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RJplots.py
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RJplots.py
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import numpy as np
import matplotlib.pyplot as plt
### The following are outward facing functions which may be called
### The main function of the package, returns the RJ-values of a 2D image (2d-array) as well as the classification of the structure.
def get_rj(image):
J1,J2,com,theta = moments(image)
RJ1 = (J1 - J2)/np.sqrt(2)
RJ2 = (J1 + J2)/np.sqrt(2)
RJ2 = RJ2/(-RJ1 + np.sqrt(2))
cla = classification(RJ1,RJ2)
return RJ1,RJ2,cla
### Uses the classification scheme described in the accompanying paper.
### 1 - Quasi-circular, centrally over-dense
### 2 - Quasi-circular, centrally under-dense
### 3 - Elongated, centrally over-dense
### 4 - Elongated, centrally under-dense
def classification(RJ1,RJ2):
z = np.poly1d([-0.31717289, 0.00112143, 0.47870963])
cla = -2
if(RJ1>0.47870963):
if(RJ2>0):
cla = 3
else:
cla = 4
else:
if(RJ1 < z(RJ2) and RJ1>-z(RJ2)):
if(RJ2>0):
cla = 1
else:
cla = 2
else:
if(RJ2>0):
cla = 3
else:
cla = 4
if(cla==-2):
print("Something went wrong with the classification",RJ1,RJ2)
return cla
### Creates and saves an RJ-plot given an array of RJ-values. The section which produces the axes, sets the limits and displays the colour-coded quadrants in highlighted so that it may copied to produce bespoke RJ-plots.
def make_rj_plot(RJ1,RJ2,plotname,dpi=100,markersize=1,markercolor="C0"):
fig = plt.figure(1,figsize=(10,10))
plt.plot(RJ1,RJ2,marker="o",color=markercolor,ls="None",ms=markersize)
### This following section of the code can be taken and copied to produce the axis lines and the four colour-coded quadrants
### From here:
z = np.poly1d([-0.31717289, 0.00112143, 0.47870963])
ans = 1.2303055886801646
yy = np.linspace(-ans,ans,100)
plt.plot(z(yy),yy,"r",lw=1.5)
xx = np.linspace(-0.05,np.sqrt(2),100)
plt.plot(xx,np.zeros_like(xx),"k",lw=1.5)
xx = np.linspace(-np.sqrt(2),np.sqrt(2),100)
plt.plot(np.zeros_like(xx),xx,"k",lw=1.5)
plt.xlim(-0.05,np.sqrt(2))
plt.ylim(-1,1)
y2 = np.linspace(0,ans,100)
plt.fill_between(z(y2),y2,alpha=0.15, color="y")
plt.fill_between(z(y2),-y2,0,alpha=0.15, color="b")
xx = np.linspace(np.amax(z(y2)),np.sqrt(2),100)
q = np.zeros_like(xx)
x2 = z(y2)[::-1]
y2 = y2[::-1]
x1 = np.concatenate((x2,xx))
y1 = np.concatenate((y2,q))
plt.fill_between(x1,y1,np.sqrt(2),alpha=0.15,color="g")
plt.fill_between(x1,-y1,-np.sqrt(2),alpha=0.15,color="m")
plt.xlabel("R$_1$")
plt.ylabel("R$_2$")
### To here.
plt.savefig(plotname,dpi=dpi)
### This function is from J-plots and will return the two J-values, the centre of weight of a structure, as well as its position angle.
def moments(g):
com=find_com(g)
Atot=np.count_nonzero(g)
Mtot=np.sum(g)
I1,I2,t1=i12(g,com)
first=min([I1,I2])
second=max([I1,I2])
ma=Atot*Mtot
II1=(ma - 4*np.pi*first)/(ma + 4*np.pi*first)
II2=(ma - 4*np.pi*second)/(ma + 4*np.pi*second)
return II1,II2,com,t1
### The following are functions used internally and are not necessarily meant to be called outside of RJ-plots. As such they are commented.
def find_com(grid):
com = np.array([0,0],dtype=float)
nx=grid.shape[0]
ny=grid.shape[1]
ax = np.linspace(0,nx-1,nx)
ay = np.linspace(0,ny-1,ny)
com[0] = np.sum(np.sum(grid,axis=1)*ax)
com[1] = np.sum(np.sum(grid,axis=0)*ay)
com=com/np.sum(grid)
return com
def m11(grid,com):
nx=grid.shape[0]
ny=grid.shape[1]
dr11=0
ay = np.linspace(0,ny-1,ny)
dr11 = np.sum(np.sum(grid,axis=0)*(ay-com[1])**2)
return dr11
def m22(grid,com):
nx=grid.shape[0]
ny=grid.shape[1]
dr22=0
ax = np.linspace(0,nx-1,nx)
dr22 = np.sum(np.sum(grid,axis=1)*(ax-com[0])**2)
return dr22
def m12(grid,com):
nx=grid.shape[0]
ny=grid.shape[1]
dr12=0
ax = np.linspace(0,nx-1,nx) - com[0]
ay = np.linspace(0,ny-1,ny) - com[1]
ax2 = np.array([ax,]*ny).T
ay2 = np.array([ay,]*nx)
dr12 = np.sum(grid*ay2*ax2)
return dr12
def theta(M11,M22,M12):
th=0.5*np.arctan2((2*M12),(M11-M22))
return th
def i12(grid,com):
M11=m11(grid,com)
M22=m22(grid,com)
M12=m12(grid,com)
tt=theta(M11,M22,M12)
i1=(M11*np.cos(tt)*np.cos(tt)) + \
(M22*np.sin(tt)*np.sin(tt)) + \
(M12*np.sin(2*tt))
i2=(M11*np.sin(tt)*np.sin(tt)) + \
(M22*np.cos(tt)*np.cos(tt)) - \
(M12*np.sin(2*tt))
return i1,i2,tt