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///////////////////////////////////////////////////////////////////////////////
// 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, 2022 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. //
// //
// 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)
*
* @author asedgewick 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);
}
}
