FEniCS: UMFPACK reports that the matrix being solved is singular - python

I created a divided domain with the stokes-equation in the first subdomain and the mixed-poisson-equation (darcy) in the second subdomain. I work with the UnitSquare and the subdomain 1 should be the interval from 0 to 0,5 and the subdomain 2 from 0,5 to 1.
But now i get the following error:
Solving linear variational problem.
UMFPACK problem related to call to numeric
* Warning: UMFPACK reports that the matrix being solved is singular.
UMFPACK problem related to call to solve
* Warning: UMFPACK reports that the matrix being solved is singular.
assert vmax>=vmin, "empty range, please specify vmin and/or vmax"
Assertion error: empty range, please specify vmin and/or vmax
Can anyone help?
Thanks!
Here is the code:
enter code here
#-*- coding: utf-8 -*-
from dolfin import *
import numpy as np
# Define mesh
mesh = UnitSquare(32,32)
#Subdomain 1
# Gitter übergeben
subdomains = CellFunction("uint", mesh)
# Klasse des Teilgebiets
class Domain_1(SubDomain):
def inside(self, x, on_boundary):
return between(x[0], (0, 0.5)) # Koordinatenangabe des Teilgebiets
# Objekt der Klasse erstellen
sub_domain1 = Domain_1()
sub_domain1.mark(subdomains,0)
# Definition Funktionenräume
U = FunctionSpace(mesh, "CG", 2)
V = FunctionSpace(mesh, "CG", 1)
W = U*V
# Definition Trial- und Testfunktion
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
# boundary condition
p_in = 1
p_out = 0
noslip = DirichletBC(W.sub(0), (0),
"on_boundary && \
(x[1] <= DOLFIN_EPS | x[1] >= 0.5-DOLFIN_EPS)")
inflow = DirichletBC(W.sub(1), p_in, "x[0] <= 0.0 + DOLFIN_EPS*1000")
outflow = DirichletBC(W.sub(1), p_out, "x[0] >= 0.5 - DOLFIN_EPS*1000")
bcp = [noslip,inflow, outflow]
# Definition f
f = Expression("0")
# Variationsformulierung
a = inner(grad(u), grad(v))*dx + div(v)*p*dx(0) + q*div(u)*dx(0)
L = inner(f,v)*dx(0)
# Lösung berechnen
w = Function(W)
problem = LinearVariationalProblem(a, L, w, bcp)
solver = LinearVariationalSolver(problem)
solver.solve()
(u, p) = w.split()
# Subdomain 2
# Gitter übergeben
subdomains = CellFunction("uint", mesh)
# Klasse des Teilgebiets
class Domain_2(SubDomain):
def inside(self,x,on_boundary):
return between(x[0], (0.5,1.0)) # Koordinatenangabe des Teilgebiets
# Objekt der Klasse erstellen
sub_domain2 = Domain_2()
sub_domain2.mark(subdomains,1)
# Define function spaces and mixed (product) space
BDM = FunctionSpace(mesh, "BDM", 1)
DG = FunctionSpace(mesh, "DG", 0)
CG = FunctionSpace(mesh, "CG", 1)
W = MixedFunctionSpace([BDM, DG, CG])
# Define trial and test functions
(sigma, u, p) = TrialFunctions(W)
(tau, v, q) = TestFunctions(W)
#Define pressure boundary condition
p_in = 1
p_out = 0
noslip = DirichletBC(W.sub(1), (0),
"on_boundary && \
(x[1] <= 0.5 + DOLFIN_EPS | x[1] >= 1.0-DOLFIN_EPS)")
inflow = DirichletBC(W.sub(2), p_in, "x[0] <= 0.5 + DOLFIN_EPS*1000")
outflow = DirichletBC(W.sub(2), p_out, "x[0] >= 1.0 - DOLFIN_EPS*1000")
bcp = [noslip,inflow, outflow]
# Define f
#f = Expression("0")
f = Expression("10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)")
# Define variational form
a = (dot(sigma, tau) + div(tau)*u + div(sigma)*v)*dx(1) + inner(p,q)*dx(1) + u*q*dx(1)
L = f*v*dx(1)
# Compute solution
w = Function(W)
problem = LinearVariationalProblem(a, L, w, bcp)
solver = LinearVariationalSolver(problem)
solver.solve()
(sigma, u, p) = w.split()
# plot
plot(u, axes = True, interactive=True, title = "u")
plot(p, axes = True, interactive=True, title = "p")
I forgot the dx(0) in this term. But this was not the problem.
