Texas Instruments TI-89 - Page 483

466 Appendix A: Functions and Instructions
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 466 of 132
Loop
CATALOG
Loop
block
EndLoop
Repeatedly executes the statements in
block
.
Note that the loop will be executed endlessly,
unless a
Goto
or
Exit
instruction is executed
within
block
.
block
is a sequence of statements separated
with the “:” character.
Program segment:
©
:
1
!
i
:Loop
: Ran
d(
6
)
!
d
ie
1
: Ran
d(
6
)
!
d
ie2
: If
d
ie
1
=6 an
d
d
ie2=6
: Goto En
d
: i+
1
!
i
:En
d
Loop
:L
bl
En
d
:Disp "T
h
e num
b
er of ro
ll
s is", i
©
LU
MATH/Matrix menu
LU
matrix
,
lMatName
,
uMatName
,
pMatName
[
,
tol
]
Calculates the Doolittle LU (lower-upper)
decomposition of a real or complex
matrix
.
The lower triangular matrix is stored in
lMatName
, the upper triangular matrix in
uMatName
, and the permutation matrix
(which describes the row swaps done during
the calculation) in
pMatName
.
lMatName
ù
uMatName
=
pMatName
ù
matrix
Optionally, any matrix element is treated as
zero if its absolute value is less than
tol
. This
tolerance is used only if the matrix has
floating-point entries and does not contain
any symbolic variables that have not been
assigned a value. Otherwise,
tol
is ignored.
•
If you use
¥¸
or set the mode to
Exact/Approx=APPROXIMATE
, computations
are done using floating-point arithmetic.
•
If
tol
is omitted or not used, the default
tolerance is calculated as:
5
E
ë
14
ù
max(dim(
matrix
))
ù
rowNorm(
matrix
)
The
LU
factorization algorithm uses partial
pivoting with row interchanges.
[6,12,18;5,14,31;3,8,18]
!
m1
¸




6 12 18
5 14 31
3 8 18
LU m1,lower,upper,perm
¸
Done
lower
¸




1 0 0
5/6 1 0
1/2 1/2 1
upper
¸




6 12 18
0 4 16
0 0 1
perm
¸




1 0 0
0 1 0
0 0 1
[m,n;o,p]
!
m1
¸
[]
m n
o p
LU m1,lower,upper,perm
¸
Done
lower
¸






1 0
m
o
1
upper
¸






o p
0 n
ì
m
ø
p
o
perm
¸
[]
0 1
1 0