def get_traces(locs, data, V=None, scales=None):
"""Reconstruct time traces from data, unprojecting and unscaling if needed.
Parameters
----------
locs : (l,nt) ndarray
Index locations for the time traces to extract.
data : (r,nt) or (config.DOF*config.NUM_ROMVARS,nt) ndarray
Data from which to extract the time traces, either the output of a ROM
or a high-dimensional data set.
V : (config.DOF*config.NUM_ROMVARS,r) ndarray or None
Rank-r POD basis. Only needed if `data` is low-dimensional ROM output.
scales : (config.NUM_ROMVARS,4) ndarray or None
Information for how the data was scaled (see data_processing.scale()).
Only needed if `data` is low-dimensional ROM output.
Returns
-------
traces : (l,nt) ndarray
The specified time traces.
"""
if V is not None and scales is not None:
return dproc.unscale(V[locs] @ data, scales)
else:
return data[locs]
def get_feature(key, data, V=None, scales=None):
"""Reconstruct a spatial statistical feature from data, unprojecting and
unscaling if needed.
Parameters
----------
key : str
Which statistical feature to calculate (T_mean, CH4_sum, etc.)
data : (r,nt) or (config.DOF*config.NUM_ROMVARS,nt) ndarray
Data from which to extract the features, either the output of a ROM
or a high-dimensional data set.
V : (config.DOF*config.NUM_ROMVARS,r) ndarray or None
Rank-r POD basis. Only needed if data is low-dimensional ROM output.
scales : (config.NUM_ROMVARS,2) ndarray or None
Information for how the data was scaled (see data_processing.scale()).
Only needed if `data` is low-dimensional ROM output.
Returns
-------
feature : (nt,) ndarray
The specified statistical feature.
"""
var, action = key.split('_')
print(f"{action}({var})", end='..', flush=True)
if V is not None and scales is not None:
variable = dproc.unscale(dproc.getvar(var, V) @ data, scales, var)
else:
variable = dproc.getvar(var, data)
return eval(f"variable.{action}(axis=0)")
def get_traces(locs, data, V=None, qbar=None, scales=None):
"""Reconstruct time traces from data, unprojecting and unscaling if needed.
Parameters
----------
locs : (l,nt) ndarray
Index locations for the time traces to extract.
data : (r,nt) or (config.DOF*config.NUM_ROMVARS,nt) ndarray
Data from which to extract the time traces, either the output of a ROM
or a high-dimensional data set.
V : (config.DOF*config.NUM_ROMVARS,r) ndarray or None
Rank-r POD basis. Only needed if `data` is low-dimensional ROM output.
qbar : (NUM_ROMVARS*DOF,) ndarray
Mean snapshot that the training data was shifted by after scaling
but before projection. Only needed if `data` is low-dimensional ROM
output.
scales : (config.NUM_ROMVARS,4) ndarray or None
Information for how the data was scaled (see data_processing.scale()).
Only needed if `data` is low-dimensional ROM output.
Returns
-------
traces : (l,nt) ndarray
The specified time traces.
"""
if V is not None and qbar is not None and scales is not None:
qbar = qbar.reshape((-1, 1))
return dproc.unscale((V[locs] @ data) + qbar[locs, :], scales)
else:
return data[locs]
def test_scalers(lifted_data):
"""Test data_processing.scale() and data_processing.unscale(),
including checking that they are inverses.
"""
# Shift the test data (learning the scaling simultaneously).
with utils.timed_block("Scaling lifted test data"):
shifted_data, scales = dproc.scale(lifted_data.copy())
assert np.allclose(scales[:, -2:], config.SCALE_TO)
# Verify the scales and that the shift worked for each variable.
with utils.timed_block("Verifying shift results with scales"):
for i, v in enumerate(config.ROM_VARIABLES):
s = slice(i * config.DOF, (i + 1) * config.DOF)
if v in ["vx", "vy"]:
assert -scales[i, 0] == scales[i, 1]
assert scales[i, 1] == np.abs(lifted_data[s]).max()
assert np.isclose(np.abs(shifted_data[s]).max(), 1)
else:
assert lifted_data[s].min() == scales[i, 0]
assert lifted_data[s].max() == scales[i, 1]
assert np.isclose(shifted_data[s].min(), scales[i, 2])
assert np.isclose(shifted_data[s].max(), scales[i, 3])
