COSC 311   Information on Sage   -- curve fitting

sagemath.org: Online version and downloadable version

http://doc.sagemath.org/html/en/tutorial/index.html:   Sage tutorial 

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Documentation/examples for curve fitting (find_fit):
http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html:
      
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initialize variable with data values:
data=[ (10, 100), (20, 205), (30, 199), (40, 400), (50, 500), (60, 600) ]

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create variables for use in fitting:
var('a, b, c, x')

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create models (function) to use for fitting
lin_model(x) = a * x + b

quad_model(x) = a * x^2 + b * x + c

log_model(x) = a * x * log(x) + b * x + c

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find best fit
find_fit(data, lin_model)

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Documentation/examples for plotting:
http://doc.sagemath.org/html/en/reference/plotting/sage/plot/plot.html#sage.plot.plot.plot  
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plot one of the curves:
plot(10.24*x - 24.6, 0, 600, color='red')

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Add to plot:
P = plot(10.24*x - 24.6, 0, 600, color='red')
P = P + plot(.071 * x^2 + 5.26 * x + 41.9, 0, 600, color='black')
P

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plot data points:
list_plot( data, color='blue' )

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Draw points and fitted curves:

P = list_plot( data, color='blue' )
P += plot(.071 * x^2 + 5.26 * x + 41.9, 0, 60, color='black')
P += plot(10.24*x - 24.6, 0, 60, color='red')
P