def check_kdmd_computation_simple(exact, total):
""" Check DMD computations on a problem where the
true solution is known. All variants of DMD
should identify the original eigenvalues
"""
num_snapshots = 50
A = np.array([[0.9, 0.1], [0.0, 0.8]])
X = np.random.randn(2, num_snapshots)
Y = A.dot(X)
ADMD = Y.dot(np.linalg.pinv(X))
vals, vecs = np.linalg.eig(ADMD)
inds = np.argsort(np.abs(vals))[::-1]
vals = vals[inds]
vecs = vecs[:, inds]
# DMD class with rank 2
poly = dmdtools.PolyKernel(5)
KDMD = dmdtools.KDMD(poly, None, exact, total)
KDMD.fit(X, Y)
for ii in range(len(vals)):
dmd_vals, dmd_modes = dmdtools.sort_modes_evals(KDMD, sortby="closest",
target=vals[ii])
assert np.abs(dmd_vals[0] - vals[ii]) < 1e-10
check_eigenvectors(vecs[:, ii], dmd_modes[:, 0])
def check_dmd_computation_simple_timeseries(exact, total):
""" Check DMD computations on a problem where the
true solution is known. All variants of DMD
should give identical outputs.
"""
num_snapshots = 10
A = np.array([[0.9, 0.1], [0.0, 0.8]])
# Create a time series of data
data = np.zeros((2, num_snapshots + 1))
data[:, 0] = np.random.randn(2)
for ii in range(num_snapshots):
data[:, ii + 1] = A.dot(data[:, ii])
X = data[:, :-1]
Y = data[:, 1:]
ADMD = Y.dot(np.linalg.pinv(X))
vals, vecs = np.linalg.eig(ADMD)
inds = np.argsort(np.abs(vals))[::-1]
vals = vals[inds]
vecs = vecs[:, inds]
# DMD class with rank 2
DMD = dmdtools.DMD(2, exact, total)
DMD.fit(data)
dmd_vals, dmd_modes = dmdtools.sort_modes_evals(DMD)
for ii in range(len(vals)):
assert np.abs(dmd_vals[ii] - vals[ii]) < 1e-10
check_eigenvectors(vecs[:, ii], dmd_modes[:, ii])
def check_dmd_computation_simple_timeseries(exact, total):
""" Check DMD computations on a problem where the
true solution is known. All variants of DMD
should give identical outputs.
"""
num_snapshots = 10
A = np.array([[0.9, 0.1], [0.0, 0.8]])
# Create a time series of data
data = np.zeros((2, num_snapshots+1))
data[:, 0] = np.random.randn(2)
for ii in range(num_snapshots):
data[:, ii + 1] = A.dot(data[:, ii])
X = data[:, :-1]
Y = data[:, 1:]
ADMD = Y.dot(np.linalg.pinv(X))
vals, vecs = np.linalg.eig(ADMD)
inds = np.argsort(np.abs(vals))[::-1]
vals = vals[inds]
vecs = vecs[:, inds]
# DMD class with rank 2
DMD = dmdtools.DMD(2, exact, total)
DMD.fit(data)
dmd_vals, dmd_modes = dmdtools.sort_modes_evals(DMD)
for ii in range(len(vals)):
assert np.abs(dmd_vals[ii] - vals[ii]) < 1e-10
check_eigenvectors(vecs[:, ii], dmd_modes[:, ii])
