Package com.imsl.math

Class NonNegativeLeastSquares

java.lang.Object
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:

  • Constructor Details

    • 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 Details

    • 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.

    • 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.

    • 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.

    • 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.

    • 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.

    • 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

    • 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.

    • 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, x.
      Returns:
      a double array containing the solution.

    • 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.