E-CodeLU decomposition with pivoting (exact) — a TI-89 Titanium program
LU89 is a TI-89 BASIC program for the TI-89 Titanium. Factor a 2×2 to 4×4 matrix as PA = LU with partial pivoting, in exact fractions: the row order P, every row of L and U, and the determinant.
What it asks for and what it shows
It asks for 4 values at its prompts. In the example below it shows DET, ROW ORDER P, L1, L2, L3, U1, U2, U3.
Example run
One of its oracle test cases: “3x3 with a row swap”. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Input 1 | 3 |
| Input 2 | {2,1,1} |
| Input 3 | {4,-6,0} |
| Input 4 | {-2,7,2} |
| The screen shows | |
DET= | -16 |
ROW ORDER P= | {2 1 3} |
L1= | {1 0 0} |
L2= | {1/2 1 0} |
L3= | {-1/2 1 1} |
U1= | {4 -6 0} |
U2= | {0 4 1} |
U3= | {0 0 1} |
How it's checked
5 test cases, each checked against an independent method. Replayed key by key on a virtual TI-89 Titanium, they make 41 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-89 Titanium calculator and pick “LU decomposition with pivoting (exact)” (LU89).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
Related programs
- LU decomposition of a typed matrix
- Matrix inverse from a typed matrix
- Linear system, exact answers
- Cramer's rule with every determinant
- Matrix inverse, exact
All TI-89 Titanium math programs · All TI-89 Titanium programs