I guess you mean that it is a sigmoid on each periodic domain and overall it is a monotonic nondecreasing function.
The main thing you need to do is identify a base function and the domain of periodicity. I have chosen the base function to be
f(x) = (1 - cos(pi*x)) / 2 for x in [0, 1]
which is a monotonic function that has the range [0, 1].
You can then extend the base function by adding a step function to it.
One step function is s(x) = floor(x).
/* The base function has domain [0, 1] and also range [0, 1].
The base function is
f(x) = (1 - cos(pi*x)) /2
*/
data PeriodicSigmoid;
pi = constant('pi');
do x = 1 to 6 by 0.01;
z = x - floor(x); /* z is always in [0,1] */
y = floor(x) + (1 - cos(pi*z)) /2; /* add step function to base function */
output;
end;
run;
proc sgplot data=PeriodicSigmoid;
series x=x y=y;
xaxis grid;
run;
I guess you mean that it is a sigmoid on each periodic domain and overall it is a monotonic nondecreasing function.
The main thing you need to do is identify a base function and the domain of periodicity. I have chosen the base function to be
f(x) = (1 - cos(pi*x)) / 2 for x in [0, 1]
which is a monotonic function that has the range [0, 1].
You can then extend the base function by adding a step function to it.
One step function is s(x) = floor(x).
/* The base function has domain [0, 1] and also range [0, 1].
The base function is
f(x) = (1 - cos(pi*x)) /2
*/
data PeriodicSigmoid;
pi = constant('pi');
do x = 1 to 6 by 0.01;
z = x - floor(x); /* z is always in [0,1] */
y = floor(x) + (1 - cos(pi*z)) /2; /* add step function to base function */
output;
end;
run;
proc sgplot data=PeriodicSigmoid;
series x=x y=y;
xaxis grid;
run;
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