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pyopenclAttractorFractals.py
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pyopenclAttractorFractals.py
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import numpy as np
import pyopencl as cl
from pyopencl.elementwise import ElementwiseKernel
import os
import matplotlib.pyplot as plt
from numba import jit,prange,njit
import pyopencl.array
import timeit
#//__f(X[i+ittlim*k],Y[i+ittlim*k],k1,k2,k3,k4,k5)__;
#//__g(X[i+ittlim*k],Y[i+ittlim*k],k1,k2,k3,k4,k5)__;
os.environ["PYOPENCL_CTX"]="0"
os.environ['PYOPENCL_COMPILER_OUTPUT'] = '1'
hoppalongx = "k1-X[i]"
hoppalongy = "Y[i]-sign(X[i])*( sqrt(fabs(k2*X[i]-k3)))"
def prepAttractorCl(f,g,dtype=float):
from PyToPyOpenCL import subsfunction
mapclstr=["int ittlim,float k1,float k2, float k3,float k4,float k5,float *Y,float *X","""
//i indexes row
//k indexes column i,k-1 is value bellow, k=0 innitial
for (int k=1; k<ittlim-1; k++){
X[i*ittlim+k]=__f(X[i*ittlim+k-1],Y[i*ittlim+k-1],k1,k2,k3,k4,k5,X[i*ittlim],Y[i*ittlim])__;
Y[i*ittlim+k]=__g(X[i*ittlim+k-1],Y[i*ittlim+k-1],k1,k2,k3,k4,k5,X[i*ittlim+k],Y[i*ittlim])__;
}
"""]
f=f.replace("y","Y[i] ")
f=f.replace("x","X[i] ")
g=g.replace("y","Y[i] ")
g=g.replace("x","X[i] ")
f=("float X[i],float Y[i],float k1,float k2, float k3,float k4,float k5,float X0, float Y0".split(","),f)
g=("float X[i],float Y[i],float k1,float k2, float k3,float k4,float k5,float XN, float Y0".split(","),g)
mapclstr[1]=subsfunction(f,mapclstr[1],"f",RemoveSemiColon=False)
mapclstr[1]=subsfunction(g,mapclstr[1],"g",RemoveSemiColon=False)
print(f)
print(g)
if dtype == np.float64:
mapclstr[1] = mapclstr[1].replace("float","double")
mapclstr[1] = mapclstr[1].replace("float","double")
mapclstr[0] = mapclstr[0].replace("float","double")
mapclstr[0] = mapclstr[0].replace("float","double")
for i in mapclstr[1].split("\n"):
print(i)
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mapcl = ElementwiseKernel(ctx,*mapclstr,"mapcl")
return mapcl,queue
def iterateOpencl(x1,x2,y1,y2,IttLim,mapclstr,SideLength,Consts = np.array([2.0,1.0,0.0,0.0,0.0],dtype =np.float32),dtype=np.float32):
if str(type(mapclstr[0]))=="<class 'pyopencl.elementwise.ElementwiseKernel'>":
mapcl=mapclstr[0]
queue = mapclstr[1]
precompiled=True
else:
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mapcl = ElementwiseKernel(ctx,*mapclstr,"mapcl")
if SideLength>1:
Xs,Ys=PrepAttractorData(x1,x2,y1,y2,SideLength,IttLim,dtype=dtype)
Xs=cl.array.to_device(queue, Xs)
Ys=cl.array.to_device(queue, Ys)
Xs.size=SideLength*SideLength
Ys.size=SideLength*SideLength
mapcl(int(IttLim),*Consts,Ys,Xs)
Xs=Xs.get().T
Ys=Ys.get().T
Hoppalongiterations=np.stack((Xs,Ys),axis=1)
else:#for plotting the orbit
Xs=np.zeros(IttLim)
Ys=np.zeros(IttLim)
Xs[0]=x1
Ys[0]=y1
Xs=cl.array.to_device(queue, Xs)
Ys=cl.array.to_device(queue, Ys)
Xs.size=SideLength*SideLength
Ys.size=SideLength*SideLength
mapcl(int(IttLim),*Consts,Ys,Xs)
Xs=Xs.get().T
Ys=Ys.get().T
Hoppalongiterations=np.array([Xs,Ys])
return Hoppalongiterations
@njit
def points(Xs,Ys,XCount,YCount):
Xbounds=np.linspace(np.min(Xs),np.max(Xs),XCount)#minimum Xvals to be assigned to pixel
Ybounds=np.linspace(np.min(Ys),np.max(Ys),YCount)
counts = np.zeros((XCount+2,YCount+2))
for i in range(len(Xs)):
counts[np.searchsorted(Xbounds,Xs[i],side="right"),np.searchsorted(Ybounds,Ys[i],side="right")]+=1
return counts[1:-1,1:-1]
@njit(parallel=True)
def prepdataDiff(Hoppalongiterations,SideLength,Order=2):
