def test_impulse(self):
"""Test impulse response of discrete system"""
rtol = 1e-10
atol = 1e-12
for num_states in [1, 10]:
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 3, 5]:
# Generate state-space system arrays
A, B, C = util.drss(num_states, num_inputs, num_outputs)
# Check that can give time_steps as argument
outputs = util.impulse(A, B, C)
num_time_steps = len(outputs)
outputs_true = np.zeros(
(num_time_steps, num_outputs, num_inputs))
for ti in range(num_time_steps):
outputs_true[ti] = C.dot(
np.linalg.matrix_power(A, ti).dot(B))
np.testing.assert_allclose(
outputs, outputs_true, rtol=rtol, atol=atol)
# Check can give num_time_steps as an argument
outputs = util.impulse(
A, B, C, num_time_steps=num_time_steps)
np.testing.assert_allclose(
outputs, outputs_true, rtol=rtol, atol=atol)
def test_impulse(self):
"""Test impulse response of discrete system"""
for num_states in [1, 10]:
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 3, 5]:
A, B, C = util.drss(num_states, num_inputs, num_outputs)
# Check that can give time_step
outputs = util.impulse(A, B, C)
num_time_steps = len(outputs)
outputs_true = np.zeros(
(num_time_steps, num_outputs, num_inputs))
for ti in range(num_time_steps):
outputs_true[ti] = C * (A**ti) * B
np.testing.assert_allclose(outputs,
outputs_true,
rtol=1e-7,
atol=1e-7)
# Check can give num_time_steps as an argument
outputs = util.impulse(A,
B,
C,
num_time_steps=num_time_steps)
np.testing.assert_allclose(outputs,
outputs_true,
rtol=1e-7,
atol=1e-7)
def test_impulse(self):
"""Test impulse response of discrete system"""
rtol = 1e-10
atol = 1e-12
for num_states in [1, 10]:
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 3, 5]:
# Generate state-space system arrays
A, B, C = util.drss(num_states, num_inputs, num_outputs)
# Check that can give time_steps as argument
outputs = util.impulse(A, B, C)
num_time_steps = len(outputs)
outputs_true = np.zeros(
(num_time_steps, num_outputs, num_inputs))
for ti in range(num_time_steps):
outputs_true[ti] = C.dot(
np.linalg.matrix_power(A, ti).dot(B))
np.testing.assert_allclose(outputs,
outputs_true,
rtol=rtol,
atol=atol)
# Check can give num_time_steps as an argument
outputs = util.impulse(A,
B,
C,
num_time_steps=num_time_steps)
np.testing.assert_allclose(outputs,
outputs_true,
rtol=rtol,
atol=atol)
def test_balanced_truncation(self):
"""Test balanced system is close to original."""
for num_inputs in [1, 3]:
for num_outputs in [1, 4]:
for num_states in [1, 10]:
A, B, C = util.drss(num_states, num_inputs, num_outputs)
Ar, Br, Cr = util.balanced_truncation(A, B, C)
num_time_steps = 10
y = util.impulse(A, B, C, num_time_steps=num_time_steps)
yr = util.impulse(Ar, Br, Cr, num_time_steps=num_time_steps)
np.testing.assert_allclose(yr, y, rtol=1e-5)
def test_balanced_truncation(self):
"""Test balanced system is close to original."""
