def test_svd_mass_res(file_prefix='F_m'):
"""
test SVD decomposition of mass residuals by generating SVD, saving to file and reloading
"""
from proteus.deim_utils import read_snapshots,generate_svd_decomposition
ns = get_burgers_ns("test_svd_mass_res",T=0.1,nDTout=10,archive_pod_res=True)
failed = ns.calculateSolution("run_svd_mass_res")
assert not failed
from proteus import Archiver
archive = Archiver.XdmfArchive(".","test_svd_mass_res",readOnly=True)
U,s,V=generate_svd_decomposition(archive,len(ns.tnList),'mass_residual0',file_prefix)
S_svd = np.dot(U,np.dot(np.diag(s),V))
#now load back in and test
S = read_snapshots(archive,len(ns.tnList),'mass_residual0')
npt.assert_almost_equal(S,S_svd)
def test_svd_soln():
"""
test SVD decomposition of solution by generating SVD, saving to file and reloading
"""
from proteus.deim_utils import read_snapshots, generate_svd_decomposition
ns = get_burgers_ns("test_svd_soln",
T=0.1,
nDTout=10,
archive_pod_res=True)
failed = ns.calculateSolution("run_svd_soln")
assert not failed
from proteus import Archiver
archive = Archiver.XdmfArchive(".", "test_svd_soln", readOnly=True)
U, s, V = generate_svd_decomposition(archive, len(ns.tnList), 'u', 'soln')
S_svd = np.dot(U, np.dot(np.diag(s), V))
#now load back in and test
S = read_snapshots(archive, len(ns.tnList), 'u')
npt.assert_almost_equal(S, S_svd)
def deim_approx(T=0.1,nDTout=10,m=5,m_mass=5):
"""
Follow basic setup for DEIM approximation
- generate a burgers solution, saving spatial and 'mass' residuals
- generate SVDs for snapshots
- for both residuals F_s and F_m
- pick $m$, dimension for snapshot reduced basis $\mathbf{U}_m$
- call DEIM algorithm to determine $\vec \rho$ and compute projection matrix
$\mathbf{P}_F=\mathbf{U}_m(\mathbf{P}^T\mathbf{U}_m)^{-1}$
For selected timesteps
- extract fine grid solution from archive, $\vec y$
- for both residuals F=F_s and F_m
- evaluate $\vec F(\vec y)$ at indices in $\vec \rho \rightarrow \vec c$
- apply DEIM interpolant $\tilde{\vec F} = \mathbf{P}_F\vec c$
- compute error $\|F-\tilde{\vec F}\|
- visualize
"""
from proteus.deim_utils import read_snapshots,generate_svd_decomposition
##run fine grid problem
ns = get_burgers_ns("test_deim_approx",T=T,nDTout=nDTout,archive_pod_res=True)
failed = ns.calculateSolution("run_deim_approx")
assert not failed
from proteus import Archiver
archive = Archiver.XdmfArchive(".","test_deim_approx",readOnly=True)
##perform SVD on spatial residual
U,s,V=generate_svd_decomposition(archive,len(ns.tnList),'spatial_residual0','F_s')
U_m,s_m,V_m=generate_svd_decomposition(archive,len(ns.tnList),'mass_residual0','F_m')
from proteus.deim_utils import deim_alg
##calculate DEIM indices and projection matrix
rho,PF = deim_alg(U,m)
#also 'mass' term
rho_m,PF_m = deim_alg(U_m,m_mass)
##for comparison, grab snapshots of solution and residual
Su = read_snapshots(archive,len(ns.tnList),'u')
Sf = read_snapshots(archive,len(ns.tnList),'spatial_residual0')
Sm = read_snapshots(archive,len(ns.tnList),'mass_residual0')
steps_to_test = np.arange(len(ns.tnList))
errors = np.zeros(len(steps_to_test),'d'); errors_mass = errors.copy()
F_deim = np.zeros((Sf.shape[0],len(steps_to_test)),'d')
Fm_deim = np.zeros((Sf.shape[0],len(steps_to_test)),'d')
for i,istep in enumerate(steps_to_test):
