com.imsl.math

Class BoundedVariableLeastSquares

java.lang.Object

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

Nested Classes

Modifier and Type	Class and Description
static class	BoundedVariableLeastSquares.TooManyIterException Maximum number of iterations exceeded.

Constructor Summary

Constructors

Constructor and Description
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

Modifier and Type	Method and Description
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

solve

public void solve()
           throws BoundedVariableLeastSquares.TooManyIterException

Find the solution x to the problem for the current constraints.

Throws:

BoundedVariableLeastSquares.TooManyIterException

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.

getIterations

public int getIterations()

Returns the number of iterations used to find the solution.

Returns:

an int containing the number of iterations.

getSolution

public double[] getSolution()

Returns the solution to the problem.

Returns:

a double array containing the solution.

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 \(w_j\ge{0}\). 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.

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.