def params(method=None, m=None, inpt=None, stvars=None):
node = zeros((inpt,max(m)))
weight = zeros((inpt,max(m)))
if method==4 or method==5:
for i in range(0,inpt):
node[i], weight[i] = gaussquad.gaussquad(m[i], stvars[i].dist, stvars[i].param[0], stvars[i].param[1])
if stvars[i].dist == 'BETA':
node[i] = node[i] * (stvars[i].param[3] - stvars[i].param[2]) + stvars[i].param[2]
return node,weight
def params(method=None, m=None, inpt=None, stvars=None):
node = zeros((inpt, max(m)))
weight = zeros((inpt, max(m)))
if method == 4 or method == 5:
for i in range(0, inpt):
node[i], weight[i] = gaussquad.gaussquad(m[i], stvars[i].dist,
stvars[i].param[0],
stvars[i].param[1])
if stvars[i].dist == 'BETA':
node[i] = node[i] * (stvars[i].param[3] -
stvars[i].param[2]) + stvars[i].param[2]
return node, weight
def UP_PCE(driver):
# Uses the PCE method for UP
# This routine has been updated as part of refactoring code before the port
# from MATLAB to Python/NumPy/SciPy. Sections of PCC_Computation that apply
# this method have been moved here.
# ---------------------- Setup ---------------------------
methd = "PCE"
method = 6
inpt = len(driver.inputs)
krig = driver.krig
limstate = driver.limstate
nodes = driver.nodes
order = driver.order
otpt = len(driver.outputNames)
output = driver.outputNames
stvars = driver.stvars
numbins = driver.numbins
# current settings for these two vars
ii = 0
jj = 0
# ---------------------- Model ---------------------------
mu_g = zeros(inpt)
sigma_g = ones(inpt)
node_t = zeros((inpt, nodes[0]))
weight_t = zeros((inpt, nodes[0]))
for i in range(inpt):
node_t[i], weight_t[i] = gaussquad.gaussquad(nodes[i], "NORM", mu_g[i], sigma_g[i])
x = []
for i in range(inpt):
x.append(symbols("x" + str(i)))
x = array(x)
j = fullfact(nodes)
pts = shape(j)[0]
node = zeros((pts, inpt))
wj = zeros((pts, inpt))
for y in range(pts):
for i in range(inpt):
node[y][i] = node_t[i][j[y][i]]
wj[y][i] = weight_t[i][j[y][i]]
weight = prod(wj, 1)
P = zeros(order)
P[0] = 1
for p in range(1, order):
term2 = 0
for s in range(1, p + 1):
term1 = 1
for r in range(s):
term1 = term1 * (inpt + r)
term2 = term2 + (1.0 / int(scipy.misc.factorial(s))) * term1
if p == 1:
P[p] = term2
else:
P[p] = term2 - sum(P[range(1, p + 1)])
G_s = zeros((pts, otpt))
if krig == 1:
t = strcat("SS_K", num2str(ii), num2str(jj))
load(char(t))
for j in range(pts):
# Rosenblatt Transformation
T_L = Dist.Dist(stvars, node[j], inpt)
G_s[j] = predictor(T_L, dmodel)
else:
values = []
for j in range(pts):
# Rosenblatt Transformation
# print 'Running simulation',j+1,'of',pts
T_L = Dist.Dist(stvars, node[j], inpt)
# G_s[j] = run_model(driver, T_L)
values.append(T_L)
G_s = run_list(driver, values)
indx = 0
bn = zeros((sum(P), otpt))
bd = zeros(sum(P))
for k in range(order):
vec = xvector.xvector(k, inpt)
for j in range(int(P[k])):
for i in range(pts):
L = node[i]
if k == 0:
bn[indx] = bn[indx] + weight[i] * G_s[i]
bd[indx] = bd[indx] + weight[i]
else:
h, h_sym = hermite.hermite(k, vec[j], L, x)
bn[indx] += weight[i] * G_s[i] * h
