def element_DsOF(el_nd_ids, doft):
nn = len(el_nd_ids)
nd = len(doft[0])
ix = zero_m((nn, nd), dtype=int)
for i in xrange(nn):
ix[i] = doft[el_nd_ids[i]]
return ix.flatten()
def table_of_nodal_coordinates(cord, vertices, doft, ndc=None):
if ndc is None:
ndc = zero_m((doft.shape[0], cord.shape[1]))
for i in xrange(doft.shape[0]):
if doft[i, 0] == -1:
ndc[i] = vertices[i]
for i in xrange(doft.shape[0]):
if doft[i, 0] != -1:
ndc[i] = cord[doft[i, 0]]
return ndc
def table_of_nodal_DsOF(v, fixed):
dof_per_node = 1
dof_table = zero_m((v, dof_per_node), dtype=int)
for s in fixed:
dof_table[support_node_index(s)] = -1
ndof = 0
j = 0
for i in xrange(v):
if dof_table[i, j] != -1:
dof_table[i, j] = ndof
ndof += 1
return (ndof, dof_table)
def _FDM_it(ndof,
tdof,
vertices,
edges,
q,
lin_solver=cg,
i_tol=1e-5,
callbacks=no_callbacks):
mD, mDf = mDmDf(ndof, tdof, vertices, edges, q)
x0 = zero_m(mDf.shape)
xyz = nodal_coordinates_it(mD, mDf, x0, vertices, tdof, lin_solver, i_tol,
callbacks)
return xyz
def multistepFDM_cg(vertices,
edges,
fixed,
q,
fcs=[],
lcs=[],
l0cs=[],
steps=250,
lin_solver=cg,
i_tol=1e-5,
callbacks=no_callbacks,
cond_num=False):
v = len(vertices)
q0 = copy(q)
ndof, tdof = table_of_nodal_DsOF(v, fixed)
mD, mDf = mDmDf(ndof, tdof, vertices, edges, q0)
if cond_num == True:
print('01', ' max =', mD.max(), ' nrm1 =', sm_norm(inv(mD), 1),
' nrmF =', sm_norm(inv(mD)), ' cn =', cond(mD.A, 1))
x0 = zero_m(mDf.shape)
cc = __solve_lin_syst_it(mD, -mDf, x0, lin_solver, i_tol, None, callbacks)
xyz = table_of_nodal_coordinates(cc, vertices, tdof)
l = list_of_element_lengths(edges, xyz)
f = list_of_element_forces(l, q0)
for i in xrange(2, steps + 1):
for fj in fcs:
q0[fj[0]] = fj[1] / l[fj[0]]
for lj in lcs:
q0[lj[0]] = f[lj[0]] / lj[1]
for l0j in l0cs:
i0 = l0j[0]
l0 = l0j[1][0]
ae0 = l0j[1][1]
ffj = f[i0]
ll = (ae0 + ffj) * l0 / ae0
q0[i0] = ffj / ll
mD, mDf = mDmDf(ndof, tdof, vertices, edges, q0)
if i % 10 == 1:
print(i, ' max =', mD.max(), ' nrm1 =', sm_norm(inv(mD), 1),
' nrmF =', sm_norm(inv(mD)), ' cn =', cond(mD.A, 1))
cc = __solve_lin_syst_it(mD, -mDf, x0, lin_solver, i_tol, None,
callbacks)
xyz = table_of_nodal_coordinates(cc, vertices, tdof)
l = list_of_element_lengths(edges, xyz)
f = list_of_element_forces(l, q0)
return (xyz, f, q0)
def mDmDf(ndof, doft, vertices, edges, q):
ii = []
jj = []
aij = []
mDf = zero_m((ndof, 3))
for j in xrange(len(edges)):
eni = edges[j]
i0, i1 = element_DsOF(eni, doft)
if i0 != -1:
ii.append(i0)
jj.append(i0)
aij.append(q[j])
if i1 != -1:
ii.append(i0)
jj.append(i1)
aij.append(-q[j])
else:
nc = vertices[eni[1]]
mDf[i0, 0] -= q[j] * nc[0]
mDf[i0, 1] -= q[j] * nc[1]
mDf[i0, 2] -= q[j] * nc[2]
if i1 != -1:
ii.append(i1)
jj.append(i1)
aij.append(q[j])
if i0 != -1:
ii.append(i1)
jj.append(i0)
aij.append(-q[j])
else:
nc = vertices[eni[0]]
mDf[i1, 0] -= q[j] * nc[0]
mDf[i1, 1] -= q[j] * nc[1]
mDf[i1, 2] -= q[j] * nc[2]
mD = csc_matrix((aij, (ii, jj)), shape=(ndof, ndof))
return mD, mDf
def multistepFDM_inexact(nodes,
elems,
supports,
qs,
fcs=[],
lcs=[],
l0cs=[],
tol_f=1e-3,
tol_l=1e-3,
abs_error=True,
lin_solver=cg,
i_tol_min=None,
i_tol_max=0.1,
damping=1e-2,
latest=True,
steps=250,
callbacks=no_callbacks):
if abs_error == False:
def force_diff(f, fs):
df = []
for ff in fs:
df.append(abs(f[ff[0]] - ff[1]) / ff[1])
