qrtsol#

Purpose#

Computes the solution of \(R'x = b\) where R is an upper triangular matrix.

Format#

x = qrtsol(b, R)#

Parameters:

b (PxL matrix) – data
R (PxP matrix) – upper triangular matrix

Returns:

x (PxL matrix) – solution of \(R'x = b\) where R is an upper triangular matrix

Remarks#

qrtsol() applies a forward solve to \(R'x = b\) to solve for x. Generally R will be the R matrix from a QR factorization. qrtsol() may be used, however, in any situation where R is upper triangular. If R is lower triangular, transpose before calling qrtsol().

If R is not transposed, use qrsol().

Examples#

// Upper triangular matrix R
r = { 3 1,
      0 2 };
b = { 7, 4 };

// Solve R'*x = b by passing R' (lower triangular) to qrtsol
x = qrtsol(b, r');

print "Solution x:";
print x;
print "R'*x (should equal b):";
print (r' * x);

The above code produces the following output:

Solution x:

   2.3333333
  0.83333333

R'*x (should equal b):

   7.0000000
   4.0000000

Source#

qrsol.src