I have coded the laplacien function for a non-regular mesh (created with the scipy.spatial.Delaunay function).
I have not errors but the results are not correct : the eigenvectors are correct but the eigenvalues are too high (in absolute value).
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import scipy.spatial
def rect_drum(L,H,U):
vals = []
val = 0
k = 1
l = 1
while val >= -U:
while val >= -U:
val = -np.pi**2*((k/L)**2+(l/H)**2)
if val >= -U:
vals.append(val)
l += 1
l = 1
k += 1
val = -np.pi**2*((k/L)**2+(l/H)**2)
return np.array(vals)
def count_vp(tab,U):
#count the n eigenvalues greater than equal to -U in the array tab
return tab[tab>=-U]
def in_curve(f,fargs,shape,a):
points = [] # the points inside the curve
for j in range(shape[0]):
for i in range(shape[1]):
if f(i*a,j*a,*fargs) < 0:
points.append([i*a,j*a])
return np.array(points)
def triang(points,a,f,fargs,bord):
tri_points = points.copy()
tri_points[:,1] *= np.sqrt(3)
tri_points2 = np.vstack((points,bord))
tri_points2[:,1] *= np.sqrt(3)
tri_points2[:,0] += a/2
tri_points2[:,1] += np.sqrt(3)/2*a
fin = np.vstack((tri_points,tri_points2))
i = 0
eps = 0.01
while i < len(fin):
if f(fin[i,0]+eps,fin[i,1]+eps,*fargs) > 0:
fin = np.delete(fin,i,0)
i -= 1
i += 1
return np.vstack((fin,bord)),len(fin),len(bord)
def tri_ang(points,ind,p0):
# sort the points in trigonometric order
vec=np.arctan2((points-p0)[:,1],(points-p0)[:,0])
values = []
dtype = [('val',float),('n',int)]
for i in range(len(vec)):
values.append((vec[i],i))
values = np.sort(np.array(values,dtype),order='val')
new_points = []
new_ind = []
for tup in values:
new_points.append(points[tup[1]])
new_ind.append(ind[tup[1]])
return np.array(new_points),np.array(new_ind)
def M(points,tri,Nint):
indptr,ind = tri.vertex_neighbor_vertices
W = np.zeros((Nint,Nint)) # cotangents matrix
A = np.zeros((Nint,1)) # surfaces vertex array for each point i (A[i])
for i in range(Nint):
tot = 0
nhb_ind = ind[indptr[i]:indptr[i+1]] # indices of the points close to the point of index k
nhb = points[nhb_ind] # their coordinates
nhb,nhb_ind = tri_ang(nhb,nhb_ind,points[i]) #the coordinates (nhb) and (nhb_ind) of each neighbor of i
for j in range(len(nhb_ind)):
vec = nhb[j]-points[i] # a vector connecting the point to his neighbor of index 0
vec_av = nhb[j-1]-points[i] # another vector but with the Vosin from before
if j+1 >= len(nhb_ind):
k = 0
else:
k = j+1
vec_ap = nhb[k]-points[i] # another vector but with the next neighbor
# another vector but with the next neighbor
A[i] += 0.5/3*np.linalg.norm(np.cross(vec,vec_av))
if nhb_ind[j] < Nint:
# we use the vector and scalar product to calculate the cotangents: A.B/||AxB||
cotan_alpha = np.dot(vec_av,vec_av-vec)/np.linalg.norm(np.cross(vec_av,vec_av-vec))
cotan_beta = np.dot(vec_ap,vec_ap-vec)/np.linalg.norm(np.cross(vec_ap,vec_ap-vec))
# Wij value :
W[i,nhb_ind[j]] = -0.5*(cotan_alpha+cotan_beta)
tot += cotan_alpha+cotan_beta
W[i,i] = -0.5*tot # diagonal values
return (1/A)*W
def rect(x,y,L,H,x0=0,y0=0):
if 0<x-x0<L and 0<y-y0<H:
return -1
else:
return 1
