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Newton.py
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Newton.py
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#from numba import jit
import equations
import math
import numpy as np
#@jit(nopython=True) # Set "nopython" mode for best performance, equivalent to @njit
def Jac(func,x,k):
epsfcn = 1.0e-3
epsmch = 1.0e-3
eps = math.sqrt(max(epsfcn,epsmch))
Jfun=[[0 for i in range(len(x))] for i in range (len(x))]
#print(x)
wa1=func(x,k)[0]
for i in range(len(x)):
temp=x[i]
#print(temp)
h=eps*abs(temp)
if (h==0):
h=eps
#if i == 80:
# print(temp, h, temp+h)
x[i]=temp+h
fvec=func(x,k)[0]
x[i]=temp
for j in range(len(x)):
Jfun[j][i]=(-wa1[j]+fvec[j])/h
#if i == 47:
# print("Newton",j,i,wa1[j], fvec[j], (-wa1[j]+fvec[j]))
return Jfun
#@jit(nopython=True) # Set "nopython" mode for best performance, equivalent to @njit
def broyden(func,x,k,type):
fun=equations.conservation_eqs
f=np.matrix(fun(x,k)[0])
J=np.matrix(Jac(fun,x,k))
# IJ=np.linalg.inv(J)
IJ=J.I
dx=np.ones(x.shape)
i=0
iter=0
#while(np.max(dx)>0.0001):
while(np.linalg.norm(f)>0.0001) and (iter<500):
f_previous=f
x_previous=x
x=x-np.array(f*IJ.T)[0]
f=np.matrix(fun(x,k)[0])
# print('x',x)
# print('f',f)
df=f-f_previous
dx=x-x_previous
# #
# #-------------------------------------------------------
# #using good broyden
# dx=np.array([dx])
# df=np.array([df])
# dx=dx.T
# df=df.T
# IJ = IJ+(dx-IJ*df)*(dx.T*IJ)/np.inner(dx.T*IJ,df)
# #-------------------------------------------------------
IJ=IJ-np.outer(IJ*f.T,dx)*IJ/np.inner(dx,dx+(IJ*f.T).T)
#print(i)
iter+=1
#print(iter,np.linalg.norm(f))
# input("Pausing! Press Enter to continue...")
#J=J+np.outer((df-dx*J.T),dx)/np.linalg.norm(x)**2
#IJ=J.I
return x, fun(x,k)
#=====================================================
# newton solvers
# separate for rat/human, same method with different
# damping coefficients
#=====================================================
# rat newton solver
def newton_rat(func,x,k,cell):
if cell.species != 'rat' and cell.species != 'mou':
raise Exception('newton_rat only for rat or mouse model')
fun=equations.conservation_eqs
f=np.matrix(fun(x,k)[0])
#print(np.matrix(fun(x,k)[0]))
#print(len(x))
TOLpcn = 1
i = 1
iter = 0
if k==0:
maxiter = 300
else:
maxiter = 150
# check
if np.isnan(np.linalg.norm(f)):
if cell.segment == 'CCD' or cell.segment == 'OMCD' or cell.segment == 'IMCD':
raise Exception(cell.segment + ' norm(f) is Nan')
else:
raise Exception(cell.segment + ' ' + cell.type + ' norm(f) is Nan')
while(np.linalg.norm(f) > 0.0001) and (iter<maxiter+1): #(iter<300)
if np.linalg.norm(f)>1e14 or np.isnan(np.linalg.norm(f)):
if cell.segment == 'CCD' or cell.segment == 'OMCD' or cell.segment == 'IMCD':
raise Exception('Newton solver diverged in ' + cell.segment + ' at cell number: ' + str(k))