bd[indx] += weight[i] * (h ** 2)
indx += 1
b = zeros((sum(P), otpt))
for l in range(otpt):
b[:, l] = bn[:, l] / bd
indx = 0
U_sum = 0
for k in range(order):
vec = xvector.xvector(k, inpt)
for j in range(int(P[k])):
if k == 0:
U_sum = b[0]
else:
h, h_sym = hermite.hermite(k, vec[j], L, x)
U_sum = U_sum + b[indx] * N(h_sym)
indx += 1
U = U_sum
U_s = zeros((pts, otpt))
G_mean = zeros(otpt)
G_kurt = zeros(otpt)
G_skew = zeros(otpt)
covar_m = zeros((otpt, otpt))
for i in range(pts):
for k in range(otpt):
U_s[i][k] = U[k].subs(dict(zip(x, node[i])))
for k in range(otpt):
# G_mean[k] = sum(matrix(weight) * matrix(U_s[:, k]).transpose())
G_mean[k] = sum(weight * U_s[:, k])
for k in range(otpt):
for j in range(k, otpt):
covar_m[k, j] = sum(weight * (U_s[:, k] - G_mean[k]) * (G_s[:, j] - G_mean[j]))
covar_m[j, k] = covar_m[k, j]
G_skew[k] = sum(weight * (U_s[:, k] - G_mean[k]) ** 3) / covar_m[k, k] ** 1.5
G_kurt[k] = sum(weight * (U_s[:, k] - G_mean[k]) ** 4) / covar_m[k, k] ** 2
CovarianceMatrix = covar_m.transpose()
Moments = {"Mean": G_mean, "Variance": diag(CovarianceMatrix), "Skewness": G_skew, "Kurtosis": G_kurt}
# ---------------------- Analyze ---------------------------
if any(Moments["Variance"] == 0):
print "Warning: One or more outputs does not vary over given parameter variation."
# Calculate the PCC for the FFNI method
if otpt > 1:
PCC = [0] * (otpt + 1)
else:
PCC = [0] * otpt
dtype = [0] * otpt
Inv1 = [0] * otpt
Inv2 = [0] * otpt
m1 = [0] * otpt
m2 = [0] * otpt
a1 = [0] * otpt
a2 = [0] * otpt
alph = [0] * otpt
beta = [0] * otpt
lo = [0] * otpt
hi = [0] * otpt
C_Y_pdf = [0] * otpt
if any(Moments["Variance"] == 0):
print "Warning: One or more outputs does not vary over given parameter variation."
for k in range(otpt):
PCC[k], dtype[k], Inv1[k], m1[k], m2[k], a1[k], a2[k], alph[k], beta[k], lo[k], hi[k] = pearscdf.pearscdf(
limstate[k],
Moments["Mean"][k],
sqrt(CovarianceMatrix[k, k]),
Moments["Skewness"][k],
Moments["Kurtosis"][k],
methd,
k,
output,
)
if dtype[k] != None:
if iscomplex(a1[k]):
a1[k] = [a1[k].real, a1[k].imag]
if iscomplex(a2[k]):
a2[k] = [a2[k].real, a2[k].imag]
C_Y_pdf[k] = estimate_complexity.with_distribution(
dtype[k], limstate[k], Moments["Mean"][k], Moments["Variance"][k], numbins
)
sigma_mat = matrix(sqrt(diag(CovarianceMatrix)))
seterr(invalid="ignore") # ignore problems with divide-by-zero, just give us 'nan' as usual
CorrelationMatrix = CovarianceMatrix / multiply(sigma_mat, sigma_mat.transpose())
Distribution = {"PearsonType": dtype, "m1": m1, "m2": m2, "a1": a1, "a2": a2, "Complexity": C_Y_pdf}
Plotting = {"alpha": alph, "beta": beta, "lo": lo, "hi": hi}
CorrelationMatrix = where(isnan(CorrelationMatrix), None, CorrelationMatrix)
if otpt > 1 and not 0 in PCC[0:otpt]:
lower = zeros(otpt) - inf
PCC[otpt] = mvstdnormcdf(lower, Inv1, CorrelationMatrix)
Results = {
"Moments": Moments,
"CorrelationMatrix": CorrelationMatrix,
"CovarianceMatrix": CovarianceMatrix,
"Distribution": Distribution,
"Plotting": Plotting,
"PCC": PCC,
}
return Results
def UP_PCE(problem, driver):