def rect_rim(L,H,a,x0=0,y0=0):
tab1 = np.arange(x0,L+x0,a)[:,np.newaxis]
h = np.hstack((tab1,H*np.ones((len(tab1),1))+y0))
b = np.hstack((tab1,np.zeros((len(tab1),1))+y0))
tab2 = np.arange(y0+a,H+y0,a)[:,np.newaxis]
g = np.hstack((np.zeros((len(tab2),1))+x0,tab2))
d = np.hstack((L*np.ones((len(tab2),1))+x0,tab2))
hp = np.array([[L+x0,H+y0]])
bp = np.array([[L+x0,0]])
return np.vstack((h,b,g,d,hp,bp))
# sample with a square 1*1
L = 1
H = 1
dl = 0.05
sol = in_curve(rect,[L,H],(100,100),dl)
sol_tri,Nint,Nbord = triang(sol,dl,rect,[L,H],rect_rim(L,H,dl))
# plt.plot(sol_tri[:,0],sol_tri[:,1],linestyle="",marker="+",label="tri")
# plt.plot(sol[:,0],sol[:,1],linestyle="",marker="x")
# plt.legend()
# plt.show()
# triangulation
tri = scipy.spatial.Delaunay(sol_tri)
# plt.triplot(sol_tri[:,0],sol_tri[:,1],tri.simplices)
# plt.show()
M = M(sol_tri,tri,Nint)
valp,vecp = np.linalg.eig(M) # eigenvalues and eigenvectors
vecp = np.real(vecp)
# comparison with the exact solution:
T = 1000
U = np.arange(0,T,1)
NUsim = np.array([len(count_vp(valp,u)) for u in U])
NU = np.array([len(rect_drum(L,H,u)) for u in U])
plt.plot(U,NUsim,label='simulation')
plt.plot(U,NU,label='exacts')
plt.legend()
plt.show()
# 3D plot of an eigenvector
vecp_tot = np.vstack((vecp,np.zeros((Nbord,Nint))))
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_trisurf(sol_tri[:,0],sol_tri[:,1],vecp_tot[:,0],triangles=tri.simplices)
plt.show()
The laplacian is the function named "M".
The "in_curve function" return the points inside a curve defined by f(x,y,*fargs) < 0 (a square in the sample).
The "triang" function return points with added points (triangle meshs). The fonction uses an another function for the rim of the curve (for most precision), in the sample it is the "rect_rim" function.
I used the formula given at https://en.wikipedia.org/wiki/Discrete_Laplace_operator ("mesh laplacians").
I have solve my problem : it's a sign and a rim problems.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import scipy.spatial
def rect_drum(L,H,U):
vals = []
val = 0
k = 1
l = 1
while val >= -U:
while val >= -U:
val = -np.pi**2*((k/L)**2+(l/H)**2)
if val >= -U:
vals.append(val)
l += 1
l = 1
k += 1
val = -np.pi**2*((k/L)**2+(l/H)**2)
return np.array(vals)
def count_vp(tab,U):
#count the n eigenvalues greater than equal to -U in the array tab
return tab[tab>=-U]
def in_curve(f,fargs,shape,a):
points = [] # the points inside the curve
for j in range(shape[0]):
for i in range(shape[1]):
if f(i*a,j*a,*fargs) < 0:
points.append([i*a,j*a])
return np.array(points)
def triang(points,a,f,fargs,bord):
tri_points = points.copy()
tri_points[:,1] *= np.sqrt(3)
tri_points2 = np.vstack((points,bord))
tri_points2[:,1] *= np.sqrt(3)
tri_points2[:,0] += a/2
tri_points2[:,1] += np.sqrt(3)/2*a
fin = np.vstack((tri_points,tri_points2))
i = 0
eps = 0.01
while i < len(fin):
if f(fin[i,0]+eps,fin[i,1]+eps,*fargs) > 0:
fin = np.delete(fin,i,0)
i -= 1
i += 1
return np.vstack((fin,bord)),len(fin),len(bord)
def tri_ang(points,ind,p0):
