def main(data_sizes: List, approximation_ranks: List, increments: List,
singular_values: RowVector, used_data_factory: Callable,
results_path: str, experiment_type: str, power_method_iterations,
_seed) -> None:
""" The main function of this project
This functions performs the desired experiment according to the given configuration.
The function runs the random_svd and random_id for every combination of data_size, approximation rank and increment
given in the config and saves all the results to a csv file in the results folder (given in the configuration).
"""
seed(_seed) # Seed the interpolative package of Scipy for later usage.
results_log = DataLog(LogFields) # Initializing an empty results log.
random_svd_with_run_time: Callable = measure_time(random_svd)
random_id_with_run_time: Callable = measure_time(random_id)
for data_size in data_sizes:
data_matrix: Matrix = used_data_factory(data_size, singular_values)
for approximation_rank in approximation_ranks:
next_singular_value: Scalar = singular_values[approximation_rank + 1] if \
approximation_rank < len(singular_values) else singular_values[-1]
for increment in increments:
# Executing all the tested methods.
print(
f'n={data_size}, k={approximation_rank}, l={approximation_rank + increment}'
)
random_svd_approximation, svd_duration = random_svd_with_run_time(
data_matrix, approximation_rank, increment)
random_svd_accuracy: Scalar = estimate_spectral_norm_diff(
data_matrix, random_svd_approximation,
power_method_iterations)
print(
f'runtime={svd_duration}, accuracy={random_svd_accuracy}')
random_id_approximation, id_duration = random_id_with_run_time(
data_matrix, approximation_rank, increment)
random_id_accuracy: Scalar = estimate_spectral_norm_diff(
data_matrix, random_id_approximation,
power_method_iterations)
print(f'runtime={id_duration}, accuracy={random_id_accuracy}')
# Appending all the experiment results to the log.
results_log.append(LogFields.DataSize, data_size)
results_log.append(LogFields.ApproximationRank,
approximation_rank)
results_log.append(LogFields.Increment,
increment + approximation_rank)
results_log.append(LogFields.NextSingularValue,
next_singular_value)
results_log.append(LogFields.RandomSVDAccuracy,
random_svd_accuracy)
results_log.append(LogFields.RandomIDAccuracy,
random_id_accuracy)
results_log.append(LogFields.RandomSVDDuration, svd_duration)
results_log.append(LogFields.RandomIDDuration, id_duration)
results_log.save_log(experiment_type + " results",
results_folder_path=results_path)
def check_id(self, dtype):
# Test ID routines on a Hilbert matrix.
# set parameters
n = 300
eps = 1e-12
# construct Hilbert matrix
A = hilbert(n).astype(dtype)
if np.issubdtype(dtype, np.complexfloating):
A = A * (1 + 1j)
L = aslinearoperator(A)
# find rank
S = np.linalg.svd(A, compute_uv=False)
try:
rank = np.nonzero(S < eps)[0][0]
except:
rank = n
# print input summary
_debug_print("Hilbert matrix dimension: %8i" % n)
_debug_print("Working precision: %8.2e" % eps)
_debug_print("Rank to working precision: %8i" % rank)
# set print format
fmt = "%8.2e (s) / %5s"
# test real ID routines
_debug_print("-----------------------------------------")
_debug_print("Real ID routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_id / idzp_id ...", )
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_aid / idzp_aid ...", )
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rid / idzp_rid ...", )
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(L, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_id / idzr_id ...", )
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_aid / idzr_aid ...", )
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rid / idzr_rid ...", )
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(L, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# check skeleton and interpolation matrices
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_(np.allclose(B, A[:, idx[:k]], eps))
assert_(np.allclose(B.dot(P), A, eps))
# test SVD routines
_debug_print("-----------------------------------------")
_debug_print("SVD routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_svd / idzp_svd ...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_asvd / idzp_asvd...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rsvd / idzp_rsvd...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(L, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_svd / idzr_svd ...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_asvd / idzr_asvd ...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rsvd / idzr_rsvd ...", )
t0 = time.clock()
U, S, V = pymatrixid.svd(L, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# ID to SVD
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
Up, Sp, Vp = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
B = U.dot(np.diag(S).dot(V.T.conj()))
assert_(np.allclose(A, B, eps))
# Norm estimates
s = svdvals(A)
norm_2_est = pymatrixid.estimate_spectral_norm(A)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
B = A.copy()
B[:, 0] *= 1.2
s = svdvals(A - B)
norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
# Rank estimates
B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=dtype)
for M in [A, B]:
ML = aslinearoperator(M)
rank_tol = 1e-9
rank_np = np.linalg.matrix_rank(M, norm(M, 2) * rank_tol)
rank_est = pymatrixid.estimate_rank(M, rank_tol)
rank_est_2 = pymatrixid.estimate_rank(ML, rank_tol)
assert_(rank_est >= rank_np)
assert_(rank_est <= rank_np + 10)
assert_(rank_est_2 >= rank_np - 4)
assert_(rank_est_2 <= rank_np + 4)
def check_id(self, dtype):
