def drx_numba(network, factor=1.0, tol=0.1, steps=10000, summary=0, update=False):
""" Run Numba accelerated dynamic relaxation analysis.
Parameters
----------
network : obj
Network to analyse.
factor : float
Convergence factor.
tol : float
Tolerance value.
steps : int
Maximum number of steps.
summary : int
Print summary at end (1:yes or 0:no).
update : bool
Update the co-ordinates of the Network.
Returns
-------
array
Vertex co-ordinates.
array
Edge forces.
array
Edge lengths.
"""
# Setup
tic1 = time()
args = _args(network, factor, summary, steps, tol)
toc1 = time() - tic1
# Solver
tic2 = time()
tol, steps, summary, m, n, u, v, X, f0, l0, k0, ind_c, ind_t, B, P, S, rows, cols, vals, nv, M, factor, V, inds, indi, indf, EIx, EIy, beams, C = args
drx_solver_numba(tol, steps, summary, m, n, u, v, X, f0, l0, k0, ind_c, ind_t, B, P, S, rows, cols, vals, nv,
M, factor, V, inds, indi, indf, EIx, EIy, beams)
_, l = uvw_lengths(C, X) # noqa: E741
f = f0 + k0 * (l.ravel() - l0)
toc2 = time() - tic2
# Summary
if summary:
print('\n\nNumba DR -------------------')
print('Setup time: {0:.3f} s'.format(toc1))
print('Solver time: {0:.3f} s'.format(toc2))
print('----------------------------------')
# Update
if update:
k_i = network.key_index()
uv_i = network.uv_index()
for key in network.vertices():
x, y, z = X[k_i[key], :]
network.set_vertex_attributes(key, 'xyz', [x, y, z])
for uv in network.edges():
i = uv_i[uv]
network.set_edge_attribute(uv, 'f', float(f[i]))
return X, f, l
def drx_solver_numpy(tol, steps, factor, C, Ct, X, M, k0, l0, f0, ind_c, ind_t,
P, S, B, V, refresh, beams, inds, indi, indf, EIx, EIy,
callback, **kwargs):
""" NumPy and SciPy dynamic relaxation solver.
Parameters
----------
tol : float
Tolerance value.
steps : int
Maximum number of steps.
factor : float
Convergence factor.
C : array
Connectivity matrix.
Ct : array
Transposed connectivity matrix.
X : array
Nodal co-ordinates.
M : array
Mass matrix.
k0 : array
Initial edge axial stiffnesses.
l0 : array
Initial edge lengths.
f0 : array
Initial edge forces.
ind_c : list
Indices of compression only edges.
ind_t : list
Indices of tension only edges.
P : array
Nodal loads Px, Py, Pz.
S : array
Shear forces Sx, Sy, Sz.
B : array
Constraint conditions Bx, By, Bz.
V : array
Nodal velocities Vx, Vy, Vz.
refresh : int
Update progress every n steps.
beams : int
Beam data flag 1 or 0.
inds : array
Indices of beam element start nodes.
indi : array
Indices of beam element intermediate nodes.
indf : array
Indices of beam element finish nodes beams.
EIx : array
Nodal EIx flexural stiffnesses.
EIy : array
Nodal EIy flexural stiffnesses.
callback : obj
Callback function.
Returns
-------
array
Vertex co-ordinates.
array
Edge forces.
array
Edge lengths.
"""
res = 1000 * tol
ts, Uo = 0, 0
M = factor * tile(M.reshape((-1, 1)), (1, 3))
while (ts <= steps) and (res > tol):
uvw, l = uvw_lengths(C, X)
f = f0 + k0 * (l.ravel() - l0)
if ind_t:
f[ind_t] *= f[ind_t] > 0
if ind_c:
f[ind_c] *= f[ind_c] < 0
if beams:
S = _beam_shear(S, X, inds, indi, indf, EIx, EIy)
q = f[:, newaxis] / l
qt = tile(q, (1, 3))
R = (P - S - Ct.dot(uvw * qt)) * B
res = mean(normrow(R))
V += R / M
Un = sum(M * V**2)
if Un < Uo:
V *= 0
Uo = Un
X += V
if refresh:
if (ts % refresh == 0) or (res < tol):
print('Step:{0} Residual:{1:.3f}'.format(ts, res))
if callback:
callback(X, **kwargs)
ts += 1
return X, f, l
def drx_solver(tol, steps, factor, C, Ct, X, ks, l0, f0, ind_c, ind_t, P, S, B,
M, V, refresh, beams, inds, indi, indf, EIx, EIy, callback,
**kwargs):
""" NumPy and SciPy dynamic relaxation solver.