In the first part of the code (Stokes) I tried to write the no slip condition in the following way:
# Randbedingungen
def top_bottom(x, on_boundary):
return x[1] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS
noslip = Constant((0.0,0.0))
bc0 = DirichletBC(W.sub(0), noslip, top_bottom)
p_in = 1
p_out = 0
inflow = DirichletBC(W.sub(1), p_in, "x[0] <= 0.0 + DOLFIN_EPS*1000")
outflow = DirichletBC(W.sub(1), p_out, "x[0] >= 0.5 - DOLFIN_EPS*1000")
bcp = [bc0, inflow, outflow]
# Definition f
f = Expression("(0.0, 0.0)")
# Variationsformulierung Stokes
a = inner(grad(u), grad(v))*dx(0) + div(v)*p*dx(0) + q*div(u)*dx(0)
L = inner(f,v)*dx(0)
But now I get the following error:
Shape mismatch: line 56, in <module> L = inner(f,v)*dx(0
Can anyone help? Thanks!

I think there are several mistakes here. In the first part of the code I think you are using Taylor-Hood elements to solve Stokes equation. If this us the case, then U should be:
U = VectorFunctionSpace(mesh, "CG", 2)
Also in this part of the code:
a = inner(grad(u), grad(v))*dx + div(v)*p*dx(0) + q*div(u)*dx(0)
L = inner(f,v)*dx(0)
I don't know why you are not using dx(0) for the first term. I encourage you to look at the demos at: http://fenicsproject.org/documentation/dolfin/dev/python/demo/index.html
You might get some more tips.

Related

How can I know the dimension of my variable?

I get this error :
ValueError: operands could not be broadcast together with shapes (365,) (2,)
But I'm surprised by this (2,).
How do I know which variable does this dimension (2,) please?
Because none of my variables should have it.
Thank you for your help !
Here, you can see the first script, where I define my function. It include a loop and also another function so I don't know if I can.
I have a lot of variable with (365, ) for the dimension because, it's function of the time, so for 365 days.
I have some fixed variable like the soil parameter, so the dimension for these is (1,)
But I don't know which variable get (2,) dimension ?
import pandas as pd
import numpy as np
def SA(MO = 0,
ETPr = 0,
SWSa = 0,
pb = 1.70 ):
DB = pd.read_excel("~/Documents/Spider/Data/data_base.xlsx", sheet_name = "DB")
DB1 = pd.read_excel("~/Documents/Spider/Bilan_Courgette.xlsx", sheet_name = "sol")
DB2 = pd.read_excel("~/Documents/Spider/Bilan_Courgette.xlsx", sheet_name = "culture")
#Calculs inter. pour déterminer ET0/day
#Array qui reprend "date" en une série 1 -> 365
JourDeLAnnee = pd.Series(range(1,366))
#Mauves
dist_TS = 1+(0.033*np.cos(0.0172 * JourDeLAnnee))
decli_So = 0.409*np.sin((0.0172 * JourDeLAnnee)-1.39)
lat = 0.87266463
ang_Hor_So =np.arccos(-np.tan(lat)*np.tan(decli_So))
gamma = 0.067
#Jaunes
delta = 2504*np.exp((17.27*DB.tsa_by_day)/(DB.tsa_by_day +237.3))/(DB.tsa_by_day +237.3)**2
rg = DB.ens_by_day / 1000000 * 86400
