lusol

Purpose

Computes the solution of \(LUx = b\) where L is a lower triangular
matrix and U is an upper triangular matrix.

Format

x = lusol(b, L, U)
Parameters:
  • b (PxK matrix) – data
  • L (PxP matrix) – lower triangular matrix
  • U (PxP matrix) – upper triangular matrix
Returns:

x (PxK matrix) – solution of LUx = b.

Examples

A = { 3 -1 5,
      -2 0 5,
      7 2 -2};

b = { 6 -4,
      3 2,
      7 -5};

// Lower decomposition
{ l, u } = lu(A);

// Solve system of equations
X = lusol(b, l, u);
x =   0.87654  -1.00000
      1.38272   1.00000
      0.95062   0.00000

Remarks

If b has more than one column, each column is solved for separately, i.e., lusol() solves \(LUx[., i] = b[., i]\).