#hoppalong iterations is all of the points every hoppalong orbit visited so sidelength by side length by Niterations
resultrange=np.zeros((SideLength,SideLength))
for i in prange((SideLength**2)):
resultrange[i%SideLength,i//SideLength] = np.sum((np.ediff1d(Hoppalongiterations[:,0,i]))**Order+np.ediff1d(Hoppalongiterations[:,1,i])**Order)
return resultrange
@njit(parallel=True)
def prepdataMaxMin(Hoppalongiterations,SideLength,width=200,height=200):
#hoppalong iterations is all of the points every hoppalong orbit visited so sidelength by side length by Niterations
print("preping data")
resultrange=np.zeros((SideLength,SideLength))
for i in prange((SideLength**2)):
agg=points(Hoppalongiterations[:,0,i],Hoppalongiterations[:,1,i],width,height)#creates density map of locations of ith hoppalong orbit
rangs = np.zeros(agg.shape[0],dtype=np.float32)
for j in range(agg.shape[0]):
rangs[j]=(np.max(agg[j,:])-np.min(agg[j,:]))#finds ranges of each jump
rang=np.sum(rangs)
resultrange[i%SideLength,i//SideLength] = rang#/dist
#print("fin preping data")
#print(np.shape(resultrange))
return resultrange
def AttractorExplorer(x1,x2,y1,y2,N,f,g,SideLength,Res2 = 300,N2=40000,args = np.array([2.0,1.0,0.0,0.0,0.0],dtype =np.float64),dtype=np.float64,cmaporbit="jet",Aggfunc=prepdataMaxMin,orbitstart=(0,0)):
from matplotlib import gridspec
print((f,g))
mapcl=prepAttractorCl(f,g,dtype=dtype)
print(mapcl)
plt.ion()
extent = [x1,x2,y1,y2]
Hoppalongiterations =iterateOpencl(*extent,N,mapcl,SideLength,Consts=args)
resultrange = Aggfunc(Hoppalongiterations,SideLength)
#Hoppalongiterations = points(Hoppalongiterations[:,0,0],Hoppalongiterations[:,1,0],1000,1000)
fig=plt.figure()
fig.set_size_inches(12,6)
fig.set_label("Attractor Explorer")
gs = gridspec.GridSpec(1, 2, width_ratios=[1,1],
wspace=0.2, hspace=0.0, top=0.95, bottom=0.05, left=0.17, right=0.845)
#fig, ax = plt.subplots(2)
ax=[plt.subplot(gs[0,0]),plt.subplot(gs[0,1])]
#plt.tight_layout()
ax[0].set_title("Function of Whole Domain/Heuristic for size of pattern")
ax[1].set_title("Orbit of input Function X0,Y0 = "+str((orbitstart)))
ax[0].spines['left'].set_position(('zero'))
ax[0].spines['bottom'].set_position('zero')
# Move left y-axis and bottim x-axis to centre, passing through (0,0)
ax[1].spines['left'].set_position('center')
ax[1].spines['bottom'].set_position('center')
ax[0].spines['left'].set_position('center')
ax[0].spines['bottom'].set_position('center')
# Eliminate upper and right axes
ax[1].spines['right'].set_color('none')
ax[1].spines['top'].set_color('none')
ax[0].spines['right'].set_color('none')
ax[0].spines['top'].set_color('none')
# Show ticks in the left and lower axes only
ax[1].xaxis.set_ticks_position('bottom')
ax[1].yaxis.set_ticks_position('left')
ax[0].xaxis.set_ticks_position('bottom')
ax[0].yaxis.set_ticks_position('left')
ax[0].imshow(resultrange,extent=extent)
Orbit = iterateOpencl(orbitstart[0],0,orbitstart[1],0,N2,mapcl,1,Consts=args)
Orbit = points(Orbit[0,:],Orbit[1,:],Res2,Res2)
Orbit= np.log2(Orbit,np.zeros_like(Orbit), where=(Orbit!=0))#= points(Hoppalongiterations[:,0,0],Hoppalongiterations[:,1,0],Res2,Res2)
ax[1].imshow(Orbit,cmap=cmaporbit)
plt.draw()
def onclick(event):
if event.key == "control":
ax[1].set_title("Orbit of input Function X0,Y0 = "+str((round(event.xdata,4),round(event.ydata,4))))
Orbit = iterateOpencl(event.xdata,0,event.ydata,0,N2,mapcl,1,Consts=args)
Orbit = points(Orbit[0,:],Orbit[1,:],Res2,Res2)
