# Arbitrary data.
parallel = MR.parallel_default_instance
nx = 50
ny = 30
nz = 20
x = N.linspace(0, 1, nx)
y = N.logspace(1, 2, ny)
z = N.linspace(0, 1, nz)**2
if parallel.is_rank_zero():
for snap in direct_snapshots + adjoint_snapshots:
snap.put(CustomVector([x, y, z], N.random.random((nx, ny, nz))))
parallel.barrier()
# Compute and save Balanced POD modes.
my_BPOD = MR.BPODHandles(inner_product)
my_BPOD.sanity_check(direct_snapshots[0])
L_sing_vecs, sing_vals, R_sing_vecs = \
my_BPOD.compute_decomp(direct_snapshots, adjoint_snapshots)
# less than 10% error
sing_vals_norm = sing_vals / N.sum(sing_vals)
num_modes = N.nonzero(N.cumsum(sing_vals_norm) > 0.9)[0][0] + 1
mode_nums = range(num_modes)
direct_modes = [CustomVecHandle('direct_mode%d.pkl'%i) for i in mode_nums]
adjoint_modes = [CustomVecHandle('adjoint_mode%d.pkl'%i) for i in mode_nums]
my_BPOD.compute_direct_modes(mode_nums, direct_modes)
my_BPOD.compute_adjoint_modes(mode_nums, adjoint_modes)
]
# Create random snapshot data
nx = 50
ny = 30
nz = 20
x = np.linspace(0, 1, nx)
y = np.logspace(1, 2, ny)
z = np.linspace(0, 1, nz)**2
if parallel.is_rank_zero():
for snap in direct_snapshots + adjoint_snapshots:
snap.put(CustomVector([x, y, z], np.random.random((nx, ny, nz))))
parallel.barrier()
# Compute and save balanced POD modes
my_BPOD = mr.BPODHandles(inner_product)
my_BPOD.sanity_check(direct_snapshots[0])
sing_vals, L_sing_vecs, R_sing_vecs = my_BPOD.compute_decomp(
direct_snapshots, adjoint_snapshots)
# Choose modes so that BPOD projection has less than 10% error
sing_vals_norm = sing_vals / np.sum(sing_vals)
num_modes = np.nonzero(np.cumsum(sing_vals_norm) > 0.9)[0][0] + 1
mode_nums = list(mr.range(num_modes))
direct_modes = [
CustomVecHandle('%s/direct_mode%d.pkl' % (out_dir, i)) for i in mode_nums
]
adjoint_modes = [
CustomVecHandle('%s/adjoint_mode%d.pkl' % (out_dir, i)) for i in mode_nums
]
my_BPOD.compute_direct_modes(mode_nums, direct_modes)
import numpy as N
import modred as MR
# Define the handles for the snapshots
num_vecs = 30
direct_snapshots = [MR.VecHandleArrayText('direct_vec%d.txt' % i)
for i in range(num_vecs)]
adjoint_snapshots = [MR.VecHandleArrayText('adjoint_vec%d.txt' % i)
for i in range(num_vecs)]
# Save arbitrary data in text files
x = N.linspace(0, N.pi, 200)
for i, snap in enumerate(direct_snapshots):
snap.put(N.sin(x*i))
for i, snap in enumerate(adjoint_snapshots):
snap.put(N.cos(0.5*x*i))
# Calculate and save BPOD modes
my_BPOD = MR.BPODHandles(N.vdot, max_vecs_per_node=10)
L_sing_vecs, sing_vals, R_sing_vecs = \
my_BPOD.compute_decomp(direct_snapshots, adjoint_snapshots)
num_modes = 10
mode_nums = range(num_modes)
direct_modes = [MR.VecHandleArrayText('direct_mode%d' % i)
for i in mode_nums]
adjoint_modes = [MR.VecHandleArrayText('adjoint_mode%d' % i)
for i in mode_nums]
my_BPOD.compute_direct_modes(mode_nums, direct_modes)
my_BPOD.compute_adjoint_modes(mode_nums, adjoint_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
# Define the handles for the snapshots
num_vecs = 30
direct_snapshots = [
mr.VecHandleArrayText('direct_vec%d.txt' % i) for i in range(num_vecs)
]
adjoint_snapshots = [
mr.VecHandleArrayText('adjoint_vec%d.txt' % i) for i in range(num_vecs)
]
# Save arbitrary data in text files
x = np.linspace(0, np.pi, 200)
for i, snap in enumerate(direct_snapshots):
snap.put(np.sin(x * i))
for i, snap in enumerate(adjoint_snapshots):
snap.put(np.cos(0.5 * x * i))
# Calculate and save BPOD modes
my_BPOD = mr.BPODHandles(np.vdot, max_vecs_per_node=10)
sing_vals, L_sing_vecs, R_sing_vecs = my_BPOD.compute_decomp(
direct_snapshots, adjoint_snapshots)
num_modes = 10
mode_nums = list(range(num_modes))
direct_modes = [mr.VecHandleArrayText('direct_mode%d' % i) for i in mode_nums]
adjoint_modes = [
mr.VecHandleArrayText('adjoint_mode%d' % i) for i in mode_nums
]
my_BPOD.compute_direct_modes(mode_nums, direct_modes)
my_BPOD.compute_adjoint_modes(mode_nums, adjoint_modes)
mr.VecHandleArrayText('%s/direct_vec%d.txt' % (out_dir, i))
for i in mr.range(num_vecs)
]
adjoint_snapshots = [
mr.VecHandleArrayText('%s/adjoint_vec%d.txt' % (out_dir, i))
for i in mr.range(num_vecs)
]
# Save random snapshot data in text files
x = np.linspace(0, np.pi, 200)
for i, snap in enumerate(direct_snapshots):
snap.put(np.sin(x * i))
for i, snap in enumerate(adjoint_snapshots):
snap.put(np.cos(0.5 * x * i))
# Calculate and save BPOD modes
my_BPOD = mr.BPODHandles(inner_product=np.vdot, max_vecs_per_node=10)
sing_vals, L_sing_vecs, R_sing_vecs = my_BPOD.compute_decomp(
direct_snapshots, adjoint_snapshots)
num_modes = 10
mode_nums = list(mr.range(num_modes))
direct_modes = [
mr.VecHandleArrayText('%s/direct_mode%d' % (out_dir, i)) for i in mode_nums
]
adjoint_modes = [
mr.VecHandleArrayText('%s/adjoint_mode%d' % (out_dir, i))
for i in mode_nums
]
my_BPOD.compute_direct_modes(mode_nums, direct_modes)
my_BPOD.compute_adjoint_modes(mode_nums, adjoint_modes)