如何拟合余弦函数? [英] How can I fit a cosine function?

问题描述

我写了一个python函数来获取以下余弦函数的参数:

I wrote a python function to get the parameters of the following cosine function:

param = Parameters()    
param.add( 'amp', value = amp_guess, min = 0.1 * amp_guess, max = amp_guess )

param.add( 'off', value = off_guess, min = -10, max = 10 )

param.add( 'shift', value = shift_guess[0], min = 0, max = 2 * np.pi, )

fit_values = minimize( self.residual, param, args = ( azi_unique, los_unique ) )

def residual( self, param, azi, data ):
        """
        Parameters
        ----------

        Returns
        -------
        """
        amp = param['amp'].value
        off = param['off'].value
        shift = param['shift'].value
        model = off + amp * np.cos( azi - shift )
        return model - data

在Matlab中如何获取余弦函数的幅度，偏移和位移?

In Matlab how can get the amplitude, offset and shift of the cosine function?

推荐答案

MATLAB在优化工具箱中具有一个名为lsqcurvefit的函数:

MATLAB has a function called lsqcurvefit in the optimisation toolbox:

lsqcurvefit(fun,X0,xdata,ydata,lbound,ubound);

其中，fun是要拟合的函数，x0是初始参数猜测值，xdata和ydata是不言自明的，lbound和ubound是参数的上下限.因此，例如，您可能具有以下功能:

where fun is the function to fit, x0 is the initial parameter guess, xdata and ydata are self-explanatory, and lbound and ubound are the lower and upper bounds to the parameters. So, for instance, you might have a function:

% x(1) = amp
% x(2) = shift
% x(3) = offset
% note cosd instead of cos, because your data appears to be in degrees
cosfit = @(x,xdata) x(1) .* cosd(xdata - x(2)) + x(3);

然后您将调用lsqcurvefit函数，如下所示:

You would then call the lsqcurvefit function as follows:

guess = [7,150,0.5];
lbound = [-10,0,-10]
ubound = [10,360,10]
fit_values = lsqcurvefit(cosfit,guess,azi_unique,los_unique,lbound,ubound);

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