Hi,
I have issues writning a formula to solve the following equation in SAS.
I have the following 10 observations (below).
Var1 is unknown ( Var1 have the same for all observations)
Var2 is known.
The value for Var3 for each observation is calculated using the following formula (EXP(Var1+Var2)/(1+EXP(Var1+Var2))
Known is also that the sum of Var3 for all ten observations is 5. This means that Var1 is about -0.56.
I now want SAS to automatic solve X for me
Thanks for help!
/Thomas
obs | var1 | var2 | var3 |
1 | X | 0.1 | EXP(X+0.1)/(1+EXP(X+0.1)) |
2 | X | 0.2 | EXP(X+0.2)/(1+EXP(X+0.2)) |
3 | X | 0.3 | EXP(X+0.3)/(1+EXP(X+0.3)) |
4 | X | 0.4 | EXP(X+0.4)/(1+EXP(X+0.4)) |
5 | X | 0.5 | EXP(X+0.5)/(1+EXP(X+0.5)) |
6 | X | 0.6 | EXP(X+0.6)/(1+EXP(X+0.6)) |
7 | X | 0.7 | EXP(X+0.7)/(1+EXP(X+0.7)) |
8 | X | 0.8 | EXP(X+08)/(1+EXP(X+0.8)) |
9 | X | 0.9 | EXP(X+0.9)/(1+EXP(X+0.9)) |
10 | X | 1.0 | EXP(X+1.0)/(1+EXP(X+1.0)) |
You need to put you equation in your code, not as a variable. Should not be any problem since the equation logic is the same for all rows.
Thanks for reply,
I have var3 in the code but I have problems to solve the equation due to the sum of all 10 observations:
Equation: sum of (EXP(Var1+Var2)/(1+EXP(Var1+Var2)) for all 10 observations =5
and I want SAS to solve Var1 for me (Var2 is known)
Thanks for further guidance if there are any procedures to solve equations loike this
/Thomas
It looks like that you are trying to look for a root .You might want post it at IML forum . Rick might have a good idea. Here is my GA code.
But My root X=-6.392141 not -0.56 .
data have;
input obs var1 $ var2 var3 : $40.;
cards;
1 X 0.1 EXP(X+0.1)/(1+EXP(X+0.1))
2 X 0.2 EXP(X+0.2)/(1+EXP(X+0.2))
3 X 0.3 EXP(X+0.3)/(1+EXP(X+0.3))
4 X 0.4 EXP(X+0.4)/(1+EXP(X+0.4))
5 X 0.5 EXP(X+0.5)/(1+EXP(X+0.5))
6 X 0.6 EXP(X+0.6)/(1+EXP(X+0.6))
7 X 0.7 EXP(X+0.7)/(1+EXP(X+0.7))
8 X 0.8 EXP(X+08)/(1+EXP(X+0.8))
9 X 0.9 EXP(X+0.9)/(1+EXP(X+0.9))
10 X 1.0 EXP(X+1.0)/(1+EXP(X+1.0))
;
run;
proc sql;
select var3 into : list separated by '+' from have;
quit;
%put &list ;
proc iml;
start func(x);
v=abs(&list-5);
return (v);
finish;
id=gasetup(1,1,1234);
call gasetobj(id,0,"func");
call gasetsel(id,100,1,0.95);
call gasetcro(id,0.05,4);
call gasetmut(id,0.05);
call gainit(id,10000,{-10,10});
niter = 100;
summary = j(niter,2);
mattrib summary [c = {"Min Value", "Avg Value"} l=""];
do i = 1 to niter;
call garegen(id);
call gagetval(value, id);
summary[i,1] = value[1];
summary[i,2] = value[:];
end;
call gagetmem(mem, value, id, 1);
print mem[ l="best member:"],
"Min Value: " value[l = ""] ;
iteration = t(1:niter);
print iteration summary;
call gaend(id);
quit;
Xia Keshan
It can be solved with proc fcmp :
proc fcmp outlib=sasuser.fcmp.test;
function myFunc(x, A
do i = 1 to dim(A);
sum + exp(x + A)/(1 + exp(x + A));
end;
return(sum);
endsub;
function solveForX(A
array solvopts[1] initial;
initial = initX;
return (solve("myFunc", solvopts, sum, ., A));
endsub;
run;
options cmplib=sasuser.fcmp;
data _null_;
array var2{10};
do i = 1 to 10;
var2{i} = i / 10;
output;
end;
expectedSum = 5;
initialGuess = -0.5;
x = solveForX(var2, expectedSum, initialGuess);
put x=;
run;
PG
Thanks thats brilliant!
A following question. In my example the values of var2 went from 0.1 to 1.
However, values for var2 might be different not following the a specific pattern (below). Is it possible to use the same proc fcmp-model and add the dataset I want to use to the array?
