def solve(nelem, h, deg, alpha, beta, gamma, k=None, b=None, c=None, f=None):
#
# Cast polynomial degree to enums
deg = POLYNOMIAL(deg)
#
# Check inputs make sense
assert (nelem > 0)
assert (nelem == len(h))
assert (deg in [POLYNOMIAL.LINEAR, POLYNOMIAL.QUADRATIC])
assert (len(alpha) == 2)
assert (len(beta) == 2)
assert (len(gamma) == 2)
#
# Make sure functions are callable on ndarrays
#
# NOTE: functions passed as None will be treated
# as a constant equal to zero.
x_test = linspace(0, 1, 3)
callable_functions = [k, b, c, f]
for fun in callable_functions:
if fun is not None:
try:
fun(x_test)
except:
try:
fun = lambda x: float(fun)
except:
raise (Exception(
"One of the functions k, b, c, f is neither callable on ndarrays nor a number. Aborting!"
))
else:
fun = lambda x: 0.
#
# Assemble the system
K = construct_stiffness()
F = construct_load()
#
# Solve the system
u = np_solve(K, F)
#
# Solve auxiliary equations
if False:
print("Hello")
#
return u
gamma = [1., 4.]
k = lambda x: 2. + x
k = vectorize(k)
b = lambda x: 0.
b = vectorize(b)
c = lambda x: 0.
c = vectorize(c)
f = lambda x: -6 - 4 * x
f = vectorize(f)
K, K0, KN = construct_stiffness(elements, polynomial_order, alpha, beta, gamma,
k, b, c)
savetxt("stiffness_quad.csv", K, delimiter=" & ", fmt="%.2f")
F = construct_load(elements, polynomial_order, alpha, beta, gamma, K0, KN, f,
k)
savetxt("load_quad.csv", F, delimiter=" \\\\ ", fmt="%.2f")
x = linspace(0, 1, 100)
t = lambda x: (1 + x)**2
t = vectorize(t)
y = t(x)
# print("COND: ", cond(K))
xx = linspace(0, 1, nelems * polynomial_order + 1)
uu = np_solve(K, F).flatten()
u = set_essential_boundary_conditions(alpha, gamma, uu)
plt.cla()
plt.plot(x, y, 'k-', label='True Sol.')