Package org.ejml.dense.block

Class InnerTriangularSolver_DDRB

java.lang.Object
org.ejml.dense.block.InnerTriangularSolver_DDRB
public class InnerTriangularSolver_DDRB extends Object

Contains triangular solvers for inner blocks of a DMatrixRBlock.

Algorithm for lower triangular inverse:
 for i=1:m
     for j=1:i-1
         val = 0
         for k=j:i-1
             val = val - L(i,k) * X(k,j)
         end
         x(i,j) = val / L(i,i)
     end
     x(i,i) = 1 / L(i,i)
 end

  • Constructor Summary

    Constructors
    Constructor
    Description
    InnerTriangularSolver_DDRB()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static void
    invertLower(double[] L, double[] L_inv, int m, int offsetL, int offsetL_inv)
    Inverts a square lower triangular matrix: L = L-1
    static void
    invertLower(double[] L, int m, int offsetL)
    Inverts a square lower triangular matrix: L = L-1
    static void
    solveL(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)
    Solves for non-singular lower triangular matrices using forward substitution.
    static void
    solveLTransB(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)
    Solves for non-singular lower triangular matrices using forward substitution.
    static void
    solveTransL(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)
    Solves for non-singular transposed lower triangular matrices using backwards substitution:
    B = L-TB

    where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.
    static void
    solveTransU(double[] U, double[] b, int m, int n, int strideU, int offsetU, int offsetB)
    Solves for non-singular upper triangular matrices using forward substitution.
    static void
    solveU(double[] U, double[] b, int m, int n, int strideU, int offsetU, int offsetB)
    Solves for non-singular upper triangular matrices using backwards substitution.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • InnerTriangularSolver_DDRB

      public InnerTriangularSolver_DDRB()

  • Method Details

    • invertLower

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

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

      Parameters:
      L - Lower triangular matrix being inverted. Not modified.
      L_inv - Where the inverse is stored. Can be the same as L. Modified.
      m - The number of rows and columns.
      offsetL - which index does the L matrix start at.
      offsetL_inv - which index does the L_inv matrix start at.

    • invertLower

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

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

      Parameters:
      L - Lower triangular matrix being inverted. Over written with inverted matrix. Modified.
      m - The number of rows and columns.
      offsetL - which index does the L matrix start at.

    • solveL

      public static void solveL(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)

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

      where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.

      Parameters:
      L - An m by m non-singular lower triangular matrix. Not modified.
      b - An m by n matrix. Modified.
      m - size of the L matrix
      n - number of columns in the B matrix.
      strideL - number of elements that need to be added to go to the next row in L
      offsetL - initial index in L where the matrix starts
      offsetB - initial index in B where the matrix starts

    • solveTransL

      public static void solveTransL(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)

      Solves for non-singular transposed lower triangular matrices using backwards substitution:
      B = L-TB

      where B is a (m by n) matrix, L is a lower triangular (m by m) matrix.

      Parameters:
      L - An m by m non-singular lower triangular matrix. Not modified.
      b - An m by n matrix. Modified.
      m - size of the L matrix
      n - number of columns in the B matrix.
      strideL - number of elements that need to be added to go to the next row in L
      offsetL - initial index in L where the matrix starts
      offsetB - initial index in B where the matrix starts

    • solveLTransB

      public static void solveLTransB(double[] L, double[] b, int m, int n, int strideL, int offsetL, int offsetB)

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

      where B is a (n by m) matrix, L is a lower triangular (m by m) matrix.

      Parameters:
      L - An m by m non-singular lower triangular matrix. Not modified.
      b - An n by m matrix. Modified.
      m - size of the L matrix
      n - number of columns in the B matrix.
      offsetL - initial index in L where the matrix starts
      offsetB - initial index in B where the matrix starts

    • solveU

      public static void solveU(double[] U, double[] b, int m, int n, int strideU, int offsetU, int offsetB)

      Solves for non-singular upper triangular matrices using backwards substitution.
      B = U-1B

      where B (m by n) is a matrix, U is a (m by m ) upper triangular matrix.

      Parameters:
      U - An m by m non-singular upper triangular matrix. Not modified.
      b - An m by n matrix. Modified.
      m - size of the L matrix
      n - number of columns in the B matrix.
      offsetU - initial index in L where the matrix starts
      offsetB - initial index in B where the matrix starts

    • solveTransU

      public static void solveTransU(double[] U, double[] b, int m, int n, int strideU, int offsetU, int offsetB)

      Solves for non-singular upper triangular matrices using forward substitution.
      B = U-TB

      where B (m by n) is a matrix, U is a (m by m ) upper triangular matrix.

      Parameters:
      U - An m by m non-singular upper triangular matrix. Not modified.
      b - An m by n matrix. Modified.
      m - size of the L matrix
      n - number of columns in the B matrix.
      offsetU - initial index in L where the matrix starts
      offsetB - initial index in B where the matrix starts