for num_inputs in [1, 3]:
for num_outputs in [1, 4]:
for num_states in [1, 10]:
A, B, C = util.drss(num_states, num_inputs, num_outputs)
Ar, Br, Cr = util.balanced_truncation(A, B, C)
num_time_steps = 10
y = util.impulse(A, B, C, num_time_steps=num_time_steps)
yr = util.impulse(Ar,
Br,
Cr,
num_time_steps=num_time_steps)
np.testing.assert_allclose(yr, y, rtol=1e-3, atol=1e-3)
def test_impulse(self):
"""Test impulse response of discrete system"""
for num_states in [1, 10]:
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 3, 5]:
A, B, C = util.drss(num_states, num_inputs, num_outputs)
# Check that can give time_step
outputs = util.impulse(A, B, C)
num_time_steps = len(outputs)
outputs_true = np.zeros((num_time_steps, num_outputs, num_inputs))
for ti in range(num_time_steps):
outputs_true[ti] = C * (A**ti) * B
np.testing.assert_allclose(outputs, outputs_true)
# Check can give num_time_steps as an argument
outputs = util.impulse(A, B, C, num_time_steps=num_time_steps)
np.testing.assert_allclose(outputs, outputs_true)
def test_assemble_Hankel(self):
""" Tests Hankel arrays are symmetric given
``[CB CAB CA**P CA**(P+1)B ...]``."""
rtol = 1e-10
atol = 1e-12
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 4]:
for sample_interval in [1]:
num_time_steps = 50
num_states = 5
A, B, C = util.drss(num_states, num_inputs, num_outputs)
time_steps = make_time_steps(num_time_steps,
sample_interval)
Markovs = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = Markovs[time_steps]
if sample_interval == 2:
time_steps, Markovs = era.make_sampled_format(
time_steps, Markovs)
my_ERA = era.ERA(verbosity=0)
my_ERA._set_Markovs(Markovs)
my_ERA._assemble_Hankel()
H = my_ERA.Hankel_array
Hp = my_ERA.Hankel_array2
for row in range(my_ERA.mc):
for col in range(my_ERA.mo):
np.testing.assert_equal(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
H[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_equal(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
Hp[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_allclose(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A,
time_steps[(row + col) * 2]).dot(B)),
rtol=rtol,
atol=atol)
np.testing.assert_allclose(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A, time_steps[(row + col) * 2 +
1]).dot(B)),
rtol=rtol,
atol=atol)
def test_assemble_Hankel(self):
""" Tests Hankel arrays are symmetric given
``[CB CAB CA**P CA**(P+1)B ...]``."""
rtol = 1e-10
atol = 1e-12
for num_inputs in [1,3]:
for num_outputs in [1, 2, 4]:
for sample_interval in [1]:
num_time_steps = 50
num_states = 5
A, B, C = util.drss(num_states, num_inputs, num_outputs)
time_steps = make_time_steps(
num_time_steps, sample_interval)
Markovs = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = Markovs[time_steps]
if sample_interval == 2:
time_steps, Markovs = era.make_sampled_format(
time_steps, Markovs)
my_ERA = era.ERA(verbosity=0)
my_ERA._set_Markovs(Markovs)
my_ERA._assemble_Hankel()
H = my_ERA.Hankel_array
Hp = my_ERA.Hankel_array2
for row in range(my_ERA.mc):
for col in range(my_ERA.mo):
np.testing.assert_equal(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
H[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_equal(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
Hp[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_allclose(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A, time_steps[(row + col) * 2]).dot(
B)),
rtol=rtol, atol=atol)
np.testing.assert_allclose(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A, time_steps[(row + col) * 2 + 1]).dot(
B)),
rtol=rtol, atol=atol)
def test_assemble_Hankel(self):
""" Tests Hankel mats are symmetric given
``[CB CAB CA**P CA**(P+1)B ...]``."""