ra = 37.6 * dist_TS * ((ang_Hor_So * np.sin(lat) * np.sin(decli_So)) + \
(np.cos(lat) * np.cos(decli_So) * np.sin(ang_Hor_So)))
rso = (0.75 + (2*0.00001*120)) * ra
tw =(DB.tsa_by_day * np.arctan(0.151977 * ((DB.hra_by_day + 8.313659)**0.5))) + \
np.arctan(DB.tsa_by_day + DB.hra_by_day) - np.arctan(DB.hra_by_day - 1.676331) + \
(0.00391838 * ((DB.hra_by_day)**1.5) * np.arctan(0.023101 * DB.hra_by_day)) - 4.686035
ed = (0.611 * np.exp((17.27 * tw) / (tw + 237.3))) - (0.0008 *(DB.tsa_by_day-tw) * 101.325)
ea =((0.611 * np.exp((17.27*DB.tsa_max) / (DB.tsa_max + 237.3))) + \
(0.611 * np.exp((17.27 * DB.tsa_min) / (DB.tsa_min +237.3)))) / 2.0
rn = (0.77 * rg) - (((1.35 * (rg / rso)) - 0.35) \
* (0.34 - (0.14 * (ed**0.5))) * (4.9E-9) * ((((273+DB.tsa_max)**4)+((273+DB.tsa_min)**4))/2))
#Calcul de G
from typing import List
def get_g_constant(tsa_by_day: List[float], day: int):
assert day >= 1
return 0.38 * (tsa_by_day[day] - tsa_by_day[day-1])
def get_g_for_year(tsa_by_day: List[int]) -> List[float]:
g_list = []
for i in range(1, len(tsa_by_day)):
g_value = get_g_constant(tsa_by_day, i)
g_list.append(g_value)
return g_list
G = get_g_for_year(DB.tsa_by_day)
G = [DB.tsa_by_day[0]] + G
#Le fameux ET0
ET0 = ((0.408 * delta * (rn - G)) + (gamma * (900 /(DB.tsa_by_day + 273)) * DB.vtt_by_day * (ea - ed))) / \
(delta + (0.067*(1+(0.34 * DB.vtt_by_day))))
# Calcul des paramètres du sol
Profil = 500
pb = 100 / ((MO / 224000) + ((100-MO) / (1.64)))
Os = 0.6355+0.0013* DB1.A -0.1631* pb
Or = 0
lnα = (-4.3003) - (0.0097*DB1.A) + (0.0138* DB1.S ) - (0.0992*MO)
lnn = -1.0846-0.0236 * DB1.A -0.0085 * DB1.S +0.0001 * (DB1.S)**2
nn = np.exp(lnn) + 1
m = 1 - (1/nn)
lnK0 = 1.9582 + 0.0308*DB1.S - 0.6142* pb - 0.1566*MO
λ = -1.8642 - 0.1317*DB1.A + 0.0067*DB1.S
α = np.exp(lnα)
K0 = np.exp(lnK0)
θPf2 =(((1 + ((α*(10**2.5))**nn))**(-m))*( Os - Or)) + Or
θPf4 =(((1 + ((α*(10**4.2))**nn))**(-m))*( Os - Or)) + Or
SWS = θPf2 - θPf4
diff = SWS*SWSa
aj = diff / 2
θPf2New = θPf2 + aj
θPf4New = θPf4 - aj
#Calcul du volume de stock p à atteindre
p = 0.04 *(5 - ET0) + DB2.ptab[0]
θp =(1 - p) * ( θPf2New - θPf4New )+ θPf4New
Vp = θp * Profil
#Le fameux ETP
import datetime
DateS = datetime.datetime.strptime('30/03/2019','%d/%m/%Y').timetuple().tm_yday
DateR = datetime.datetime.strptime('15/09/2019','%d/%m/%Y').timetuple().tm_yday
ETP=ET0.copy()
for n in range(364):
if n >= (DateS - 1) and n <= (DateR - 1) :
ETP[n] = ET0[n] * DB2.Kc[0]
else:
ETP[n] = ET0[n] * DB2.SolNu[0]
ETP[0] = 0
ETPNew = ET0.copy()
ETPNew = ETP - ETP * ETPr
#Le Bilan Hydrique
Stock = ET0.copy()
θ = ET0.copy()
Drainage = ET0.copy()
Irrigation = ET0.copy()
Se = ET0.copy()
SeC = ET0.copy()
θ[0] = θPf2New
Stock[0] = θ[0]*Profil
for i in range(364) :
Se[i] = (θ[i] - Or)/( Os - Or)
if Se[i] > 1 :
SeC[i] = 1
else:
SeC[i] = Se[i]
Drainage[i] = K0 *(((SeC[i])**λ )*(1-(1- SeC[i]**(nn/(nn-1)))**m)**2)*10
