code: ///////////////////////////////////////////////////////////////////////////////
  // For information as to what this class does, see the Javadoc, below.       //
  // Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
  // 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
  // Ramsey, and Clark Glymour.                                                //
  //                                                                           //
  // This program is free software; you can redistribute it and/or modify      //
  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
  // (at your option) any later version.                                       //
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  // This program is distributed in the hope that it will be useful,           //
  // but WITHOUT ANY WARRANTY; without even the implied warranty of            //
  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             //
  // GNU General Public License for more details.                              //
  //                                                                           //
  // You should have received a copy of the GNU General Public License         //
  // along with this program; if not, write to the Free Software               //
  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.pitt.csb.mgm;
  
  import cern.colt.matrix.DoubleMatrix1D;
  
  /**
   * This interface should be used for non-differentiable convex functions that are decomposable such that
   * f(x) = g(x) + h(x) where g(x) is a differentiable convex function (i.e. smooth) and h(x) is a convex but not
   * necessarily differentiable (i.e. non-smooth) and has a proximal operator prox_t(x) = argmin_z 1/(2t) norm2(x-z)^2 +
   * h(z) has a solution for any t > 0. Typically g(x) will be a likelihood, and h(x) is a penalty term (as in l_1 in the
   * lasso)
   *
   *
   * Created by ajsedgewick on 8/4/15.
   */
  public abstract class ConvexProximal {
  
      /**
       * Calculate value of smooth function g(X)
       *
       * @param X input vector
       * @return value of g(X)
       */
      abstract double smoothValue(DoubleMatrix1D X);
  
      /**
       * Gradient of smooth function g(X)
       *
       * @param X input vector
       * @return vector containing gradient of g(X)
       */
      abstract DoubleMatrix1D smoothGradient(DoubleMatrix1D X);
  
  
      /**
       * Calculate value of g(X) and gradient of g(X) at the same time for efficiency reasons.
       *
       * @param X input Vector
       * @param Xout gradient of g(X)
       * @return value of g(X)
       */
      public double smooth(DoubleMatrix1D X, DoubleMatrix1D Xout){
          Xout.assign(smoothGradient(X));
          return smoothValue(X);
      }
  
      /**
       * Calculate value of h(X)
       *
       * @param X input vector
       * @return value of h(X)
       */
      abstract double nonSmoothValue(DoubleMatrix1D X);
  
      /**
       * A proximal operator is the solution to this optimization problem:
       *     prox_t(x) = argmin_z \frac{1}{2t} \|x-z\|^2_2 + h(x)
       *
       * @param t positive parameter for prox operator
       * @param X input vector
       * @return vector solution to prox_t(X)
       */
      abstract DoubleMatrix1D proximalOperator(double t, DoubleMatrix1D X);
  
      /**
       * Calculate value of h(X) and proxOperator of h(X) at the same time for efficiency reasons.
       *
       * @param t positive parameter for prox operator
       * @param X input vector
       * @param Xout vector solution to prox_t(X)
       * @return value of h(X)
       */
      public double nonSmooth(double t, DoubleMatrix1D X, DoubleMatrix1D Xout){
          Xout.assign(proximalOperator(t,X));
          return nonSmoothValue(X);
      }
  
  }
  
  