univariate_tools

Tools to fit, interpolate, and synthesize univariate data.

Installation

Method 1 - Directly from Github

pip install git+https://github.com/sandersa-nist/univariate_tools.git

Method 2 - Clone then Install

1. Use your favorite way to clone the repo or download the zip file and extract it.
2. pip install to that location (note pip expects a unix style string 'C:/univariate_tools/')

pip install <path to top folder>

Use case

Have you ever wanted to fit a really weird function of one variable? How about make a complicated synthetic time-domain signal? Have calibration data on an irregular grid and you need to interpolate? Then univariate_tools is for you! FunctionalModel is a blend of sympy and numpy functionality that lets the user do all kinds of math with functions and then fit data.

from univariate_tools import *
# lets make a composite function
line=FunctionalModel(parameters=["m","b"],variables="x",equation="m*x+b")
gaussian=FunctionalModel(parameters="alpha x0 delta",variables="x",equation="alpha*exp(-1*(x-x0)^2/(2*delta**2))")
gauss_line=line+gaussian
x_data=np.linspace(-1,1,1000)
plt.plot(x_data,gauss_line(alpha=1,x0=.1,delta=.1,m=1.2,b=.1,x=x_data))
plt.title("${0}$".format(gauss_line.to_latex()))

Workflow

Calculating Data

1. To calculate a function, first create a FunctionalModel. There should be a set of parameters, one variable, and an equation.

model = FunctionalModel(parameters=["a","b","c"],variables="x",equation="a*x**2+b*x+c")

2. Set the parameters

model.set_parameters({"a":1.25,"b":3,"c":-.4})

3. Calculate the result with an input of x

x_data = np.linspace(-10,10,1000)
y_data = model(x_data)
plt.plot(x_data,y_data)

Fitting Data

1. To fit data, start with defining a FunctionalModel.There should be a set of parameters, one variable, and an equation.

model = FunctionalModel(parameters=["m","b"],variables="x",equation="m*x+b")

2. Use model.fit_data, for more complex fits provide an initial guess

x_data = np.linspace(-10,10,1000)
y_data = 2.12*x_data+3.11
model.fit_data(x_data = x_data,y_data = y_data,initial_guess = {"m":2,"b":3})

3. The fit parameters are now in the parameter_values

model.parameter_values

{'m': 2.12, 'b': 3.11}

Simulate Data

1. Specify the parameters, variable, equation, noise characteristics, x_data

simulated_data = DataSimulator(**{"parameters":["m","b"],
                   "variables":"x",
                   "equation":"m*x+b",
                   "parameter_values":{"m":2,"b":1},
                   "output_noise_type":"normal",
                   "output_noise_width":1,
                   "output_noise_center":0,
                   "output_noise_amplitude":1.,
                   "random_seed":42,
                   "x":np.linspace(-10,10,100)})

2. Now the simulated data is in the data attribute and the x_data is in the x attribute

plt.plot(simulated_data.x,simulated_data.data)

Interpolate Data

This is a resampling of a data stream to a new x set of points, the methods are lowess, loess, 1d, gpr and spline. Each one of these methods has a different set of options that can be passed with keywords

"""
    *********************************************************************************************
    refs: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html, options for kind are
    ‘linear’, ‘nearest’, ‘nearest-up’, ‘zero’, ‘slinear’, 
    ‘quadratic’, ‘cubic’, ‘previous’, or ‘next’. ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’
    ****************************************************************************************
    https://www.statsmodels.org/dev/generated/statsmodels.nonparametric.smoothers_lowess.lowess.html
    ***********************************************************************************************
    https://scikit-learn.org/stable/modules/gaussian_process.html
    ***************************************************************
    https://docs.scipy.org/doc/scipy/tutorial/interpolate/smoothing_splines.html
    ********************************************************************************"""

1. provide the data as an x_data and y_data array (need to be the same size) and decide the new_x_data. There are parametric and non-parametric methods

    x_data = np.linspace(-6,6,500)
    signal = np.sin(x_data)+np.random.normal(scale=.5,size=len(x_data))
    plt.plot(x_data,signal,".",label="Original Data")
    for interp_type in ["lowess","loess", "1d", "gpr","spline"]:
        new_x = np.linspace(-2,2,500)
        interp_data = interpolate_data(x_data=x_data,y_data=signal,new_x_data=new_x,method=interp_type)
        plt.plot(new_x,interp_data,label=interp_type)
    plt.legend()
    plt.show()
    

Reverse Regressor

This is used when you have a monotonic function that represents a calibration and you have new y points. It has similar methods and options as the interpolate data function.

x_data = np.linspace(-6,6,200)
signal = 2*x_data+1+np.random.normal(scale=.2,size=len(x_data))
plt.plot(x_data,signal,".",label="Original Data",alpha=.3)

for interp_type in ["lowess","loess", "1d", "gpr","spline"]:
    try:
        new_y = np.linspace(-2,5,10)
        new_x = reverse_regressor(x_data=x_data,y_data=signal,new_y_data=new_y,method=interp_type)
        print(f"{interp_type}:{new_x},{new_y}")
        plt.plot(new_x,new_y,label=interp_type,linewidth=2,linestyle="dashed")
    except Exception as e:
        print(e)
plt.legend()
plt.show() 

Example

An example of creating a functional model, fitting data, creating composite models and simulating data.

API Documentation

The API Documentation links to the init.py file and has the primary submodules linked.

Contact

Aric Sanders [email protected]

NIST Disclaimer

Certain commercial equipment, instruments, or materials (or suppliers, or software, ...) are identified in this repository to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.