if Vp[i] - Stock[i] > 0 : #Ici stock non défini
Irrigation[i] = Vp[i] - Stock[i]
else:
Irrigation[i] = 0
Stock[i+1] = Stock[i] + DB.plu_by_day[i] - ETPNew[i] - Drainage[i] + Irrigation[i]
θ[i+1] = Stock[i+1] / Profil
return (Irrigation.sum())
After, i use a second script to do a sensitivity analysis. And It's here, when I run this script, I get the error 'ValueError: operands could not be broadcast together with shapes (365,) (2,)'
import numpy as np
from SALib.analyze import sobol
from SALib.sample import saltelli
from test import*
import matplotlib.pyplot as plt
# Set up dictionary with system parameters
problem = {
'num_vars': 4,
'names': ['MO', 'ETPr', 'SWSa', 'K0'],
'bounds': [[0, 10],
[0, 0.04135],
[0, 0.2615],
[1.40, 1.70],
]}
# Array with n's to use
nsamples = np.arange(50, 400, 50)
# Arrays to store the index estimates
S1_estimates = np.zeros([problem['num_vars'],len(nsamples)])
ST_estimates = np.zeros([problem['num_vars'],len(nsamples)])
# Loop through all n values, create sample, evaluate model and estimate S1 & ST
for i in range(len(nsamples)):
print('n= '+ str(nsamples[i]))
# Generate samples
sampleset = saltelli.sample(problem, nsamples[i],calc_second_order=False)
# Run model for all samples
output = [SA(*sampleset[j,:]) for j in range(len(sampleset))]
# Perform analysis
results = sobol.analyze(problem, np.asarray(output), calc_second_order=False,print_to_console=False)
# Store estimates
ST_estimates[:,i]=results['ST']
S1_estimates[:,i]=results['S1']
np.save('ST_estimates.npy', ST_estimates)
np.save('S1_estimates.npy', S1_estimates)
S1_estimates = np.load('S1_estimates.npy')
ST_estimates = np.load('ST_estimates.npy')
# Generate figure showing evolution of indices
fig = plt.figure(figsize=(18,9))
ax1 = fig.add_subplot(1,2,1)
handles = []
for j in range(problem['num_vars']):
handles += ax1.plot(nsamples, S1_estimates[j,:], linewidth=5)
ax1.set_title('Evolution of S1 index estimates', fontsize=20)
ax1.set_ylabel('S1', fontsize=18)
ax1.set_xlabel('Number of samples (n)', fontsize=18)
ax1.tick_params(axis='both', which='major', labelsize=14)
ax2 = fig.add_subplot(1,2,2)
for j in range(problem['num_vars']):
ax2.plot(nsamples, ST_estimates[j,:], linewidth=5)
ax2.set_title('Evolution of ST index estimates', fontsize=20)
ax2.set_ylabel('ST', fontsize=18)
ax2.tick_params(axis='both', which='major', labelsize=14)
ax2.set_xlabel('Number of samples (n)', fontsize=18)
fig.legend(handles, problem['names'], loc = 'right', fontsize=11)
plt.savefig('indexevolution.png')
# Calculate parameter rankings
S1_ranks = np.zeros_like(S1_estimates)
ST_ranks = np.zeros_like(ST_estimates)
for i in range(len(nsamples)):
orderS1 = np.argsort(S1_estimates[:,i])
orderST = np.argsort(ST_estimates[:,i])
S1_ranks[:,i] = orderS1.argsort()
ST_ranks[:,i] = orderST.argsort()
Thank you for your help !