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 4]:
for sample_interval in [1]:
num_time_steps = 50
num_states = 5
A, B, C = util.drss(num_states, num_inputs, num_outputs)
time_steps = make_time_steps(num_time_steps,
sample_interval)
Markovs = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = Markovs[time_steps]
if sample_interval == 2:
time_steps, Markovs = era.make_sampled_format(
time_steps, Markovs)
myERA = era.ERA(verbosity=0)
myERA._set_Markovs(Markovs)
myERA._assemble_Hankel()
H = myERA.Hankel_mat
Hp = myERA.Hankel_mat2
for row in range(myERA.mc):
for col in range(myERA.mo):
np.testing.assert_allclose(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
H[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_allclose(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
Hp[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
np.testing.assert_allclose(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C * (A**time_steps[(row + col) * 2]) * B)
np.testing.assert_allclose(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C * (A**time_steps[(row + col) * 2 + 1]) * B)
def test_compute_model(self):
"""
Test ROM Markov params similar to those given
- generates data
- assembles Hankel array
- computes SVD
- forms the ROM discrete arrays A, B, and C (D = 0)
- Tests Markov parameters from ROM are approx. equal to full plant's
"""
num_time_steps = 40
num_states_plant = 12
num_states_model = num_states_plant // 3
for num_inputs in [1, 3]:
for num_outputs in [1, 2]:
for sample_interval in [1, 2, 4]:
time_steps = make_time_steps(num_time_steps,
sample_interval)
A, B, C = util.drss(num_states_plant, num_inputs,
num_outputs)
my_ERA = era.ERA(verbosity=0)
Markovs = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = Markovs[time_steps]
if sample_interval == 2:
time_steps, Markovs =\
era.make_sampled_format(time_steps, Markovs)
num_time_steps = time_steps.shape[0]
A_path_computed = join(self.test_dir, 'A_computed.txt')
B_path_computed = join(self.test_dir, 'B_computed.txt')
C_path_computed = join(self.test_dir, 'C_computed.txt')
A, B, C = my_ERA.compute_model(Markovs, num_states_model)
my_ERA.put_model(A_path_computed, B_path_computed,
C_path_computed)
#sing_vals = my_ERA.sing_vals[:num_states_model]
# Flatten vecs into 2D X and Y arrays:
# [B AB A**PB A**(P+1)B ...]
#direct_vecs_flat = direct_vecs.swapaxes(0,1).reshape(
# (num_states_model,-1)))
# Exact grammians from Lyapunov eqn solve
#gram_cont = util.solve_Lyapunov(A, B*B.H)
#gram_obs = util.solve_Lyapunov(A.H, C.H*C)
#print(np.sort(np.linalg.eig(gram_cont)[0])[::-1])
#print(sing_vals)
#np.testing.assert_allclose(gram_cont.diagonal(),
# sing_vals, atol=.1, rtol=.1)
#np.testing.assert_allclose(gram_obs.diagonal(),
# sing_vals, atol=.1, rtol=.1)
#np.testing.assert_allclose(np.sort(np.linalg.eig(
# gram_cont)[0])[::-1], sing_vals,
# atol=.1, rtol=.1)
#np.testing.assert_allclose(np.sort(np.linalg.eig(
# gram_obs)[0])[::-1], sing_vals,
# atol=.1, rtol=.1)
# Check that the diagonals are largest entry on each row
#self.assertTrue((np.max(np.abs(gram_cont),axis=1) ==
# np.abs(gram_cont.diagonal())).all())
#self.assertTrue((np.max(np.abs(gram_obs),axis=1) ==
# np.abs(gram_obs.diagonal())).all())
# Check the ROM Markov params match the full plant's
Markovs_model = np.zeros(Markovs.shape)
for ti, tv in enumerate(time_steps):
Markovs_model[ti] = C.dot(
np.linalg.matrix_power(A, tv).dot(B))
#print(
# 'Computing ROM Markov param at time step %d' % tv)
"""
import matplotlib.pyplot as PLT
for input_num in range(num_inputs):
PLT.figure()
PLT.hold(True)
for output_num in range(num_outputs):
PLT.plot(time_steps[:50],
# Markovs_model[:50, output_num,input_num], 'ko')
PLT.plot(time_steps[:50],Markovs[:50,
# output_num, input_num],'rx')
PLT.plot(time_steps_dense[:50],
# Markovs_dense[:50, output_num, input_num],'b--')
PLT.title('input %d to outputs'%input_num)
PLT.legend(['ROM','Plant','Dense plant'])
PLT.show()
"""
np.testing.assert_allclose(Markovs_model.squeeze(),
Markovs.squeeze(),
rtol=0.5,
atol=0.5)
np.testing.assert_equal(
util.load_array_text(A_path_computed), A)
np.testing.assert_equal(
util.load_array_text(B_path_computed), B)
np.testing.assert_equal(
util.load_array_text(C_path_computed), C)
def test_compute_model(self):
"""
Test ROM Markov params similar to those given when the reduced system
has the same number of states as the full system.
