def solve_for_DMD(self):
'''
Solve for the ritz_values, mode_norms and build_coefficients.
'''
self.dmd = modred.DMDHandles(vec_containers.inner_product)
ritz_vals, mode_norms, build_coeffs = self.dmd.compute_decomp(
self.direct_snapshots)
fd_ritz = open((self.directory + 'ritz.cPickle'), 'w')
cPickle.dump(ritz_vals, fd_ritz)
fd_ritz.close()
fd_mode = open((self.directory + 'mode.cPickle'), 'w')
cPickle.dump(mode_norms, fd_mode)
fd_mode.close()
fd_coeffs = open((self.directory + 'coeffs.cPickle'), 'w')
cPickle.dump(build_coeffs, fd_coeffs)
fd_coeffs.close()
print 'ritz_vals', ritz_vals
print 'mode_norms', mode_norms
ny = 100
x_grid = 1. - np.cos(np.linspace(0, np.pi, nx))
y_grid = np.linspace(0, 1., ny)**2
Y, X = np.meshgrid(y_grid, x_grid)
# Create random snapshot data
num_vecs = 100
snapshots = [
mr.VecHandlePickle('%s/vec%d.pkl' % (out_dir, i))
for i in mr.range(num_vecs)
]
if parallel.is_rank_zero():
for i, snap in enumerate(snapshots):
snap.put(np.sin(X * i) + np.cos(Y * i))
parallel.barrier()
# Calculate DMD modes and save them to pickle files
weighted_IP = mr.InnerProductTrapz(x_grid, y_grid)
my_DMD = mr.DMDHandles(inner_product=weighted_IP)
my_DMD.compute_decomp(snapshots)
my_DMD.put_decomp('%s/eigvals.txt' % out_dir,
'%s/R_low_order_eigvecs.txt' % out_dir,
'%s/L_low_order_eigvecs.txt' % out_dir,
'%s/correlation_array_eigvals.txt' % out_dir,
'%s/correlation_array_eigvecs.txt' % out_dir)
mode_indices = [1, 4, 5, 0, 10]
modes = [
mr.VecHandlePickle('%s/mode%d.pkl' % (out_dir, i)) for i in mode_indices
]
my_DMD.compute_exact_modes(mode_indices, modes)
num_vecs = 100
nx = 80
ny = 100
x_grid = 1. - np.cos(np.linspace(0, np.pi, nx))
y_grid = np.linspace(0, 1., ny)**2
Y, X = np.meshgrid(y_grid, x_grid)
snapshots = [
mr.VecHandlePickle('%s/vec%d.pkl' % (out_dir, i)) for i in range(num_vecs)
]
if parallel.is_rank_zero():
for i, snap in enumerate(snapshots):
snap.put(np.sin(X * i) + np.cos(Y * i))
parallel.barrier()
weighted_IP = mr.InnerProductTrapz(x_grid, y_grid)
# Calculate DMD modes and save them to pickle files
my_DMD = mr.DMDHandles(weighted_IP)
my_DMD.compute_decomp(snapshots)
my_DMD.put_decomp('%s/eigvals.txt' % out_dir,
'%s/R_low_order_eigvecs.txt' % out_dir,
'%s/L_low_order_eigvecs.txt' % out_dir,
'%s/correlation_mat_eigvals.txt' % out_dir,
'%s/correlation_mat_eigvecs.txt' % out_dir)
mode_indices = [1, 4, 5, 0, 10]
modes = [
mr.VecHandlePickle('%s/mode%d.pkl' % (out_dir, i)) for i in mode_indices
]
my_DMD.compute_exact_modes(mode_indices, modes)
def modal_decomposition(obj, kind='pod', obj2=None, wanted_modes='all',
max_vecs_per_node=1000, verbose=True):
"""
Compute POD modes of the given fields using the snapshot method.
Parameters
----------
obj : TemporalFields, Profile or Points object
Fields to extract modes from
obj2 : same as obj
Only used as second dataset for BPOD
kind : string, optional
Kind of decomposition, can be 'pod' (default), 'bpod' or 'dmd'.
wanted_modes : string or number or array of numbers
If 'all', extract all modes,
If a number, extract first modes,
If an array, extract the associated modes.
max_vecs_per_node : integer, optional
Number of fields that can be charged in memory.