TypeError: 'int' object is not callable Modeling in python

I am getting the following error in python, and I am not sure why. I am trying to model how meth affects mice.
Here is my code, and the functions that are created in my code:
from scipy import array, linspace
from scipy import integrate
from matplotlib.pyplot import *
def Temp2(z, t, Ta, Te, wexc, yexc, winhib, yinhib, whd, yhd, wexctoinhib, winhibtomdl, whdtospn, yspn, Tt):
# Dependence of Meth Concentration
# dx
# -- = -x/Ta
# dt
#
# dy
# -- = x/Ta - y/Te
# dt
# x = interperitoneal
# y = blood
# Ta is the time constant of Meth in the absorbtion
# Te is the time constant of Meth in elimination
x = z[0] # Rabbits density
y = z[1] # Sheep density
T = z[2]
D = int(x=1)
yt = D(Ta/Te -1)**-1 * (e**-t/Ta - e**-t/Te)
Pexc = (1+tanhx)*[wexc*yt*yexc]
Pinhib = (1+tanhx)*[winhib*yt*yinhib]
Phd = (1+tanhx)*[whd*yt*yhd]
Pmdl = wexctoinghib*Pexc-winhibtomdl*Pinhib
Pspn = Pmdl + whdtospn*Phd+yspn
V = array([-x/Ta, x/Ta - y/Te, (Pspn-(T-T0))/Tt])
return V
def main():
# set up our initial conditions
IC0 = 1
BC0 = 0
T0 = 37
z0 = array([IC0, BC0, T0])
# Parameters
Ta = 8.25
Te = 57.5
wexc = 1.225
yexc = -0.357
winhib = 1.335
yinhib = 1.463
whd = 0.872
yhd = -3.69
wexctoinhib = 7.47
winhibtomdl = 6.38
whdtospn = 5.66
yspn = -3.35
Tt = 89.2
# choose the time's we'd like to know the approximate solution
t = linspace(0., 1., 60)
# and solve
xode= integrate.odeint(Temp2, z0, t, args=(Ta, Te, wexc, yexc, winhib, yinhib, whd, yhd, wexctoinhib, winhibtomdl, whdtospn, yspn, Tt))
print (xode)
main()
Ignore the #s as they do not relate to what the code is saying. Here is the error I am getting:
yt = D(Ta/Te -1)**-1 * (e**-t/Ta - e**-t/Te)
TypeError: 'int' object is not callable
I am not sure what is wrong, and how I can fix this? Can anyone help me?
The issue is here
yt = D(Ta/Te -1)**-1 * (e**-t/Ta - e**-t/Te)
There is no implicit multiplication in python, so when you attempt to do D(Ta/Te - 1) it is being interpreted as a function call rather than D multiplied by what is in the bracket.
Rewrite it like this
yt = D*(Ta/Te -1)**-1 * (e**-t/Ta - e**-t/Te)

Numerical issue in scipy.ode.integrate solver

I am using ode solver to solve stiff problem (since odeint function could not able to solve it). But by this way also I have some warnings and my plot get saturate at some point. Here is image What should I do? Here is the list of warnings:
DVODE-- Warning..internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). solver will continue anyway
In above, R1 = 0.3667661010318D+00 R2 = 0.1426374862242D-16
DVODE-- Warning..internal T (=R1) and H (=R2) are
such that in the machine, T + H = T on the next step
(H = step size). solver will continue anyway
In above, R1 = 0.3667661010318D+00 R2 = 0.1426374862242D-16
DVODE-- Above warning has been issued I1 times.
