Package org.ejml.dense.row.decomposition

Class TriangularSolver_DDRM

java.lang.Object
org.ejml.dense.row.decomposition.TriangularSolver_DDRM
public class TriangularSolver_DDRM
extends java.lang.Object

This contains algorithms for solving systems of equations where T is a non-singular triangular matrix:

T*x = b

where x and b are vectors, and T is an n by n matrix. T can either be a lower or upper triangular matrix.

These functions are designed for use inside of other algorithms. To use them directly is dangerous since no sanity checks are performed.

  • Constructor Summary

    Constructors 
    Constructor Description
    TriangularSolver_DDRM()  

  • Method Summary

    Modifier and Type Method Description
    static void invertLower​(double[] L, double[] L_inv, int m)  
    static void invertLower​(double[] L, int m)
    Inverts a square lower triangular matrix: L = L-1
    static void solveL​(double[] L, double[] b, int n)
    Solves for non-singular lower triangular matrices using forward substitution.
    static void solveL​(double[] L, double[] b, int m, int n)
    L is a m by m matrix B is a m by n matrix
    static void solveTranL​(double[] L, double[] b, int n)
    This is a forward substitution solver for non-singular lower triangular matrices.
    static void solveU​(double[] U, double[] b, int n)
    This is a forward substitution solver for non-singular upper triangular matrices.
    static void solveU​(double[] U, double[] b, int sideLength, int minRow, int maxRow)  
    static void solveU​(double[] U, int startU, int strideU, int widthU, double[] b, int startB, int strideB, int widthB)
    This is a forward substitution solver for non-singular upper triangular matrices which are a sub-matrix inside a larger.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

  • Method Details

    • invertLower

      public static void invertLower​(double[] L, int m)

      Inverts a square lower triangular matrix: L = L-1

    • invertLower

      public static void invertLower​(double[] L, double[] L_inv, int m)

    • solveL

      public static void solveL​(double[] L, double[] b, int n)

      Solves for non-singular lower triangular matrices using forward substitution.
      b = L-1b

      where b is a vector, L is an n by n matrix.

      Parameters:
      L - An n by n non-singular lower triangular matrix. Not modified.
      b - A vector of length n. Modified.
      n - The size of the matrices.

    • solveL

      public static void solveL​(double[] L, double[] b, int m, int n)
      L is a m by m matrix B is a m by n matrix

    • solveTranL

      public static void solveTranL​(double[] L, double[] b, int n)

      This is a forward substitution solver for non-singular lower triangular matrices.
      b = (LT)-1b

      where b is a vector, L is an n by n matrix.

      L is a lower triangular matrix, but it comes up with a solution as if it was an upper triangular matrix that was computed by transposing L.

      Parameters:
      L - An n by n non-singular lower triangular matrix. Not modified.
      b - A vector of length n. Modified.
      n - The size of the matrices.

    • solveU

      public static void solveU​(double[] U, double[] b, int n)

      This is a forward substitution solver for non-singular upper triangular matrices.
      b = U-1b

      where b is a vector, U is an n by n matrix.

      Parameters:
      U - An n by n non-singular upper triangular matrix. Not modified.
      b - A vector of length n. Modified.
      n - The size of the matrices.

    • solveU

      public static void solveU​(double[] U, double[] b, int sideLength, int minRow, int maxRow)

    • solveU

      public static void solveU​(double[] U, int startU, int strideU, int widthU, double[] b, int startB, int strideB, int widthB)

      This is a forward substitution solver for non-singular upper triangular matrices which are a sub-matrix inside a larger. The columns of 'b' are solved for individually
      b = U-1b

      where b is a matrix, U is an n by n matrix.

      Parameters:
      U - Matrix containing the upper triangle system
      startU - Index of the first element in U
      strideU - stride between rows
      widthU - How wide the square matrix is
      b - Matrix containing the solution to the system. Overwritten with the solution.
      startB - Index of the first element in B
      strideB - stride between rows
      widthB - How wide the matrix is. Length is the same as U's width