def performance(oppr, opps, oppc, W, L):
opp = zip(oppr, opps, oppc, W, L)
ret = [0.0, 0.0, 0.0, 0.0]
meanok = True
for cat in xrange(0,3):
spopp = [o for o in opp if o[2] == cat]
sW = sum([o[3] for o in spopp])
sL = sum([o[4] for o in spopp])
if sW == 0 and sL == 0:
ret[cat+1] = NA
meanok = False
elif sW == 0:
ret[cat+1] = MININF
meanok = False
elif sL == 0:
ret[cat+1] = INF
meanok = False
else:
gen_phi = lambda p, x: pdf(x, loc=p[0], scale=sqrt(1+p[1]**2))
gen_Phi = lambda p, x: max(min(cdf(x, loc=p[0], scale=sqrt(1+p[1]**2)), 1-LOG_CAP), LOG_CAP)
def logL(x):
ret = 0.0
for p in spopp:
gP = gen_Phi(p,x)
ret += p[3] * log(gP) + p[4] * log(1-gP)
return ret
def DlogL(x):
ret = 0.0
for p in spopp:
gp = gen_phi(p,x)
gP = gen_Phi(p,x)
ret += (float(p[3])/gP - float(p[4])/(1-gP)) * gp
return ret
def D2logL(x):
ret = 0.0
for p in spopp:
gp = gen_phi(p,x)
gP = gen_Phi(p,x)
alpha = gp/gP
beta = gp/(1-gP)
sb = sqrt(1+p[1]**2)
Mv = pi/sqrt(3)/sb * tanh(pi/2/sqrt(3)*(x-p[0])/sb)
ret -= p[3]*alpha*(alpha+Mv) + p[4]*beta*(beta-Mv)
return ret
perf = maximize(logL, DlogL, D2logL, 0.0, method=None)[0]
ret[cat+1] = perf
if meanok:
ret[0] = sum(ret[1:]) / 3
else:
ret[0] = NA
return ret
def update(myr, mys, oppr, opps, oppc, W, L, text='', pr=False, Ncats=3):
"""This function updates the rating of a player according to the ratings of the opponents and the games
against them."""
# If no games were played, do nothing.
if len(W) == 0:
return(myr, mys, [None] * (Ncats+1), [None] * (Ncats+1))
# Add fake games to prevent infinities
(oppr, opps, oppc, W, L) = fix_ww(myr, mys, oppr, opps, oppc, W, L)
if pr:
print text
print oppr
print opps
print oppc
print W
print L
played_cats = sorted(unique(oppc)) # The categories against which the player played
played_cats_p1 = [p+1 for p in played_cats]
tot = sum(myr[array(played_cats)+1]) # The sum relative rating against those categories
# (will be kept constant)
M = len(W) # Number of opponents
C = len(played_cats) # Number of different categories played
# Convert global categories to local
def loc(x):
return array([played_cats.index(c) for c in x])
# Convert local categories to global
def glob(x):
return array([played_cats[c] for c in x])
# Extends a M-vector to an M+1-vector according to the restriction given
# (that the sum of relative ratings against the played categories is constant)
def extend(x):
return hstack((x, tot-sum(x[1:])))
# Ensure that arrays are 1-dimensional
def dim(x):
if x.ndim == 0:
x = array([x])
return x
# Prepare some vectors and other numbers that are needed to form objective functions, derivatives and
# Hessians
DM = zeros((M,C))
DMex = zeros((M,C+1))
DM[:,0] = 1
DMex[:,0] = 1
for j in range(0,M):
lc = loc([oppc[j]])[0]