# Redo the shift with the given scales and compare the results.
with utils.timed_block("Verifying repeat shift with given scales"):
shifted_data2, _ = dproc.scale(lifted_data.copy(), scales)
assert np.allclose(shifted_data2, shifted_data)
# Undo the shift and compare the results.
with utils.timed_block("Verifying inverse scaling"):
unshifted_data = dproc.unscale(shifted_data, scales)
assert np.allclose(unshifted_data, lifted_data)
# Check the inverse property for a subset of the variables.
with utils.timed_block("Repeating experiment with nontrivial varindices"):
variables = np.random.choice(config.ROM_VARIABLES,
size=4,
replace=False)
subset = np.vstack([dproc.getvar(v, lifted_data) for v in variables])
shifted_subset, _ = dproc.scale(subset.copy(), scales, variables)
unshifted_subset = dproc.unscale(shifted_subset, scales, variables)
assert np.allclose(unshifted_subset, subset)
def errors_in_time(trainsize, r, regs, cutoff=60000):
"""Plot spatially averaged errors, and the projection error, in time.
Parameters
----------
trainsize : int
Number of snapshots used to train the ROM.
r : int
Dimension of the ROM.
regs : two positive floats
Regularization hyperparameters used to train the ROM.
cutoff : int
Numer of time steps to plot.
"""
# Load and simulate the ROM.
t, V, scales, q_rom = simulate_rom(trainsize, r, regs, cutoff)
# Load and lift the true results.
data, _ = utils.load_gems_data(cols=cutoff)
with utils.timed_block("Lifting GEMS data"):
data_gems = dproc.lift(data[:, :cutoff])
del data
# Shift and project the data (unscaling done later by chunk).
with utils.timed_block("Projecting GEMS data to POD subspace"):
data_shifted, _ = dproc.scale(data_gems.copy(), scales)
data_proj = V.T @ data_shifted
del data_shifted
# Initialize the figure.
fig, axes = plt.subplots(3, 3, figsize=(12, 6), sharex=True)
# Compute and plot errors in each variable.
for var, ax in zip(config.ROM_VARIABLES, axes.flat):
with utils.timed_block(f"Reconstructing results for {var}"):
Vvar = dproc.getvar(var, V)
gems_var = dproc.getvar(var, data_gems)
proj_var = dproc.unscale(Vvar @ data_proj, scales, var)
pred_var = dproc.unscale(Vvar @ q_rom, scales, var)
with utils.timed_block(f"Calculating error in {var}"):
denom = np.abs(gems_var).max(axis=0)
proj_error = np.mean(np.abs(proj_var - gems_var), axis=0) / denom
pred_error = np.mean(np.abs(pred_var - gems_var), axis=0) / denom
# Plot results.
ax.plot(t,
proj_error,
'-',
lw=1,
label="Projection Error",
c=config.GEMS_STYLE['color'])
ax.plot(t,
pred_error,
'-',
lw=1,
label="ROM Error",
c=config.ROM_STYLE['color'])
ax.axvline(t[trainsize], color='k')
ax.set_ylabel(config.VARTITLES[var])
# Format the figure.
for ax in axes[-1, :]:
ax.set_xlim(t[0], t[-1])
ax.set_xticks(np.arange(t[0], t[-1] + .001, .002))
ax.set_xlabel("Time [s]", fontsize=12)
# Make legend centered below the subplots.
fig.tight_layout(rect=[0, .1, 1, 1])
leg = axes[0, 0].legend(ncol=2,
fontsize=14,
loc="lower center",
bbox_to_anchor=(.5, 0),
bbox_transform=fig.transFigure)
for line in leg.get_lines():
line.set_linestyle('-')
line.set_linewidth(5)
# Save the figure.
utils.save_figure(f"errors"
f"_{config.TRNFMT(trainsize)}"
f"_{config.DIMFMT(r)}"
f"_{config.REGFMT(regs)}.pdf")
def point_traces(trainsize, r, regs, elems, cutoff=60000):
"""Plot the time trace of each variable in the original data at the monitor
location, and the time trace of each variable of the ROM reconstruction at
the same locations. One figure is generated per variable.
