I am trying to figure out what it is I don't understand here.

I am following <http://www.scipy.org/Cookbook/FittingData> and trying to fit a sine wave. The real problem is satellite magnetometer data which makes a nice sine wave on a spinning spacecraft. I created a dataset then am trying to fit it to recover the inputs.

Here is my code:

```
import numpy as np
from scipy import optimize

from scipy.optimize import curve_fit, leastsq

import matplotlib.pyplot as plt

class Parameter:
    def __init__(self, value):
            self.value = value

    def set(self, value):
            self.value = value

    def __call__(self):
            return self.value

def fit(function, parameters, y, x = None):
    def f(params):
        i = 0
        for p in parameters:
            p.set(params[i])
            i += 1
        return y - function(x)

    if x is None: x = np.arange(y.shape[0])
    p = [param() for param in parameters]
    return optimize.leastsq(f, p, full_output=True, ftol=1e-6, xtol=1e-6)

# generate a perfect data set (my real data have tiny error)
def mysine(x, a1, a2, a3):
    return a1 * np.sin(a2 * x + a3)

xReal = np.arange(500)/10.
a1 = 200.
a2 = 2*np.pi/10.5  # omega, 10.5 is the period
a3 = np.deg2rad(10.) # 10 degree phase offset
yReal = mysine(xReal, a1, a2, a3)

# plot the real data
plt.figure(figsize=(15,5))
plt.plot(xReal, yReal, 'r', label='Real Values')

# giving initial parameters
amplitude = Parameter(175.)
frequency = Parameter(2*np.pi/8.)
phase = Parameter(0.0)

# define your function:
def f(x): return amplitude() * np.sin(frequency() * x + phase())

# fit! (given that data is an array with the data to fit)
out = fit(f, [amplitude, frequency, phase], yReal, xReal)
period = 2*np.pi/frequency()
print amplitude(), period, np.rad2deg(phase())

xx = np.linspace(0, np.max(xReal), 50)
plt.plot( xx, f(xx) , label='fit')
plt.legend(shadow=True, fancybox=True)

```

Which makes this plot:
![enter image description here](https://i.stack.imgur.com/91cGN.png)

The recovered fit parameters of `[44.2434221897 8.094832581 -61.6204033699]` have no resemblance to what I started with.

Any thoughts on what I am not understanding or doing wrong?

```
scipy.__version__
'0.10.1'

```

---

Edit:
Fixing one parameter was suggested. In the example above fixing the amplitude to `np.histogram(yReal)[1][-1]` still produces unacceptable output. Fits: `[175.0 8.31681375217 6.0]` Should I try a different fitting method? Suggestions on which?

![enter image description here](https://i.stack.imgur.com/KFEwf.png)