# Uses the PCE method for UP
# This routine has been updated as part of refactoring code before the port
# from MATLAB to Python/NumPy/SciPy. Sections of PCC_Computation that apply
# this method have been moved here.
# ---------------------- Setup ---------------------------
methd = 'PCE'
method = 6
inpt = len(driver.inputs)
krig = driver.krig
limstate= driver.limstate
nodes = driver.nodes
order = driver.order
otpt = len(driver.outputNames)
output = driver.outputNames
stvars = driver.stvars
numbins = driver.numbins
#current settings for these two vars
ii = 0
jj = 0
# ---------------------- Model ---------------------------
mu_g = zeros(inpt)
sigma_g = ones(inpt)
node_t = zeros((inpt,nodes[0]))
weight_t = zeros((inpt,nodes[0]))
for i in range(inpt):
node_t[i], weight_t[i] = gaussquad.gaussquad(nodes[i], 'NORM', mu_g[i], sigma_g[i])
x=[]
for i in range(inpt):
x.append(symbols('x'+str(i)))
x=array(x)
j=fullfact(nodes);
pts = shape(j)[0]
node=zeros((pts,inpt))
wj=zeros((pts,inpt))
for y in range(pts):
for i in range(inpt):
node[y][i] = node_t[i][j[y][i]]
wj[y][i] = weight_t[i][j[y][i]]
weight=prod(wj,1);
P = zeros(order)
P[0] = 1
for p in range(1,order):
term2 = 0
for s in range(1,p+1):
term1 = 1
for r in range(s):
term1 = term1 * (inpt + r)
term2 = term2 + (1.0 / int(scipy.misc.factorial(s))) * term1
if p == 1:
P[p] = term2
else:
P[p] = term2 - sum(P[range(1,p+1)])
G_s = zeros((pts, otpt))
if krig == 1:
t = strcat('SS_K', num2str(ii), num2str(jj))
load(char(t))
for j in range(pts):
#Rosenblatt Transformation
T_L = Dist.Dist(stvars, node[j], inpt)
G_s[j] = predictor(T_L, dmodel)
else:
values = []
for j in range(pts):
#Rosenblatt Transformation
# print 'Running simulation',j+1,'of',pts
T_L = Dist.Dist(stvars, node[j], inpt)
# G_s[j] = run_model(driver, T_L)
values.append(T_L)
G_s = run_list(problem, driver, values)
indx = 0
bn = zeros((sum(P), otpt))
bd = zeros(sum(P))
for k in range(order):
vec = xvector.xvector(k, inpt)
for j in range(int(P[k])):
for i in range(pts):
L=node[i]
if k == 0:
bn[indx] = bn[indx] + weight[i] * G_s[i]
bd[indx] = bd[indx] + weight[i]
else:
h, h_sym = hermite.hermite(k, vec[j], L, x)
bn[indx] += weight[i] * G_s[i] * h
bd[indx] += weight[i] * (h ** 2)
indx+=1
b = zeros((sum(P),otpt))
for l in range(otpt):
b[:, l] = bn[:, l] / bd
indx = 0
U_sum = 0
for k in range(order):
vec = xvector.xvector(k, inpt)
for j in range(int(P[k])):
if k == 0:
U_sum = b[0]
else:
h, h_sym = hermite.hermite(k, vec[j], L, x)
U_sum = U_sum + b[indx] * N(h_sym)
indx+=1
U = U_sum
U_s = zeros((pts,otpt))
G_mean = zeros(otpt)