if lc < C-1:
DM[j,lc+1] = 1
else:
DM[j,1:] = -1
DMex[j,lc+1] = 1
mbar = oppr
sbar = sqrt(opps**2 + 1)
gen_phi = lambda j, x: pdf(x, loc=mbar[j], scale=sbar[j])
gen_Phi = lambda j, x: max(min(cdf(x, loc=mbar[j], scale=sbar[j]), 1-LOG_CAP), LOG_CAP)
alpha = pi/2/sqrt(3)
myrc = myr[[0]+played_cats_p1]
mysc = mys[[0]+played_cats_p1]
# Objective function
def logL(x):
Mv = x[0] + extend(x)[loc(oppc)+1]
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
if pr:
print ':::', x, Mv, Phi
return sum(W*log(Phi) + L*log(1-Phi))
def logE(x):
return sum(log(1 - tanh(alpha*(extend(x)-myrc)/mysc)**2))
#logF = lambda x: logL(x) + logE(x)
logF = lambda x: logL(x)
# Derivative
def DlogL(x):
Mv = x[0] + extend(x)[loc(oppc)+1]
phi = array([gen_phi(i,Mv[i]) for i in range(0,M)])
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
vec = (W/Phi - L/(1-Phi)) * phi
return array(vec * matrix(DM))[0]
def DlogE(x):
ret = -2*alpha*tanh(alpha*(extend(x)-myrc)/mysc)/mysc
print ret
return ret
#DlogF = lambda x: DlogL(x) + DlogE(x)
DlogF = lambda x: DlogL(x)
# Hessian
def D2logL(x, DM, C):
Mv = x[0] + extend(x)[loc(oppc)+1]
phi = array([gen_phi(i,Mv[i]) for i in range(0,M)])
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
alpha = phi/Phi
beta = phi/(1-Phi)
Mvbar = pi/sqrt(3)/sbar * tanh(pi/2/sqrt(3)*(Mv-mbar)/sbar)
coeff = - W*alpha*(alpha+Mvbar) - L*beta*(beta-Mvbar)
ret = zeros((C,C))
for j in range(0,M):
ret += coeff[j] * outer(DM[j,:], DM[j,:])
return ret
def D2logE(x):
return diag(-2*alpha**2*(1 - tanh(alpha*(extend(x)-myrc)/mysc)**2)/mysc**2)
#D2logF = lambda x: D2logL(x,DM,C) + D2logE(x)
D2logF = lambda x: D2logL(x,DM,C)
# Prepare initial guess in unrestricted format and maximize
x = hstack((myr[0], myr[played_cats_p1]))[0:-1]
x = maximize(logF, DlogF, D2logF, x, method='powell', disp=pr)
x = dim(x)
# If maximization failed, return the current rating and print an error message
if x == None:
print 'Failed to converge for %s' % text
return (myr, mys, [None]*(Ncats+1), [None]*(Ncats+1))
# Extend to restricted format
devs = sqrt(-1/diag(D2logL(x, DMex, C+1)))
#devs = -1/diag(D2logL(x, DMex, C+1))
devs = maximum(devs, RATINGS_MIN_DEV)
rats = extend(x)
if pr:
print devs
print rats
# Compute new RD and rating for the indices that can change
news = zeros(len(myr))
newr = zeros(len(myr))
ind = [0] + [f+1 for f in played_cats]
#news[ind] = devs
#newr[ind] = rats
news[ind] = 1./sqrt(1./devs**2 + 1./mys[ind]**2)
newr[ind] = (rats/devs**2 + myr[ind]/mys[ind]**2) * news[ind]**2
if pr:
print news
print newr
# Enforce the restriction of sum relative rating against played categories should be constant
ind = ind[1:]
m = (sum(newr[ind]) - tot)/len(ind)
newr[ind] -= m
newr[0] += m
if pr:
