import matrix
import LCD
import math
import random


# approximate sin(t) = a*t^2 + b*t + c over 0<t<1.5

t = matrix.linspace(0,0.1,1.59)
t = matrix.transpose([t])
n = len(t)

Y = matrix.zeros(n, 1)
for i in range(0,n):
    Y[i][0] = math.sin(t[i][0])
    
t2 = matrix.power(t,2)
t0 = matrix.power(t,0)
B = matrix.append(t2,t)
B = matrix.append(t,t0)

Bt = matrix.transpose(B)
BtB = matrix.mult(Bt,B)
BtBi = matrix.inv(BtB)
BtY = matrix.mult(Bt,Y)
A = matrix.mult(BtBi,BtY)
matrix.display(A)

Navy = LCD.RGB(0,0,5)
Pink = LCD.RGB(150,50,50)
White = LCD.RGB(150,150,150)
LtBlue = LCD.RGB(50,50,150)

LCD.Init()
LCD.Clear(Navy)

Yf = matrix.mult(B, A)
Data = matrix.append(Y, Yf)

LCD.Plot(t,Data)