3617.sagews

import numpy                        #import to use numpy package
from numpy import *                #import everything in numpy

#input data :
#        [Time              (t)][3   ,5   ,7   ,8   ,9  ] (sec)
#        [Signal  Strength  (m)][400 ,500 ,550 ,600 ,730] (millivolts)
#approximate with : m=f(t)=c+b*sin(t)+a*tan(t)

A0 = numpy.ones((1,5))              #create matrix (1x5) of scalar 1
A3 = numpy.matrix([3,5,7,8,9],dtype=float)  
					      #create data matrix t(1x5)
A1=sin(A3)                             #matrix sin(t)(1x5)
A2=tan(A3)                             #matrix tan(t) (1x5)
A=concatenate((A0,A1,A2))          #combine A0, A1, A2 into A
Y = matrix([400,500,550,600,730],dtype=float)      
					       #create data matrix Y(1x5)
Y=Y.T                                   #transpose of Y
X=linalg.inv(A*A.T)*A*Y       #calculate suitable set of [c,b,a]
print "Coefficients = "
print X
plot(X[0,0]+X[1,0]*sin(x)+X[2,0]*tan(x), (x,0,10)) + list_plot(zip(A3.T,Y)) 
			        #plot the approximate curve and data points