print newr
# Ratings against non-played categories should be kept as before.
ind = setdiff1d(range(0,len(myr)), [0] + ind)
news[ind] = mys[ind]
newr[ind] = myr[ind]
if pr:
print news
print newr
# Keep new RDs between MIN_DEV and INIT_DEV
news = minimum(news, RATINGS_INIT_DEV)
news = maximum(news, RATINGS_MIN_DEV)
if pr:
print news
# Ensure that mean relative rating is zero
m = mean(newr[1:])
newr[1:] -= m
newr[0] += m
if pr:
print newr
# Extend the performance ratings to global indices
devsex = [None] * (Ncats + 1)
ratsex = [None] * (Ncats + 1)
devsex[0] = devs[0]
ratsex[0] = rats[0]
for c in played_cats:
devsex[c+1] = devs[played_cats.index(c)+1]
ratsex[c+1] = rats[played_cats.index(c)+1]
if pr:
print '------------ Finished'
return (newr, news, ratsex, devsex)
def performance(oppr, opps, oppc, W, L, text='', pr=False):
opp = list(zip(oppr, opps, oppc, W, L))
ret = [0.0, 0.0, 0.0, 0.0]
meanok = True
if pr:
print('Now performance for %s' % text)
for cat in range(0,3):
spopp = [o for o in opp if o[2] == cat]
sW = sum([o[3] for o in spopp])
sL = sum([o[4] for o in spopp])
if sW == 0 and sL == 0:
ret[cat+1] = PRF_NA
meanok = False
elif sW == 0:
ret[cat+1] = PRF_MININF
meanok = False
elif sL == 0:
ret[cat+1] = PRF_INF
meanok = False
else:
gen_phi = lambda p, x: pdf(x, loc=p[0], scale=sqrt(1+p[1]**2))
gen_Phi = lambda p, x: max(min(cdf(x, loc=p[0], scale=sqrt(1+p[1]**2)), 1-LOG_CAP), LOG_CAP)
def logL(x):
ret = 0.0
for p in spopp:
gP = gen_Phi(p,x)
ret += p[3] * log(gP) + p[4] * log(1-gP)
return ret
def DlogL(x):
ret = 0.0
for p in spopp:
gp = gen_phi(p,x)
gP = gen_Phi(p,x)
ret += (float(p[3])/gP - float(p[4])/(1-gP)) * gp
return ret
def D2logL(x):
ret = 0.0
for p in spopp:
gp = gen_phi(p,x)
gP = gen_Phi(p,x)
alpha = gp/gP
beta = gp/(1-gP)
sb = sqrt(1+p[1]**2)
Mv = pi/sqrt(3)/sb * tanh(pi/2/sqrt(3)*(x-p[0])/sb)
ret -= p[3]*alpha*(alpha+Mv) + p[4]*beta*(beta-Mv)
return ret
perf, init = nan, 1.0
while isnan(perf):
perf = maximize_1d(logL, DlogL, D2logL, init)
init -= 0.1
ret[cat+1] = perf
if meanok:
ret[0] = sum(ret[1:]) / 3
else:
ret[0] = PRF_NA
return ret
def update(myr, mys, oppr, opps, oppc, W, L, text='', pr=False, Ncats=3):
"""This function updates the rating of a player according to the ratings of the opponents and the games
against them."""
if len(W) == 0:
return(myr, mys)
if pr:
print(text)
print(oppr, len(oppr))
print(opps, len(opps))
print(oppc, len(oppc))
print(W, len(W))
print(L, len(L))
played_cats = sorted(unique(oppc)) # The categories against which the player played
played_cats_p1 = [p+1 for p in played_cats]
tot = sum(myr[array(played_cats)+1]) # The sum relative rating against those categories
# (will be kept constant)
M = len(W) # Number of opponents
C = len(played_cats) # Number of different categories played
# Convert global categories to local
def loc(x):
return array([played_cats.index(c) for c in x])
# Convert local categories to global
def glob(x):
return array([played_cats[c] for c in x])
# Extends a M-vector to an M+1-vector according to the restriction given
# (that the sum of relative ratings against the played categories is constant)
def extend(x):
return hstack((x, tot-sum(x[1:])))
# Ensure that arrays are 1-dimensional
def dim(x):
if x.ndim == 0:
x = array([x])
return x
