ltrisol

Purpose

Computes the solution of \(Lx = b\) where L is a lower triangular matrix.

Format

x = ltrisol(b, L)

Parameters:

• b (PxK matrix) – data

• L (PxP matrix) – lower triangular matrix

Returns:

x (PxK matrix) – solution of \(Lx = b\).

Examples

rndseed 123131;

// Create lower triangular matrix
l = lowmat(rndn(4, 4));

// Create random b matrix
b = rndn(4, 1);

print "b/l ="; b/l;

x = ltrisol(b, l);

print "x ="; x;

This code produces

b/l =

  1.31626
  3.24920
 -4.95390
  4.62379
x =

  1.31626
  3.24920
 -4.95390
  4.62379

Remarks

ltrisol() applies a forward solve to \(Lx = b\) to solve for x. If b has more than one column, each column will be solved for separately, i.e., ltrisol() will apply a forward solve to \(L*x[., i] = b[., i]\).