Re: rearranging equations
- To: mathgroup at smc.vnet.net
- Subject: [mg22453] Re: [mg22505] rearranging equations
- From: BobHanlon at aol.com
- Date: Wed, 8 Mar 2000 02:21:52 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
f[x_] := 7 + 3x + 2x^2;
data = Sort[Table[{x = 10*Random[], f[x]}, {6}]];
Clear[x];
As expected, the quadratic fit to the data arrives at the quadratic
definition used to generate the data
y == Fit[data, {1, x, x^2}, x]
y == 6.999999999999996 + 3.0000000000000133*x + 2.*x^2
Inverting the quadratic equation
(x == (x /. #)) & /@ Solve[%, x] // Simplify
{x == -0.7500000000000033 - 0.7071067811865476*
Sqrt[-5.874999999999986 + 1.*y],
x == -0.7500000000000033 + 0.7071067811865476*
Sqrt[-5.874999999999986 + 1.*y]}
Note that x is not quadratic in y. However, the quadratic terms of the series
expansion are
Series[#[[2]], {y, 0, 2}] & /@ % // Normal
{-0.7500000000000033 - 1.713913650100259*I +
0.14586499149789472*I*y + 0.006207020914804047*I*y^2,
-0.7500000000000033 + 1.713913650100259*I -
0.14586499149789472*I*y - 0.006207020914804047*I*y^2}
Extracting the coefficients
CoefficientList[#, y] & /@ %
{{-0.7500000000000033 - 1.713913650100259*I,
0.14586499149789472*I, 0.006207020914804047*I},
{-0.7500000000000033 + 1.713913650100259*I,
-0.14586499149789472*I, -0.006207020914804047*I}}
Bob Hanlon
In a message dated 3/4/2000 3:49:44 AM, cdeacon at .physics.mun.ca writes:
>Suppose I take some data and use Fit or Regress to obtain values for
>a,b and in the equation y=a+bx+cx^2.
>
>Is there a simple Mathematica function that will let me rewrite the
>equation as x=A+By+Cy^2 and obtain values for A, B and C?
>