Parameters:
tol (float): Tolerance limit.
steps (int): Maximum number of steps.
factor (float): Convergence factor.
C (array): Connectivity matrix.
Ct (array): Transposed connectivity matrix.
X (array): Nodal co-ordinates.
ks (array): Initial edge axial stiffnesses.
l0 (array): Initial edge lengths.
f0 (array): Initial edge forces.
ind_c (list): Indices of compression only edges.
ind_t (list): Indices of tension only edges.
P (array): Nodal loads Px, Py, Pz.
S (array): Shear forces Sx, Sy, Sz.
B (array): Constraint conditions.
M (array): Mass matrix.
V (array): Nodal velocities Vx, Vy, Vz.
refresh (int): Update progress every n steps.
beams (bool): Dictionary of beam information.
inds (list): Indices of beam element start nodes.
indi (list): Indices of beam element intermediate nodes.
indf (list): Indices of beam element finish nodes beams.
EIx (array): Nodal EIx flexural stiffnesses.
EIy (array): Nodal EIy flexural stiffnesses.
callback (obj): Callback function.
Returns:
array: Updated nodal co-ordinates.
array: Updated forces.
array: Updated lengths.
"""
res = 1000 * tol
ts, Uo = 0, 0
M = factor * tile(M, (1, 3))
while (ts <= steps) and (res > tol):
uvw, l = uvw_lengths(C, X)
f = f0 + ks * (l - l0)
if ind_t:
f[ind_t] *= f[ind_t] > 0
if ind_c:
f[ind_c] *= f[ind_c] < 0
if beams:
S = _beam_shear(S, X, inds, indi, indf, EIx, EIy)
q = f / l
qt = tile(q, (1, 3))
R = (P - S - Ct.dot(uvw * qt)) * B
res = mean(normrow(R))
V += R / M
Un = sum(M * V**2)
if Un < Uo:
V *= 0
Uo = Un
X += V
if refresh:
if (ts % refresh == 0) or (res < tol):
print('Step:{0} Residual:{1:.3g}'.format(ts, res))
if callback:
callback(X, **kwargs)
ts += 1
return X, f, l
def drx_numba(network,
factor=1.0,
tol=0.1,
steps=10000,
summary=0,
update=False):
""" Run Numba accelerated dynamic relaxation analysis.
Parameters
----------
network (obj): Network to analyse.
factor (float): Convergence factor.
tol (float): Tolerance value.
steps (int): Maximum number of steps.
summary (int): Print summary at end.
update (bool): Update the co-ordinates of the Network.
Returns
-------
array: Vertex co-ordinates.
array: Edge forces.
array: Edge lengths.
"""
# Setup
tic1 = time()
X, B, P, Pn, S, V, E, A, C, Ct, f0, l0, ind_c, ind_t, u, v, M, ks = _create_arrays(
network)
try:
inds, indi, indf, EIx, EIy = _beam_data(network)
inds = array(inds)
indi = array(indi)
indf = array(indf)
EIx = EIx.ravel()
EIy = EIy.ravel()
beams = 1
except AttributeError:
z0, z1 = array([0]), array([0.])
inds, indi, indf, EIx, EIy = z0, z0, z0, z1, z1
beams = 0
# Arrays
f0_ = f0.ravel()
ks_ = ks.ravel()
l0_ = l0.ravel()
M_ = M.ravel()
if not ind_c:
ind_c = [-1]
if not ind_t:
ind_t = [-1]
ind_c = array(ind_c)
ind_t = array(ind_t)
rows, cols, vals = find(Ct)
toc1 = time() - tic1
# Solver
tic2 = time()
X = drx_solver(tol, steps, factor, u, v, X, ks_, l0_, f0_, ind_c, ind_t,
rows, cols, vals, P, S, B, M_, summary, inds, indi, indf,
EIx, EIy, beams)
_, l = uvw_lengths(C, X)
f = f0 + ks * (l - l0)
toc2 = time() - tic2
# Summary
if summary:
print('\n\nNumba DR -------------------')
print('Setup time: {0:.3g}s'.format(toc1))
print('Solver time: {0:.3g}s'.format(toc2))
print('----------------------------------')
# Update
if update:
i_k = network.index_key()
for i in sorted(list(network.vertices()), key=int):
x, y, z = X[i, :]
network.set_vertex_attributes(i_k[i], {'x': x, 'y': y, 'z': z})
uv_i = network.uv_index()
for edge in network.edges():
i = uv_i[edge]
network.set_edge_attribute(edge, 'f', float(f[i]))
return X, f, l