupton_2d(kk , f , sigma)
return xs
def spoly_centroid(data , A , f , sigma):
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(7, f , 0 , np.array([3.5,3.5]))
image = signal.convolve2d(data , kernel , mode = "same")
bp = np.where(image==image.max()) #brightest pixel in the smoothed image
cen = [bp[1][0] , bp[0][0]]
k = image[cen[1]-1:cen[1]+2,cen[0]-1:cen[0]+2]
if (k.shape!= (3,3)):
center = np.array([0.,0.])
X = np.arange(6)*0.
else:
C = cov(f , sigma)
X = regression(A , C , k.flatten())
a , b , c, d , e , f = X
matrix = np.array([[2.*d , e],[e , 2.*f]])
#matrix = matrix + (np.max(np.abs(matrix))/9.)*np.array([[1,0],[0,1]])
matrix = matrix + (sigma/np.sqrt(4.*np.pi*f**2.))*np.array([[1,0],[0,1]]) #add maximum per pixel variance
#of the smoothed image to the
# diagonal elements of the curvature
#matrix
vector = np.array([-1.*b , -1.*c])
center = np.dot(np.linalg.inv(matrix) , vector)
#center = (c*e - b*f)/(2.*d*f - 2.*e**2.) , (b*e - c*d)/(2.*d*f - 2.*e**2.)
return np.array(cen) + np.array([.5,.5]) + center
def sdss_centroid(data, f, sigma):
"""
Inputs: image = postage_stamp of star
f = FWHM of smoothing kernel
sigma = variance of the background Gaussian noise
------------------------------------------------------------
Output:
x & y coordinate of centroid
"""
size = data.shape[0]
zero = size / 2 + .5
kernel = profile.makeGaussian(17, f, 0, np.array([zero, zero]))
smoothed_image = signal.convolve2d(data, kernel, mode="same")
image = smoothed_image / np.sum(smoothed_image)
bp = np.where(
(image == image.max())) #brightest pixel in the smoothed image
cen = [bp[0][0], bp[1][0]]
kk = image[cen[0] - 1:cen[0] + 2, cen[1] - 1:cen[1] + 2]
if (kk.shape != 3):
cen = [size / 2, size / 2]
kk = image[cen[0] - 1:cen[0] + 2, cen[1] - 1:cen[1] + 2]
xs = lupton_2d(kk, f, sigma)
return xs
def sdss_centroid(data , f , sigma):
"""
Inputs: image = postage_stamp of star
f = FWHM of smoothing kernel
sigma = variance of the background Gaussian noise
------------------------------------------------------------
Output:
x & y coordinate of centroid
"""
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(7 , f , 0 , np.array([3.5,3.5]))
smoothed_image = signal.convolve2d(data , kernel , mode = "same")
image = smoothed_image#/np.sum(smoothed_image)
bp = np.where((image==image.max())) #brightest pixel in the smoothed image
cen = [bp[0][0] , bp[1][0]]
kk = image[cen[0]-1:cen[0]+2 , cen[1]-1:cen[1]+2]
if (kk.shape!= (3,3)):
xs = np.array([0.,0.])
else:
xs = lupton_2d(kk , f , sigma)
center_t = np.array(xs) + np.array([.5,.5]) + cen
return np.array([center_t[1] , center_t[0]])
def find_centroid(data , f , sigma):
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(7, f , 0 , np.array([3.5,3.5]))
img = signal.convolve2d(data , kernel , mode = "same")
xi, yi = np.unravel_index(np.argmax(img), img.shape)
if (xi >= 1 and xi < img.shape[0] - 1 and yi >= 1 and yi < img.shape[1] - 1):
ox, oy = fit_3x3(img[xi-1:xi+2, yi-1:yi+2] , sigma)
else:
ox , oy = 0. , 0.
return xi + ox + .5 , yi + oy + .5
def find_centroid(data , f , sigma):
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(17, f , 0 , np.array([8.5,8.5]))
img = signal.convolve2d(data , kernel , mode = "same")
xi, yi = np.unravel_index(np.argmax(img), img.shape)
if (xi >= 1 and xi < img.shape[0] - 1 and yi >= 1 and yi < img.shape[1] - 1):
ox, oy = fit_3x3(img[xi-1:xi+2, yi-1:yi+2] , sigma)
else:
ox , oy = 0. , 0.