# sort the points in trigonometric order
vec=np.arctan2((points-p0)[:,1],(points-p0)[:,0])
values = []
dtype = [('val',float),('n',int)]
for i in range(len(vec)):
values.append((vec[i],i))
values = np.sort(np.array(values,dtype),order='val')
new_points = []
new_ind = []
for tup in values:
new_points.append(points[tup[1]])
new_ind.append(ind[tup[1]])
return np.array(new_points),np.array(new_ind)
def Laplacian(points,tri,Nint):
indptr,ind = tri.vertex_neighbor_vertices
W = np.zeros((Nint,Nint)) # cotangents matrix
A = np.zeros((Nint,1)) # surfacesvertex aray of point i (A[i])
for i in range(Nint):
tot = 0
nhb_ind = ind[indptr[i]:indptr[i+1]] # indices of the points close to the point of index k
nhb = points[nhb_ind] # their coordinates
nhb,nhb_ind = tri_ang(nhb,nhb_ind,points[i]) #the coordinates (nhb) and (nhb_ind) of each neighbor of i
for j in range(len(nhb_ind)):
vec = nhb[j]-points[i] # a vector connecting the point to his neighbor of index 0
vec_av = nhb[j-1]-points[i] # another vector but with the Vosin from before
if j+1 >= len(nhb_ind):
k = 0
else:
k = j+1
vec_ap = nhb[k]-points[i] # another vector but with the next neighbor
# we use the cross product to calculate the areas of the triangles: ||AxB||/2:
A[i] += 0.5/3*np.linalg.norm(np.cross(vec,vec_av))
# we use the cross product and scalar product to calculate the cotangents: A.B/||AxB||
cotan_alpha = np.dot(vec_av,vec_av-vec)/np.linalg.norm(np.cross(vec_av,vec_av-vec))
cotan_beta = np.dot(vec_ap,vec_ap-vec)/np.linalg.norm(np.cross(vec_ap,vec_ap-vec))
tot += cotan_alpha+cotan_beta
if nhb_ind[j] < Nint:
W[i,nhb_ind[j]] = 0.5*(cotan_alpha+cotan_beta)
W[i,i] = -0.5*tot # diagonal values
return (1/A)*W
def rect(x,y,L,H,x0=0,y0=0):
if 0<x-x0<L and 0<y-y0<H:
return -1
else:
return 1
def rect_rim(L,H,a,x0=0,y0=0):
tab1 = np.arange(x0,L+x0,a)[:,np.newaxis]
h = np.hstack((tab1,H*np.ones((len(tab1),1))+y0))
b = np.hstack((tab1,np.zeros((len(tab1),1))+y0))
tab2 = np.arange(y0+a,H+y0,a)[:,np.newaxis]
g = np.hstack((np.zeros((len(tab2),1))+x0,tab2))
d = np.hstack((L*np.ones((len(tab2),1))+x0,tab2))
hp = np.array([[L+x0,H+y0]])
bp = np.array([[L+x0,0]])
return np.vstack((h,b,g,d,hp,bp))
# sample with a square 1*1
L = 1
H = 1
dl = 0.04
sol = in_curve(rect,[L,H],(100,100),dl)
sol_tri,Nint,Nbord = triang(sol,dl,rect,[L,H],rect_rim(L,H,dl))
# triangulation
tri = scipy.spatial.Delaunay(sol_tri)
M = Laplacian(sol_tri,tri,Nint)
valp,vecp = np.linalg.eig(M) # eigenvalues and eigenvectors
vecp = np.real(vecp)
# comparison with the exact solution:
T = 1000
U = np.arange(0,T,1)
NUsim = np.array([len(count_vp(valp,u)) for u in U])
NU = np.array([len(rect_drum(L,H,u)) for u in U])
plt.plot(U,NUsim,label='simulation')
plt.plot(U,NU,label='exacts')
plt.legend()
plt.show()
# 3D plot of an eigenvector
mode = 0 # change this for an another mode
vecp_tot = np.vstack((vecp,np.zeros((Nbord,Nint))))
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_trisurf(sol_tri[:,0],sol_tri[:,1],vecp_tot[:,mode],triangles=tri.simplices)
plt.show()
Notes :
1- The hight eigenvalues are false : it's an effect of discretisation.
