code: def test_fit():
      from brainiak.reprsimil.brsa import BRSA
      import brainiak.utils.utils as utils
      import scipy.stats
      import numpy as np
      import os.path
  
      np.random.seed(10)
      file_path = os.path.join(
          os.path.dirname(__file__), "example_design.1D"
      )
      # Load an example design matrix
      design = utils.ReadDesign(fname=file_path)
  
      # concatenate it by 2 times, mimicking 2 runs of itenditcal timing
      n_run = 2
      design.design_task = np.tile(
          design.design_task[:, :-1], [n_run, 1]
      )
      design.n_TR = design.n_TR * n_run
  
      # start simulating some data
      n_V = 50
      n_C = np.size(design.design_task, axis=1)
      n_T = design.n_TR
  
      noise_bot = 0.5
      noise_top = 5.0
      noise_level = (
          np.random.rand(n_V) * (noise_top - noise_bot) + noise_bot
      )
      # noise level is random.
  
      # AR(1) coefficient
      rho1_top = 0.8
      rho1_bot = -0.2
      rho1 = np.random.rand(n_V) * (rho1_top - rho1_bot) + rho1_bot
  
      # generating noise
      noise = np.zeros([n_T, n_V])
      noise[0, :] = (
          np.random.randn(n_V) * noise_level / np.sqrt(1 - rho1**2)
      )
      for i_t in range(1, n_T):
          noise[i_t, :] = (
              noise[i_t - 1, :] * rho1
              + np.random.randn(n_V) * noise_level
          )
  
      # ideal covariance matrix
      ideal_cov = np.zeros([n_C, n_C])
      ideal_cov = np.eye(n_C) * 0.6
      ideal_cov[0:4, 0:4] = 0.2
      for cond in range(0, 4):
          ideal_cov[cond, cond] = 2
      ideal_cov[5:9, 5:9] = 0.9
      for cond in range(5, 9):
          ideal_cov[cond, cond] = 1
      L_full = np.linalg.cholesky(ideal_cov)
  
      # generating signal
      snr_level = 5.0  # test with high SNR
      # snr = np.random.rand(n_V)*(snr_top-snr_bot)+snr_bot
      # Notice that accurately speaking this is not snr. the magnitude of signal
      # depends
      # not only on beta but also on x.
      inten = np.random.rand(n_V) * 20.0
  
      # parameters of Gaussian process to generate pseuso SNR
      tau = 1.0
      smooth_width = 5.0
      inten_kernel = 1.0
  
      coords = np.arange(0, n_V)[:, None]
  
      dist2 = np.square(coords - coords.T)
  
      inten_tile = np.tile(inten, [n_V, 1])
      inten_diff2 = (inten_tile - inten_tile.T) ** 2
  
      K = (
          np.exp(
              -dist2 / smooth_width**2 / 2.0
              - inten_diff2 / inten_kernel**2 / 2.0
          )
          * tau**2
          + np.eye(n_V) * tau**2 * 0.001
      )
  
      L = np.linalg.cholesky(K)
      snr = np.exp(np.dot(L, np.random.randn(n_V))) * snr_level
      sqrt_v = noise_level * snr
      betas_simulated = (
          np.dot(L_full, np.random.randn(n_C, n_V)) * sqrt_v
      )
      signal = np.dot(design.design_task, betas_simulated)
  
      # Adding noise to signal as data
      Y = signal + noise + inten
  
      scan_onsets = np.linspace(0, design.n_TR, num=n_run + 1)
  
      # Test fitting with GP prior.
      brsa = BRSA(
          GP_space=True,
          GP_inten=True,
          n_iter=5,
          init_iter=10,
          auto_nuisance=False,
          tol=2e-3,
      )
  
      # We also test that it can detect baseline regressor included in the
      # design matrix for task conditions
      wrong_design = np.insert(design.design_task, 0, 1, axis=1)
      with pytest.raises(ValueError) as excinfo:
          brsa.fit(
              X=Y,
              design=wrong_design,
              scan_onsets=scan_onsets,
              coords=coords,
              inten=inten,
          )
      assert (
          "Your design matrix appears to have included baseline time series."
          in str(excinfo.value)
      )
      # Now we fit with the correct design matrix.
      brsa.fit(
          X=Y,
          design=design.design_task,
          scan_onsets=scan_onsets,
          coords=coords,
          inten=inten,
      )
  
      # Check that result is significantly correlated with the ideal covariance
      # matrix
      u_b = brsa.U_
      u_i = ideal_cov
      p = scipy.stats.spearmanr(
          u_b[np.tril_indices_from(u_b)], u_i[np.tril_indices_from(u_i)]
      )[1]
      assert p < 0.01, (
          "Fitted covariance matrix does not correlate with ideal covariance "
          "matrix!"
      )
      # check that the recovered SNRs makes sense
      p = scipy.stats.pearsonr(brsa.nSNR_, snr)[1]
      assert (
          p < 0.01
      ), "Fitted SNR does not correlate with simulated SNR!"
      assert np.isclose(
          np.mean(np.log(brsa.nSNR_)), 0
      ), "nSNR_ not normalized!"
      p = scipy.stats.pearsonr(brsa.sigma_, noise_level)[1]
      assert (
          p < 0.01
      ), "Fitted noise level does not correlate with simulated noise level!"
      p = scipy.stats.pearsonr(brsa.rho_, rho1)[1]
      assert (
          p < 0.01
      ), "Fitted AR(1) coefficient does not correlate with simulated values!"
  