- generates data
- assembles Hankel array
- computes SVD
- forms the ROM discrete arrays A, B, and C (D = 0)
- Tests Markov parameters from ROM are approx. equal to full plant's
Also, unrelated:
- Tests that saved ROM mats are equal to those returned in memory
"""
# Set test tolerances (for infinity norm of transfer function
# difference)
tf_abs_tol = 1e-6
tf_rel_tol = 1e-4
# Set time parameters for discrete-time simulation
dt = 0.1
num_time_steps = 1000
# Set size of plant and model. For test, don't reduce the system, just
# check that it comes back close to the original plant. Also, note that
# using more than 8 states causes poorly conditioned TF coeffs
# (https://github.com/scipy/scipy/issues/2980)
num_states_plant = 8
num_states_model = num_states_plant
# Loop through different numbers of inputs, numbers of outputs, and
# sampling intervals
for num_inputs in [1, 3]:
for num_outputs in [1, 2]:
for sample_interval in [1, 2, 4]:
# Define time steps at which to save data. These will be of
# the form [0, 1, p, p + 1, 2p, 2p + 1, ...] where p is the
# sample interval.
time_steps = make_time_steps(
num_time_steps, sample_interval)
# # Create a state space system
# A_plant, B_plant, C_plant = util.drss(
# num_states_plant, num_inputs, num_outputs)
A_plant = util.load_array_text(
join(self.data_dir, 'A_in%d_out%d.txt') % (
num_inputs, num_outputs))
B_plant = util.load_array_text(
join(self.data_dir, 'B_in%d_out%d.txt') % (
num_inputs, num_outputs))
C_plant = util.load_array_text(
join(self.data_dir, 'C_in%d_out%d.txt') % (
num_inputs, num_outputs))
# Simulate an impulse response using the state space system.
# This will generate Markov parameters at all timesteps [0,
# 1, 2, 3, ...]. Only keep data at the desired time steps,
# which are separated by a sampling interval (see above
# comment).
Markovs = util.impulse(
A_plant, B_plant, C_plant,
time_steps[-1] + 1)[time_steps]
# Compute a model using ERA
my_ERA = era.ERA(verbosity=0)
A_model, B_model, C_model = my_ERA.compute_model(
Markovs, num_states_model)
# Save ERA model to disk
A_path_computed = join(self.out_dir, 'A_computed.txt')
B_path_computed = join(self.out_dir, 'B_computed.txt')
C_path_computed = join(self.out_dir, 'C_computed.txt')
my_ERA.put_model(
A_path_computed, B_path_computed, C_path_computed)
# Check normalized Markovs
rtol = 1e-5 # 1e-6
atol = 1e-5 # 1e-10
Markovs_model = util.impulse(
A_model, B_model, C_model,
time_steps[-1] + 1)[time_steps]
max_Markov = np.amax(Markovs)
eigs_plant = np.linalg.eig(A_plant)[0]
eigs_model = np.linalg.eig(A_model)[0]
# print 'markovs shape', Markovs.shape
# print 'max plant eig', np.abs(eigs_plant).max()
# print 'max model eig', np.abs(eigs_model).max()
# print 'max plant markov', max_Markov
# print 'max model markov', np.amax(Markovs_model)
# print 'markov diffs', (
# Markovs - Markovs_model).squeeze().max()
'''
import matplotlib.pyplot as plt
plt.figure()
plt.semilogy(np.abs(Markovs).squeeze(), 'b')
plt.semilogy(np.abs(Markovs_model).squeeze(), 'r--')
plt.axis(
[0, time_steps[-1], Markovs.min(), Markovs.max()])
'''
np.testing.assert_allclose(
Markovs_model.squeeze(),
Markovs.squeeze(),
rtol=rtol, atol=atol)
# plt.show()
'''