return max(df)
def length_diff(l, ls):
dl = []
for ll in ls:
dl.append(abs(l[ll[0]] - ll[1]) / ll[1])
return max(dl)
def l0_diff(l, f, l0s):
dl = []
for ll in l0s:
i0 = ll[0]
l0 = ll[1][0]
ae0 = ll[1][1]
dl.append(abs(unstrained_length(l[i0], f[i0], ae0) - l0) / l0)
return max(dl)
else:
def force_diff(f, fs):
df = []
for ff in fs:
df.append(abs(f[ff[0]] - ff[1]))
return max(df)
def length_diff(l, ls):
dl = []
for ll in ls:
dl.append(abs(l[ll[0]] - ll[1]))
return max(dl)
def l0_diff(l, f, l0s):
dl = []
for ll in l0s:
i0 = ll[0]
l0 = ll[1][0]
ae0 = ll[1][1]
dl.append(abs(unstrained_length(l[i0], f[i0], ae0) - l0))
return max(dl)
qs0 = copy(qs)
ndof, tdof = table_of_nodal_DsOF(len(nodes), supports)
mD, mDf = mDmDf(ndof, tdof, nodes, elems, qs0)
x0 = zero_m(mDf.shape)
# nb1 = max (map (bind_2nd (v_norm, inf), mDf))
# nb1 = 1/nb1 if nb1 > 100 else 1e-2
# nb1 /= 2*sqrt (3.)
nb = 5e-3
i_tol0 = i_tol_min if i_tol_min != None else min(tol_f, tol_l) * nb
print('i_tol_min =', i_tol0)
cc = __solve_lin_syst_it(mD, -mDf, x0, lin_solver, i_tol0, None, callbacks)
nc = table_of_nodal_coordinates(cc, nodes, tdof)
l = list_of_element_lengths(elems, nc)
f = list_of_element_forces(l, qs0)
rfd = rld = rl0d = 1e-13
if fcs != []:
rfd1 = rfd
rfd = force_diff(f, fcs)
if lcs != []:
rld1 = rld
rld = length_diff(l, lcs)
if l0cs != []:
rl0d1 = rl0d
rl0d = l0_diff(l, f, l0cs)
print(1, i_tol0, rfd, rld, rl0d)
if rfd < tol_f and rld < tol_l and rl0d < tol_l:
print('steps:', 1)
if fcs != []:
print('maximal force error: ', rfd)
if lcs != []:
print('maximal length error: ', rld)
if l0cs != []:
print('maximal unstrained length error: ', rl0d)
return (nc, f, qs0)
i_tol1 = i_tol_max
gamma_f = i_tol0 * (1 - sqrt(tol_f)) / tol_f**2
gamma_l = i_tol0 * (1 - sqrt(tol_l)) / tol_l**2
for i in xrange(2, steps + 1):
if rfd >= tol_f:
for fj in fcs:
qs0[fj[0]] = fj[1] / l[fj[0]]
if rld >= tol_l:
for lj in lcs:
qs0[lj[0]] = f[lj[0]] / lj[1]
if rl0d >= tol_l:
for l0j in l0cs:
i0 = l0j[0]
l0 = l0j[1][0]
ae0 = l0j[1][1]
ffj = f[i0]
ll = (ae0 + ffj) * l0 / ae0
qs0[i0] = ffj / ll
mD, mDf = mDmDf(ndof, tdof, nodes, elems, qs0)
# nb1 = max (map (bind_2nd (v_norm, inf), -mDf))
# nb1 = 1/nb1 if nb1 > 100 else 1e-2
# nb1 /= 2*sqrt (3.)
# i_tol0 = i_tol if i_tol != None else min (tol_f, tol_l) * nb
x1 = cc if latest else x0
minrfd = minrld = minrl0d = 0.0
if fcs != []:
minrfd = min(damping * rfd**3 / rfd1**2, gamma_f * rfd**2)
if lcs != []:
minrld = min(damping * rld**3 / rld1**2, gamma_l * rld**2)
if l0cs != []:
minrl0d = min(damping * rl0d**3 / rl0d1**2, gamma_l * rl0d**2)
i_tol1 = min(i_tol_max, i_tol1, max(minrfd, minrld, minrl0d, i_tol0))
cc = __solve_lin_syst_it(mD, -mDf, x1, lin_solver, i_tol1, None,
callbacks)
# cc = __solve_lin_syst_it (mD, -mDf, x1, lin_solver, i_tol1, x1, callbacks)
nc = table_of_nodal_coordinates(cc, nodes, tdof)
# nc = table_of_nodal_coordinates (cc, nodes, tdof, nc)
l = list_of_element_lengths(elems, nc)
f = list_of_element_forces(l, qs0)
if fcs != []:
rfd1 = rfd
rfd = force_diff(f, fcs)
if lcs != []:
rld1 = rld
rld = length_diff(l, lcs)
if l0cs != []:
rl0d = l0_diff(l, f, l0cs)
if i % 10 == 1:
print(i, i_tol1, rfd, rld, rl0d)
if rfd < tol_f and rld < tol_l and rl0d < tol_l:
break
if i == steps:
print('WARNING: maximal number of steps (' + str(steps) +
') reached !')