else:
raise Exception('Newton solver diverged in '+ cell.type + ' ' + cell.segment + ' at cell number: ' + str(k))
elif iter == maxiter:
if cell.segment == 'CCD' or cell.segment == 'OMCD' or cell.segment == 'IMCD':
print('Warning!!: Newton solver did not converge in <'+str(iter)+' iterations in ' + cell.segment + ' cell number ' + str(k) + '\n')
else:
print('Warning!!: Newton solver did not converge in <'+str(iter)+' iterations in ' + cell.type + ' ' + cell.segment + ' cell number ' + str(k) + '\n')
print('error size: '+ str(np.linalg.norm(f)))
print('\n')
i += 1
J = np.matrix(Jac(fun,x,k))
#print(J[:,78])
#print(len(x))
#print(J.shape)
#print(np.where(~J.any(axis=1))[0])
#u, c = np.unique(J, axis=0, return_counts=True)
#print((c>1).any())
#print(np.linalg.det(J))
IJ = J.I
F = np.matrix(fun(x,k)[0])
# PCT
if cell.segment == 'PT':
amp = 1.0
# S3
elif cell.segment == 'S3':
amp = 1.0
# SDL
elif cell.segment == 'SDL':
amp = 1.0
# LDL
elif cell.segment == 'LDL':
if iter>75:
amp = 0.9
elif iter>100:
amp = 0.7
else:
amp = 1.0
# LAL
elif cell.segment == 'LAL':
amp = 1.0
# mTAL
elif cell.segment == 'mTAL':
if np.linalg.norm(f)>5000:
if k==0:
amp = 0.2
else:
amp = 0.5
elif np.linalg.norm(f)>1500:
if k==0:
amp = 0.2
else:
amp = 0.5
elif np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.95
elif iter>100:
amp = 0.95
else:
amp = 1.0
# cTAL
elif cell.segment == 'cTAL':
if np.linalg.norm(f)>5000:
amp = 0.2
elif np.linalg.norm(f)>2000:
amp = 0.1 # change for female 0.3
elif np.linalg.norm(f)>1000:
amp = 0.5
elif np.linalg.norm(f)>100:
amp = 0.9
elif iter>100:
if np.linalg.norm(f)>1:
amp = 0.9
else:
amp = 0.95
else:
amp = 1.0
# DCT
elif cell.segment == 'DCT':
amp = 1.0
'''
if k==0:
amp = 0.2
else:
amp = 1
'''
# CNT
elif cell.segment == 'CNT':
# amp = 0.6
if np.linalg.norm(f)>1e9:
amp = 0.25
elif np.linalg.norm(f)>1e6:
amp = 0.45
elif np.linalg.norm(f)>5000:
if cell.type == 'jux2':
if k==0:
amp = 0.5
else:
amp = 0.5
elif cell.type == 'jux3':
if k==0:
amp = 1.0
else:
amp = 0.75
elif cell.type == 'jux4':
if k==0:
amp = 1.0 #0.4
else:
amp = 0.5
elif cell.type == 'jux5':
if k==0:
if cell.HT == 'N':
amp = 0.3
else:
amp = 0.5
else:
amp = 0.25
elif cell.type == 'jux1':
if k==0:
amp = 1.0
else:
amp = 0.5
else:
if k==0:
amp = 0.5
else:
amp = 0.4
elif np.linalg.norm(f)>1500:
if k==0:
amp = 0.4
else:
amp = 0.6
elif np.linalg.norm(f)>1000:
if k==0:
amp = 0.5
else:
amp = 0.7
elif iter > 100:
if np.linalg.norm(f)<1:
amp = 0.8 #1.0
else:
amp = 0.65
elif iter > 50:
if np.linalg.norm(f)>1:
amp = 0.75
else:
amp = 1.0
else:
if np.linalg.norm(f)>1:
amp = 0.5
else:
amp = 1.0
# CCD
elif cell.segment == 'CCD':
if np.linalg.norm(f)>1e8:
amp = 0.2
elif np.linalg.norm(f)>5000:
if k==0:
amp = 0.5 # 0.5
else:
amp = 0.5 #0.5
