def __call__(self, eps, lambd, xi, E_mod, theta, A):
'''
Implements the response function with arrays as variables.
first extract the variable discretizations from the orthogonal grid.
'''
# NOTE: as each variable is an array oriented in different direction
# the algebraic expressions (-+*/) perform broadcasting,. i.e. performing
# the operation for all combinations of values. Thus, the resulgin eps
# is contains the value of local strain for any combination of
# global strain, xi, theta and lambda
#
eps_ = (eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd))
# cut off all the negative strains due to delayed activation
#
eps_ *= Heaviside(eps_)
# broadcast eps also in the xi - dimension
# (by multiplying with array containing ones with the same shape as xi )
#
eps_grid = eps_ * Heaviside(xi - eps_)
# cut off all the realizations with strain greater than the critical one.
#
# eps_grid[ eps_grid >= xi ] = 0
# transform it to the force
#
q_grid = E_mod * A * eps_grid
return q_grid
def __call__(self, w, fu, qf, L, A, E_mod, z, phi, f):
'''Lexically optimized expresseion - each result is
calculated only once.
Further optimization possible by printing out the shape
and doing inplace operation where possible.
However, this does not seem to have a significant effect.
'''
t4 = sqrt(w * E_mod * A * qf)
t5 = f * phi
t6 = exp(t5)
t7 = t4 * t6
t11 = Heaviside(fu * A - 0.1000000000e1 * t7)
t12 = exp(t5);
t14 = 0.5000000000e0 * L
t15 = cos(phi)
t17 = z / t15
t18 = t14 - t17
t19 = pow(t18, 0.20e1)
t24 = t12 * qf * t19 / E_mod / A
t25 = t24 - w
t26 = Heaviside(t25)
t28 = Heaviside(t18)
t32 = t18 * qf
t38 = (t32 + t32 / (t14 - t17 - t24) * t25) * t6
t39 = Heaviside(t38)
t40 = Heaviside(-t25)
res = 0.1000000000e1 * t7 * t11 * t26 * t28 + t38 * t39 * t40
return res
def __call__(self, eps, lambd, xi, E_mod, theta, A):
'''
Implements the response function with arrays as variables.
first extract the variable discretizations from the orthogonal grid.
'''
eps_ = (eps - theta * (1 + lambd)) / ((1 + theta) * (1 + lambd))
eps_ *= Heaviside(eps_)
eps_grid = eps_ * Heaviside(xi - eps_)
q_grid = E_mod * A * eps_grid
return q_grid
def __call__(self, e, la, xi):
''' Response function of a single fiber '''
return la * e * Heaviside(xi - e)