it will not be issued again for this problem
In above message, I1 = 2
DVODE-- At current T (=R1), MXSTEP (=I1) steps
taken on this call before reaching TOUT
In above message, I1 = 500
In above message, R1 = 0.3667661010318D+00
My code:
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as si
def func():
#arguments:::
w = 1./3.
xi = 2.86
phi1 = 1.645
phi2 = 2.* 1.202
gt = 10.**(-60)
Lt = (1.202*gt)/np.pi
Lin = 10.**-5
Lf = 0.49
dt = 0.0001
gin = gt*Lt/Lin
xin = (-np.log((3. - (xi**2)*Lin)/(3. - (xi**2)*Lt)) + np.log(Lin/Lt))/4.0
uin = -(np.log(Lin/Lt))/2.
state0 = [gin,xin,uin]
print state0
def eq(L, state):
g = state[0]
x = state[1]
u = state[2]
N = (-2.*g/(6.*np.pi + 5.*g))*(18./(1. - 2.*L) + 5.*np.log(1.- 2.*L) - phi1 + 6. )
B = (-(2. - N)*L) - ((g/np.pi)* (5.*np.log(1.-2.*L) - phi2 + (5.*N/40.)))
Eqs = np.zeros((3))
gdl = Eqs[0] = ((2.+N)*g)/B
xdl = Eqs[1] = -(2./(3.*(1.+w)))* (1./(1.-(xi**2)*L/3.))*(1./B)
udl = Eqs[2]= 1./B
return Eqs
ode = si.ode(eq)
# BDF method suited to stiff systems of ODEs
ode.set_integrator('vode',nsteps=500,method='bdf')
ode.set_initial_value(state0,Lin)
L = []
G = []
while ode.successful() and ode.t < Lf:
ode.integrate(ode.t + dt)
L.append(ode.t)
G.append(ode.y)
lam = np.vstack(L)
g,x,u = np.vstack(G).T
return g,x,u,lam
r= func()
L = r[3]
g = r[0]
lng = np.log10(g)
x = r[1]
u = r[2]
w = 1./3.
xi = 2.86
O_A = np.zeros(len(L))
q = np.zeros(len(L))
for i in np.arange(len(L)):
O_A[i] = xi**2*L[i]/3.
alpha = 2./ ((3.+3.*w) * (1.- (L[i]*xi**2)/3.) )
q[i] = 1./alpha - 1.
n = np.zeros(len(L)) #eta(n)
b = np.zeros(len(L))
for j in np.arange(len(L)):
n[j] =(-2.*g[j]/(6.*np.pi + 5.*g[j]))*(18./(1. - 2.*L[j]) + 5.*np.log(1.- 2.*L[j]) - 1.645 + 6. )
b[j]= (-(2. - n[j])*L[j]) - ((g[j]/np.pi)* (5.*np.log(1.-2.*L[j]) - 2.* 1.202 + ((5.*n[j])/4.)))
P = np.zeros(len(x))
for k in np.arange(len(x)):
C = (((3. - (xi**2)*L[k])/g[k])**(3./4.)) * (((2.*L[k] + (u[k]*b[k]))*xi**2) + (n[k] * (3.- L[k]*xi**2)) )
P[k] = (np.exp(3.*x[k])) * (np.exp(4.*u[k])) * C
plt.figure()
plt.plot(L,P)
plt.xlabel('Lambda ---->')
plt.ylabel('P ----->')
plt.title('lambda Vs P')
plt.show()

Magnus Force, Drag force , Serve Ball Trajectory

I am trying to put into this code. Main focus for the code would be to combine all of the forces, hitting at various launch angles and print out the graph of figure 42.3.