# Prepare some vectors and other numbers that are needed to form objective functions, derivatives and
# Hessians
DM = zeros((M,C))
DMex = zeros((M,C+1))
DM[:,0] = 1
DMex[:,0] = 1
for j in range(0,M):
lc = loc([oppc[j]])[0]
if lc < C-1:
DM[j,lc+1] = 1
else:
DM[j,1:] = -1
DMex[j,lc+1] = 1
mbar = oppr
sbar = sqrt(opps**2 + 1)
gen_phi = lambda j, x: pdf(x, loc=mbar[j], scale=sbar[j])
gen_Phi = lambda j, x: max(min(cdf(x, loc=mbar[j], scale=sbar[j]), 1-LOG_CAP), LOG_CAP)
alpha = pi/2/sqrt(3)
myrc = myr[[0]+played_cats_p1]
mysc = mys[[0]+played_cats_p1]
# {{{ Objective function
def logL(x):
Mv = x[0] + extend(x)[loc(oppc)+1]
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
if pr:
print(':::', x, Mv, Phi)
return sum(W*log(Phi) + L*log(1-Phi))
def logE(x):
return sum(log(1 - tanh(alpha*(extend(x)-myrc)/mysc)**2))
logF = lambda x: logL(x) + logE(x)
# }}}
# {{{ Derivative
def DlogL(x):
Mv = x[0] + extend(x)[loc(oppc)+1]
phi = array([gen_phi(i,Mv[i]) for i in range(0,M)])
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
vec = (W/Phi - L/(1-Phi)) * phi
return array(vec * matrix(DM))[0]
def DlogE(x):
ret = -2*alpha*tanh(alpha*(extend(x)-myrc)/mysc)/mysc
ret = ret[0:-1] - ret[-1]
return ret
DlogF = lambda x: DlogL(x) + DlogE(x)
# }}}
# {{{ Hessian
def D2logL(x, DM, C):
Mv = x[0] + extend(x)[loc(oppc)+1]
phi = array([gen_phi(i,Mv[i]) for i in range(0,M)])
Phi = array([gen_Phi(i,Mv[i]) for i in range(0,M)])
alpha = phi/Phi
beta = phi/(1-Phi)
Mvbar = pi/sqrt(3)/sbar * tanh(pi/2/sqrt(3)*(Mv-mbar)/sbar)
coeff = - W*alpha*(alpha+Mvbar) - L*beta*(beta-Mvbar)
ret = zeros((C,C))
for j in range(0,M):
ret += coeff[j] * outer(DM[j,:], DM[j,:])
return ret
def D2logE(x):
diags = -2*alpha**2*(1 - tanh(alpha*(extend(x)-myrc)/mysc)**2)/mysc**2
diags, final = diags[0:-1], diags[-1]
return diag(diags) + final
def D2logEx(x):
diags = -2*alpha**2*(1 - tanh(alpha*(extend(x)-myrc)/mysc)**2)/mysc**2
return diag(diags)
D2logF = lambda x: D2logL(x,DM,C) + D2logE(x)
# }}}
# Prepare initial guess in unrestricted format and maximize
x = hstack((myr[0], myr[played_cats_p1]))[0:-1]
x = maximize(logF, DlogF, D2logF, x, disp=pr)
x = dim(x)
# If maximization failed, return the current rating and print an error message
if x == None:
print('Failed to converge for %s' % text)
return (myr, mys, [None]*(Ncats+1), [None]*(Ncats+1))
# Extend to restricted format
D2 = D2logL(x, DMex, C+1) + D2logEx(x)
devs = sqrt(-1/diag(D2))
rats = extend(x)
if pr:
print(devs)
print(rats)
# Compute new RD and rating for the indices that can change
news = zeros(len(myr))
newr = zeros(len(myr))
ind = [0] + [f+1 for f in played_cats]
news[ind] = devs
newr[ind] = rats
if pr:
print(news)
print(newr)
# Enforce the restriction of sum relative rating against played categories should be constant
ind = ind[1:]
m = (sum(newr[ind]) - tot)/len(ind)
newr[ind] -= m
newr[0] += m
if pr:
print(newr)
# Ratings against non-played categories should be kept as before.
ind = setdiff1d(range(0,len(myr)), [0] + ind)
news[ind] = mys[ind]
newr[ind] = myr[ind]
if pr:
print(news)
print(newr)
# Keep new RDs between MIN_DEV and INIT_DEV
news = minimum(news, INIT_DEV)
news = maximum(news, MIN_DEV)
if pr:
print(news)
# Ensure that mean relative rating is zero
m = mean(newr[1:])
newr[1:] -= m
newr[0] += m
if pr:
print(newr)
print('------------ Finished')
return (newr, news)