return xi + ox + .5 , yi + ox + .5
def BP(data, f):
size = data.shape[0]
zero = size / 2 + .5
kernel = profile.makeGaussian(size, f, 0, np.array([zero, zero]))
smoothed_image = signal.convolve2d(data, kernel, mode="same")
data = smoothed_image #/np.sum(smoothed_image)
bp = np.where((data == data.max())) #brightest pixel in the smoothed image
cen = [bp[0][0], bp[1][0]]
#kk = data[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2]
return cen
def BP(data , f): size = data.shape[0] zero = size/2 + .5 kernel = profile.makeGaussian(size , f , 0 , np.array([zero,zero])) smoothed_image = signal.convolve2d(data , kernel , mode = "same") data = smoothed_image#/np.sum(smoothed_image) bp = np.where((data==data.max())) #brightest pixel in the smoothed image cen = [bp[0][0] , bp[1][0]] #kk = data[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2] return cen
def find_centroid(data, FWHM, sigma):
size = data.shape[0]
zero = size / 2 + .5
##q = np.int(2.*FWHM)
##Q = 2*q+1
##kernel = profile.makeGaussian(Q, FWHM , 0 , np.array([Q/2.,Q/2.]))
""" incorporating referee's comment """
kernel = profile.makeGaussian(size, FWHM, 0,
np.array([size / 2., size / 2.]))
img = signal.convolve2d(data, kernel, mode="same")
xi, yi = np.unravel_index(np.argmax(img), img.shape)
if (xi >= 1 and xi < img.shape[0] - 1 and yi >= 1
and yi < img.shape[1] - 1):
ox, oy = fit_3x3(img[xi - 1:xi + 2, yi - 1:yi + 2], sigma)
else:
ox, oy = 0., 0.
return xi + ox + .5, yi + oy + .5
def BP(data , f):
"""
Inputs: data
f = FWHM of the smoothing kernel
"""
size = data.shape[0]
zero = size/2 + .5
kernel = profile.makeGaussian(17 , f , 0 , np.array([zero,zero]))
smoothed_image = signal.convolve2d(data , kernel , mode = "same")
data = smoothed_image#/np.sum(smoothed_image)
bp = np.where((data==data.max())) #brightest pixel in the smoothed image
cen = [bp[0][0] , bp[1][0]]
#kk = data[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2]
"""
if (kk.shape!= 3):
cen = [size/2 , size/2]
kk = data[cen[0]-1:cen[0]+2,cen[1]-1:cen[1]+2]
cen = [size/2 , size/2]
"""
return cen
import c3 import profile y = profile.makeGaussian(33,6,0,(14.78,18.1)) print -16.5+14.78 , -16.5+18.1 print c3.find_centroid(y)
import sampler import profile import matplotlib.pyplot as plt from matplotlib.colors import LogNorm M , H = 25 , 3 y = profile.makeGaussian(H*M, H*M/6. ,0.1, (H*M/2.+0.83*H, H*M/2.+1.45*H)) hx, hy, hf = sampler.test_imatrix_new(M, H, -1.45, -0.83) qw = hx.dot(y).dot(hy) qq = y.flatten().dot(hf).reshape(M,M) plt.subplot(1,3,1) plt.imshow(y, interpolation = "None" , origin = "lower") plt.colorbar() plt.subplot(1,3,2) plt.imshow(qw, interpolation = "None" , origin = "lower") plt.colorbar() plt.subplot(1,3,3) plt.imshow(qq, interpolation = "None" , origin = "lower") plt.colorbar() plt.show() M , H = 25 , 3 y = profile.makeGaussian(M, M/5. ,0.1, (M/2.+0.83, M/2.+1.45)) y /= y.sum()
C = np.kron(np.eye(m) , np.ones(n)).T print D.shape , C.shape s = np.dot(D,C)/n w = np.dot(s,v) print v print w print v.sum() , w.sum() from scipy import ndimage import profile from matplotlib.colors import LogNorm image = profile.makeGaussian(18 , 4. , 0.1 ,(8.1,7.8)) ii = ndimage.interpolation.zoom(image, 3, output=None, order=3) def srmatrix(n,m): D = np.kron(np.eye(n) , np.ones(m).reshape(1,m).T).T C = np.kron(np.eye(m) , np.ones(n).reshape(1,n)).T return np.dot(D,C)#np.kron(np.dot(D,C) , np.dot(D,C)) from pylab import * i = np.dot(srmatrix(54,18) , np.dot(image , srmatrix(54,18).T)) #i = np.dot(image,srmatrix(10,17).T).reshape(10,10) imshow(image, interpolation ="None") show()