use curveFit.frink

/** This performs tests on the file curveFit.frink which tries to fit data
    to linear and quadratic curves.
*/

    
// Linear data
data = [ [0, 1], [1, 3], [2, 5] ]
printFit[data]

// Test to verify that units of measure can be fitted correctly.
// THIS EXAMPLE IS ACTUALLY AMAZING!
// It derives the gravitic equation given just 3 points on a curve of
// time and height (and none of those points are forced to be zero, nor are
// the initial height, nor the initial velocity.)  It derives the initial
// velocity at t=0,  the acceleration of gravity, and the initial height at t=0
// given 3 points on the trajectory of an object.
// This is incredibly impressive.
// To generate points, see the Frink solver at:
//   tinyurl.com/2p8pntcd
// This represents the [time, height] data of a projectile being launched from
// an initial height of 2 meters at t=0 s and an initial upward velocity of
// 40 m/s at t = 0 s:
data = [ [1 s, 32.19335 m], [2 s, 42.7734 m], [4.1 s, 1.1502135 m] ]
printFit[data]

// This is the above but with heights rounded to the nearest 0.1 m.
// data = [ [1 s, 32.2 m], [2 s, 42.8 m], [4.1 s, 1.2 m] ]
// printFit[data]


// This demonstrates a purely symbolic result!
symbolicMode[true]
data = [ [x1, y1], [x2, y2], [x3, y3] ]
printFit[data]

printFit[data] :=
{
   println["\n\nFor data: "]
   println[formatTableBoxed[data]]
   println["linear: " + inputForm[linearFit[data]]]
   f = linearFitFunction[data]
   println["\nlinear function: " + inputForm[f]]
   println["\nquadratic: " + inputForm[quadraticFit[data]]]
   f = quadraticFitFunction[data]
   println["\nquadratic function: " + inputForm[f]]
}