Orbit= np.log2(Orbit,np.zeros_like(Orbit), where=(Orbit!=0))#= points(Hoppalongiterations[:,0,0],Hoppalongiterations[:,1,0],Res2,Res2)
ax[1].imshow(Orbit,cmap=cmaporbit)
ax[1].xaxis.set_ticks_position('bottom')
ax[1].yaxis.set_ticks_position('left')
ax[1].spines['right'].set_color('none')
ax[1].spines['top'].set_color('none')
ax[1].spines['left'].set_position('center')
ax[1].spines['bottom'].set_position('center')
plt.draw()
else:
print("Control click to generate new orbit originating from mouse coords")
def onpress(event):
if event.key == "m":
extent=[*ax[0].get_xlim(),*ax[0].get_ylim()]
print("regening map with borders")
print(extent)
Hoppalongiterations =iterateOpencl(*extent,N,mapcl,SideLength,Consts=args)
Zoomedmap = Aggfunc(Hoppalongiterations,SideLength)
ax[0].imshow(Zoomedmap,extent=extent)
plt.draw()
#print((event.xdata,event.ydata))
cid = fig.canvas.mpl_connect('button_press_event', onclick)
cid=fig.canvas.mpl_connect('key_press_event', onpress)
plt.show(block=True)
@njit(parallel=True)
def PrepAttractorData(x1,x2,y1,y2,SideLength,IttLim,dtype):
xvals = np.linspace(x1,x2,SideLength)
yvals = np.linspace(y1,y2,SideLength)#creates start vals
xvalsOrdered = np.zeros(SideLength**2)#empty containers for start vals ordered
yvalsOrdered = np.zeros(SideLength**2)
for i in prange(SideLength):
yvalsOrdered[i*SideLength:i*SideLength+SideLength]=yvals[i]#every y val repeated side length times
xvalsOrdered[i*SideLength:i*SideLength+SideLength]=xvals#whole xval arr repeated for each row
Xs=np.zeros((SideLength**2,IttLim))
Ys=np.zeros((SideLength**2,IttLim))#includes space for itterated values
Xs[:,0]=xvalsOrdered.astype(dtype)
Ys[:,0]=yvalsOrdered.astype(dtype)
return Xs,Ys
if __name__ == '__main__':
SideLength = 500
IttLim=50
dtype=np.float64
Consts = np.array([2,1,0],dtype =dtype)
x1,x2,y1,y2=-2,2,-2,2
extent=[x1,x2,y1,y2]
hoppalongx = "k1- X[i]"
hoppalongy = "Y[i]-sign(X[i])*( sqrt(fabs(k2*X[i]-k3)))"
dejongx="sin(k1*Y[i])+cos(X[i]*k2)"
dejongy="sin(k3*X[i])+cos(Y[i]*k4)"
#info and start vals for https://www.researchgate.net/publication/263469351_ABOUT_WHAT_IS_CALLED_GUMOWSKI-MIRA_MAP
Gumowski_MiraF = "(k2*x + (2*(1-k2)*x*x/(1.0 + x*x)))"
Gumowski_Mirax="k1*y+k3*y*(1-k3*y*y)+"+Gumowski_MiraF
Gumowski_Miray="-x+"+Gumowski_MiraF.replace("x","XN") #(k2 * XN + (2*(1 - k2)*XN*XN/(1.0 + XN*XN)))"
AttractorExplorer(*extent,IttLim,hoppalongx,hoppalongy,SideLength,Res2=500,N2=int(1e6),args=[2,1, 0, 0, 0],orbitstart=(0, 0),Aggfunc=prepdataDiff)
"""
time = timeit.default_timer()
Xs,Ys=PrepAttractorData(*extent,SideLength,IttLim,dtype=dtype)
print(timeit.default_timer()-time)
#Xs[:,0]=np.array([1,2]).astype(dtype)
#Ys[:,0]=np.array([1,2]).astype(dtype)
prepAttractorCl()
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
Xs=cl.array.to_device(queue, Xs)
Ys=cl.array.to_device(queue, Ys)
Xs.size=SideLength*SideLength
Ys.size=SideLength*SideLength
mapcl(int(IttLim),2.0,1.0,0.0,0.0,0.0,Ys,Xs)
Xs=Xs.get().T
Ys=Ys.get().T
print(timeit.default_timer()-time)
Hoppalongiterations=np.stack((Xs,Ys),axis=1)
mapclstr=["float k1,float k2, float k3, float *Xs,float *Ys,float *resY,float *resX","""
#resY[i] =k1- Xs[i];
#resX[i]= Ys[i]-sign(Xs[i])*( sqrt(fabs(k2*Xs[i]-k3)));
#Xs[i]=resX[i];
#Ys[i]=resY[i];
"""
]
#Hoppalongiterations = iterateOpencl(*extent,N,mapclstr,SideLength)
print(timeit.default_timer()-time)
resultrange = prepdataMaxMin(Hoppalongiterations,SideLength)
print(timeit.default_timer()-time)
plt.imshow(resultrange,extent=extent)
plt.show()
"""