(More is faster but can lead to MemoryError)
verbose : boolean, optional
If 'True', display information.
Returns
-------
modal_field : ModalField object
.
Notes
-----
You can use partially masked fields as input.
If so, the asked values are lineary interpolated before doing the
decomposition.
"""
# check if modred is available
if not MODRED:
raise Exception("This feature need 'modred' to be installed")
# Test parameters
if not isinstance(obj, (TemporalFields)):
raise TypeError()
if kind == "bpod":
if obj2 is None:
raise ValueError()
if not isinstance(obj2, obj.__class__):
raise TypeError()
if not obj2.shape == obj.shape:
raise ValueError()
if not isinstance(kind, STRINGTYPES):
raise TypeError()
if kind not in ['pod', 'bpod', 'dmd']:
raise ValueError()
if isinstance(wanted_modes, STRINGTYPES):
if not wanted_modes == 'all':
raise ValueError()
wanted_modes = np.arange(len(obj.fields))
elif isinstance(wanted_modes, NUMBERTYPES):
wanted_modes = np.arange(wanted_modes)
elif isinstance(wanted_modes, ARRAYTYPES):
wanted_modes = np.array(wanted_modes)
if wanted_modes.min() < 0 or wanted_modes.max() > len(obj.fields):
raise ValueError()
else:
raise TypeError()
try:
max_vecs_per_node = int(max_vecs_per_node)
except:
raise TypeError()
# getting datas
if isinstance(obj, TemporalScalarFields):
obj_type = 'TSF'
snaps, props = _tsf_to_POD(obj)
if kind == "bpod":
snaps2, _ = _tsf_to_POD(obj2)
elif isinstance(obj, TemporalVectorFields):
obj_type = 'TVF'
snaps, props = _tvf_to_POD(obj)
if kind == "bpod":
snaps2, _ = _tvf_to_POD(obj2)
else:
raise TypeError()
globals().update(props)
# Setting the decomposition mode
eigvals = None
eigvect = None
ritz_vals = None
mode_norms = None
growth_rate = None
pulsation = None
if kind == 'pod':
my_decomp = modred.PODHandles(np.vdot,
max_vecs_per_node=max_vecs_per_node,
verbosity=verbose)
eigvals, eigvect = my_decomp.compute_decomp(snaps)
del snaps
wanted_modes = wanted_modes[wanted_modes < len(eigvals)]
eigvect = np.array(eigvect)
eigvect = eigvect[:, wanted_modes]
eigvals = Profile(wanted_modes, eigvals[wanted_modes], mask=False,
unit_x=props['unit_times'], unit_y='')
elif kind == 'bpod':
my_decomp = modred.BPODHandles(np.vdot,
max_vecs_per_node=max_vecs_per_node,
verbosity=verbose)
eigvect, eigvals, eigvect_l = my_decomp.compute_decomp(snaps, snaps2)
del snaps
del snaps2
wanted_modes = wanted_modes[wanted_modes < len(eigvals)]
eigvect = np.array(eigvect)
eigvect = eigvect[:, wanted_modes]
eigvals = Profile(wanted_modes, eigvals[wanted_modes], mask=False,
unit_x=props['unit_times'], unit_y='')
elif kind == 'dmd':
my_decomp = modred.DMDHandles(np.vdot,
max_vecs_per_node=max_vecs_per_node,
verbosity=verbose)
ritz_vals, mode_norms, build_coeffs = my_decomp.compute_decomp(snaps)
del snaps
wanted_modes = wanted_modes[wanted_modes < len(ritz_vals)]
# supplementary charac
delta_t = props['times'][1] - props['times'][0]
lambd_i = np.imag(ritz_vals)
lambd_r = np.real(ritz_vals)
lambd_mod = np.abs(ritz_vals)
lambd_arg = np.zeros((len(ritz_vals)))
mask = np.logical_and(lambd_i == 0, lambd_r <= 0)
filt = np.logical_not(mask)
lambd_arg[mask] = np.pi
lambd_arg[filt] = 2*np.arctan(lambd_i[filt]/(lambd_r[filt] +
lambd_mod[filt]))
sigma = np.log(lambd_mod)/delta_t
