Suppose we have the following measurements
X_0 = [0, 1]; Y_0 = 15
X_1 = [1, 0]; Y_1 = 8
X_2 = [1, 1]; Y_2 = 80
X_3 = [3, 4]; Y_3 = 100
X_4 = [1, 15]; Y_4 = 150
subjected to a>=4, c<=30
(we could handle other constraints as well: Ax <= b, Aeq x = beq, c(x) <= 0, h(x) = 0)
"""
from openopt import DFP
from numpy import inf
f = lambda z, X: z[0]**3 + z[1]*X[0] + z[2]*X[1] + z[3]*(X[0]+X[1])**2
initEstimation = [0] * 4 # start point for solver: [0, 0, 0, 0]
X = ([0, 1], [1, 0], [1, 1], [3, 4], [1, 15]) # list, tuple, numpy array or array-like are OK as well
Y = [15, 8, 80, 100, 150]
lb = [4, -inf, -inf, -inf]
ub = [inf, inf, 30, inf]
p = DFP(f, initEstimation, X, Y, lb=lb, ub=ub)
# optional: derivative
p.df = lambda z, X: [3*z[0]**2, X[0], X[1], (X[0]+X[1])**2]
r = p.solve('nlp:ralg', plot=0, iprint = 10)
print('solution: '+str(r.xf)+'\n||residuals||^2 = '+str(r.ff)+'\nresiduals: '+str([f(p.xf, X[i])-Y[i] for i in xrange(len(Y))]))
#solution: [ 3.99999936 5.99708861 -12.25696614 1.04221073]
#||residuals||^2 = 5992.63887806
#residuals: [37.785213926923028, 63.039268675751572, -18.091065285780857, -15.968303801844399, 2.9485118103557397]
X_0 = [0, 1]; Y_0 = 15
X_1 = [1, 0]; Y_1 = 8
X_2 = [1, 1]; Y_2 = 80
X_3 = [3, 4]; Y_3 = 100
X_4 = [1, 15]; Y_4 = 150
subjected to a>=4, c<=30
(we could handle other constraints as well: Ax <= b, Aeq x = beq, c(x) <= 0, h(x) = 0)
"""
from openopt import DFP
from numpy import inf
f = lambda z, X: z[0]**3 + z[1] * X[0] + z[2] * X[1] + z[3] * (X[0] + X[1])**2
initEstimation = [0] * 4 # start point for solver: [0, 0, 0, 0]
X = ([0, 1], [1, 0], [1, 1], [3, 4], [1, 15]
) # list, tuple, numpy array or array-like are OK as well
Y = [15, 8, 80, 100, 150]
lb = [4, -inf, -inf, -inf]
ub = [inf, inf, 30, inf]
p = DFP(f, initEstimation, X, Y, lb=lb, ub=ub)
# optional: derivative
p.df = lambda z, X: [3 * z[0]**2, X[0], X[1], (X[0] + X[1])**2]
r = p.solve('nlp:ralg', plot=0, iprint=10)
print('solution: ' + str(r.xf) + '\n||residuals||^2 = ' + str(r.ff) +
'\nresiduals: ' + str([f(p.xf, X[i]) - Y[i] for i in xrange(len(Y))]))
#solution: [ 3.99999936 5.99708861 -12.25696614 1.04221073]
#||residuals||^2 = 5992.63887806
#residuals: [37.785213926923028, 63.039268675751572, -18.091065285780857, -15.968303801844399, 2.9485118103557397]
subjected to a>=4, c<=30
(we could handle other constraints as well: Ax <= b, Aeq x = beq, c(x) <= 0, h(x) = 0)
"""
from openopt import DFP
from numpy import *
f = lambda z, X: (z[0]**3 + z[1] * X[0] + z[2] * X[1] + z[3] * (X[0] + X[
1])**2, 2 * z[0] + 3 * z[1] * X[0] + 4 * z[2] * X[1] + 5 * z[3] *
(X[0] + X[1])**2)
#f = (lambda z, X: z[0]**3 + z[1]*X[0] + z[2]*X[1] + z[3]*(X[0]+X[1])**2,
#lambda z, X: 2*z[0] + 3*z[1]*X[0] + 4*z[2]*X[1] + 5*z[3]*(X[0]+X[1])**2)
df = lambda z, X: ([3 * z[0]**2, X[0], X[1], (X[0] + X[1])**2],
[2, 3 * X[0], 4 * X[1], 5 * (X[0] + X[1])**2])
initEstimation = [0] * 4 # start point for solver: [0, 0, 0, 0]
X = ([0, 1], [1, 0], [1, 1], [3, 4], [1, 15]
) # list, tuple, numpy array or array-like are OK as well
Y = [[15, 1], [8, 16], [80, 800], [100, 120], [150, 1500]]
lb = [4, -inf, -inf, -inf]
ub = [inf, inf, 30, inf]
p = DFP(f, initEstimation, X, Y, df=df, lb=lb, ub=ub)
r = p.solve('nlp:ralg', plot=0, iprint=10)
print('solution: ' + str(r.xf) + '\n||residuals||^2 = ' + str(r.ff) +
'\nresiduals: ')
rr = [array(f(p.xf, X[i])) - array(Y[i]) for i in xrange(len(Y))]
print(rr)
#solution: [ 3.99999936 -1.9497013 18.25467922 0.24926213]
#||residuals||^2 = 653639.695247
#residuals:
#[array([ 67.50391074, 81.26502627]), array([ 54.29953022, -12.60279452]), array([ 1.30199584, -719.84514565]), array([ 43.38342685, 223.59677693]), array([ 249.68156224, -83.51282276])]
F(x0, x1) = a^3 + b * x0 + c * x1 + d * (x0^2+x1^2)
Suppose we have the following measurements
X_0 = [0, 1]; Y_0 = 15
X_1 = [1, 0]; Y_1 = 8
X_2 = [1, 1]; Y_2 = 80
X_3 = [3, 4]; Y_3 = 100
X_4 = [1, 15]; Y_4 = 150
subjected to a>=4, c<=30
(we could handle other constraints as well: Ax <= b, Aeq x = beq, c(x) <= 0, h(x) = 0)
"""
from openopt import DFP
from numpy import inf
f = lambda z, X: z[0]**3 + z[1]*X[0] + z[2]*X[1] + z[3]*(X[0]+X[1])**2
df = lambda z, X: [3*z[0]**2, X[0], X[1], (X[0]+X[1])**2]
initEstimation = [0] * 4 # start point for solver: [0, 0, 0, 0]
X = ([0, 1], [1, 0], [1, 1], [3, 4], [1, 15]) # list, tuple, numpy array or array-like are OK as well
Y = [15, 8, 80, 100, 150]
lb = [4, -inf, -inf, -inf]
ub = [inf, inf, 30, inf]
p = DFP(f, initEstimation, X, Y, df = df, lb=lb, ub=ub)
r = p.solve('nlp:ralg', plot=0, iprint = 10)
print('solution: '+str(r.xf)+'\n||residuals||^2 = '+str(r.ff)+'\nresiduals: '+str([f(p.xf, X[i])-Y[i] for i in xrange(len(Y))]))
#solution: [ 3.99999936 5.99708861 -12.25696614 1.04221073]
#||residuals||^2 = 5992.63887806
#residuals: [37.785213926923028, 63.039268675751572, -18.091065285780857, -15.968303801844399, 2.9485118103557397]