#solution on the fine grid
u = Su[:,istep]
#spatial residual evaluated from fine grid
F = Sf[:,istep]
#deim approximation on the fine grid
F_deim[:,istep] = np.dot(PF,F[rho])
errors[i] = np.linalg.norm(F-F_deim[:,istep])
#repeat for 'mass residual'
Fm= Sm[:,istep]
#deim approximation on the fine grid
Fm_deim[:,istep] = np.dot(PF_m,Fm[rho])
errors_mass[i] = np.linalg.norm(Fm-Fm_deim[:,istep])
#
np.savetxt("deim_approx_errors_space_test_T={0}_nDT={1}_m={2}.dat".format(T,nDTout,m),errors)
np.savetxt("deim_approx_errors_mass_test_T={0}_nDT={1}_m={2}.dat".format(T,nDTout,m_mass),errors_mass)
return errors,errors_mass,F_deim,Fm_deim
def deim_approx(T=0.1, nDTout=10, m=5, m_mass=5):
"""
Follow basic setup for DEIM approximation
- generate a burgers solution, saving spatial and 'mass' residuals
- generate SVDs for snapshots
- for both residuals F_s and F_m
- pick $m$, dimension for snapshot reduced basis $\mathbf{U}_m$
- call DEIM algorithm to determine $\vec \rho$ and compute projection matrix
$\mathbf{P}_F=\mathbf{U}_m(\mathbf{P}^T\mathbf{U}_m)^{-1}$
For selected timesteps
- extract fine grid solution from archive, $\vec y$
- for both residuals F=F_s and F_m
- evaluate $\vec F(\vec y)$ at indices in $\vec \rho \rightarrow \vec c$
- apply DEIM interpolant $\tilde{\vec F} = \mathbf{P}_F\vec c$
- compute error $\|F-\tilde{\vec F}\|
- visualize
"""
from proteus.deim_utils import read_snapshots, generate_svd_decomposition
##run fine grid problem
ns = get_burgers_ns("test_deim_approx",
T=T,
nDTout=nDTout,
archive_pod_res=True)
failed = ns.calculateSolution("run_deim_approx")
assert not failed
from proteus import Archiver
archive = Archiver.XdmfArchive(".", "test_deim_approx", readOnly=True)
##perform SVD on spatial residual
U, s, V = generate_svd_decomposition(archive, len(ns.tnList),
'spatial_residual0', 'F_s')
U_m, s_m, V_m = generate_svd_decomposition(archive, len(ns.tnList),
'mass_residual0', 'F_m')
from proteus.deim_utils import deim_alg
##calculate DEIM indices and projection matrix
rho, PF = deim_alg(U, m)
#also 'mass' term
rho_m, PF_m = deim_alg(U_m, m_mass)
##for comparison, grab snapshots of solution and residual
Su = read_snapshots(archive, len(ns.tnList), 'u')
Sf = read_snapshots(archive, len(ns.tnList), 'spatial_residual0')
Sm = read_snapshots(archive, len(ns.tnList), 'mass_residual0')
steps_to_test = np.arange(len(ns.tnList))
errors = np.zeros(len(steps_to_test), 'd')
errors_mass = errors.copy()
F_deim = np.zeros((Sf.shape[0], len(steps_to_test)), 'd')
Fm_deim = np.zeros((Sf.shape[0], len(steps_to_test)), 'd')
for i, istep in enumerate(steps_to_test):
#solution on the fine grid
u = Su[:, istep]
#spatial residual evaluated from fine grid
F = Sf[:, istep]
#deim approximation on the fine grid
F_deim[:, istep] = np.dot(PF, F[rho])
errors[i] = np.linalg.norm(F - F_deim[:, istep])
#repeat for 'mass residual'
Fm = Sm[:, istep]
#deim approximation on the fine grid
Fm_deim[:, istep] = np.dot(PF_m, Fm[rho])
errors_mass[i] = np.linalg.norm(Fm - Fm_deim[:, istep])
#
np.savetxt(
"deim_approx_errors_space_test_T={0}_nDT={1}_m={2}.dat".format(
T, nDTout, m), errors)
np.savetxt(
"deim_approx_errors_mass_test_T={0}_nDT={1}_m={2}.dat".format(
T, nDTout, m_mass), errors_mass)
return errors, errors_mass, F_deim, Fm_deim