858
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:
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
Summary of Contents for Voyage 200
Page 36: ...Getting Started 36 D B D B Press Result ...
Page 45: ...Getting Started 45 3 0 D B D D B D Press Result ...
Page 46: ...Getting Started 46 D 2 0 0 2 D B Scroll down to October and press Press Result ...
Page 60: ...Getting Started 60 B D Press Result ...
Page 139: ...Previews 139 8 Complete the operation Press 2 d Steps and keystrokes Display 5 f 2 ...
Page 453: ...Differential Equation Graphing 453 ...
Page 468: ...Tables 468 ...
Page 777: ...Activities 777 ...