JMSLTM Numerical Library 6.1

com.imsl.math
Class BoundedVariableLeastSquares

java.lang.Object
  extended by com.imsl.math.BoundedVariableLeastSquares
All Implemented Interfaces:
Serializable, Cloneable

public class BoundedVariableLeastSquares
extends Object
implements Serializable, Cloneable

Solve a linear least-squares problem with bounds on the variables. BoundedVariableLeastSquares solves the least-squares problem

min_x | Ax-b|^2

subject to the conditions

alpha_k le x_k le beta_k

for all k.

This algorithm is a generalization of NonNegativeLeastSquares, that solves the least-squares problem, Ax = b, subject to all x_j ge 0. NonNegativeLeastSquares is based on the subroutine NNLS which appeared in Lawson and Hanson (1974). The additional work on bounded variable least squares was published in a later reprint (Lawson and Hanson, 1995).

See Also:
NonNegativeLeastSquares, Example, Serialized Form

Nested Class Summary
static class BoundedVariableLeastSquares.TooManyIterException
          Maximum number of iterations exceeded.
 
Constructor Summary
BoundedVariableLeastSquares(double[][] a, double[] b, double[] lowerBound, double[] upperBound)
          Construct a new BoundedVariableLeastSquares instance to solve Ax-b subject to bounds on the variables.
 
Method Summary
 double[] getDualSolution()
          Returns the dual solution vector, w.
 int getIterations()
          Returns the number of iterations used to find the solution.
 double getResidualNorm()
          Returns the euclidean norm of the residual vector, |Ax-b|^2.
 double[] getSolution()
          Returns the solution to the problem.
 void setMaxIterations(int maxIterations)
          Sets the maximum number of iterations.
 void setTolerance(double tolerance)
          Sets the internal tolerance used to determine the relative linear dependence of a column vector for a variable moved from its initial value.
 void solve()
          Find the solution x to the problem for the current constraints.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

BoundedVariableLeastSquares

public BoundedVariableLeastSquares(double[][] a,
                                   double[] b,
                                   double[] lowerBound,
                                   double[] upperBound)
Construct a new BoundedVariableLeastSquares instance to solve Ax-b subject to bounds on the variables. Each upper bound must be greater than or equal to the corresponding lower bound.

Parameters:
a - the double input matrix.
b - a double array of length a.length.
lowerBound - a double array of length n containing lower bounds. Use Double.NEGATIVE_INFINITY for variables which are not bounded below.
upperBound - a double array of length n containing upper bounds. Use Double.POSITIVE_INFINITY for variables which are not bounded above.
Method Detail

getDualSolution

public double[] getDualSolution()
Returns the dual solution vector, w. If x_j is at neither its upper nor lower bound then w_j=0. If x_j is at its lower bound then w_j
 le{0}. If x_j is at its upper bound then w_jge{0}. If the upper and lower bound for the j -th variable are equal, fixing the value of x_j, then the value of w_j is arbitrary.

Returns:
a double array containing the dual solution vector, w.

getIterations

public int getIterations()
Returns the number of iterations used to find the solution.

Returns:
an int containing the number of iterations.

getResidualNorm

public double getResidualNorm()
Returns the euclidean norm of the residual vector, |Ax-b|^2.

Returns:
a double containing the euclidean norm of the residual vector.

getSolution

public double[] getSolution()
Returns the solution to the problem.

Returns:
a double array containing the solution.

setMaxIterations

public void setMaxIterations(int maxIterations)
Sets the maximum number of iterations.

Parameters:
maxIterations - an int specifying the maximum number of iterations. The default is three times a[0].length.

setTolerance

public void setTolerance(double tolerance)
Sets the internal tolerance used to determine the relative linear dependence of a column vector for a variable moved from its initial value.

Parameters:
tolerance - a double value specifying the tolerance. The default value is 1.0e-7.

solve

public void solve()
           throws BoundedVariableLeastSquares.TooManyIterException
Find the solution x to the problem for the current constraints.

Throws:
BoundedVariableLeastSquares.TooManyIterException

JMSLTM Numerical Library 6.1

Copyright © 1970-2010 Visual Numerics, Inc.
Built July 30 2010.