G_kurt = zeros(otpt)
G_skew = zeros(otpt)
covar_m = zeros((otpt,otpt))
for i in range(pts):
for k in range(otpt):
U_s[i][k] = U[k].subs(dict(zip(x, node[i])))
for k in range(otpt):
# G_mean[k] = sum(matrix(weight) * matrix(U_s[:, k]).transpose())
G_mean[k] = sum(weight * U_s[:, k])
for k in range(otpt):
for j in range(k,otpt):
covar_m[k, j] = sum(weight * (U_s[:, k] - G_mean[k]) * (G_s[:, j] - G_mean[j]))
covar_m[j, k] = covar_m[k, j]
G_skew[k] = sum(weight * (U_s[:, k] - G_mean[k]) ** 3) / covar_m[k, k] ** 1.5
G_kurt[k] = sum(weight * (U_s[:, k] - G_mean[k]) ** 4) / covar_m[k, k] ** 2
CovarianceMatrix = covar_m.transpose()
Moments = {'Mean': G_mean, 'Variance': diag(CovarianceMatrix), 'Skewness': G_skew, 'Kurtosis': G_kurt}
# ---------------------- Analyze ---------------------------
if any(Moments['Variance']==0):
print "Warning: One or more outputs does not vary over given parameter variation."
# Calculate the PCC for the FFNI method
if otpt>1:
PCC = [0]*(otpt+1)
else:
PCC = [0]*otpt
dtype = [0]*otpt
Inv1 = [0]*otpt
Inv2 = [0]*otpt
m1 = [0]*otpt
m2 = [0]*otpt
a1 = [0]*otpt
a2 = [0]*otpt
alph = [0]*otpt
beta = [0]*otpt
lo = [0]*otpt
hi = [0]*otpt
C_Y_pdf = [0]*otpt
if any(Moments['Variance']==0):
print "Warning: One or more outputs does not vary over given parameter variation."
for k in range(otpt):
PCC[k],dtype[k],Inv1[k],m1[k],m2[k],a1[k],a2[k],alph[k],beta[k],lo[k],hi[k] =\
pearscdf.pearscdf(limstate[k], Moments['Mean'][k], sqrt(CovarianceMatrix[k, k]), Moments['Skewness'][k], Moments['Kurtosis'][k], methd, k, output)
if dtype[k] != None:
if iscomplex(a1[k]):
a1[k] = [a1[k].real, a1[k].imag]
if iscomplex(a2[k]):
a2[k] = [a2[k].real, a2[k].imag]
C_Y_pdf[k] = estimate_complexity.with_distribution(dtype[k],limstate[k],Moments['Mean'][k],Moments['Variance'][k],numbins)
sigma_mat=matrix(sqrt(diag(CovarianceMatrix)))
seterr(invalid='ignore') #ignore problems with divide-by-zero, just give us 'nan' as usual
CorrelationMatrix= CovarianceMatrix/multiply(sigma_mat,sigma_mat.transpose())
Distribution = {'PearsonType': dtype, 'm1': m1, 'm2': m2, 'a1': a1, 'a2': a2, 'Complexity': C_Y_pdf}
Plotting = {'alpha': alph, 'beta': beta, 'lo': lo, 'hi': hi}
CorrelationMatrix=where(isnan(CorrelationMatrix), None, CorrelationMatrix)
if otpt > 1 and not 0 in PCC[0:otpt]:
lower = zeros(otpt)-inf
PCC[otpt] = mvstdnormcdf(lower, Inv1, CorrelationMatrix)
Results = {'Moments': Moments, 'CorrelationMatrix': CorrelationMatrix,
'CovarianceMatrix': CovarianceMatrix, 'Distribution': Distribution, 'Plotting': Plotting, 'PCC': PCC}
return Results