Parameters
----------
trainsize : int
Number of snapshots used to train the ROM.
r : int
Dimension of the ROM.
regs : two positive floats
Regularization hyperparameters used to train the ROM.
elems : list(int) or ndarray(int)
Indices in the spatial domain at which to compute the time traces.
cutoff : int
Numer of time steps to plot.
"""
if elems is None:
elems = config.MONITOR_LOCATIONS
# Get the indicies for each variable.
elems = np.atleast_1d(elems)
nelems = elems.size
nrows = (nelems // 2) + (1 if nelems % 2 != 0 else 0)
elems = np.concatenate(
[elems + i * config.DOF for i in range(config.NUM_ROMVARS)])
# Load and lift the true results.
data, _ = utils.load_gems_data(rows=elems[:nelems * config.NUM_GEMSVARS])
with utils.timed_block("Lifting GEMS time trace data"):
traces_gems = dproc.lift(data[:, :cutoff])
# Load and simulate the ROM.
t, V, scales, q_rom = simulate_rom(trainsize, r, regs, cutoff)
# Reconstruct and rescale the simulation results.
simend = q_rom.shape[1]
with utils.timed_block("Reconstructing simulation results"):
traces_rom = dproc.unscale(V[elems] @ q_rom, scales)
# Save a figure for each variable.
xticks = np.arange(t[0], t[-1] + .001, .002)
for i, var in enumerate(config.ROM_VARIABLES):
fig, axes = plt.subplots(nrows,
2 if nelems > 1 else 1,
figsize=(9, 3 * nrows),
sharex=True)
axes = np.atleast_2d(axes)
for j, ax in enumerate(axes.flat):
idx = j + i * nelems
ax.plot(t, traces_gems[idx, :], lw=1, **config.GEMS_STYLE)
ax.plot(t[:simend], traces_rom[idx, :], lw=1, **config.ROM_STYLE)
ax.axvline(t[trainsize], color='k', lw=1)
ax.set_xlim(t[0], t[-1])
ax.set_xticks(xticks)
ax.set_title(f"Location ${j+1}$", fontsize=12)
ax.locator_params(axis='y', nbins=2)
for ax in axes[-1, :]:
ax.set_xlabel("Time [s]", fontsize=12)
for ax in axes[:, 0]:
ax.set_ylabel(config.VARLABELS[var], fontsize=12)
# Single legend to the right of the subplots.
fig.tight_layout(rect=[0, 0, .85, 1])
leg = axes[0, 0].legend(loc="center right",
fontsize=14,
bbox_to_anchor=(1, .5),
bbox_transform=fig.transFigure)
for line in leg.get_lines():
line.set_linewidth(2)
# Save the figure.
utils.save_figure("pointtrace"
f"_{config.TRNFMT(trainsize)}"
f"_{config.DIMFMT(r)}"
f"_{config.REGFMT(regs)}_{var}.pdf")
def main(timeindices,
variables=None,
snaptype=["gems", "rom", "error"],
trainsize=None,
r=None,
reg=None):
"""Convert a snapshot in .h5 format to a .dat file that matches the format
of grid.dat. The new file is saved in `config.tecplot_path()` with the same
filename and the new file extension .dat.
Parameters
----------
timeindices : ndarray(int) or int
Indices (one-based) in the full time domain of the snapshots to save.
variables : str or list(str)
The variables to scale, a subset of config.ROM_VARIABLES.
Defaults to all variables.
snaptype : {"rom", "gems", "error"} or list(str)
Which kinds of snapshots to save. Options:
* "gems": snapshots from the full-order GEMS data;
* "rom": reconstructed snapshots produced by a ROM;
* "error": absolute error between the full-order data
and the reduced-order reconstruction.
