832 Appendix A: Functions and Instructions
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:
5Eë 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(møpì nøo)øo
m
2
+o
2
o
m
2
+o
2
møsign(møpì nøo)
m
2
+o
2
rm ¸
m
2
+o
2
møn+oøp
m
2
+o
2
0
|
møpì nøo
|
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
¸
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