#!/usr/bin/env python

# ----------------------------------------------------------------------------------- #
# 
# Python/ROOT macro for discussing size of errors in measurement of g with pendulum.
# 
# For more information on error propagation, see:
#     R. J. Barlow: page 48-61 
#     P. R. Bevington: page 36-48
# 
# Author: Troels C. Petersen (NBI)
# Email:  petersen@nbi.dk
# Date:   13th of November 2016
# 
# ----------------------------------------------------------------------------------- #



# ----------------------------------------------------------------------------------- #
# 
# This exercise is primarily analytical (one of the few/only), and concerns itself
# with planning an experiment measuring the gravitational acceleration, g.
# 
# 1) A simple pendulum of length L = 14m is planned to be used for a measurement of g.
#    Given that g = 4pi^2 L T^-2 is around 10, what is the expected period T roughly?
# 
# 2) Try to evaluate how accurately you would be able to measure the pendulum length L?
#    Remember that you will have both a 14+m measuring tape and a laser distance
#    measurer (LDS) nominally precise to about 1mm, and that you will have several
#    repeated measurements from all members of the team, but also that some/most of
#    of the errors will not be statistical (and hence not reduce with repeated
#    measurements) and also that the pendulum length probably is a combination of
#    several length measurements.
# 
# 3) Given your estimate in 2), calculate how accurately you will have to measure
#    the period T, if L and T are to contribute equally to the uncertainty on g.
# 
# The outline code below is only in case you want to verify your above calculations,
# and/or see if you can program this up yourself from (almost) scratch, and not required.
# 
# ----------------------------------------------------------------------------------- #

from ROOT import *
from math import sqrt, atan, sin, cos


# Define the squaring function:
def sqr( a ) : return a*a


#---------------------------------------------------------------------------------- 
# Error propagation
#---------------------------------------------------------------------------------- 

# Setting what to be shown in statistics box:
gStyle.SetOptStat(1110)   # Print for stat: Entries, Mean, and RMS
gStyle.SetOptFit(1111)    # Print for fit:  Everything!

# Set parameters:
Nexp = 10000           # Number of experiments
pi = TMath.Pi()
SavePlots = False
r = TRandom3()

# Define histograms:
Hist_g_errorL = TH1F( "Hist_g_errorL", "Hist_g_errorL", 200, 9.0, 11.0)
Hist_g_errorT = TH1F( "Hist_g_errorT", "Hist_g_errorT", 200, 9.0, 11.0)


#----------------------------------------------------------------------------------
# Define parameters for two random numbers (Gaussianly distributed):
#----------------------------------------------------------------------------------

L  = 14.000   # Pendulum length
eL =  0.0     # Error on L         - estimate this yourself
T  =  0.0     # Pendulum period    - calculate yourself
eT =  0.0     # Error on T         - calculate yourself



#----------------------------------------------------------------------------------
# Loop over process:
#----------------------------------------------------------------------------------

for i in range( Nexp ) : 
    continue


#----------------------------------------------------------------------------------
# Plot in a new window:
#----------------------------------------------------------------------------------
c1 = TCanvas("c1", "", 100, 20, 1000, 600)

Hist_g_errorL.Draw()
Hist_g_errorT.Draw("same")

c1.Update()
if (SavePlots) : c1.SaveAs("PendulumErrorProb.pdf")

raw_input( ' ... Press enter to exit ... ' )


#---------------------------------------------------------------------------------- 
# 
# 
#----------------------------------------------------------------------------------