def test1():
import numpy as np
import pylab
from scipy import sparse
from regreg.algorithms import FISTA
from regreg.atoms import l1norm
from regreg.container import container
from regreg.smooth import quadratic
Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14
sparsity = l1norm(500, lagrange=1.0)
#Create D
D = (np.identity(500) + np.diag([-1]*499,k=1))[:-1]
D = sparse.csr_matrix(D)
fused = l1norm.linear(D, lagrange=19.5)
loss = quadratic.shift(-Y, lagrange=0.5)
p = container(loss, sparsity, fused)
soln1 = blockwise([sparsity, fused], Y)
solver = FISTA(p)
solver.fit(max_its=800,tol=1e-10)
soln2 = solver.composite.coefs
#plot solution
pylab.figure(num=1)
pylab.clf()
pylab.scatter(np.arange(Y.shape[0]), Y, c='r')
pylab.plot(soln1, c='y', linewidth=6)
pylab.plot(soln2, c='b', linewidth=2)
def test2():
import numpy as np
import pylab
from scipy import sparse
from regreg.algorithms import FISTA
from regreg.atoms import l1norm
from regreg.container import container
from regreg.smooth import quadratic
n1, n2 = l1norm(1), l1norm(1)
Y = np.array([30.])
loss = quadratic.shift(-Y, lagrange=0.5)
blockwise([n1, n2], Y)
import pylab import numpy as np import scipy.sparse from regreg.algorithms import FISTA from regreg.smooth import quadratic from regreg.atoms import l1norm, maxnorm from regreg.seminorm import seminorm D = (np.diag(np.ones(500)) - np.diag(np.ones(499),1))[:-1] DT = scipy.sparse.csr_matrix(D.T) D = scipy.sparse.csr_matrix(D) Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14 loss = quadratic.shift(-Y, l=0.5) penalty = l1norm(D, l=20) problem = loss.add_seminorm(seminorm(penalty)) solver = FISTA(problem) solver.fit(max_its=100, tol=1e-10) solution = solver.problem.coefs l1_soln = np.fabs(D * solution).sum() tfocs_penalty = maxnorm(499, l=l1_soln) tfocs_loss = quadratic.affine(DT, -Y, l=0.5) tfocs_loss.coefs = np.zeros(499) tfocs_problem = tfocs_loss.add_seminorm(tfocs_penalty) tfocs_solver = FISTA(tfocs_problem) tfocs_solver.debug = True tfocs_solver.fit(max_its=1000, tol=1e-10)
from regreg.algorithms import FISTA from regreg.smooth import quadratic from regreg.atoms import l1norm, maxnorm from regreg.seminorm import seminorm sparsity = l1norm(500, l=1.3) D = (np.identity(500) + np.diag([-1] * 499, k=1))[:-1] D = scipy.sparse.csr_matrix(D) fused = l1norm(D, l=20) penalty = seminorm(sparsity, fused) Y = np.random.standard_normal(500) Y[100:150] += 7 Y[250:300] += 14 loss = quadratic.shift(-Y, l=0.5) problem = loss.add_seminorm(penalty) solver = FISTA(problem) solver.fit(max_its=100, tol=1e-10) solution = solver.problem.coefs import pylab pylab.scatter(np.arange(Y.shape[0]), Y, c='r') pylab.plot(solution, color='yellow', linewidth=5) l1_fused = np.fabs(D * solution).sum() l1_sparsity = np.fabs(solution).sum() new_fused = l1norm(D, l=l1_fused) new_sparsity = l1norm(500, l=l1_sparsity) conjugate = quadratic.shift(Y, l=0.5)
