qrsol#

Purpose#

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

Format#

x = qrsol(b, R)#

Parameters:

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

Returns:

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

Remarks#

qrsol() applies a backsolve to \(Rx = b\) to solve for x. Generally R will be the R matrix from a QR factorization. qrsol() may be used, however, in any situation where R is upper triangular.

Examples#

// Upper triangular matrix R and right-hand side b
r = { 3 1,
      0 2 };
b = { 7, 4 };

// Solve R*x = b
x = qrsol(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:

   1.6666667
   2.0000000

R*x (should equal b):

   7.0000000
   4.0000000

Source#

qrsol.src