Owner's Manual

836 Appendix A: Functions and Instructions
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
: Rand(6)! die1
: Rand(6)! die2
: If die1=6 and die2=6
: Goto End
: i+1! i
:EndLoop
:Lbl End
:Disp "The number of rolls 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:
5Eë 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
møp
o
perm ¸
[]
0 1
1 0