2- If dl is too small, we have false eigenvectors and eigenvalues (at the top of valp and firsts vectors of vecp), it's probably due to the quality of the meshing.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy import linalg, optimize
%matplotlib inline
Data load
data = pd.read_csv("D:/Stat/TimeSeries/KRW_month_0617_1.csv",index_col="Date") / 100
para = open("D:/Stat/TimeSeries/KRW_month_0617_1.txt").readlines()[0:2]
data.index = pd.to_datetime(data.index)
Parameters
cond = []
params = []
time = []
for i in para:
j = i.split()
for k in j:
cond.append(k)
cond = cond[1:]
for i in range(len(cond)):
cond[i] = round(float(cond[i]),4)
params = cond[0:23]
time = cond[23:]
maturity = np.array(time[1:])
timegap = 1/cond[23]
Functions We need
def Paramcheck(Params, checkStationary = 1):
result = 0
Kappa = np.array([[params[20],0,0], [0,params[21],0], [0,0,params[22]]])
Sigma = np.array([[params[1],0,0], [params[2],params[3],0], [params[4],params[5],params[6]]])
State = np.array([params[7], params[8], params[9]])
Lambda = params[0]
SigmaEps = np.identity(10)
for i in range(10):
SigmaEps[i][i] = params[i+10]
for i in range(len(Sigma)):
if Sigma[i][i] < 0:
result = 1
for j in SigmaEps:
if np.any(SigmaEps) < 0:
result = 1
if Lambda < 0.05 or Lambda > 2:
result = 1
elif State[0] < 0:
result = 1
elif Kappa[0][0] < 0:
result = 1
if result == 0 and checkStationary > 0:
if max(np.linalg.eigvals(-Kappa).real) > 0:
result = 2
return result
def CheckDet(x):
if x == np.inf or x == np.nan:
result = 1
elif x < 0:
result = 2
elif abs(x) < 10**-250:
result = 3
else:
result = 0
return result
def NS_factor(lambda_val, maturity):
col1 = np.ones(len(maturity))
col2 = (1 - np.exp(-lambda_val*maturity))/(lambda_val*maturity)
col3 = col2 - np.exp(-lambda_val*maturity)
factor = np.array([col1,col2,col3]).transpose()
return factor
def DNS_Kalman_filter(Params, *args):
N = Paramcheck(Params)
if N == 0:
Kappa = np.array([[params[20],0,0], [0,params[21],0], [0,0,params[22]]])
Sigma = np.array([[params[1],0,0], [params[2],params[3],0],
[params[4],params[5],params[6]]])
State = np.array([params[7], params[8], params[9]])
Lambda = params[0]
SigmaEps = np.identity(10)
for i in range(10):
SigmaEps[i][i] = params[i+10]
Obs_Yield = args[0]
Obs_Date = args[1]
Timegap = args[2]
Obs_Mty = args[3]
Finalstate = args[4]
Mty_length = len(Obs_Mty)
B = NS_factor(lambda_val = Lambda,maturity = Obs_Mty)
H_large = SigmaEps **2
N_obs = len(Obs_Date)
LLH_vec = np.zeros(N_obs)
phi1 = linalg.expm(-Kappa*Timegap)
phi0 = (np.identity(3)-phi1) # State
Eigenvalues = np.linalg.eig(Kappa)[0]
Eigen_vec = np.linalg.eig(Kappa)[1]
Eigen_vec_inv = np.linalg.inv(Eigen_vec)
S = Eigen_vec_inv # Sigma # Sigma.transpose() # Eigen_vec_inv.transpose()
Atilde = np.dot(Sigma[0], Sigma[0])
Btilde = np.dot(Sigma[1], Sigma[1])
Ctilde = np.dot(Sigma[2], Sigma[2])
Dtilde = np.dot(Sigma[0], Sigma[1])
Etilde = np.dot(Sigma[0], Sigma[2])
Ftilde = np.dot(Sigma[1], Sigma[2])
res1= Atilde* Obs_Mty* Obs_Mty/6
res2= Btilde*(1/(2*Lambda**2) - (1-np.exp(-Lambda*Obs_Mty))/(Lambda**3*Obs_Mty) + (1-
np.exp(-2*Lambda*Obs_Mty))/(4*Lambda**3*Obs_Mty))
res3= Ctilde*(1/(2*Lambda**2) + np.exp(-Lambda*Obs_Mty)/(Lambda**2)-
Obs_Mty*np.exp(-2*Lambda*Obs_Mty)/(4*Lambda) -
3*np.exp(-2*Lambda*Obs_Mty)/(4*Lambda**2) - 2*(1-np.exp(-
Lambda*Obs_Mty))/(Lambda**3*Obs_Mty) + 5*(1-
np.exp(-2*Lambda*Obs_Mty))/(8*Lambda**3*Obs_Mty))
res4= Dtilde*(Obs_Mty/(2*Lambda) + np.exp(-Lambda*Obs_Mty)/(Lambda**2) - (1-np.exp(-
Lambda*Obs_Mty))/(Lambda**3*Obs_Mty))
res5= Etilde*(3*np.exp(-Lambda*Obs_Mty)/(Lambda**2) + Obs_Mty/(2*Lambda)+Obs_Mty*np.exp(-
Lambda*Obs_Mty)/(Lambda) - 3*(1-np.exp(-Lambda*Obs_Mty))/(Lambda**3*Obs_Mty))
res6= Ftilde*(1/(Lambda**2) + np.exp(-Lambda*Obs_Mty)/(Lambda**2) -
np.exp(-2*Lambda*Obs_Mty)/(2*Lambda**2) - 3*(1-np.exp(-
Lambda*Obs_Mty))/(Lambda**3*Obs_Mty) + 3*(1-
np.exp(-2*Lambda*Obs_Mty))/(4*Lambda**3*Obs_Mty))
val = res1 + res2 + res3 + res4 + res5 + res6
