I have data
data = {{5, 580}, {10, 570}, {15, 565}, {20, 562}, {25, 560}};
I have fitting function
A[x_] := a*Sqrt[1 - x/b]
I expect value a = 600, b = 300. Using
FindFit[data, A[x], {a, b}, x]
I instead error message:
"indFit::nrlnum: "The function value {-580.`+2.` I,-570.`+3.` I,-565.`+3.7416573867739413` I,-562.`+4.358898943540674` I,-560.`+4.898979485566356` I} is not a list of real numbers with dimensions {5} at {a,b} = {1.`,1.`}""
How to use FindIt to get a and b?
Transforming the data can be helpful, e.g.
dt = {#1, Log@#2} & @@@ data
nlm = NonlinearModelFit[dt, c + Log[b - x]/2, {{c, 10}, {b, 30}}, x]
dtf = {#1, #2^2} & @@@ data
{a0, b0} = {Exp[c] Sqrt[b], b} /. nlm["BestFitParameters"]
lm = LinearModelFit[dtf, {1, x}, x]
{a1, b1} = {Sqrt@#1, -#1/#2} & @@ lm["BestFitParameters"]
Legended[Show[
Plot[{Exp[nlm[x]], Sqrt[lm[x]]}, {x, 5, 25},
PlotStyle -> {Blue, {Red, Dashed}}], ListPlot[data],
PlotRange -> {540, 600}],
Placed[LineLegend[{Blue, {Red, Dashed}}, {"Log transform",
"Squaring"}], {0.5, 0.8}]]
TableForm[{{a0, b0}, {a1, b1}},
TableHeadings -> {{"Log Transform", "Squaring"}, {"a", "b"}}]
FindFit[data,A[x],{{a,600},{b,300}},x]will specify starting points. Just FYI though, I'd probably defineAasfitfun[x_,a_,b_]:=...and doFindFit[data, fitfun[x,a,b],{{a,600},{b,300}},x]. Better to avoid capital letters in your defs. to avoid clashing with MMA functions, and prevent your function from messing up ifa,bend up with global defs. I'd also look intoNonlinearModelFit$\endgroup$FindFittries values that make theSqrtcomplex. Restrictingbfixes that :FindFit[data, {A[x], b > 25}, {a, b}, x]$\endgroup$