def test_are_we_saveobjective_agnostic():
"""Test whether the reconstruction is the same unrespective to the
'saveobjective flag'
"""
## Generate data
np.random.seed(42)
A = np.genfromtxt('./demodata/fourierbasis.csv') # Measurement matrix
f = cstools.generate_1D(512, .95) # Signal
y = cstools.measure(f,A)
rec_save = pySPIRALTAP.SPIRALTAP(y,A,1e-6,
maxiter=100,
miniter=5,
penalty='canonical',
noisetype='gaussian',
stopcriterion=3,
tolerance=1e-8,
alphainit=1,
alphamin=1e-30,
alphamax=1e30,
alphaaccept=1e30,
logepsilon=1e-10,
saveobjective=True,
savereconerror=False,
savesolutionpath=False,
truth=f,
verbose=0, savecputime=False)[0]
rec_nosave = pySPIRALTAP.SPIRALTAP(y,A,1e-6,
maxiter=100,
miniter=5,
penalty='canonical',
noisetype='gaussian',
stopcriterion=3,
tolerance=1e-8,
alphainit=1,
alphamin=1e-30,
alphamax=1e30,
alphaaccept=1e30,
logepsilon=1e-10,
saveobjective=False,
savereconerror=False,
savesolutionpath=False,
truth=f,
verbose=0,savecputime=False)[0]
er = ((rec_save- rec_nosave)**2).sum()/(rec_save**2).sum()
print("L2 error between the two reconstructions : ", er)
assert er == 0
def reconstruct_1Dspiral(measure,
basis,
maxiter=500,
verbose=0,
W=[],
penalty='canonical',
noisetype='gaussian'):
"""Reconstruct using pySPIRALTAP and default parameters"""
## ==== Parameters
tau = 1e-6
tolerance = 1e-8
## ==== Create function handles
y = measure #.reshape((measure.size,1))
AT = lambda x: basis.transpose().dot(x)
A = lambda x: basis.dot(x)
finit = y.sum() * AT(y).size / AT(y).sum() / AT(
np.ones_like(y)).sum() * AT(y)
rec_l1 = pySPIRALTAP.SPIRALTAP(
y,
A,
tau,
AT=AT,
W=W,
maxiter=maxiter,
miniter=5,
penalty=penalty,
noisetype=noisetype,
#initialization=finit,
stopcriterion=3,
tolerance=tolerance,
alphainit=1,
alphamin=1e-30,
alphamax=1e30,
alphaaccept=1e30,
logepsilon=1e-10,
verbose=verbose)[0]
return rec_l1
def run_spiral(y,Ao,f,finit=None, penalty='canonical', W=[], WT=[]):
"""Simple wrapper for SPIRAL function. All the parameters are preset."""
## Set regularization parameters and iteration limit:
tau = 1e-6
maxiter = 100
tolerance = 1e-8
verbose = 0
## Setup function handles for computing A and A^T:
AT = lambda x: Ao.transpose().dot(x)
A = lambda x: Ao.dot(x)
if finit==None: ## rescaled least-square to initialize finit
finit = y.sum()*AT(y).size/AT(y).sum()/AT(np.ones_like(y)).sum() * AT(y)
return pySPIRALTAP.SPIRALTAP(y,A,tau,
AT=AT,
W=W,
WT=WT,
maxiter=maxiter,
miniter=5,
penalty=penalty,
noisetype='gaussian',
initialization=finit,
stopcriterion=3,
tolerance=tolerance,
alphainit=1,
alphamin=1e-30,
alphamax=1e30,
alphaaccept=1e30,
logepsilon=1e-10,
saveobjective=True,
savereconerror=False,
savesolutionpath=False,
truth=f,
verbose=verbose, savecputime=False)[0]
finit = y.sum() * AT(y).size / AT(y).sum() / AT(
np.ones_like(y)).sum() * AT(y)
# ==== Run the algorithm:
## Demonstrating all the options for our algorithm:
resSPIRAL = pySPIRALTAP.SPIRALTAP(y,
A,
tau,
AT=AT,
maxiter=maxiter,
miniter=5,
penalty='canonical',
noisetype='gaussian',
initialization=finit,
stopcriterion=3,
tolerance=tolerance,
alphainit=1,
alphamin=1e-30,
alphamax=1e30,
alphaaccept=1e30,
logepsilon=1e-10,
saveobjective=True,
savereconerror=True,
savesolutionpath=False,
truth=f,
verbose=verbose,
savecputime=True)
## Deparse outputs
fhatSPIRAL = resSPIRAL[0]
parSPIRAL = resSPIRAL[1]
iterationsSPIRAL = parSPIRAL['iterations']
objectiveSPIRAL = parSPIRAL['objective']