814 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
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