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Appendix A: Functions and Instructions 841
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
mat4
44
4data MATH/List menu
mat4
44
4data
mat,data
[,row1][,col1][,row2][,col2]
Converts a matrix to data.
Each argument
[,row1][,col1][,row2][,col2] can
be individually omitted. If
row1
is omitted the
default is 1. If
col1 is omitted the default is 1. If
row2 is omitted, the default is “max row.” If col2
is omitted, the default is “max column.”
mat4data,m1,d1,1,,,1 ¸
Done