Texas Instruments TI-89 Voyage 200, Руководство пользователя

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Appendix A: Functions and Instructions 859
QR
MATH/Matrix menu
QR
matrix
,
qMatName
,
rMatName [
,
tol ]
Calculates the Householder QR factorization of a
real or complex
matrix
. The resulting Q and R
matrices are stored to the specified
MatNames
.
The Q matrix is unitary. The R matrix is upper
triangular.
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 floating-point number (9.) in
m1
causes
results to be calculated in floating-point form.
[1,2,3;4,5,6;7,8,9.]
!
m1
¸






1 2 3
4 5 6
7 8 9.
QR m1,qm,rm
¸
Done
qm
¸






.123… .904… .408…
.492… .301…
ë
.816…
.861…
ë
.301… .408…
rm
¸






8.124… 9.601… 11.078…
0. .904… 1.809…
0. 0. 0.
[m,n;o,p]
!
m1
¸
[ ]
m n
o p
The QR factorization is computed numerically
using Householder transformations. The symbolic
solution is computed using Gram-Schmidt. The
columns in
qMatName are the orthonormal basis
vectors that span the space defined by
matrix
.
QR m1,qm,rm
¸
Done
qm
¸






m
m
2
+ o
2
ë
sign(m
ø
p
ì
n
ø
o)
ø
o
m
2
+ o
2
o
m
2
+ o
2
m
ø
sign(m
ø
p
ì
n
ø
o)
m
2
+ o
2
rm
¸






m
2
+ o
2
m
ø
n+o
ø
p
m
2
+ o
2
0
|
m
ø
p
ì
n
ø
o
|
m
2
+ o
2
QuadReg
MATH/Statistics/Regressions menu
QuadReg
list1
,
list2
[
, [
list3
] [ ,
list4
,
list5
]
]
Calculates the quadratic polynomial regression
and updates the system statistics variables.
All the lists must have equal dimensions except
for
list5
.
list1
represents xlist.
list2
represents ylist.
list3
represents frequency.
list4
represents category codes.
list5
represents category include list.
In function graphing mode:
{0,1,2,3,4,5,6,7}
!
L1
¸
{1 2 3
...
}
{4,3,1,1,2,2,3,3}
!
L2
¸
{4 3 1
...
}
QuadReg L1,L2
¸
Done
ShowStat
¸