elif np.linalg.norm(f)>1000:
if k==0:
amp = 0.5#0.7
else:
amp = 0.5 #0.75
elif iter>75:
amp = 0.75
elif iter>50:
if np.linalg.norm(f)>1:
amp = 0.8
else:
amp = 0.95
elif iter>30:
if np.linalg.norm(f)>20:
amp = 0.8
elif np.linalg.norm(f)>5:
amp = 0.9
else:
amp = 1.0
else:
amp = 1.0
# OMCD
elif cell.segment == 'OMCD':
if k==0:
amp = 0.1
elif np.linalg.norm(f)>1e6:
amp = 0.4 #0.45
elif np.linalg.norm(f)>1e4:
amp = 0.4 #0.65
elif np.linalg.norm(f)>5000:
if k==0:
amp = 0.75
else:
amp = 0.6 #1.0
elif np.linalg.norm(f)>1000:
if k==0:
amp = 0.8
else:
amp = 0.8 #1.0
elif np.linalg.norm(f)>100:
amp = 0.3 #1.0
elif iter>115:
amp = 0.6
elif iter>75:
amp = 0.6 #0.65
else:
amp = 0.8
# IMCD
elif cell.segment == 'IMCD':
if cell.sex == 'female' or cell.sex == 'male':
if k==0:
amp = 0.12
else:
amp = 0.5
# male
elif np.linalg.norm(f)>5000:
if k==0:
amp = 0.07
else:
amp = 0.5
elif np.linalg.norm(f)>1000:
amp = 1.0 # 0.5
elif iter>100:
if np.linalg.norm(f)>100:
amp = 0.9
elif np.linalg.norm(f)>50:
amp = 0.75
elif np.linalg.norm(f)>1:
amp = 0.5
else:
amp = 0.5
elif iter>75:
if np.linalg.norm(f)>100:
amp = 0.95
elif np.linalg.norm(f)>10:
amp = 0.85
elif np.linalg.norm(f)>1:
amp = 0.9
else:
amp = 1.0
elif iter>50:
if np.linalg.norm(f)>10:
amp = 0.8
else:
amp = 0.9
else:
amp = 1.0
else:
print('What is this segment?', cell.segment)
raise Exception('cell.segment is not characterized')
delta = amp*np.array(F*IJ.T)[0]
x-= delta
f = np.matrix(fun(x,k)[0])
iter+=1
#print(iter, np.linalg.norm(f))
TOLpcn = np.max(delta/x)
return x, fun(x,k)
# human newton solver
def newton_human(func,x,k,cell):
if cell.species != 'hum':
raise Exception('newton_human only for human model')
fun=equations.conservation_eqs
f=np.matrix(fun(x,k))
TOLpcn = 1
i = 1
iter = 0
while(np.linalg.norm(f) > 0.0001) and (iter<150): #(iter<300)
i += 1
J = np.matrix(Jac(fun,x,k))
IJ = J.I
F = np.matrix(fun(x,k))
# PCT
if cell.segment == 'PT':
amp = 1.0
# S3
elif cell.segment == 'S3':
if cell.diabete == 'Non' and cell.unx == 'Y':
if cell.sex == 'male':
amp = 1.0
if cell.sex == 'female':
amp = 0.6
else:
amp = 1.0
# SDL
elif cell.segment == 'SDL':
amp = 1.0
# LDL
elif cell.segment == 'LDL':
amp = 1.0
# LAL
elif cell.segment == 'LAL':
amp = 1.0
# mTAL
elif cell.segment == 'mTAL':
if cell.inhib == 'ACE':
if np.linalg.norm(f)>100:
amp = 0.2
else:
amp = 0.8
elif cell.diabete == 'Non':
if np.linalg.norm(f)>100:
amp=0.2
else:
amp=1.0
elif cell.diabete == 'Moderate':
if np.linalg.norm(f)>100:
amp = 0.2
else:
amp = 1.0
elif cell.diabete == 'Severe':
if np.linalg.norm(f)>100:
amp = 0.2
else:
amp = 1.0
else:
amp = 1.0
elif cell.segment == 'cTAL':
if np.linalg.norm(f)>100:
amp = 0.2
else:
amp = 1.0
# MD
elif cell.segment == 'MD':
if np.linalg.norm(f)>100:
amp = 0.2
else:
amp = 0.8
# DCT
elif cell.segment == 'DCT':
if cell.inhib == 'ACE':