from numpy import *
from matplotlib import*
from matplotlib.pyplot import *
from __future__ import division
Basic info
Dimeter = 0.067
r = (Dimeter/2) # radius of sphere (meters)
s = 1.0 # spin in revolutions per second (positive is backspin)
p = 1.225 # air density in kg/m^3
dragCoef = 0.5 # drag coefficient
m = 0.0585 # mass of the ball in kilograms
g = 9.82 # gravitational constant
dt = 0.01
A = (pi*r**2)
Cd = 0.5
Cl = 1.5
v = 30
t = 0.470
n= (t/dt)
a = zeros(n)
v = zeros(n)
x = zeros(n)
Fg = zeros(n)
Fd = zeros(n)
t = zeros(n)
v[0] = 0
x[0] = 0
i = 0
A while loop to add Forces on the ball
while i <= (n-2):
Fg[i] = (m*g)
Fd[i] = (.5*p*A*Cd*(v[i]**2)*sign(-v[i]))
a[i] = ((Fg[i] + Fd[i]) / m)
v[i+1] = (v[i] + a[i]*dt)
x[i+1] = (x[i] +v[i]*dt +.5*a[i]*(dt**2))
t[i+1] = (t[i] + dt)
i = i+1
Printing out graph
print "My distance is",max(x)-min(x), "meters"
print "At t=", argmax(x)/100, "s"
plot(x,label="position")
legend()

FloatingPointError: overflow encountered in double_scalars

I've set up numpy.seterr as follows:
np.seterr(invalid='raise', over ='raise', under='raise')
And I'm getting the following error:
c = beta[j,i] + oneminusbeta[j,i]
FloatingPointError: overflow encountered in double_scalars
I've checked what beta[j,i] and oneminusbeta[j,i] are at the point of crash, and these are their values:
beta: -131.340389182
oneminusbeta: 0.0
Please note, this line of addition (beta[j,i] + oneminusbeta[j,i]) has run for thousands of lines in a loop (that performs image classification) before crashing here at this point.
How can I deal with this? Is it necessary to change the type of the numpy arrays?
This is how I've initialized them:
beta = np.empty([m,n])
oneminusbeta = np.empty([m,n])
Is it possible to cast the individual values before adding them up? Rather than changing the entire array declarations? Or is this even a serious issue? Would it be safe to simply turn off the numpy.seterr configuration and let the calculations go ahead without raising the error?
Edit
Someone suggested below, and I suspected as well, that the values being added shouldn't cause an overflow. Then how can I find out where the overflow is really happening?
This is my code:
epthreshold = 709
enthreshold = -708
f.write("weights["+str(i)+", " + str(j)+"] = math.exp(beta: " +str(beta[j,i])+ " + oneminusbeta: " + str(oneminusbeta[j,i])+")\n" )
c = beta[j,i] + oneminusbeta[j,i]
weights[i,j] = math.exp(np.clip(c, enthreshold, epthreshold))
And when I check my log file, this is the line I get:
weights[5550, 13] = math.exp(beta: -131.340389182 + oneminusbeta: 0.0)
Edit 2
Here's the rest of my code, where variables n,m and H have already been initialized to integer values:
import numba
import numpy as np
import statsmodels.api as sm
weights = np.empty([n,m])
for curr_n in range(n):
for curr_m in range(m):
weights[curr_n,curr_m] = 1.0/(n)
beta = np.empty([m,n])
oneminusbeta = np.empty([m,n])
for curr_class in range(m):
for curr_sample in range(n):
beta[curr_class,curr_sample] = 1./m
epthreshold = 709 # positive exponential threshold
enthreshold = -708
for h in range(H):
print "Boosting round %d ... " % h
z = np.empty([n,m])
for j in range(m): # computing working responses and weights, Step 2(a)(i)
for i in range(no_samples):
i_class = y[i] #get the correct class for the current sample
if h == 0:
z[i,j] = (int(j==i_class) - beta[j,i])/((beta[j,i])*(1. - beta[j,i]))
weights[i,j] = beta[j,i]*(1. - beta[j,i])
else:
if j == i_class:
z[i,j] = math.exp(np.clip(-beta[j,i],enthreshold, epthreshold))
else:
z[i,j] = -math.exp(np.clip(oneminusbeta[j,i], enthreshold, epthreshold))
f.write("weights["+str(i)+", " + str(j)+"] = math.exp(beta: " +str(beta[j,i])+ " + oneminusbeta: " + str(oneminusbeta[j,i])+")\n" )
c = beta[j,i] + oneminusbeta[j,i]
weights[i,j] = math.exp(np.clip(c, enthreshold, epthreshold))
g_h = np.zeros([1,1])
j = 0
# Calculating regression coefficients per class
# building the parameters per j class
for y1_w in zip(z.T, weights.T):
y1, w = y1_w
temp_g = sm.WLS(y1, X, w).fit() # Step 2(a)(ii)
if np.allclose(g_h,0):
g_h = temp_g.params
else:
g_h = np.c_[g_h, temp_g.params]
j = j + 1
if np.allclose(g,0):
g = g_h
else:
g = g + g_h # Step(2)(a)(iii)
# now set g(x), function coefficients according to new formula, step (2)(b)
sum_g = g.sum(axis=1)
for j in range(m):
diff = (g[:,j] - ((1./m) * sum_g))
g[:,j] = ((m-1.)/m) * diff
g_per_round[h,:,j] = g[:,j]
#Now computing beta, Step 2(c)...."