If "rom" or "error" are selected, the ROM is selected by the
remaining arguments.
trainsize : int
Number of snapshots used to train the ROM.
r : int
Number of retained modes in the ROM.
reg : float
Regularization factor used to train the ROM.
"""
utils.reset_logger(trainsize)
# Parse parameters.
timeindices = np.sort(np.atleast_1d(timeindices))
simtime = timeindices.max()
t = utils.load_time_domain(simtime + 1)
# Parse the variables.
if variables is None:
variables = config.ROM_VARIABLES
elif isinstance(variables, str):
variables = [variables]
varnames = '\n'.join(f'"{v}"' for v in variables)
if isinstance(snaptype, str):
snaptype = [snaptype]
for stype in snaptype:
if stype not in ("gems", "rom", "error"):
raise ValueError(f"invalid snaptype '{stype}'")
# Read the grid file.
with utils.timed_block("Reading Tecplot grid data"):
# Parse the header.
grid_path = config.grid_data_path()
with open(grid_path, 'r') as infile:
grid = infile.read()
if int(re.findall(r"Elements=(\d+)", grid)[0]) != config.DOF:
raise RuntimeError(f"{grid_path} DOF and config.DOF do not match")
num_nodes = int(re.findall(r"Nodes=(\d+)", grid)[0])
end_of_header = re.findall(r"DT=.*?\n", grid)[0]
headersize = grid.find(end_of_header) + len(end_of_header)
# Extract geometry information.
grid_data = grid[headersize:].split()
x = grid_data[:num_nodes]
y = grid_data[num_nodes:2 * num_nodes]
cell_volume = grid_data[2 * num_nodes:3 * num_nodes]
connectivity = grid_data[3 * num_nodes:]
# Extract full-order data if needed.
if ("gems" in snaptype) or ("error" in snaptype):
gems_data, _ = utils.load_gems_data(cols=timeindices)
with utils.timed_block("Lifting selected snapshots of GEMS data"):
lifted_data = dproc.lift(gems_data)
true_snaps = np.concatenate(
[dproc.getvar(v, lifted_data) for v in variables])
# Simulate ROM if needed.
if ("rom" in snaptype) or ("error" in snaptype):
# Load the SVD data.
V, _ = utils.load_basis(trainsize, r)
# Load the initial conditions and scales.
X_, _, _, scales = utils.load_projected_data(trainsize, r)
# Load the appropriate ROM.
rom = utils.load_rom(trainsize, r, reg)
# Simulate the ROM over the time domain.
with utils.timed_block(f"Simulating ROM with r={r:d}, reg={reg:.0e}"):
x_rom = rom.predict(X_[:, 0], t, config.U, method="RK45")
if np.any(np.isnan(x_rom)) or x_rom.shape[1] < simtime:
raise ValueError("ROM unstable!")
# Reconstruct the results (only selected variables / snapshots).
with utils.timed_block("Reconstructing simulation results"):
x_rec = dproc.unscale(V[:, :r] @ x_rom[:, timeindices], scales)
x_rec = np.concatenate([dproc.getvar(v, x_rec) for v in variables])
dsets = {}
if "rom" in snaptype:
dsets["rom"] = x_rec
if "gems" in snaptype:
dsets["gems"] = true_snaps
if "error" in snaptype:
with utils.timed_block("Computing absolute error of reconstruction"):
abs_err = np.abs(true_snaps - x_rec)
dsets["error"] = abs_err
# Save each of the selected snapshots in Tecplot format matching grid.dat.
for j, tindex in enumerate(timeindices):
header = HEADER.format(varnames, tindex, t[tindex], num_nodes,
config.DOF,
len(variables) + 2, "SINGLE " * len(variables))
for label, dset in dsets.items():
if label == "gems":
save_path = config.gems_snapshot_path(tindex)
if label in ("rom", "error"):
folder = config.rom_snapshot_path(trainsize, r, reg)
save_path = os.path.join(folder, f"{label}_{tindex:05d}.dat")
with utils.timed_block(f"Writing {label} snapshot {tindex:05d}"):
with open(save_path, 'w') as outfile:
# Write the header.
outfile.write(header)
