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poly2d.py
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import itertools
import numpy as np
# fitsh functions translated into python from fitsh-0.9.3 by Pal et al.
xscale=2400.0
yscale=4600.0
def polyfit2d(x, y, z, order=3):
ncols = (order + 1)**2
G = np.zeros((x.size, ncols))
ij = itertools.product(range(order+1), range(order+1))
for k, (i,j) in enumerate(ij):
G[:,k] = x**i * y**j
m, _, _, _ = np.linalg.lstsq(G, z)
return m
def polyval2d(x, y, m):
order = int(np.sqrt(len(m))) - 1
ij = itertools.product(range(order+1), range(order+1))
z = np.zeros_like(x)
for a, (i,j) in zip(m, ij):
z += a * x**i * y**j
return z
def fitsh_eval_2d_poly(x,y,order,coeff,ox,oy,scale):
x=(x-ox)/scale
y=(y-oy)/scale
if order==0:
return coeff[0]
elif order==1:
return coeff[0]+x*coeff[1]+y*coeff[2]
else:
ret=0.0
m=order*(order+1)/2
n=order
ym=1.0
yf=1
while n>=0:
i=n
p=m
w=coeff[m]
k=order
while i>=1:
w=w*x/i
p=p-k
w=w+coeff[p]
i=i-1
k=k-1
ret=ret+w*ym
ym=ym*y/yf
yf=yf+1
n=n-1
m=m+1
return ret
def fitsh_get_jacobi(dxfit,dyfit,params):
order = params[0]
offsetx = params[1]
offsety = params[2]
scale = params[3]
jnvar = order*(order+1)/2
jxx = np.zeros(jnvar)
jxy = np.zeros(jnvar)
jyx = np.zeros(jnvar)
jyy = np.zeros(jnvar)
k=0
for i in range(order):
for j in range(i+1):
jxx[k] = jxx[k] + dxfit[k+i+1]/scale
jxy[k] = jxy[k] + dxfit[k+i+2]/scale
jyx[k] = jyx[k] + dyfit[k+i+1]/scale
jyy[k] = jyy[k] + dyfit[k+i+1]/scale
k=k+1
return [jxx,jxy,jyx,jyy]
def fitsh_invertpoly2d(x,y,dxfit,dyfit,params):
#Apply fitsh's inverse polynomial transform
#fitsh function transformation_eval_invert_2d
order = params[0]
offsetx = params[1]
offsety = params[2]
scale = params[3]
wx = x-dxfit[0]
wy = y-dyfit[0]
mxx = dxfit[1]
mxy = dxfit[2]
myx = dyfit[1]
myy = dyfit[2]
det = 1.0/(mxx*myy-mxy*myx)
imxx = +myy*det
imxy = -mxy*det
imyx = -myx*det
imyy = +mxx*det
x0 = imxx*wx + imxy*wy
y0 = imyx*wx + imyy*wy
jxx,jxy,jyx,jyy = fitsh_get_jacobi(dxfit,dyfit,params)
n = 100
px0 = x0
py0 = y0
if order>=2:
for i in range(n):
mxx = fitsh_eval_2d_poly(x0,y0,order-1,jxx,offsetx,offsety,scale)
mxy = fitsh_eval_2d_poly(x0,y0,order-1,jxy,offsetx,offsety,scale)
myx = fitsh_eval_2d_poly(x0,y0,order-1,jyx,offsetx,offsety,scale)
myy = fitsh_eval_2d_poly(x0,y0,order-1,jyy,offsetx,offsety,scale)
det=1.0/(mxx*myy-mxy*myx)
imxx=+myy*det
imxy=-mxy*det
imyx=-myx*det
imyy=+mxx*det
wx=fitsh_eval_2d_poly(x0,y0,order,dxfit,offsetx,offsety,scale)-x
wy=fitsh_eval_2d_poly(x0,y0,order,dyfit,offsetx,offsety,scale)-y
dx=imxx*wx+imxy*wy
dy=imyx*wx+imyy*wy
x0=x0-dx
y0=y0-dy
return x0,y0
def fitsh_projection_get_matrix(ra0,dec0):
mproj = np.zeros(shape=[3,3])
ra=ra0*np.pi/180.0
dec=dec0*np.pi/180.0
sr0=np.sin(ra)
cr0=np.cos(ra)
sd0=np.sin(dec)
cd0=np.cos(dec)
mproj[0,0] = + sr0
mproj[0,1]=-cr0
mproj[0,2]=0.0
mproj[1,0]=-sd0*cr0
mproj[1,1]=-sd0*sr0
mproj[1,2]=+cd0
mproj[2,0]=-cd0*cr0
mproj[2,1]=-cd0*sr0
mproj[2,2]=-sd0
return mproj
def fitsh_projection_do_matrix_coord(mproj,rain,decin):
ra = rain*np.pi/180.0
dec = decin*np.pi/180.0
sr=np.sin(ra)
cr=np.cos(ra)
sd=np.sin(dec)
cd=np.cos(dec)
x=cd*cr
y=cd*sr
z=sd
rx=mproj[0,0]*x+mproj[0,1]*y+mproj[0,2]*z
ry=mproj[1,0]*x+mproj[1,1]*y+mproj[1,2]*z
rz=mproj[2,0]*x+mproj[2,1]*y+mproj[2,2]*z
m=1.0/np.sqrt(1-rx**2-ry**2) #gnomic projection
rx = rx*m
ry = ry*m
return [-rx*180.0/np.pi,ry*180.0/np.pi]
def fitsh_projection_do_inverse_matrix_coord(mproj,x,y):
z=1.0-x**2-y**2
z=-np.sqrt(z);
px=mproj[0,0]*x+mproj[1,0]*y+mproj[2,0]*z
py=mproj[0,1]*x+mproj[1,1]*y+mproj[2,1]*z
pz=mproj[0,2]*x+mproj[1,2]*y+mproj[2,2]*z
rde=np.asin(pz)*180.0/np.pi
rra=np.atan2(py,px)*180.0/np.pi
if rra<0.0:
rra=rra+360.0
return [rra,rdec]