# Use Scipy to check that transfer function of ERA model is
# close to transfer function of full model. Do so by
# computing the infinity norm (H_inf) of the difference
# between the transfer functions. Since Scipy can't handle
# MIMO transfer functions, loop through each input-output
# pair individually.
for input_idx in range(num_inputs):
for output_idx in range(num_outputs):
# Compute transfer functions
tf_plant = scipy.signal.StateSpace(
A_plant, B_plant[:, input_idx:input_idx + 1],
C_plant[output_idx:output_idx + 1, :],
0, dt=dt).to_tf()
tf_model = scipy.signal.StateSpace(
A_model,
B_model[:, input_idx:input_idx + 1],
C_model[output_idx:output_idx + 1, :],
0, dt=dt).to_tf()
tf_diff = util.sub_transfer_functions(
tf_plant, tf_model, dt=dt)
# Compute transfer function norms
tf_plant_inf_norm = util.compute_inf_norm_discrete(
tf_plant, dt)
tf_diff_inf_norm = util.compute_inf_norm_discrete(
tf_diff, dt)
# Test values
print 'err_frac', (
tf_diff_inf_norm / tf_plant_inf_norm)
self.assertTrue(
tf_diff_inf_norm / tf_plant_inf_norm <
tf_rel_tol)
'''
# Also test that saved reduced model mats are equal to those
# returned in memory
np.testing.assert_equal(
util.load_array_text(A_path_computed), A_model)
np.testing.assert_equal(
util.load_array_text(B_path_computed), B_model)
np.testing.assert_equal(
util.load_array_text(C_path_computed), C_model)
def test_assemble_Hankel(self):
""" Tests Hankel arrays are symmetric and accurate given Markov params
``[CB CAB CA**P CA**(P+1)B ...]``."""
rtol = 1e-10
atol = 1e-12
for num_inputs in [1, 3]:
for num_outputs in [1, 2, 4]:
for sample_interval in [1]:
num_time_steps = 50
num_states = 8
# A, B, C = util.drss(num_states, num_inputs, num_outputs)
time_steps = make_time_steps(
num_time_steps, sample_interval)
A = util.load_array_text(
join(self.data_dir, 'A_in%d_out%d.txt') % (
num_inputs, num_outputs))
B = util.load_array_text(
join(self.data_dir, 'B_in%d_out%d.txt') % (
num_inputs, num_outputs))
C = util.load_array_text(
join(self.data_dir, 'C_in%d_out%d.txt') % (
num_inputs, num_outputs))
impulse_response = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = impulse_response[time_steps]
if sample_interval == 2:
time_steps, Markovs = era.make_sampled_format(
time_steps, Markovs)
my_ERA = era.ERA(verbosity=0)
my_ERA._set_Markovs(Markovs)
my_ERA._assemble_Hankel()
H = my_ERA.Hankel_array
Hp = my_ERA.Hankel_array2
for row in range(my_ERA.mc):
for col in range(my_ERA.mo):
# Test values in H are accurate using that, roughly,
# H[r,c] = C * A^(r+c) * B.
np.testing.assert_allclose(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A, time_steps[(row + col) * 2]).dot(
B)),
rtol=rtol, atol=atol)
