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qnewton.py
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import numpy as np
import copy
import sys
a = 3.00
b = 2.00
k = 1.000
k1 = 0.100
k2 = 0.03 #float(sys.argv[1])
#A = 1
#B = 0.5
#v = 2
'''def update(X,E,h,Xs):
print("update %f,%f -> %f,%f"%(X[h][0],X[h][1],Xs[0],Xs[1]))
X[h] = Xs
newX = X
E[h] = getE(Xs)
newE = E
return newX, newE
def findh(E):
Emax = -100.0
h = -1
for i in range(len(E)):
if E[i] > Emax:
h = i
Emax = E[i]
return h, Emax
def conv(dx):
thresh = 0.002
cv = abs(dx[0]) < thresh and abs(dx[1]) < thresh
return cv
'''
def constrain(X, Xmin, Xmax):
#print(X)
over = np.heaviside(X - Xmax, 0.0)
under = np.heaviside(X - Xmin, 0.0)
X = X*(1.0-over) + Xmax*over
X = X*under + Xmin*(1.0-under)
#print(X)
return X
def qn_iter(X, getf, getE, t2N, N2t, maxstep=0.05, maxiter=25, debug=False):
#Xmin, Xmax = Xrange
conv = False
E = getE(X)
f, hdiag = getf(X)
print('cycle maxq dE maxg')
print(" 0 %.6f"% abs(f).max())
if debug: print( 'X', X, 'f', f)
if np.dot(f.T, f) < 1e-10 :
conv = True
return X, conv
nx = len(X)
oldE = E
oldX = copy.copy(X)
oldf = copy.copy(f)
oldalpha = 0.5
#oldG = np.identity(nx)
oldG = np.diag(hdiag**(-1))
while(True):
q = -oldalpha*oldf
q = constrain(q, -maxstep, maxstep)
X = oldX + q
#X = constrain(X, Xmin, Xmax)
E = getE(X)
f, hdiag = getf(X)
dE = E - oldE
#print(dE)
if dE > 1e-4:
print("reset alpha")
oldalpha /= 2
else:
#print(" 1 %.3f %.3f %.3f "%(abs(q).max(), dE, abs(f).max()))
dump_cyc(1, q, dE, f)
if debug: print('q', q, 'X', X, 'f', f)
#print("Start Forming U")
U = -1*np.dot(oldG, f + oldf*(oldalpha-1))
d = f - oldf
#print("U: ", U, "d:", d)
aa = 1.0/np.dot(U.T, d)
T = np.dot(U.T, U)
#print("a: %f T: %f"%(aa,T), "aUf: %f"%((1/aa)*np.dot(U,oldf)))
if (1/aa < 1e-5*T) or (abs((1/aa)*np.dot(U.T,oldf)) > 1e-5):
#if False:
print("reset G")
#G = np.identity(nx)
G = np.diag(hdiag**(-1))
alpha = 0.5
else:
G = oldG + aa*np.einsum('i,j->ij', U, U)
alpha = 1
break
cyc = 2
while(True):
oldX = copy.copy(X)
oldE = E
oldalpha = alpha
oldG = copy.copy(G)
oldf = copy.copy(f)
#print(oldX, oldE)
q = -oldalpha*np.dot(oldG, oldf)
q = constrain(q, -maxstep, maxstep)
X = oldX + q
#X = constrain(X, Xmin, Xmax)
E = getE(X)
dE = E - oldE
f, hdiag = getf(X)
#print("Cycle %d X: "%cyc, X, "E:", E, 'f:', f)
dump_cyc(cyc, q, dE, f)
if debug: print('q', q, 'X', X, 'f', f)
U = -1*np.dot(oldG, f + oldf*(oldalpha-1))
d = f - oldf
#print(U, d)
aa = 1.0/np.dot(U.T, d)
T = np.dot(U.T, U)
#print("a: %f T: %.9f"%(aa,T), "aUf: %.9f"% ((1/aa)*np.dot(U,oldf)))
if (abs(aa*T > 1e5)) or (abs((1/aa)*np.dot(U.T,oldf)) > 1e-5):
#if False:
print("reset G")
#break
#G = np.identity(nx)
G = np.diag(hdiag**(-1))
alpha = 0.5
else:
G = oldG + aa*np.einsum('i,j->ij',U, U)
alpha = 1
if check_conv(f, q, dE):
print("occ opt converged")
conv = True
break
else:
cyc += 1
if cyc > maxiter:
print("conv not met")
break
return X, conv
def check_conv(f, q, dE):
normf = np.linalg.norm(f)
maxf = abs(f).max()
normq = np.linalg.norm(q)
maxq = abs(q).max()
conv = normf < 1e-6 and maxf < 1e-5 and normq < 1e-5 and maxq < 7e-5 and dE < 5e-8
return conv
def dump_cyc(cyc, q, dE, f):
print(" %2d %-9.5g %-9.5g %-9.5g "%(cyc, abs(q).max(), dE, abs(f).max()))
'''
'''