class LassoNorm(BaseNorm):
      
      #Implements the LASSO (ℓ₁) norm:
      #     Omega(w) = lambda1 * ||w||₁.
      #The quadratic surrogate for each coordinate is given by
      #     |w_i| ≈ w_i^2/(|w_i| + eps)
      #to smooth the non-differentiability.
      
      def __init__(self, lambda1):
          self.lambda1 = lambda1

      def penalty(self, w):
          return self.lambda1 * np.sum(np.abs(w))

      def quadratic_approximation(self, w, eps=1e-8):
          diag_entries = 1.0 / (np.abs(w) + eps)
          return self.lambda1 * np.diag(diag_entries)
      
      def __repr__(self):
          return f"{self.__class__.__name__}(lambda1={self.lambda1})"

import numpy as np

from dual_spls.plug_norm import ElasticNetNorm, d_spls_generic, mm_dual_norm_generic


if __name__ == '__main__':
    np.random.seed(0)
    n_samples, n_features = 100, 20
    X = np.random.randn(n_samples, n_features)
    y = np.random.randn(n_samples)
    ncp = 3  # number of latent components

    # --- Example with Elastic Net norm ---
    enet_norm = ElasticNetNorm(lambda1=0.5, lambda2=0.1)
    w_enet, dual_val_enet = mm_dual_norm_generic(np.random.randn(n_features), enet_norm, rho=10.0, ppnu=0.8)
    print("Elastic Net dual update:")
    print("w =", w_enet)
    print("Dual value =", dual_val_enet)

    # Run the dual-sPLS procedure with the Elastic Net norm.
    model = d_spls_generic(X, y, ncp, enet_norm, rho=10.0, ppnu=0.8, verbose=True)
    print("\nDual-sPLS model output keys:", model.keys())