Package org.ddogleg.optimization.math

Class HessianSchurComplement_Base<S extends DMatrix>

java.lang.Object
org.ddogleg.optimization.math.HessianSchurComplement_Base<S>
All Implemented Interfaces:
HessianMath, HessianSchurComplement<S>
Direct Known Subclasses:
HessianSchurComplement_DDRM, HessianSchurComplement_DSCC
public abstract class HessianSchurComplement_Base<S extends DMatrix> extends Object implements HessianSchurComplement<S>
The approximate Hessian matrix (J'*J) is assumed to have the following block triangle form: [A B;C D]. The system being solved for is as follows: [A B;C D] [x_1;x_2] = [b_1;b_2]. Then the following steps are followed to solve it:
  1. D' = D - C*inv(A)*B and b_2' = b_2 - C*inv(A)*b_1
  2. D'*x_2 = b_2'
  3. A*x_1 = b_1 - B*x_2
[1] Triggs, Bill, et al. "Bundle adjustment—a modern synthesis." International workshop on vision algorithms. Springer, Berlin, Heidelberg, 1999.

  • Field Details

  • Constructor Details

  • Method Details

    • init

      public void init(int numParameters)
      Description copied from interface: HessianMath
      Initialize Hessian to be in its initial state with the specified dimensions
      Specified by:
      init in interface HessianMath
      Parameters:
      numParameters - Number of optimization parameters. Hessian will be N by N

    • innerVectorHessian

      public double innerVectorHessian(DMatrixRMaj v)
      Vector matrix inner product of Hessian in block format.

      [A B;C D]*[x;y] = [c;d]
      A*x + B*y = c
      C*x + D*y = d
      [x;y]T[A B;C D]*[x;y] = [x;y]T*[c;d]

      Specified by:
      innerVectorHessian in interface HessianMath
      Parameters:
      v - row vector
      Returns:
      v'*H*v = v'*[A B;C D]*v

    • extractDiagonals

      public void extractDiagonals(DMatrixRMaj diag)
      Description copied from interface: HessianMath
      Extracts diagonal elements from the hessian and stores them in the vector diag
      Specified by:
      extractDiagonals in interface HessianMath
      Parameters:
      diag - vector

    • setDiagonals

      public void setDiagonals(DMatrixRMaj diag)
      Description copied from interface: HessianMath
      Sets the diagonal elements in the Hessian to the provided vector
      Specified by:
      setDiagonals in interface HessianMath
      Parameters:
      diag - vector

    • divideRowsCols

      public void divideRowsCols(DMatrixRMaj scaling)
      Description copied from interface: HessianMath
      Applies row and column division using the scaling vector. B = inv(diag(s))*B*inv(diag(s))
      Specified by:
      divideRowsCols in interface HessianMath

    • initializeSolver

      public boolean initializeSolver()
      Description copied from interface: HessianMath
      Initializes the solver
      Specified by:
      initializeSolver in interface HessianMath
      Returns:
      true if successful

    • solve

      public boolean solve(DMatrixRMaj gradient, DMatrixRMaj step)
      Description copied from interface: HessianMath
      Solves the system step = inv(B)*Y
      Specified by:
      solve in interface HessianMath
      Parameters:
      gradient - (Input) vector
      step - (output) vector

    • computeGradient

      public void computeGradient(S jacLeft, S jacRight, DMatrixRMaj residuals, DMatrixRMaj gradient)
      Computes the gradient using Schur complement
      Specified by:
      computeGradient in interface HessianSchurComplement<S extends DMatrix>
      Parameters:
      jacLeft - (Input) Left side of Jacobian
      jacRight - (Input) Right side of Jacobian
      residuals - (Input) Residuals
      gradient - (Output) Gradient

    • innerProduct

      protected abstract double innerProduct(double[] a, int offsetA, S B, double[] c, int offsetC)

    • extractDiag

      protected abstract void extractDiag(S input, DMatrixRMaj output)

    • divideRowsCols

      protected abstract void divideRowsCols(double[] diagA, int offsetA, S B, double[] diagC, int offsetC)

    • multTransA

      protected abstract void multTransA(S A, S B, S C)

    • multTransA

      protected abstract void multTransA(S A, DMatrixRMaj B, DMatrixRMaj C)

    • add

      protected abstract void add(double alpha, S A, double beta, S B, S C)

    • mult

      protected abstract void mult(S A, DMatrixRMaj B, DMatrixRMaj C)