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 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 signal_approximator, smooth_function
Y = np.random.standard_normal(500)
Y[100:150] += 7
Y[250:300] += 14
sparsity = l1norm(500, l=1.0)
# Create D
D = (np.identity(500) + np.diag([-1] * 499, k=1))[:-1]
D = sparse.csr_matrix(D)
fused = l1norm(D, l=19.5)
p = container(loss, sparsity, fused)
soln1 = blockwise(pen, Y)
solver = FISTA(p.problem())
solver.fit(max_its=800, tol=1e-10)
soln2 = solver.problem.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 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 signal_approximator, smooth_function
Y = np.random.standard_normal(500)
Y[100:150] += 7
Y[250:300] += 14
sparsity = l1norm(500, l=1.0)
#Create D
D = (np.identity(500) + np.diag([-1] * 499, k=1))[:-1]
D = sparse.csr_matrix(D)
fused = l1norm(D, l=19.5)
p = container(loss, sparsity, fused)
soln1 = blockwise(pen, Y)
solver = FISTA(p.problem())
solver.fit(max_its=800, tol=1e-10)
soln2 = solver.problem.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)
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 = l2normsq.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 = l2normsq.shift(Y, l=0.5) from regreg.constraint import constraint loss_constraint = constraint(conjugate, new_fused, new_sparsity)
from regreg.algorithms import FISTA from regreg.atoms import positive_part from regreg.container import container from regreg.smooth import l2normsq n = 100 Y = np.random.standard_normal(n) Y[:-30] += np.arange(n - 30) * 0.2 D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:] nisotonic = positive_part.linear(-sparse.csr_matrix(D), l=3) loss = l2normsq.shift(-Y, l=0.5) p = container(loss, nisotonic) solver = FISTA(p.problem()) vals = solver.fit(max_its=25000, tol=1e-05) soln = solver.problem.coefs.copy() nisotonic.atoms[0].l = 100. solver.fit(max_its=25000, tol=1e-05) soln2 = solver.problem.coefs.copy() nisotonic.atoms[0].l = 1000. solver.fit(max_its=25000, tol=1e-05) soln3 = solver.problem.coefs.copy() X = np.arange(n) pylab.clf() pylab.scatter(X, Y)
from regreg.atoms import positive_part from regreg.container import container from regreg.smooth import l2normsq n = 100 Y = np.random.standard_normal(n) Y[:-30] += np.arange(n-30) * 0.2 D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:] nisotonic = positive_part.linear(-sparse.csr_matrix(D), l=3) loss = l2normsq.shift(-Y,l=0.5) p = container(loss, nisotonic) solver=FISTA(p.problem()) vals = solver.fit(max_its=25000, tol=1e-05) soln = solver.problem.coefs.copy() nisotonic.atoms[0].l = 100. solver.fit(max_its=25000, tol=1e-05) soln2 = solver.problem.coefs.copy() nisotonic.atoms[0].l = 1000. solver.fit(max_its=25000, tol=1e-05) soln3 = solver.problem.coefs.copy() X = np.arange(n) pylab.clf() pylab.scatter(X, Y)
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) tfocs_dual_solution = tfocs_problem.coefs tfocs_primal_solution = Y - DT * tfocs_dual_solution
import numpy as np import pylab from scipy import sparse from regreg.algorithms import FISTA from regreg.atoms import nonnegative from regreg.container import container from regreg.smooth import signal_approximator, smooth_function n = 100 Y = np.random.standard_normal(n) Y[:-30] += np.arange(n - 30) * 0.2 D = (np.identity(n) - np.diag(np.ones(n - 1), -1))[1:] isotonic = nonnegative.linear(sparse.csr_matrix(D)) loss = signal_approximator(Y) p = container(loss, isotonic) solver = FISTA(p.problem(initial=np.zeros(n))) solver.debug = True vals = solver.fit(max_its=25000, tol=1e-08, backtrack=True) soln = solver.problem.coefs X = np.arange(n) pylab.clf() pylab.scatter(X, Y) pylab.step(X, soln, 'r--')
