I'm solving an optimization problem to do a constrained nonlinear regression using experimental data. I use scipy minimize and it works with the original data, but it doesn't work when I do a simple data transformation. For the transformed data I use the excel solver solution for the same problem as the initial condition so it should work butcan't figure out why it doesn not. Please any help is appreciated. Thanks beforehand btw.
Here is the code with the original data (works) and the transformation (does not work)
import numpy as np
from scipy.optimize import Bounds, minimize
def yp(x, time, mode = 'fit'):
y1 = x[0] + x[1]*time
y2 = x[2] + (x[3] - x[2])*np.exp(-x[5]*(time - x[4])/(x[3] - x[2]))
comparison = time < x[4]
yp = y1*comparison + y2*(~comparison)
if mode == 'fit':
return yp
elif mode == 'calc':
return y1, y2
else:
print('Unsupported mode, returning default behavior for fitting data')
return yp
def objective(x, time, y):
ypred = yp(x, time)
z = sum((ypred - y)**2)
return z
#***********************
#Original data
#***********************
data_x = np.array([0,30,60,90,120,150,180,210,240,270,300,330,360,420,480,540,600,720,840])
data_y = np.array([11.06468023,10.03242418,9.771158736,8.873720137,8.618127786,
8.397702515,7.581607582,7.131636821,6.537043245,6.358885017,
5.898468977,5.25275811,4.983989976,4.141791045,2.602472349,
2.07395813,1.078129376,0.551764193,0.480052971])
x0 = [11.5, -0.0211, 0.6, 3.26, 400, 0.01919]
lbound = [9, -0.1, 0.3, 1, 200, 0]
ubound = [14, -1e-5, 1, 4, 800, 0.1]
bounds = Bounds(lbound,ubound)
constraint = dict(type = 'ineq',
fun = lambda x: 0.1 - abs(x[0] + x[1]*x[4] - x[3]))
res = minimize(fun = objective,
x0 = x0,
args = (data_x, data_y),
method = 'SLSQP',
constraints = constraint,
options = {'disp':True},
bounds = bounds)
print(res)
Optimization terminated successfully (Exit mode 0)
Current function value: 0.6681037696841838
Iterations: 20
Function evaluations: 149
Gradient evaluations: 20
fun: 0.6681037696841838
jac: array([ 1.19826198e-03, 5.93313336e-01, 9.38165262e-02, 6.77183270e-04,
1.15633011e-05, -3.35602835e-02])
message: 'Optimization terminated successfully'
nfev: 149
nit: 20
njev: 20
status: 0
success: True
x: array([ 1.06185481e+01, -1.59476490e-02, 3.00000000e-01, 3.86162000e+00,
4.29964822e+02, 2.80661182e-02])
#***********************
#Transformed data
#***********************
data_y_rel = data_y/data_y[0]
x0_rel = [1, -0.00207571, 0.03, 0.359269446, 313.497571, 0.001970666]
lbound_rel = [1, -0.1, 0.03, 0.1, 200, 0]
ubound_rel = [1, -1e-5, 0.1, 0.4, 800, 0.1]
bounds_rel = Bounds(lbound_rel,ubound_rel)
constraint_rel = dict(type = 'ineq',
fun = lambda x: 0.01 - abs(x[0] + x[1]*x[4] - x[3]))
res_rel = minimize(fun = objective,
x0 = x0_rel,
args = (data_x, data_y_rel),
method = 'SLSQP',
constraints = constraint_rel,
options = {'disp':True},
bounds = bounds_rel)
print(res_rel)
Inequality constraints incompatible (Exit mode 4)
Current function value: 0.1593965203706159
Iterations: 1
Function evaluations: 7
Gradient evaluations: 1
fun: 0.1593965203706159
jac: array([ nan, -2.88985475e+02, -1.53672213e-01, -1.13128023e+00,
-1.58630125e-03, 5.45240970e+01])
message: 'Inequality constraints incompatible'
nfev: 7
nit: 1
njev: 1
status: 4
success: False
x: array([ 1.00000000e+00, -2.07571000e-03, 3.00000000e-02, 3.59269446e-01,
3.13497571e+02, 1.97066600e-03])
C:\Users\username\Anaconda3\lib\site-packages\scipy\optimize\_numdiff.py:519: RuntimeWarning: invalid value encountered in true_divide
J_transposed[i] = df / dx