Package wsh.opt

Class QuadraticSolver

  • public class QuadraticSolver
extends java.lang.Object
    Minimize a simple quadratic objective function. Finds the x that minimizes the quadratic function 0.5 x'Hx + b'x . Solves Hx + b = 0 for x (the Normal Equations of a least-squares problem) b is the gradient for x=0, and H is the hessian. The algorithm is a conjugate gradient. A is an approximate inverse Hessian, making AH more diagonal and improving convergence. A may also include a model-dependent conditioning to converge earlier on eigenfunction of most importance. The algorithm assumes that the application of H dominates the cost. 
     x = p = u = 0;
 beta = 0;
 g = b;
 a = A g;
 q = H a;
 do {
 p = -a + beta p
 u = Hp = -q + beta u
 scalar = -p'g/p'u
 x = x + scalar p
 if (done) return x
 g = H x + b = g + scalar u
 a = A g
 q = H a
 beta = p'H A g / p'H p = p'q/p'u
 }

    Also contains a solver for a least-squares inverse of a linear transform, using QuadraticTransform as a wrapper.

    • Constructor Summary

      Constructors 
      Constructor Description
      QuadraticSolver​(Quadratic quadratic)
      Implement the Quadratic interface and pass to this constructor.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      Vect solve​(int numberIterations, Monitor monitor)
      Return a new solution after the number of conjugate gradient iterations.
      static Vect solve​(VectConst data, VectConst referenceModel, LinearTransform linearTransform, boolean dampOnlyPerturbation, int conjugateGradIterations, Monitor monitor)
      Solve quadratic objective function for linear transform.

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • QuadraticSolver

        public QuadraticSolver​(Quadratic quadratic)
        Implement the Quadratic interface and pass to this constructor. Pass a vector b to the constructor (a copy is cloned internally). This solver calls Vect and Quadratic methods. Does not call Vect.multiplyInverseCovariance().
        Parameters:
        quadratic - Defines the Hessian quadratic term.

    • Method Detail

      • solve

        public Vect solve​(int numberIterations,
                  Monitor monitor)
        Return a new solution after the number of conjugate gradient iterations.
        Parameters:
        numberIterations - is the number of iterations to perform.
        monitor - If non-null, then track all progress.
        Returns:
        Optimized solution

      • solve

        public static Vect solve​(VectConst data,
                         VectConst referenceModel,
                         LinearTransform linearTransform,
                         boolean dampOnlyPerturbation,
                         int conjugateGradIterations,
                         Monitor monitor)
        Solve quadratic objective function for linear transform. Minimizes 
         [F(m+x)-data]'N[F(m+x)-data] + (m+x)'M(m+x)
        if dampOnlyPerturbation is true and 
         [F(m+x)-data]'N[F(m+x)-data] + (x)'M(x)
        if dampOnlyPerturbation is false.
        Parameters:
        data - The data to be fit.
        referenceModel - Initialize with this model.
        linearTransform - Describes the linear transform.
        dampOnlyPerturbation - If true then, only damp perturbations to reference model. If false, then damp the reference model plus the perturbation.
        conjugateGradIterations - The specified number of conjugate gradient iterations.
        monitor - Report progress here, if non-null.
        Returns:
        Result of optimization