V_mat = np.zeros([3,3])
V_lim = np.zeros([3,3])
for i in range(3):
for j in range(3):
V_mat[i][j] = S[i][j]*(1-np.exp(-(Eigenvalues[i] +
Eigenvalues[j])*Timegap))/(Eigenvalues[i] + Eigenvalues[j])
V_lim[i][j] = S[i][j]/(Eigenvalues[i] + Eigenvalues[j])
Q = (Eigen_vec # V_mat # Eigen_vec.transpose()).real
Sigma_lim = (Eigen_vec # V_lim # Eigen_vec.transpose()).real
for i in range(N_obs):
y = Obs_Yield[i]
xhat = phi0 + phi1 # State
y_implied = B # xhat
v = y - y_implied + val
Sigmahat = phi1 # Sigma_lim # phi1.transpose() + Q
F = B # Sigmahat # B.transpose() + H_large
detF = np.linalg.det(F)
if CheckDet(detF) > 0:
N = 3
break
Finv = np.linalg.inv(F)
State = xhat + Sigmahat # B.transpose() # Finv # v
Sigma_lim = Sigmahat - Sigmahat # B.transpose() # Finv # B # Sigmahat
LLH_vec[i] = np.log(detF) + v.transpose() # Finv # v
if N == 0:
if Finalstate:
yDate = Obs_Date[-1]
result = np.array([yDate,State])
else:
result = 0.5 * (sum(LLH_vec) + Mty_length*N_obs*np.log(2*np.pi))
else:
result = 7000000
return result
I made a code that does Arbitrage Free Nelson-Siegel model. Data is return rates of bond (1Y,1.5Y, ... ,20Y). I wanna optimize that function with scipy optimize.minimize function with fixed *args.
Suppose that Initial parmas are verified that it's close to optimized params from empirical experiments using Dynamic Nelson-Siegel Model.
LLC_new = 0
while True:
LLC_old = LLC_new
OPT = optimize.minimize(x0=params,fun=DNS_Kalman_filter, args=
(data.values,data.index,timegap,maturity,0))
params = OPT.x
LLC_new = round(OPT.fun,5)
print("Current LLC: %0.5f" %LLC_new)
if LLC_old == LLC_new:
OPT_para = params
FinalState = DNS_Kalman_filter(params,data.values,data.index,timegap,maturity,True)
break
Result is
Current LLC: -7613.70146
Current LLC: -7613.70146
LLC(log-likelihood value) isn't maximized. It's not a result I desire using Optimizer.
Is there any solution for that?
In R, there is optim() function works as similar as scipy.optimize.minimize() which works really well. I also have a R code for that very similar to this Python code.
When I run code below, I get:
TypeError: Cannot cast array data from dtype('O') to dtype('int64') according to the rule 'safe'
But I don't know where is dtype('O') and dtype('int64'). Does anyone know where is to parse?
import collections
import numpy as np
import math
import pandas as pd
def pre_prob(y):
y_dict = collections.Counter(y)
pre_probab = np.ones(2)
for i in range(0, 2):
pre_probab[i] = y_dict[i]/y.shape[0]
return pre_probab
def mean_var(X, y):
n_features = X.shape[1]
m = np.ones((2, n_features))
v = np.ones((2, n_features))
n_0 = np.bincount(y)[np.nonzero(np.bincount(y))[0]][0]
x0 = np.ones((n_0, n_features))
x1 = np.ones((X.shape[0] - n_0, n_features))
k = 0
for i in range(0, X.shape[0]):
if y[i] == 0:
x0[k] = X[i]
k = k + 1
k = 0
for i in range(0, X.shape[0]):
if y[i] == 1:
x1[k] = X[i]
k = k + 1
for j in range(0, n_features):
m[0][j] = np.mean(x0.T[j])
v[0][j] = np.var(x0.T[j])*(n_0/(n_0 - 1))
m[1][j] = np.mean(x1.T[j])
v[1][j] = np.var(x1.T[j])*((X.shape[0]-n_0)/((X.shape[0]- n_0) - 1))
return m, v # mean and variance
def prob_feature_class(m, v, x):
n_features = m.shape[1]
pfc = np.ones(2)
for i in range(0, 2):
product = 1
for j in range(0, n_features):
product = product * (1/math.sqrt(2*3.14*v[i][j])) * math.exp(-0.5* pow((x[j] - m[i][j]),2)/v[i][j])
pfc[i] = product
return pfc
def GNB(X, y, x):
m, v = mean_var(X, y)
pfc = prob_feature_class(m, v, x)
pre_probab = pre_prob(y)
pcf = np.ones(2)
total_prob = 0
for i in range(0, 2):
total_prob = total_prob + (pfc[i] * pre_probab[i])
for i in range(0, 2):
pcf[i] = (pfc[i] * pre_probab[i])/total_prob
prediction = int(pcf.argmax())
return m, v, pre_probab, pfc, pcf, prediction
I need to optimize a non-convex problem (max likelihood), and when I try quadratic optmiziation algorithms such as bfgs, Nelder-Mead, it fails to find the extremum, I frequently get saddle point, instead.