Q = 0.
e = 0.
for j in range(m):
# Calculating beta and oneminusbeta for class j
aj = 0.0
for i in range(no_samples):
i_class = y[i]
X1 = X[i].reshape(1, no_features)
g1 = g[:,j].reshape(no_features, 1)
gc = g[:,i_class].reshape(no_features, 1)
dot = 1. + float(np.dot(X1, g1)) - float(np.dot(X1,gc))
aj = dot
sum_e = 0.
a_q = []
a_q.append(0.)
for j2 in range(m): # calculating sum of e's except for all j except where j=i_class
if j2 != i_class: # g based on j2, not necessarily g1?
g2 = g[:,j2].reshape(no_features, 1)
dot1 = 1. + float(np.dot(X1, g2)) - float(np.dot(X1,gc))
e2 = math.exp(np.clip(dot1,enthreshold, epthreshold))
sum_e = sum_e + e2
a_q.append(dot1)
if (int(j==i_class) == 1):
a_q_arr = np.array(a_q)
alpha = np.array(a_q_arr[1:])
Q = mylogsumexp(f,a_q_arr, 1, 0)
sumalpha = mylogsumexp(f,alpha, 1, 0)
beta[j,i] = -Q
oneminusbeta[j,i] = sumalpha - Q
else:
alpha = a_q
alpha = np.array(alpha[1:])
a_q_arr = np.array(a_q)
Q = mylogsumexp(f,a_q_arr, 0, aj)
sumalpha = log(math.exp(np.clip(Q, enthreshold, epthreshold)) - math.exp(np.clip(aj, enthreshold, epthreshold)))
beta[j,i] = aj - Q
oneminusbeta[j,i] = sumalpha - Q
and the function mylogsumexp is:
def mylogsumexp(f, a, is_class, maxaj, axis=None, b=None):
np.seterr(over="raise", under="raise", invalid="raise")
threshold = -sys.float_info.max
maxthreshold = sys.float_info.max
epthreshold = 709 # positive exponential threshold
enthreshold = -708
a = asarray(a)
if axis is None:
a = a.ravel()
else:
a = rollaxis(a, axis)
if is_class == 1:
a_max = a.max(axis=0)
else:
a_max = maxaj
#bnone = " none "
if b is not None:
a_max = maxaj
b = asarray(b)
if axis is None:
b = b.ravel()
else:
b = rollaxis(b, axis)
a = np.clip(a - a_max, enthreshold, epthreshold)
midout = np.sum(np.exp(a), axis=0)
midout = 1.0 + np.clip(midout - math.exp(a_max), threshold, maxthreshold)
out = np.log(midout)
else:
a = np.clip(a - a_max, enthreshold, epthreshold)
out = np.log(np.sum(np.exp(a)))
out += a_max
if out == float("inf"):
out = maxthreshold
if out == float("-inf"):
out = threshold
return out

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