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Roots of a function: Difference between revisions
+AutoHotkey by Laszlo
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2nd root found at x = 2.1844288770224760190097e 0 (Approximately)
3rd root found at x = 0.0000000000000000000000e 0 (Exactly)</pre>
=={{header|AutoHotkey}}==
Poly(x) is a test function of one variable. <br>We search for its roots.
roots() searches for intervals within given limits,
shifted by a given “step”, where our function has different<br> signs at the endpoints. Having found such an interval, the root() function searches for<br> a value where our
function is 0, within a given tolerance. <br>
It also sets ErrorLevel to info about the root found.<br>
ahk
[http://www.autohotkey.com/forum/viewtopic.php?t=44657&postdays=0&postorder=asc&start=139 discussion]
<lang autohotkey>MsgBox % roots("poly", -0.99, 2, 0.1, 1.0e-5)
MsgBox % roots("poly", -1, 3, 0.1, 1.0e-5)
roots(f,x1,x2,step,tol) { ; search for roots in intervals of length "step", within tolerance "tol"
x := x1, y := %f%(x), s := (y>0)-(y<0)
Loop % ceil((x2-x1)/step) {
x += step, y := %f%(x), t := (y>0)-(y<0)
If (s=0 || s!=t)
res .= root(f, x-step, x, tol) " [" ErrorLevel "]`n"
s := t
}
Sort res, UN ; remove duplicate endpoints
Return res
}
root(f,x1,x2,d) { ; find x in [x1,x2]: f(x)=0 within tolerance d, by bisection
If (!y1 := %f%(x1))
Return x1, ErrorLevel := "Exact"
If (!y2 := %f%(x2))
Return x2, ErrorLevel := "Exact"
If (y1*y2>0)
Return "", ErrorLevel := "Need different sign ends!"
Loop {
x := (x2+x1)/2, y := %f%(x)
If (y = 0 || x2-x1 < d)
Return x, ErrorLevel := y ? "Approximate" : "Exact"
If ((y>0) = (y1>0))
x1 := x, y1 := y
Else
x2 := x, y2 := y
}
}
poly(x) {
Return ((x-3)*x+2)*x
}</lang>
=={{header|C++}}==
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