# utrisol¶

## Purpose¶

Computes the solution of $$Ux = b$$ where $$U$$ is an upper triangular matrix.

## Format¶

x = utrisol(b, U)
Parameters: b (PxK matrix) – data U (PxP upper triangular matrix) – data x (PxK matrix) – solution of $$Ux = b$$.

## Example¶

// Create upper triangular matrix
U = { 9.8    -0.32     0.66       1.28,
0     9.32    -0.25    -0.0084,
0        0     8.37       0.54,
0        0        0      10.17 };

b = { -0.7,
1.5,
-0.8,
-0.003 };

// Solve the system of equations
x = utrisol(b, U);

b_pred = U * x;


The above code will make the following assignments:

 x = -0.0597827
0.158381
-0.0955604
-0.000294985

b_pred = -0.7
1.5
-0.8
-0.003


## Remarks¶

utrisol() applies a back solve to $$Ux = b$$ to solve for $$x$$. If $$b$$ has more than one column, each column is solved for separately, i.e., utrisol() applies a back solve to $$U * x[., i] = b[., i]$$.