Hyperbolic Tan Fit
$begingroup$
I am trying to fit some data to a hyperbolic tan function of the following form:
$y=frac{1}{2}Big[(a+b)+(b-a)tanh{frac{x-t_0}{omega}}Big]$
where:
a = upper limit of range
b = lower limit of range
$t_0$ = inflection point
$omega$ = width? (not too sure)
I want the upper range to be $alpha$, so $a = alpha$, and also to reach this upper range when $x=0$, so $y=alpha, x = 0$.
I have found this is an impossible condition to meet, I am guessing because the function asymptotically approaches $alpha$, so it can't quite equal it.
Are there any tricks I can implement to get the result/conditions I want?
algebra-precalculus functions
edited Jan 25 at 20:26
KReiser
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
$endgroup$
add a comment |
$begingroup$
I am trying to fit some data to a hyperbolic tan function of the following form:
$y=frac{1}{2}Big[(a+b)+(b-a)tanh{frac{x-t_0}{omega}}Big]$
where:
a = upper limit of range
b = lower limit of range
$t_0$ = inflection point
$omega$ = width? (not too sure)
I want the upper range to be $alpha$, so $a = alpha$, and also to reach this upper range when $x=0$, so $y=alpha, x = 0$.
I have found this is an impossible condition to meet, I am guessing because the function asymptotically approaches $alpha$, so it can't quite equal it.
Are there any tricks I can implement to get the result/conditions I want?
algebra-precalculus functions
edited Jan 25 at 20:26
KReiser
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
$endgroup$
add a comment |
$begingroup$
I am trying to fit some data to a hyperbolic tan function of the following form:
$y=frac{1}{2}Big[(a+b)+(b-a)tanh{frac{x-t_0}{omega}}Big]$
where:
a = upper limit of range
b = lower limit of range
$t_0$ = inflection point
$omega$ = width? (not too sure)
I want the upper range to be $alpha$, so $a = alpha$, and also to reach this upper range when $x=0$, so $y=alpha, x = 0$.
I have found this is an impossible condition to meet, I am guessing because the function asymptotically approaches $alpha$, so it can't quite equal it.
Are there any tricks I can implement to get the result/conditions I want?
algebra-precalculus functions
edited Jan 25 at 20:26
KReiser
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
$endgroup$
I am trying to fit some data to a hyperbolic tan function of the following form:
$y=frac{1}{2}Big[(a+b)+(b-a)tanh{frac{x-t_0}{omega}}Big]$
where:
a = upper limit of range
b = lower limit of range
$t_0$ = inflection point
$omega$ = width? (not too sure)
I want the upper range to be $alpha$, so $a = alpha$, and also to reach this upper range when $x=0$, so $y=alpha, x = 0$.
I have found this is an impossible condition to meet, I am guessing because the function asymptotically approaches $alpha$, so it can't quite equal it.
Are there any tricks I can implement to get the result/conditions I want?
algebra-precalculus functions
algebra-precalculus functions
edited Jan 25 at 20:26
KReiser
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
edited Jan 25 at 20:26
KReiser
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
edited Jan 25 at 20:26
KReiser
9,87121435
edited Jan 25 at 20:26
KReiser
9,87121435
edited Jan 25 at 20:26
KReiser
9,87121435
9,87121435
asked Jan 25 at 19:55
ScientizedScientized
20118
asked Jan 25 at 19:55
ScientizedScientized
20118
asked Jan 25 at 19:55
ScientizedScientized
20118
20118
add a comment |
add a comment |
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