You can download data from here.
import numpy as np
import csv
from scipy.stats import norm
f=open('data.csv','r')
reader = csv.reader(f)
headers = next(reader)
column={}
for h in headers:
column[h] = []
for row in reader:
for h,v in zip(headers, row):
column[h].append(float(v))
ini=[-0.0002,-0.01,.002,-0.09,-0.04,0.01,-0.02,-.0004]
for i in range(0,len(x[0])):
ini.append(float(x[0][i]))
x_header = list(Coef_headers)
N = 19 # no of observations
I = 4
P =7
Yobs=np.zeros(N)
Yobs[:] = column['size']
X=np.zeros((N,P))
X[:,0] = column['costTon']
X[:,1] = column['com1']
X[:,2] = column['com3']
X[:,3] = column['com4']
X[:,4] = column['com5']
X[:,5] = column['night']
X[:,6] = 1 #constant
def myfunction(B):
beta = B[0.299,18.495,2.181,2.754,3.59,2.866,-12.846]
theta = 30
U=np.zeros((N,I))
mm=np.zeros(I)
u = np.zeros((N,I))
F = np.zeros((N,I))
G = np.zeros(N)
l = 0
s1 = np.expm1(-theta)
for n in range (0,N):
m = 0
U[n,0] = B[0]*column['cost_van'][n]+ B[4]*column['cap_van'][n]
U[n,1] = B[1]+ B[5]*column['ex'][n]+ B[8]*column['dist'][n]+ B[0]*column['cost_t'][n]+ B[4]*column['cap_t'][n]
U[n,2] = B[2]+ B[6]*column['ex'][n]+ B[9]*column['dist'][n] + B[0]*column['cost_Ht'][n]+ B[4]*column['cap_Ht'][n]
U[n,3] = B[3]+ B[7]*column['ex'][n]+ B[10]*column['dist'][n]+ B[0]*column['cost_tr'][n]+ B[4]*column['cap_tr'][n]
for i in range(0,I):
mm[i]=np.exp(U[n,i])
m= sum(mm)
for i in range(0,I):
u[n,i]=1/(1+ np.exp(U[n,i]- np.log(m-np.exp(U[n,i]))))
F[n,i] = np.expm1(-u[n,i]*theta)
CDF = np.zeros(N)
Y = X.dot(beta)
resid = 0
for n in range (0,N):
resid = resid + (np.square(Yobs[n]-Y[n]))
SSR = resid / N
dof = N - P - 1
s2 = resid/dof # MSE, or variance: the mean squarred error of residuals
for n in range(0,N):
CDF[n] = norm.cdf((Yobs[n]+1),SSR,s2) - norm.cdf((Yobs[n]-1),SSR,s2)
G[n] = np.expm1(-CDF[n]*theta)
k = column['Choice_Veh'][n]-1
l = l + (np.log10(1+(F[n,k]*G[n]/s1))/(-theta))
loglikelihood = np.log10(l)
return -loglikelihood
rranges = np.repeat(slice(-10, 10, 1),11, axis = 0)
a = rranges
from scipy import optimize
resbrute = optimize.brute(myfunction, rranges, full_output=True,finish=optimize.fmin)
print("# global minimum:", resbrute[0])
print("function value at global minimum :", resbrute[1])
Now, I decided to go for grid search and tried scipy.optimize.brute, but I get this error. In fact, my real variables are 47, I decreased it to 31 to work, but still doesn't. please help.
File "C:\...\site-packages\numpy\core\numeric.py", line 1906, in indices
res = empty((N,)+dimensions, dtype=dtype)
ValueError: array is too big.