%pylab inline
import pandas as pd
import scipy.optimize as op

Populating the interactive namespace from numpy and matplotlib

a = pd.read_csv("Vibrationbeam.csv")
a['L'] = a['L']/100
a['L_unc'] = 0.01
a['F_unc'] = 0.1
a

a = a.loc[delete(a.index,[1,5])]
a

plot(a['L'],a['F'],'o')

[<matplotlib.lines.Line2D at 0x26899b154e0>]

errorbar(a['L'],a['F'],a['F_unc'],fmt='r.')
ylabel("frequency (Hz)")
xlabel("length (m)")

<matplotlib.text.Text at 0x26899a8f9b0>

x = a['L']
y = a['F']
y_unc = a['F_unc']

def f(x,m,b):
    return m*x + b

# do the fit

# method 0: no uncertainty included
##ans = op.curve_fit(f,x,y,p0=[1.0,1.0])

# method 1: use uncertainty as relative weight
ans = op.curve_fit(f,x,y,p0=[1.0,1.0], sigma=y_unc)

# method 2 (preferred): use uncertainty as absolute sigma
ans = op.curve_fit(f,x,y,p0=[1.0,1.0], sigma=y_unc, absolute_sigma=True)


# interpret results of fit
m,b = ans[0]
m_unc,b_unc = sqrt(diag(ans[1]))

print("m = %.2f +/- %.2f"%(m,m_unc))
print("b = %.2f +/- %.2f"%(b,b_unc))

# plot results
errorbar(x,y,y_unc, fmt='r.', label="data")
xx = linspace(0.15,.26)
plot(xx,f(xx,m,b),label="fit")
legend(loc="upper right")
xlabel("length (m)")
ylabel("frequency (Hz)")


# plot residuals (obs - fit results)
figure()
errorbar(x, y-f(x,m,b), y_unc, fmt="r.")
hlines(0.1,0.15,.26)
xlabel("length (m)")
ylabel("residual (y - fit)")
ylim(-100,150)

m = -652.00 +/- 0.61
b = 197.96 +/- 0.12

(-100, 150)

x = a['L']
y = a['F']
y_unc = a['F_unc']

def f(x,m,b):
    return m*x**b

# do the fit

# method 0: no uncertainty included
##ans = op.curve_fit(f,x,y,p0=[1.0,1.0])

# method 1: use uncertainty as relative weight
ans = op.curve_fit(f,x,y,p0=[1.0,1.0], sigma=y_unc)

# method 2 (preferred): use uncertainty as absolute sigma
ans = op.curve_fit(f,x,y,p0=[1.0,1.0], sigma=y_unc, absolute_sigma=True)


# interpret results of fit
m,b = ans[0]
m_unc,b_unc = sqrt(diag(ans[1]))

print("m = %.2e +/- %.2e"%(m,m_unc))
print("b = %.2e +/- %.2e"%(b,b_unc))

# plot results
errorbar(x,y,y_unc, fmt='r.', label="data")
xx = linspace(0.15,.26)
plot(xx,f(xx,m,b),label="fit")
legend(loc="upper right")
xlabel("length (m)")
ylabel("frequency (Hz)")


# plot residuals (obs - fit results)
figure()
errorbar(x, y-f(x,m,b), y_unc, fmt="r.")
hlines(0.1,0.15,.26)
xlabel("length (m)")
ylabel("residual (y - fit)")
ylim(-100,150)

m = 2.59e+00 +/- 9.21e-03
b = -1.98e+00 +/- 2.04e-03

(-100, 150)

	L	F	L_unc	F_unc
0	0.1558	102.0	0.01	0.1
1	0.1558	646.5	0.01	0.1
2	0.1558	103.8	0.01	0.1
3	0.1558	103.0	0.01	0.1
4	0.1558	104.0	0.01	0.1
5	0.1650	53.0	0.01	0.1
6	0.1650	91.0	0.01	0.1
7	0.1650	91.0	0.01	0.1
8	0.1650	91.0	0.01	0.1
9	0.1650	91.0	0.01	0.1
10	0.1745	81.5	0.01	0.1
11	0.1745	82.0	0.01	0.1
12	0.1745	82.0	0.01	0.1
13	0.1745	82.0	0.01	0.1
14	0.1745	81.5	0.01	0.1
15	0.1845	73.5	0.01	0.1
16	0.1845	73.5	0.01	0.1
17	0.1845	73.5	0.01	0.1
18	0.1845	73.5	0.01	0.1
19	0.1845	73.5	0.01	0.1
20	0.2162	53.5	0.01	0.1
21	0.2162	53.5	0.01	0.1
22	0.2162	53.5	0.01	0.1
23	0.2162	53.0	0.01	0.1
24	0.2162	53.5	0.01	0.1
25	0.2455	42.0	0.01	0.1
26	0.2455	42.0	0.01	0.1
27	0.2455	42.0	0.01	0.1
28	0.2455	42.0	0.01	0.1
29	0.2455	42.5	0.01	0.1

	L	F	L_unc	F_unc
0	0.1558	102.0	0.01	0.1
2	0.1558	103.8	0.01	0.1
3	0.1558	103.0	0.01	0.1
4	0.1558	104.0	0.01	0.1
6	0.1650	91.0	0.01	0.1
7	0.1650	91.0	0.01	0.1
8	0.1650	91.0	0.01	0.1
9	0.1650	91.0	0.01	0.1
10	0.1745	81.5	0.01	0.1
11	0.1745	82.0	0.01	0.1
12	0.1745	82.0	0.01	0.1
13	0.1745	82.0	0.01	0.1
14	0.1745	81.5	0.01	0.1
15	0.1845	73.5	0.01	0.1
16	0.1845	73.5	0.01	0.1
17	0.1845	73.5	0.01	0.1
18	0.1845	73.5	0.01	0.1
19	0.1845	73.5	0.01	0.1
20	0.2162	53.5	0.01	0.1
21	0.2162	53.5	0.01	0.1
22	0.2162	53.5	0.01	0.1
23	0.2162	53.0	0.01	0.1
24	0.2162	53.5	0.01	0.1
25	0.2455	42.0	0.01	0.1
26	0.2455	42.0	0.01	0.1
27	0.2455	42.0	0.01	0.1
28	0.2455	42.0	0.01	0.1
29	0.2455	42.5	0.01	0.1