from regreg.algorithms import FISTA from regreg.atoms import l1norm from regreg.container import container from regreg.smooth import l2normsq Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14 loss = l2normsq.shift(-Y, coef=0.5) sparsity = l1norm(len(Y), 1.4) # TODO should make a module to compute typical Ds D = sparse.csr_matrix((np.identity(500) + np.diag([-1]*499,k=1))[:-1]) fused = l1norm.linear(D, 25.5) problem = container(loss, sparsity, fused) solver = FISTA(problem.composite()) solver.fit(max_its=100, tol=1e-10) solution = solver.composite.coefs delta1 = np.fabs(D * solution).sum() delta2 = np.fabs(solution).sum() fused_constraint = l1norm.linear(D, bound=delta1) sparsity_constraint = l1norm(500, bound=delta2) constrained_problem = container(loss, fused_constraint, sparsity_constraint) constrained_solver = FISTA(constrained_problem.composite()) constrained_solver.composite.lipshitz = 1.01 vals = constrained_solver.fit(max_its=10, tol=1e-06, backtrack=False, monotonicity_restart=False) constrained_solution = constrained_solver.composite.coefs
from regreg.smooth import l2normsq 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 = l2normsq.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 = l2normsq.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) tfocs_dual_solution = tfocs_problem.coefs tfocs_primal_solution = Y - DT * tfocs_dual_solution
import numpy as np
import pylab
from scipy import sparse
from regreg.algorithms import FISTA
from regreg.atoms import nonnegative
from regreg.container import container
from regreg.smooth import signal_approximator, smooth_function
n = 100
Y = np.random.standard_normal(n)
Y[:-30] += np.arange(n-30) * 0.2
D = (np.identity(n) - np.diag(np.ones(n-1),-1))[1:]
isotonic = nonnegative.linear(sparse.csr_matrix(D))
loss = signal_approximator(Y)
p = container(loss, isotonic)
solver=FISTA(p.problem(initial=np.zeros(n)))
solver.debug=True
vals = solver.fit(max_its=25000, tol=1e-08, backtrack=True)
soln = solver.problem.coefs
X = np.arange(n)
pylab.clf()
pylab.scatter(X, Y)
pylab.step(X, soln, 'r--')
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 signal_approximator
Y = np.random.standard_normal(500); Y[100:150] += 7; Y[250:300] += 14
sparsity = l1norm(500, l=1.3)
#Create D
D = (np.identity(500) + np.diag([-1]*499,k=1))[:-1]
D = sparse.csr_matrix(D)
fused = l1norm.linear(D, l=25.5)
loss = signal_approximator(Y)
problem = container(loss, sparsity, fused)
solver = FISTA(problem.problem())
solver.fit(max_its=800,tol=1e-10)
soln = solver.problem.coefs
#plot solution
pylab.figure(num=1)
pylab.clf()
pylab.plot(soln, c='g')
pylab.scatter(np.arange(Y.shape[0]), Y)
from regreg.atoms import l1norm
from regreg.container import container
from regreg.smooth import l2normsq
Y = np.random.standard_normal(500)
Y[100:150] += 7
Y[250:300] += 14
loss = l2normsq.shift(-Y, coef=0.5)
sparsity = l1norm(len(Y), 1.4)
# TODO should make a module to compute typical Ds
D = sparse.csr_matrix((np.identity(500) + np.diag([-1] * 499, k=1))[:-1])
fused = l1norm.linear(D, 25.5)
problem = container(loss, sparsity, fused)
solver = FISTA(problem.composite())
solver.fit(max_its=100, tol=1e-10)
solution = solver.composite.coefs
delta1 = np.fabs(D * solution).sum()
delta2 = np.fabs(solution).sum()
fused_constraint = l1norm.linear(D, bound=delta1)
sparsity_constraint = l1norm(500, bound=delta2)
constrained_problem = container(loss, fused_constraint, sparsity_constraint)
constrained_solver = FISTA(constrained_problem.composite())
constrained_solver.composite.lipshitz = 1.01
vals = constrained_solver.fit(max_its=10,
tol=1e-06,
backtrack=False,
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 signal_approximator Y = np.random.standard_normal(500) Y[100:150] += 7 Y[250:300] += 14 sparsity = l1norm(500, l=1.3) #Create D D = (np.identity(500) + np.diag([-1] * 499, k=1))[:-1] D = sparse.csr_matrix(D) fused = l1norm.linear(D, l=25.5) loss = signal_approximator(Y) problem = container(loss, sparsity, fused) solver = FISTA(problem.problem()) solver.fit(max_its=800, tol=1e-10) soln = solver.problem.coefs #plot solution pylab.figure(num=1) pylab.clf() pylab.plot(soln, c='g') pylab.scatter(np.arange(Y.shape[0]), Y)