else:
print('steps:', i)
if fcs != []:
print('maximal force error: ', rfd)
if lcs != []:
print('maximal length error: ', rld)
if l0cs != []:
print('maximal unstrained length error: ', rl0d)
return (nc, f, qs0)
def multistepFDM_wtol_cg(vertices,
edges,
fixed,
q,
fcs=[],
lcs=[],
l0cs=[],
tol_f=1e-3,
tol_l=1e-3,
abs_error=True,
lin_solver=cg,
i_tol=None,
latest=True,
steps=250,
callbacks=no_callbacks):
if abs_error == False:
def force_diff(f, fs):
df = []
for ff in fs:
df.append(abs(f[ff[0]] - ff[1]) / ff[1])
return max(df)
def length_diff(l, ls):
dl = []
for ll in ls:
dl.append(abs(l[ll[0]] - ll[1]) / ll[1])
return max(dl)
def l0_diff(l, f, l0s):
dl = []
for ll in l0s:
i0 = ll[0]
l0 = ll[1][0]
ae0 = ll[1][1]
dl.append(abs(unstrained_length(l[i0], f[i0], ae0) - l0) / l0)
return max(dl)
else:
def force_diff(f, fs):
df = []
for ff in fs:
df.append(abs(f[ff[0]] - ff[1]))
return max(df)
def length_diff(l, ls):
dl = []
for ll in ls:
dl.append(abs(l[ll[0]] - ll[1]))
return max(dl)
def l0_diff(l, f, l0s):
dl = []
for ll in l0s:
i0 = ll[0]
l0 = ll[1][0]
ae0 = ll[1][1]
dl.append(abs(unstrained_length(l[i0], f[i0], ae0) - l0))
return max(dl)
q0 = copy(q)
v = len(vertices)
ndof, tdof = table_of_nodal_DsOF(v, fixed)
mD, mDf = mDmDf(ndof, tdof, vertices, edges, q0)
x0 = zero_m(mDf.shape)
nb = 5e-3
i_tol = i_tol if i_tol != None else min(tol_f, tol_l) * nb
print('i_tol =', i_tol)
cc = __solve_lin_syst_it(mD, -mDf, x0, lin_solver, i_tol, None, callbacks)
xyz = table_of_nodal_coordinates(cc, vertices, tdof)
l = list_of_element_lengths(edges, xyz)
f = list_of_element_forces(l, q0)
rfd = rld = rl0d = 0
if fcs != []:
rfd = force_diff(f, fcs)
if lcs != []:
rld = length_diff(l, lcs)
if l0cs != []:
rl0d = l0_diff(l, f, l0cs)
print(1, rfd, rld)
if rfd < tol_f and rld < tol_l and rl0d < tol_l:
print('steps:', 1)
if fcs != []:
print('maximal force error: ', rfd)
if lcs != []:
print('maximal length error: ', rld)
if l0cs != []:
print('maximal unstrained length error: ', rl0d)
return (xyz, f, q0)
for i in xrange(2, steps + 1):
if rfd >= tol_f:
for fj in fcs:
q0[fj[0]] = fj[1] / l[fj[0]]
if rld >= tol_l:
for lj in lcs:
q0[lj[0]] = f[lj[0]] / lj[1]
if rl0d >= tol_l:
for l0j in l0cs:
i0 = l0j[0]
l0 = l0j[1][0]
ae0 = l0j[1][1]
ffj = f[i0]
ll = (ae0 + ffj) * l0 / ae0
q0[i0] = ffj / ll
mD, mDf = mDmDf(ndof, tdof, vertices, edges, q0)
x1 = cc if latest else x0
cc = __solve_lin_syst_it(mD, -mDf, x1, lin_solver, i_tol, None,
callbacks)
xyz = table_of_nodal_coordinates(cc, vertices, tdof)
l = list_of_element_lengths(edges, xyz)
f = list_of_element_forces(l, q0)
if fcs != []:
rfd = force_diff(f, fcs)
if lcs != []:
rld = length_diff(l, lcs)
if l0cs != []:
rl0d = l0_diff(l, f, l0cs)
if i % 10 == 1:
print(i, rfd, rld)
if rfd < tol_f and rld < tol_l and rl0d < tol_l:
break
if i == steps:
print('WARNING: maximal number of steps (' + str(steps) +
') reached !')
else:
print('steps:', i)
if fcs != []:
print('maximal force error: ', rfd)
if lcs != []:
print('maximal length error: ', rld)
if l0cs != []:
print('maximal unstrained length error: ', rl0d)
return (xyz, f, q0)