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LU
MATH/Matrix menu
matrix
lMatName
LU
,
Calculates the Doolittle LU (lower-upper)
decomposition of a real or complex
lower triangular matrix is stored in
upper triangular matrix in
permutation matrix (which describes the row
swaps done during the calculation) in
lMatName
Optionally, any matrix element is treated as zero
if its absolute value is less than
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,
If you use ¥ ¸ or set the mode to
Exact/Approx=APPROXIMATE
are done using floating-point arithmetic.
If
tol
tolerance is calculated as:
ë 14 ù max(dim(
5
E
ù rowNorm(
The
LU
pivoting with row interchanges.
mat4 4 4 4 data
MATH/List menu
mat4 4 4 4 data
mat,data
Converts a matrix to data.
Each argument
be individually omitted. If
default is 1. If
row2
is omitted, the default is "max column."
840
uMatName
pMatName
,
,
uMatName
ù
=
uMatName
pMatName
is ignored.
tol
is omitted or not used, the default
matrix
))
matrix
)
factorization algorithm uses partial
[,row1][,col1][,row2][,col2]
[,row1][,col1][,row2][,col2]
row1
is omitted the default is 1. If
col1
is omitted, the default is "max row." If
[6,12,18;5,14,31;3,8,18] ! m1 ¸
tol
[
]
,
. The
matrix
, the
lMatName
, and the
LU m1,lower,upper,perm ¸
.
pMatName
ù
matrix
lower ¸
. This tolerance
tol
upper ¸
perm ¸
, computations
[m,n;o,p] ! m1 ¸
LU m1,lower,upper,perm ¸
lower ¸
upper ¸
perm ¸
mat 4 data,m1,d1,1,,,1 ¸
Done
can
is omitted the
col2
Appendix A: Functions and Instructions
6 12 18
5 14 31
3 8
18
Done
1
0
0
5/6 1
0
1/2 1/2 1
6 12 18
0 4
16
0 0
1
1 0 0
0 1 0
0 0 1
[ ]
m n
o p
Done
1 0
m
o 1
o p
m ø p
0 n ì
o
[ ]
0 1
1 0
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