/Thomas
obs | var1 | var2 | var3 |
1 | X | 0.15 | EXP(X+0.15)/(1+EXP(X+0.15)) |
2 | X | 0.03 | EXP(X+0.03)/(1+EXP(X+0.03)) |
3 | X | 0.23 | EXP(X+0.23)/(1+EXP(X+0.23)) |
4 | X | 0.44 | EXP(X+0.44)/(1+EXP(X+0.44)) |
5 | X | 0.16 | EXP(X+0.16)/(1+EXP(X+0.16)) |
6 | X | 0.7 | EXP(X+0.7)/(1+EXP(X+0.7)) |
7 | X | 0.12 | EXP(X+0.12)/(1+EXP(X+0.12)) |
8 | X | 0.32 | EXP(X+0.32)/(1+EXP(X+0.32)) |
9 | X | 0.22 | EXP(X+0.22)/(1+EXP(X+0.22)) |
10 | X | 0.82 | EXP(X+0.82)/(1+EXP(X+0.82)) |
Replace the _null_ step with
/* Prepare equation parameters in a dataset */
data var2;
input eqNo var2_1-var2_10 expectedSum initialGuess;
datalines;
1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 5 -0.5
2 0.15 0.03 0.23 0.44 0.16 0.7 0.12 0.32 0.22 0.82 5 -0.5
;
/* solve equations */
data want;
set var2;
array var2Array{*} var2_:;
x = solveForX(var2Array, expectedSum, initialGuess);
run;
proc print data=want noobs; run;
PG
Thank you all for your relies!
I tried the solution by PGstats and it worked well for me
thanks
thomas
You mean creating a VAR3 variable ,right ?
Surprise! This time I got root X=-0.55 . There must be some wrong in your original var3.
data have;
input obs var1 $ var2;
var3=cats('EXP(X+',var2,')/(1+EXP(X+',var2,'))');
cards;
1 X 0.1
2 X 0.2
3 X 0.3
4 X 0.4
5 X 0.5
6 X 0.6
7 X 0.7
8 X 0.8
9 X 0.9
10 X 1.0
;
run;
proc sql;
select var3 into : list separated by '+' from have;
quit;
%put &list ;
proc iml;
start func(x);
v=abs(&list-5);
return (v);
finish;
id=gasetup(1,1,1234);
call gasetobj(id,0,"func");
call gasetsel(id,100,1,0.95);
call gasetcro(id,0.05,4);
call gasetmut(id,0.05);
call gainit(id,10000,{-10,10});
niter = 100;
summary = j(niter,2);
mattrib summary [c = {"Min Value", "Avg Value"} l=""];
do i = 1 to niter;
call garegen(id);
call gagetval(value, id);
summary[i,1] = value[1];
summary[i,2] = value[:];
end;
call gagetmem(mem, value, id, 1);
print mem[ l="best member:"],
"Min Value: " value[l = ""] ;
iteration = t(1:niter);
print iteration summary;
call gaend(id);
quit;
Xia Keshan
Here is How to find a root by Rick . But I don't agree with him a little bit .
This is a one-dimensional root-finding problem: Find the value of alpha such that
sum( logistic(alpha + var2) ) = 5
or
sum( logistic(alpha + var2) ) - 5 = 0.
Just do an internet search for "find root sas."
A pedestrian approach.
let us generalize a bit the function for which one is looking for roots.
The following applies 3 parameters (p1,p2,p3) to a slightly generalized function given in the Question.
************************************************;
**** if you want, create sets of parameters ****;
************************************************;
data t_param(keep=zSteps i p1 p2 p3);
do k= 1 to 5;
zSteps=10*(k=1)+20*(k=2)+40*(k=3)+50*(k=4)+100*(k=5);
do i=1 to zSteps;
p1=10/zSteps;
p2=(1/zSteps)*i;
p3=(1/zSteps)*i;
output;
end;
end;
run;
**************************************************;
**** macro funk() can be an arbitrary function ***;
**************************************************;
%macro funk(d1,d2,d3);
%global fnc;
%let fnc = &d1*exp(x+&d2)/(1+exp(x+&d3));
&fnc.
%mend;
*****************************************;
**** table t_root collects the roots ****;
*****************************************;
data t_root(keep=zSteps ySteps yRoot);
array pp1(1000);
array pp2(1000);
array pp3(1000);
array fnk(10000);
ySteps=400;
LHS_eqn=5; **** this is equation the Left-Hand-Side value ****;
nn=0;
call missing(of pp1(*));
call missing(of pp2(*));
call missing(of pp3(*));
call missing(of fnk(*));
*********************************************;
**** load the matrices pp1() pp2() pp3() ****;
*********************************************;
do until (last.zSteps);
nn+1;
set t_param;
by zSteps;
pp1(nn)=p1; pp2(nn)=p2; pp3(nn)=p3;
end;
********************************;
**** find f(x) from -1 to 1 ****;
********************************;
do yIter=1 to ySteps;
x=-1.0+2*(yIter/ySteps);
FF=-1*LHS_eqn;
do c1=1 to nn;
f1=pp1(c1); f2=pp2(c1); f3=pp3(c1);
FF = FF + %funk(f1,f2,f3);
end;
fnk(yIter)=FF;
end;
*********************************;
**** find roots from -1 to 1 ****;
*********************************;
do yIter=1 to (ySteps-1);
sgn1=sign(fnk(yIter+1));
sgn0=sign(fnk(yIter+0));
if (sgn1=0) then do; yRoot=-1.0+2*((yIter+1)/ySteps); output; end;
else if not(sgn0=0) and not(sgn1=sgn0) then do;
yRoot= -1.0+2*((yIter+1)/ySteps);
abs1=abs(fnk(yIter+1));
abs0=abs(fnk(yIter+0));
yRoot=yRoot -(2/ySteps)*(abs1/(abs0+abs1));
output;
end;
end;
run;
table t_root becomes:
ySteps zSteps yRoot
==========================
400 10 -0.5500
400 20 -0.5250
400 40 -0.5125
400 50 -0.5100
400 100 -0.5050
==========================
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