TI-86:
Angle Between Vectors, Vandermonde Matrix, Least Squares Algorithm,
Chebyshev Polynomials (1st Kind)
The
TI-86 has one of the best interfaces for a graphing calculator I ever
had the joy to work with. The TI-86 is an update of the TI-85. Here
are some programs for the TI-86.
Angle
Between Vectors
The
program vangle calculates the angle between two angles. The angle is
calculated in degrees.
TI-86
Program vangle
(75 bytes)
Prompt
V1
Prompt
V2
Disp
cos⁻¹ (dot(V1,V2)/(norm V1*V2))
Example:
[2, -3, 4] and [8, 1, -2]
Angle:
83.5823268926°
Vandermonde
Matrix
The
program vander creates a matrix based on a list of coefficients.
Example:
{x, y, z} produces the matrix
[
[x^0, x^1, x^2], [y^0, y^1, y^2], [z^0, z^1, z^2] ]
TI-86
Program vander
(125
bytes)
Input
“List: “, L1
dimL
L1 → N
{N,
N} → dimL MA
For(R,
1, N)
For(C,
1, N)
L1(R)^(C-1)
→ MA(R,C)
End
End
Disp
“MA=”
Pause
MA
Example:
{2, 4, 7}
Result:
[ [1, 2, 4], [1, 4, 16], [1, 7, 49] ]
Least
Square Algorithm
The
program LSQ taxes the matrices X and Y (Y is a one-column matrix),
and calculates
(X^T
X)^-1 (X^T Y).
LSQ
is used to fit statistical fits with least squares.
TI-86
Program LSQ
(118
bytes)
Disp
“Least Squares”
Input
“Matrix X: “,MX
Input
“Matrix Y: “,MY
(MX^T
* MX)^-1 * (MX^T * MY) → ML
Disp
“ML= “
Pause
ML
Example:
MX
= [ [1, 3, 2.0], [1, 4, 2.3], [1, 5, 2.6], [1, 8, 2.9] ]
MY
= [ [1.6], [1.8], [2.1], [2.3] ]
Results:
ML
= [ [-0.14444444449], [-1.666666667E-2], [0.88888888889] ]
Chebyshev
Polynomials (1st Kind)
The
program tcheby calculates the numerical value of the Chebyshev
polynomials of the 1st
Kind given its point, X, and the order, N.
TI-86
Program tcheby
(127
bytes)
Prompt
X,N
If
X>1 : Goto A
If
X<-1 :="" b="" goto="" span="">
cos(N
* cos⁻¹ X) → A
Goto
C
Lbl
A
cosh(N
* cosh⁻¹ X) → A
Goto
C
Lbl
B
(-1)^N
* cosh(N * cosh⁻¹ X) → A
Lbl
C
Disp
A
Example:
X
= -2.5, N = 4, Result: 263.5
X
= 0.5, N = 4, Result: -0.5
X
= 2.5, N = 4, Result: 263.5
Eddie
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original content copyright, © 2011-2019. Edward Shore.
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