# Write the geometry data (x,y coordinates).
for i in range(0, len(x), NCOLS):
outfile.write(' '.join(x[i:i + NCOLS]) + '\n')
for i in range(0, len(y), NCOLS):
outfile.write(' '.join(y[i:i + NCOLS]) + '\n')
# Write the data for each variable.
for i in range(0, dset.shape[0], NCOLS):
row = ' '.join(f"{v:.9E}"
for v in dset[i:i + NCOLS, j])
outfile.write(row + '\n')
# Write connectivity information.
for i in range(0, len(connectivity), NCOLS):
outfile.write(' '.join(connectivity[i:i + NCOLS]) +
'\n')
def temperature_average(trainsize, r, reg, cutoff=60000):
"""Get the average-in-time temperature profile for the GEMS data and a
specific ROM.
Parameters
----------
trainsize : int
Number of snapshots used to train the ROM.
r : int
Dimension of the ROM.
reg : float
Regularization hyperparameters used to train the ROM.
cutoff : int
Number of time steps to average over.
"""
utils.reset_logger(trainsize)
# Read the grid file.
with utils.timed_block("Reading Tecplot grid data"):
# Parse the header.
grid_path = config.grid_data_path()
with open(grid_path, 'r') as infile:
grid = infile.read()
if int(re.findall(r"Elements=(\d+)", grid)[0]) != config.DOF:
raise RuntimeError(f"{grid_path} DOF and config.DOF do not match")
num_nodes = int(re.findall(r"Nodes=(\d+)", grid)[0])
end_of_header = re.findall(r"DT=.*?\n", grid)[0]
headersize = grid.find(end_of_header) + len(end_of_header)
# Extract geometry information.
grid_data = grid[headersize:].split()
x = grid_data[:num_nodes]
y = grid_data[num_nodes:2 * num_nodes]
# cell_volume = grid_data[2*num_nodes:3*num_nodes]
connectivity = grid_data[3 * num_nodes:]
# Compute full-order time-averaged temperature from GEMS data.
_s = config.DOF * config.GEMS_VARIABLES.index("T")
gems_data, _ = utils.load_gems_data(rows=slice(_s, _s + config.DOF),
cols=cutoff)
with utils.timed_block("Computing time-averaged GEMS temperature"):
T_gems = gems_data.mean(axis=1)
assert T_gems.shape == (config.DOF, )
# Simulate ROM and compute the time-averaged temperature.
t, V, scales, q_rom = step4.simulate_rom(trainsize, r, reg, steps=cutoff)
with utils.timed_block("Reconstructing ROM simulation results"):
T_rom = dproc.unscale(dproc.getvar("T", V) @ q_rom, scales, "T")
T_rom = T_rom.mean(axis=1)
assert T_rom.shape == (config.DOF, )
header = HEADER.format('"T"', 0, 0, num_nodes, config.DOF, 3,
"DOUBLE " * 3)
header = header.replace("VARLOCATION=([3-3]", "VARLOCATION=([3]")
for label, dset in zip(["gems", "rom"], [T_gems, T_rom]):
if label == "gems":
save_path = os.path.join(config.tecplot_path(), "gems",
"temperature_average.dat")
elif label == "rom":
folder = config.rom_snapshot_path(trainsize, r, reg)
save_path = os.path.join(folder, "temperature_average.dat")
with utils.timed_block(f"Writing {label} temperature average"):
with open(save_path, 'w') as outfile:
# Write the header.
outfile.write(header)
# Write the geometry data (x,y coordinates).
for i in range(0, len(x), NCOLS):
outfile.write(' '.join(x[i:i + NCOLS]) + '\n')
for i in range(0, len(y), NCOLS):
outfile.write(' '.join(y[i:i + NCOLS]) + '\n')
# Write the data for each variable.
for i in range(0, dset.shape[0], NCOLS):
row = ' '.join(f"{v:.9E}" for v in dset[i:i + NCOLS])
outfile.write(row + '\n')
# Write connectivity information.
for i in range(0, len(connectivity), NCOLS):
outfile.write(' '.join(connectivity[i:i + NCOLS]) + '\n')