def get_func_deriv(k):
"""
Get the energy value and its derivative for given k value
"""
f = np.pi
spr = Spring(k)
u = spr.solve(0, f)
E = spr.F(u)
dRdk = spr.dRdk(u)
dFdk = spr.dFdk(u)
dRdq = spr.dRdq(u)
dFdq = spr.dFdq(u)
lam = spr.adjoint_solve(u)
DFDx = dFdk + lam * dRdk
return E, DFDx
# Quadrature node and weight
yq = pc.Y(q, 'name')
wq = pc.W(q)
# Set the paramter values into the element
dspr.setStiffness(yq['K'])
# Create space for fetching deterministic
# jacobian, and state vectors that go as input
uq = np.zeros((1)) # dspr.nddof
for k in range(sspr.nterms):
psiky = pc.evalOrthoNormalBasis(k, q)
uq[:] += U[k * 1:(k + 1) * 1] * psiky
fq = dspr.F(uq)
dfdxq = dspr.dFdk(uq)
dRdxq = dspr.dRdk(uq)
# Form u for this quadrature point 'y'
# Project the determinic element jacobian onto the
# stochastic basis and place in the global matrix
psiziw = wq * pc.evalOrthoNormalBasis(i, q)
# F(q,q(y))*psi(y)*rho(y)
E[i] += fq * psiziw
dFdX[i] += dfdxq * psiziw
dRdX[i] += dRdxq * psiziw
fmean = E[0]
fvar = np.sum(E[1:]**2)
fstd = np.sqrt(fvar)
