JMSLTM Numerical Library 6.1

com.imsl.math
Class NonNegativeLeastSquares

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

public class NonNegativeLeastSquares
extends Object
implements Serializable, Cloneable

Solves a linear least squares problem with nonnegativity constraints. NonNegativeLeastSquares solves the problem

min_x|Ax-b|^2

subject to the condition x ge 0.

If a starting point x_0 is provided, those entries of x_0 that are gt0 are first combined with a descent gradient component. The start point is the origin. When x_0 is not provided the algorithm uses only the gradient to verify that an optimum has been found. The algorithm completes using only the gradient components to reach an optimum. For more information, see Lawson and Hanson (1974).

See Also:
BoundedVariableLeastSquares, Example, Serialized Form

Nested Class Summary
static class NonNegativeLeastSquares.TooManyIterException
          Maximum number of iterations has been exceeded.
static class NonNegativeLeastSquares.TooMuchTimeException
          Maximum time allowed for solve is exceeded.
 
Constructor Summary
NonNegativeLeastSquares(double[][] a, double[] b)
          Construct a new NonNegativeLeastSquares instance to solve Ax-b where x is a vector of n unknowns.
 
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, x.
 void setDualTolerance(double dualTolerance)
          Sets the dual tolerance.
 void setGuess(double[] guess)
          Sets the initial guess.
 void setMaximumTime(long maximumTime)
          Sets the maximum time allowed for the solve step.
 void setMaxIterations(int maxIterations)
          Sets the maximum number of iterations.
 void setNormTolerance(double normTolerance)
          Sets the residual norm tolerance.
 void setRankTolerance(double rankTolerance)
          Sets the tolerance used for the incoming column rank deficient check.
 void solve()
          Finds the solution 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

NonNegativeLeastSquares

public NonNegativeLeastSquares(double[][] a,
                               double[] b)
Construct a new NonNegativeLeastSquares instance to solve Ax-b where x is a vector of n unknowns.

Parameters:
a - the double input matrix.
b - a double array of length a.length.
Method Detail

getDualSolution

public double[] getDualSolution()
Returns the dual solution vector, w. If x_j = 0 then w_j le 0, otherwise w_j = 0.

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, x.

Returns:
a double array containing the solution.

setDualTolerance

public void setDualTolerance(double dualTolerance)
Sets the dual tolerance. The computation stops if largest gradient is smaller than this. The default value is 0.

Parameters:
dualTolerance - a double containing the dual tolerance.

setGuess

public void setGuess(double[] guess)
Sets the initial guess.

Parameters:
guess - a double array containing the initial guess. If set, the guess is used in a two-phase algorithm where the positive components are matched with positive gradients to choose an incoming column. If not set, the algorithm uses only the gradient to verify that an optimum has been found.

setMaximumTime

public void setMaximumTime(long maximumTime)
Sets the maximum time allowed for the solve step.

Parameters:
maximumTime - a long value specifying the maximum time, in milliseconds, to be allowed for the solve step. If maximumTime is less than or equal to zero, then no time limit is imposed. By default, there is no time limit.

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.

setNormTolerance

public void setNormTolerance(double normTolerance)
Sets the residual norm tolerance.

Parameters:
normTolerance - a double containing the residual norm tolerance. The computation stops if {||mbox{rnorm}||}^2 le{mbox{normTolerance}
                      times{||b||}}, where rnorm is the residual norm. By default, the value is 0.

setRankTolerance

public void setRankTolerance(double rankTolerance)
Sets the tolerance used for the incoming column rank deficient check.

Parameters:
rankTolerance - a double value used to check for rank deficiency. The default value is 2.220e-016.

solve

public void solve()
           throws NonNegativeLeastSquares.TooManyIterException,
                  NonNegativeLeastSquares.TooMuchTimeException
Finds the solution to the problem for the current constraints.

Throws:
TooManyIterationsException - is thrown if the maximum number of iterations is exceeded.
NonNegativeLeastSquares.TooMuchTimeException - is thrown if the maximum time allowed for solve is exceeded.
NonNegativeLeastSquares.TooManyIterException

JMSLTM Numerical Library 6.1

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