      noise_new = np.zeros([n_T, n_V])
      noise_new[0, :] = (
          np.random.randn(n_V) * noise_level / np.sqrt(1 - rho1**2)
      )
      for i_t in range(1, n_T):
          noise_new[i_t, :] = (
              noise_new[i_t - 1, :] * rho1
              + np.random.randn(n_V) * noise_level
          )
  
      Y_new = signal + noise_new + inten
      ts, ts0 = brsa.transform(Y_new, scan_onsets=scan_onsets)
      p = scipy.stats.pearsonr(ts[:, 0], design.design_task[:, 0])[1]
      assert (
          p < 0.01
      ), "Recovered time series does not correlate with true time series!"
      assert np.shape(ts) == (n_T, n_C) and np.shape(ts0) == (
          n_T,
          1,
      ), "Wrong shape in returned time series by transform function!"
  
      [score, score_null] = brsa.score(
          X=Y_new, design=design.design_task, scan_onsets=scan_onsets
      )
      assert (
          score > score_null
      ), "Full model does not win over null model on data containing signal"
  
      [score, score_null] = brsa.score(
          X=noise_new + inten,
          design=design.design_task,
          scan_onsets=scan_onsets,
      )
      assert (
          score < score_null
      ), "Null model does not win over full model on data without signal"
  
      # Test fitting with lower rank, nuisance regressors and without GP prior
      rank = n_C - 1
      n_nureg = 1
      brsa = BRSA(
          rank=rank,
          n_nureg=n_nureg,
          tol=2e-3,
          n_iter=8,
          init_iter=4,
          auto_nuisance=True,
      )
      brsa.fit(X=Y, design=design.design_task, scan_onsets=scan_onsets)
      # u_b = brsa.U_
      u_i = ideal_cov
      p = scipy.stats.spearmanr(
          u_b[np.tril_indices_from(u_b)], u_i[np.tril_indices_from(u_i)]
      )[1]
      assert p < 0.01, (
          "Fitted covariance matrix does not correlate with ideal covariance "
          "matrix!"
      )
      # check that the recovered SNRs makes sense
      p = scipy.stats.pearsonr(brsa.nSNR_, snr)[1]
      assert (
          p < 0.01
      ), "Fitted SNR does not correlate with simulated SNR!"
      assert np.isclose(
          np.mean(np.log(brsa.nSNR_)), 0
      ), "nSNR_ not normalized!"
      p = scipy.stats.pearsonr(brsa.sigma_, noise_level)[1]
      assert (
          p < 0.01
      ), "Fitted noise level does not correlate with simulated noise level!"
      p = scipy.stats.pearsonr(brsa.rho_, rho1)[1]
      assert (
          p < 0.01
      ), "Fitted AR(1) coefficient does not correlate with simulated values!"
  
      assert (
          not hasattr(brsa, "bGP_")
          and not hasattr(brsa, "lGPspace_")
          and not hasattr(brsa, "lGPinten_")
      ), (
          "the BRSA object should not have parameters of GP if GP is "
          "not requested."
      )
      # GP parameters are not set if not requested
      assert (
          brsa.beta0_.shape[0] == n_nureg + 1
      ), "Shape of beta0 incorrect"
      p = scipy.stats.pearsonr(brsa.beta0_[0, :], inten)[1]
      assert (
          p < 0.01
      ), "recovered beta0 does not correlate with the baseline of voxels."
      assert np.shape(brsa.L_) == (
          n_C,
          rank,
      ), "Cholesky factor should have shape of (n_C, rank)"
  
      # Test fitting with GP over just spatial coordinates.
      brsa = BRSA(
          GP_space=True,
          baseline_single=False,
          tol=2e-3,
          n_iter=4,
          init_iter=4,
      )
      brsa.fit(
          X=Y,
          design=design.design_task,
          scan_onsets=scan_onsets,
          coords=coords,
      )
      # Check that result is significantly correlated with the ideal covariance
      # matrix
      u_b = brsa.U_
      u_i = ideal_cov
      p = scipy.stats.spearmanr(
          u_b[np.tril_indices_from(u_b)], u_i[np.tril_indices_from(u_i)]
      )[1]
      assert p < 0.01, (
          "Fitted covariance matrix does not correlate with ideal covariance "
          "matrix!"
      )
      # check that the recovered SNRs makes sense
      p = scipy.stats.pearsonr(brsa.nSNR_, snr)[1]
      assert (
          p < 0.01
      ), "Fitted SNR does not correlate with simulated SNR!"
      assert np.isclose(
          np.mean(np.log(brsa.nSNR_)), 0
      ), "nSNR_ not normalized!"
      p = scipy.stats.pearsonr(brsa.sigma_, noise_level)[1]
      assert (
          p < 0.01
      ), "Fitted noise level does not correlate with simulated noise level!"
      p = scipy.stats.pearsonr(brsa.rho_, rho1)[1]
      assert (
          p < 0.01
      ), "Fitted AR(1) coefficient does not correlate with simulated values!"
      assert not hasattr(brsa, "lGPinten_"), (
          "the BRSA object should not have parameters of lGPinten_ if only "
          "smoothness in space is requested."
      )
  
imports: import pytest
label_desc: Use image node_id 2 for calling a global function with example usage: test_fit() without return types