import os
import numpy as np
import modred as mr
# Create directory for output files
out_dir = 'rom_ex1_out'
if not os.path.isdir(out_dir):
os.makedirs(out_dir)
# Create random system and modes
nx = 100
num_inputs = 2
num_outputs = 3
num_basis_vecs = 10
A = np.mat(np.random.random((nx, nx)))
B = np.mat(np.random.random((nx, num_inputs)))
C = np.mat(np.random.random((num_outputs, nx)))
basis_vecs = np.mat(np.random.random((nx, num_basis_vecs)))
LTI_proj = mr.LTIGalerkinProjectionMatrices(basis_vecs)
A_reduced, B_reduced, C_reduced = LTI_proj.compute_model(
A * basis_vecs, B, C * basis_vecs)
LTI_proj.put_model(
'%s/A_reduced.txt' % out_dir, '%s/B_reduced.txt' % out_dir,
'%s/C_reduced.txt' % out_dir)
# Plot the first 3 modes
if plots:
for i in range(3):
PLT.figure()
PLT.hold(True)
PLT.plot(x, direct_modes[:, i].real, '-o')
PLT.plot(x, adjoint_modes[:, i].real, '-x')
PLT.xlabel('Space')
PLT.ylabel('Real(q)')
PLT.legend(['direct', 'adjoint'])
PLT.title('Direct and adjoint mode %d' % (i + 1))
# Project the linear dynamics onto the modes
projection = MR.LTIGalerkinProjectionMatrices(direct_modes,
adjoint_basis_vecs=adjoint_modes,
inner_product_weights=weights,
is_basis_orthonormal=True)
A_direct_modes = A * direct_modes
Ar, Br, Cr = projection.compute_model(A_direct_modes, B, C.dot(direct_modes))
# Verify that the model accurately reproduces the impulse response
qr = N.mat(N.zeros((r, nt), dtype=complex))
qr[:, 0] = Br
LHSr = N.identity(r) - dt / 2. * Ar
RHSr = N.identity(r) + dt / 2. * Ar
for ti in range(nt - 1):
qr[:, ti + 1] = N.linalg.solve(LHSr, RHSr * qr[:, ti])
y = C * q
yr = Cr * qr
print 'Max error in reduced system impulse response output y is', N.amax(