if cell.sex == 'male':
amp = 0.5
elif cell.sex == 'female':
amp = 0.8
else:
if cell.sex == 'female':
if cell.type == 'jux1':
amp = 0.9
elif cell.type == 'jux2':
amp = 0.7
elif cell.type == 'jux3':
amp = 0.7
elif cell.type == 'sup':
if np.linalg.norm(f)>2000:
amp = 0.5
else:
amp = 0.5
else:
amp = 1.0
else:
amp = 0.5
# CNT
elif cell.segment == 'CNT':
if np.linalg.norm(f)>5000:
if k==0:
amp = 0.2
else:
amp = 0.3
elif np.linalg.norm(f)>1000:
if k==0:
amp = 0.5
else:
amp = 0.7
else:
amp = 1.0
# CCD
elif cell.segment == 'CCD':
if np.linalg.norm(f)>5000:
if k==0:
amp = 0.25
else:
amp = 0.5
elif np.linalg.norm(f)>1000:
amp = 0.75
elif iter>50:
if np.linalg.norm(f)>1:
amp = 0.8
else:
amp = 0.95
else:
amp = 1.0
# OMCD
elif cell.segment == 'OMCD':
if np.linalg.norm(f)>100:
amp = 0.5
else:
amp = 0.8
# IMCD
elif cell.segment == 'IMCD':
if cell.inhib == 'ACE':
if np.linalg.norm(f)>100:
if k==0:
amp=0.2
else:
amp = 0.1
else:
if k==0:
amp = 1.5
else:
amp = 0.9
elif cell.diabete == 'Non' and cell.unx == 'N':
if cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.1
else:
if k==0:
amp = 0.5
else:
amp = 0.5
elif cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.27
else:
amp = 0.2
else:
if k==0:
amp = 0.8
else:
amp = 0.8
elif cell.diabete == 'Non' and cell.inhib == 'SGLT2' and cell.unx == 'Y':
if cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.1
else:
if k==0:
amp = 0.5
else:
amp = 0.5
elif cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.23
else:
amp = 0.8
else:
amp = 0.8
elif cell.diabete == 'Moderate':
if cell.inhib != 'SGLT2':
if cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.1
else:
amp = 0.5
elif cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.19
else:
amp = 0.17
else:
if k==0:
amp = 0.8
else:
amp = 0.8
elif cell.inhib == 'SGLT2':
if cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.5
else:
amp = 0.2
else:
amp = 0.8
elif cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.7
else:
amp = 0.2
else:
amp = 0.8
elif cell.diabete == 'Severe':
if cell.inhib == 'SGLT2':
if cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.1
else:
if k==0:
amp = 0.5
else:
amp = 0.5
elif cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.23
else:
amp = 0.17
else:
if k==0:
amp = 0.8
else:
amp = 0.8
else:
if cell.sex == 'female':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.2
else:
amp = 0.1
else:
if k == 0:
amp = 0.5
else:
amp = 0.5
elif cell.sex == 'male':
if np.linalg.norm(f)>100:
if k==0:
amp = 0.1
else:
amp = 0.17
else:
if k==0:
amp = 0.2
else:
amp = 0.8
else:
amp = 1.0
else:
print('What is this segment?', cell.segment)
raise Exception('cell.segment is not characterized')
delta = amp*np.array(F*IJ.T)[0]
x -= delta
f = np.matrix(fun(x,k))
iter += 1
#print(iter, np.linalg.norm(f))
TOLpcn = np.max(delta / x)
return x