# Test ID routines on a Hilbert matrix.
# set parameters
n = 300
eps = 1e-12
# construct Hilbert matrix
A = hilbert(n).astype(dtype)
if np.issubdtype(dtype, np.complexfloating):
A = A * (1 + 1j)
L = aslinearoperator(A)
# find rank
S = np.linalg.svd(A, compute_uv=False)
try:
rank = np.nonzero(S < eps)[0][0]
except:
rank = n
# print input summary
_debug_print("Hilbert matrix dimension: %8i" % n)
_debug_print("Working precision: %8.2e" % eps)
_debug_print("Rank to working precision: %8i" % rank)
# set print format
fmt = "%8.2e (s) / %5s"
# test real ID routines
_debug_print("-----------------------------------------")
_debug_print("Real ID routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_id / idzp_id ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_aid / idzp_aid ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(A, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rid / idzp_rid ...",)
t0 = time.clock()
k, idx, proj = pymatrixid.interp_decomp(L, eps)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_id / idzr_id ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_aid / idzr_aid ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(A, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rid / idzr_rid ...",)
t0 = time.clock()
idx, proj = pymatrixid.interp_decomp(L, k)
t = time.clock() - t0
B = pymatrixid.reconstruct_matrix_from_id(A[:, idx[:k]], idx, proj)
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# check skeleton and interpolation matrices
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
P = pymatrixid.reconstruct_interp_matrix(idx, proj)
B = pymatrixid.reconstruct_skel_matrix(A, k, idx)
assert_(np.allclose(B, A[:,idx[:k]], eps))
assert_(np.allclose(B.dot(P), A, eps))
# test SVD routines
_debug_print("-----------------------------------------")
_debug_print("SVD routines")
_debug_print("-----------------------------------------")
# fixed precision
_debug_print("Calling iddp_svd / idzp_svd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_asvd / idzp_asvd...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddp_rsvd / idzp_rsvd...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(L, eps)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# fixed rank
k = rank
_debug_print("Calling iddr_svd / idzr_svd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k, rand=False)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_asvd / idzr_asvd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(A, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
_debug_print("Calling iddr_rsvd / idzr_rsvd ...",)
t0 = time.clock()
U, S, V = pymatrixid.svd(L, k)
t = time.clock() - t0
B = np.dot(U, np.dot(np.diag(S), V.T.conj()))
_debug_print(fmt % (t, np.allclose(A, B, eps)))
assert_(np.allclose(A, B, eps))
# ID to SVD
idx, proj = pymatrixid.interp_decomp(A, k, rand=False)
Up, Sp, Vp = pymatrixid.id_to_svd(A[:, idx[:k]], idx, proj)
B = U.dot(np.diag(S).dot(V.T.conj()))
assert_(np.allclose(A, B, eps))
# Norm estimates
s = svdvals(A)
norm_2_est = pymatrixid.estimate_spectral_norm(A)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
B = A.copy()
B[:,0] *= 1.2
s = svdvals(A - B)
norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B)
assert_(np.allclose(norm_2_est, s[0], 1e-6))
# Rank estimates
B = np.array([[1, 1, 0], [0, 0, 1], [0, 0, 1]], dtype=dtype)
for M in [A, B]:
ML = aslinearoperator(M)
rank_np = np.linalg.matrix_rank(M, 1e-9)
rank_est = pymatrixid.estimate_rank(M, 1e-9)
rank_est_2 = pymatrixid.estimate_rank(ML, 1e-9)
assert_(rank_est >= rank_np)
assert_(rank_est <= rank_np + 10)
assert_(rank_est_2 >= rank_np)
assert_(rank_est_2 <= rank_np + 10)
def test_estimate_spectral_norm_diff(self, A):
B = A.copy()
B[:, 0] *= 1.2
s = svdvals(A - B)
norm_2_est = pymatrixid.estimate_spectral_norm_diff(A, B)
assert_(np.allclose(norm_2_est, s[0], 1e-6))