Owner's Manual

854 Appendix A: Functions and Instructions
PxlVert CATALOG
PxlVert col [, drawMode ]
Draws a vertical line down the screen at pixel
position
col .
If
drawMode = 1, draws the line (default).
If
drawMode = 0, turns off the line.
If
drawMode = -1, turns a line that is on to off or
off to on (inverts pixels along the line).
Note: Regraphing erases all drawn items. See
also LineVert.
PxlVert 50,1 ¸
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