text: from __future__ import print_function
  
  import numpy as np, regreg.api as rr
  
  from ...tests.instance import gaussian_instance
  
  from ..lasso import (ROSI,
                       ROSI_modelQ,
                       _truncation_interval,
                       _solve_restricted_problem)
  
  # earlier implmentation
  
  def solve_problem(Qbeta_bar, Q, lagrange, initial=None):
      p = Qbeta_bar.shape[0]
      loss = rr.quadratic_loss((p,), Q=Q, quadratic=rr.identity_quadratic(0, 
                                                                          0,
                                                                          -Qbeta_bar, 
                                                                          0))
      lagrange = np.asarray(lagrange)
      if lagrange.shape in [(), (1,)]:
          lagrange = np.ones(p) * lagrange
      pen = rr.weighted_l1norm(lagrange, lagrange=1.)
      problem = rr.simple_problem(loss, pen)
      if initial is not None:
          problem.coefs[:] = initial
      soln = problem.solve(tol=1.e12, min_its=500)
  
      return soln
  
  def truncation_interval(Qbeta_bar, Q, Qi_jj, j, beta_barj, lagrange):
      if lagrange[j] != 0:
          lagrange_cp = lagrange.copy()
      lagrange_cp[j] = np.inf
      restricted_soln = solve_problem(Qbeta_bar, Q, lagrange_cp)
  
      p = Qbeta_bar.shape[0]
      I = np.identity(p)
      nuisance = Qbeta_bar - I[:,j] / Qi_jj * beta_barj
      center = nuisance[j] - Q[j].dot(restricted_soln)
      upper = (lagrange[j] - center) * Qi_jj
      lower = (-lagrange[j] - center) * Qi_jj
  
      return lower, upper
  
  def test_smaller():
  
      n, p, s = 200, 100, 4
      X, y, beta = gaussian_instance(n=n,
                                     p=p,
                                     s=s)[:3]
  
      lagrange = 10. * np.ones(p)
  
      LF = ROSI.gaussian(X, y, lagrange, approximate_inverse=None)
      LF.fit()
  
      Q = X.T.dot(X)
      Qbeta_bar = X.T.dot(y)
      beta_hat = solve_problem(Qbeta_bar, Q, lagrange)
      beta_hat2 = _solve_restricted_problem(Qbeta_bar, (X, np.ones(X.shape[0])), 
                                            lagrange, min_its=500)
  
      Qi = np.linalg.inv(Q)
      beta_bar = np.linalg.pinv(X).dot(y)
  
      yield np.testing.assert_allclose, beta_hat, beta_hat2, 1.e-4, 1.e-4
      np.testing.assert_allclose(beta_hat, beta_hat2)
  
      E = LF.active
      QiE = Qi[E][:,E]
      beta_barE = beta_bar[E]
  
      S = LF.summary()
  
      for i, j in enumerate(LF.active):
          l, u = (np.array(S['lower_truncation'])[i], 
                  np.array(S['upper_truncation'])[i]) 
          lower, upper =  truncation_interval(Qbeta_bar, 
                                              Q, 
                                              QiE[i,i], 
                                              j, 
                                              beta_barE[i], 
                                              lagrange)
          yield np.testing.assert_allclose, l, lower, 1.e-4, 1.e-4
          yield np.testing.assert_allclose, u, upper, 1.e-4, 1.e-4
  
  def test_modelQ():
  
      n, p, s = 200, 50, 4
      X, y, beta = gaussian_instance(n=n,
                                     p=p,
                                     s=s,
                                     sigma=1)[:3]
  
      lagrange = 1. * np.ones(p)
  
      LF = ROSI.gaussian(X, y, lagrange, approximate_inverse=None)
      LF.fit()
      S = LF.summary(dispersion=1)
  
      LX = ROSI_modelQ(X.T.dot(X), X, y, lagrange)
      LX.fit()
      SX = LX.summary(dispersion=1)
  
      np.testing.assert_allclose(S['pvalue'], SX['pvalue'], rtol=1.e-5, atol=1.e-4)
  
  
  
  
  