omega = lambd_arg/delta_t
# creating profiles
unit_times = props['unit_times']
ritz_vals = Profile(wanted_modes, ritz_vals[wanted_modes], mask=False,
unit_x=unit_times, unit_y='')
mode_norms = Profile(wanted_modes, mode_norms[wanted_modes],
mask=False, unit_x=unit_times, unit_y='')
growth_rate = Profile(wanted_modes, sigma[wanted_modes], mask=False,
unit_x=unit_times, unit_y=1./unit_times)
pulsation = Profile(wanted_modes, omega[wanted_modes], mask=False,
unit_x=unit_times,
unit_y=make_unit('rad')/unit_times)
else:
raise ValueError("Unknown kind of decomposition : {}".format(kind))
f_shape = props['f_shape']
unit_values = props['unit_values']
unit_times = props['unit_times']
times = props['times']
ind_fields = props['ind_fields']
# Decomposing and getting modes
if kind in ['pod', 'dmd']:
modes = [modred.VecHandleInMemory(np.zeros(f_shape))
for i in np.arange(len(wanted_modes))]
my_decomp.compute_modes(wanted_modes, modes)
elif kind in ['bpod']:
modes = [modred.VecHandleInMemory(np.zeros(f_shape))
for i in np.arange(len(wanted_modes))]
adj_modes = [modred.VecHandleInMemory(np.zeros(f_shape))
for i in np.arange(len(wanted_modes))]
my_decomp.compute_direct_modes(wanted_modes, modes)
my_decomp.compute_adjoint_modes(wanted_modes, adj_modes)
# Getting temporal evolution
temporal_prof = []
if kind in ['pod']:
for n in np.arange(len(modes)):
tmp_prof = eigvect[:, n]*eigvals.y[n]**.5
tmp_prof = Profile(times, tmp_prof, mask=False,
unit_x=unit_times,
unit_y=unit_values)
temporal_prof.append(tmp_prof)
if kind in ['bpod']:
for n in np.arange(len(modes)):
tmp_prof = eigvect[:, n]*eigvals.y[n]**.5
tmp_times = times[0:len(tmp_prof)]
tmp_prof = Profile(tmp_times, tmp_prof, mask=False,
unit_x=unit_times,
unit_y=unit_values)
temporal_prof.append(tmp_prof)
elif kind == 'dmd':
for n in np.arange(len(modes)):
tmp_prof = np.real([ritz_vals.y[n]**(k) for k in ind_fields])
tmp_prof = Profile(times, tmp_prof, mask=False, unit_x=unit_times,
unit_y=obj.unit_values)
temporal_prof.append(tmp_prof)
# Returning
if obj_type == "TSF":
modes_f = _POD_to_tsf(modes, props)
elif obj_type == "TVF":
modes_f = _POD_to_tvf(modes, props)
del modes
modal_field = ModalFields(kind, props['mean_field'], modes_f, wanted_modes,
temporal_prof,
eigvals=eigvals, eigvects=eigvect,
ritz_vals=ritz_vals, mode_norms=mode_norms,
growth_rate=growth_rate, pulsation=pulsation)
return modal_field
import modred as MR
import numpy as N
num_vecs = 100
# Non-uniform grid and corresponding inner product weights.
nx = 80
ny = 100
x_grid = 1. - N.cos(N.linspace(0, N.pi, nx))
y_grid = N.linspace(0, 1., ny)**2
Y, X = N.meshgrid(y_grid, x_grid)
snapshots = [MR.VecHandlePickle('vec%d.pkl' % i) for i in range(num_vecs)]
parallel = MR.parallel_default_instance
if parallel.is_rank_zero():
for i, snap in enumerate(snapshots):
snap.put(N.sin(X * i) + N.cos(Y * i))
parallel.barrier()
weighted_IP = MR.InnerProductTrapz(x_grid, y_grid)
# Calculate DMD modes and save them to pickle files.
my_DMD = MR.DMDHandles(weighted_IP)
my_DMD.compute_decomp(snapshots)
my_DMD.put_decomp('ritz_vals.txt', 'mode_norms.txt', 'build_coeffs.txt')
mode_indices = [1, 4, 5, 0, 10]
modes = [MR.VecHandlePickle('mode%d.pkl' % i) for i in mode_indices]
my_DMD.compute_modes(mode_indices, modes)