# Test values in H are accurate using that, roughly,
# Hp[r,c] = C * A^(r+c+1) * B.
np.testing.assert_allclose(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
C.dot(
np.linalg.matrix_power(
A, time_steps[(row + col) * 2 + 1]).dot(
B)),
rtol=rtol, atol=atol)
# Test H is block symmetric
np.testing.assert_equal(
H[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
H[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
# Test Hp is block symmetric
np.testing.assert_equal(
Hp[row * num_outputs:(row + 1) * num_outputs,
col * num_inputs:(col + 1) * num_inputs],
Hp[col * num_outputs:(col + 1) * num_outputs,
row * num_inputs:(row + 1) * num_inputs])
def test_compute_model(self):
"""
Test ROM Markov params similar to those given
- generates data
- assembles Hankel array
- computes SVD
- forms the ROM discrete arrays A, B, and C (D = 0)
- Tests Markov parameters from ROM are approx. equal to full plant's
"""
num_time_steps = 40
num_states_plant = 12
num_states_model = num_states_plant // 3
for num_inputs in [1, 3]:
for num_outputs in [1, 2]:
for sample_interval in [1, 2, 4]:
time_steps = make_time_steps(
num_time_steps, sample_interval)
A, B, C = util.drss(
num_states_plant, num_inputs, num_outputs)
my_ERA = era.ERA(verbosity=0)
Markovs = util.impulse(A, B, C, time_steps[-1] + 1)
Markovs = Markovs[time_steps]
if sample_interval == 2:
time_steps, Markovs =\
era.make_sampled_format(time_steps, Markovs)
num_time_steps = time_steps.shape[0]
A_path_computed = join(self.test_dir, 'A_computed.txt')
B_path_computed = join(self.test_dir, 'B_computed.txt')
C_path_computed = join(self.test_dir, 'C_computed.txt')
A, B, C = my_ERA.compute_model(Markovs, num_states_model)
my_ERA.put_model(
A_path_computed, B_path_computed, C_path_computed)
#sing_vals = my_ERA.sing_vals[:num_states_model]
# Flatten vecs into 2D X and Y arrays:
# [B AB A**PB A**(P+1)B ...]
#direct_vecs_flat = direct_vecs.swapaxes(0,1).reshape(
# (num_states_model,-1)))
# Exact grammians from Lyapunov eqn solve
#gram_cont = util.solve_Lyapunov(A, B*B.H)
#gram_obs = util.solve_Lyapunov(A.H, C.H*C)
#print(np.sort(np.linalg.eig(gram_cont)[0])[::-1])
#print(sing_vals)
#np.testing.assert_allclose(gram_cont.diagonal(),
# sing_vals, atol=.1, rtol=.1)
#np.testing.assert_allclose(gram_obs.diagonal(),
# sing_vals, atol=.1, rtol=.1)
#np.testing.assert_allclose(np.sort(np.linalg.eig(
# gram_cont)[0])[::-1], sing_vals,
# atol=.1, rtol=.1)
#np.testing.assert_allclose(np.sort(np.linalg.eig(
# gram_obs)[0])[::-1], sing_vals,
# atol=.1, rtol=.1)
# Check that the diagonals are largest entry on each row
#self.assertTrue((np.max(np.abs(gram_cont),axis=1) ==
# np.abs(gram_cont.diagonal())).all())
#self.assertTrue((np.max(np.abs(gram_obs),axis=1) ==
# np.abs(gram_obs.diagonal())).all())
# Check the ROM Markov params match the full plant's
Markovs_model = np.zeros(Markovs.shape)
for ti, tv in enumerate(time_steps):
Markovs_model[ti] = C.dot(
np.linalg.matrix_power(A, tv).dot(
B))
#print(
# 'Computing ROM Markov param at time step %d' % tv)
"""
import matplotlib.pyplot as PLT
for input_num in range(num_inputs):
PLT.figure()
PLT.hold(True)
for output_num in range(num_outputs):
PLT.plot(time_steps[:50],
# Markovs_model[:50, output_num,input_num], 'ko')
PLT.plot(time_steps[:50],Markovs[:50,
# output_num, input_num],'rx')
PLT.plot(time_steps_dense[:50],
# Markovs_dense[:50, output_num, input_num],'b--')
PLT.title('input %d to outputs'%input_num)
PLT.legend(['ROM','Plant','Dense plant'])
PLT.show()
"""
np.testing.assert_allclose(
Markovs_model.squeeze(), Markovs.squeeze(),
rtol=0.5, atol=0.5)
np.testing.assert_equal(
util.load_array_text(A_path_computed), A)
np.testing.assert_equal(
util.load_array_text(B_path_computed), B)
np.testing.assert_equal(
util.load_array_text(C_path_computed), C)