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06-18-2016 11:38 AM

Hello dear community,

I would appreciate your help on following question, concerning the generation of a variable, which solves an equation, containing variables already existing in the data set, where the equation is not solved for the unknown but shall be solved iteratively.

In the following, I provide a simply example.

`data icctrial;`

input p e1 e2 e3 r;
datalines;
48.159278738 10 20 30 0.1
80.681818182 20 40 60 0.2
456.46644799 30 45 601 0.15
420.4413418 454 5 5 0.11
4986.8628377 5445 12 45 0.17
0.7513148009 0 0 1 0.1
11.605639731 5 6 5 0.2
2.5476889974 1 2 1 0.3
;
run;

The equation to be solved for each observation is

p=(e1)/(1+a)+e2/((1+a)**2)+e3/((1+a)**3),

with "p", "e1", "e2" and "e3" all given, "a" as the only unknown.

The solution shall be added to the data set as the variable "a" for each observation.

The data is chosen, such that "r" is the correct solution. "r" is added as a reference (sadly, only).

I would be glad, if someone would help me.

Yours sincerely,

Sinistrum

Accepted Solutions

Solution

06-19-2016
03:17 PM

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06-18-2016 09:58 PM

You can also use the** solve** function in FCMP:

```
data test;
input p e1 e2 e3;
datalines;
48.159278738 10 20 30
80.681818182 20 40 60
456.46644799 30 45 601
420.4413418 454 5 5
4986.8628377 5445 12 45
0.7513148009 0 0 1
11.605639731 5 6 5
2.5476889974 1 2 1
;
/* FCMP routine to find function roots */
proc fcmp outlib=sasuser.fcmp.test;
function fn(e1, e2, e3, a);
return ( e1/(1+a) + e2/(1+a)**2 + e3/(1+a)**3 );
endsub;
function findZero(p, e1, e2, e3, init);
array solvopts[1] initial (0);
initial = init;
return (solve("fn", solvopts, p, e1, e2, e3, .));
endsub;
run;
options cmplib=sasuser.fcmp;
data roots;
set test;
root = findZero(p, e1, e2, e3, 0.1);
run;
proc print data=roots; run;
```

which gives the same roots as proc nlin.

PG

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06-18-2016 02:30 PM

Have you looked at PROC MODEL? Do you have SAS ETS licensed?

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06-18-2016 03:27 PM - edited 06-18-2016 03:52 PM

Hello

and thank you for your reply.

Indeed, during my desperate search, I came across "PROC MODEL".

As I have never worked with SAS before, I was afraid, this was "just" a tool in order to create the standard Least-Squares-Regression output . Furthermore, I do not know, how I could assign the output of such a procedure as a variable to my existing data set.

So, maybe I should dig deeper into that topic.

I was hoping for something profane in the manner like

data icctrial; set icctrial; a = 'such that this equation here is fulfilled'; run;

and that someone would have an easy solution,

But thanks to you, I now know where to search.

I hope I will come to terms with this issue.

---

Indeed, "I" have SAS/ETS licensed.

---

EDIT:

I tried this

```
proc model data=icctrial out=egal;
exogenous p e1 e2 e3;
endogenous a ;
solve a;
p=(e1)/(1+a)+e2/((1+a)**2)+e3/((1+a)**3);
run;
```

but it gives pretty inaccurate results.

Solution

06-19-2016
03:17 PM

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06-18-2016 09:58 PM

You can also use the** solve** function in FCMP:

```
data test;
input p e1 e2 e3;
datalines;
48.159278738 10 20 30
80.681818182 20 40 60
456.46644799 30 45 601
420.4413418 454 5 5
4986.8628377 5445 12 45
0.7513148009 0 0 1
11.605639731 5 6 5
2.5476889974 1 2 1
;
/* FCMP routine to find function roots */
proc fcmp outlib=sasuser.fcmp.test;
function fn(e1, e2, e3, a);
return ( e1/(1+a) + e2/(1+a)**2 + e3/(1+a)**3 );
endsub;
function findZero(p, e1, e2, e3, init);
array solvopts[1] initial (0);
initial = init;
return (solve("fn", solvopts, p, e1, e2, e3, .));
endsub;
run;
options cmplib=sasuser.fcmp;
data roots;
set test;
root = findZero(p, e1, e2, e3, 0.1);
run;
proc print data=roots; run;
```

which gives the same roots as proc nlin.

PG

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06-18-2016 04:06 PM - edited 06-18-2016 04:14 PM

You don't need an iterative procedure to find the roots of third degree polynomials. But for a general function of one variable, you can hijack the line search of **proc nlin** in this way:

```
data test;
input p e1 e2 e3;
datalines;
48.159278738 10 20 30
80.681818182 20 40 60
456.46644799 30 45 601
420.4413418 454 5 5
4986.8628377 5445 12 45
0.7513148009 0 0 1
11.605639731 5 6 5
2.5476889974 1 2 1
;
/* Add equation number */
data parms;
set test;
eqNo + 1;
run;
/* define starting value for parameter b = 1+a */
data startingValues;
set parms;
parameter = "b";
Estimate = 1.1;
run;
/* Find 3rd degree equation root for every obs */
proc nlin data=parms outest=roots(where=(_TYPE_="FINAL"));
by eqNo p e1 e2 e3;
parameters / pdata=startingValues;
model e3 = -(-p*b**3 + e1*b**2 + e2*b);
run;
title "Polynomial roots";
proc sql;
select eqNo, p, e1, e2, e3, b-1 as a format=6.4,
e3 + (-p)*b**3 + e1*b**2 + e2*b as rootValue
from roots
order by eqNo;
quit;
```

Note: Some roots don't match your 'r' values.

PG

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06-18-2016 11:48 PM

You are looking for the root of function : F(x)=p*x**3-e1*x**2-e2*x-e3 It would be easy for SAS/IML . You can run it under SAS University Edition. data icctrial; infile cards expandtabs truncover; input p e1 e2 e3 r; datalines; 48.159278738 10 20 30 0.1 80.681818182 20 40 60 0.2 456.46644799 30 45 601 0.15 420.4413418 454 5 5 0.11 4986.8628377 5445 12 45 0.17 0.7513148009 0 0 1 0.1 11.605639731 5 6 5 0.2 2.5476889974 1 2 1 0.3 ; run; proc iml; use icctrial; read all var _num_ into x[c=vnames]; close; root=j(nrow(x),1,.); do i=1 to nrow(x); parm=x[i,1]||-x[i,2]||-x[i,3]||-x[i,4]; roots=polyroot(parm); root[i]=roots[loc(roots[,2]=0),1]-1; end; want=x||root; print want[c=(vnames||'root') l='']; quit; OUTPUT: p e1 e2 e3 r root 48.159279 10 20 30 0.1 0.1 80.681818 20 40 60 0.2 0.1898444 456.46645 30 45 601 0.15 0.1489363 420.44134 454 5 5 0.11 0.1004448 4986.8628 5445 12 45 0.17 0.1014909 0.7513148 0 0 1 0.1 0.1 11.60564 5 6 5 0.2 0.1791374 2.547689 1 2 1 0.3 0.2614769

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06-19-2016 02:24 AM - edited 06-19-2016 02:31 AM

Thank you for your answers. This is really awesome.

So, "**solve** function in FCMP" and "hijack[ing] the line search of **proc nlin**" as you mentioned, PG, are presumably exactly what I am looking for.

The data set I made up was just a simple example. In fact, I do have to solve a function of the form

,

where the variable "b" is a function of "a" (and a constant, which is given, no problem with that), too.

So the itterative procedure is indeed what I am looking for.

Thank you, Ksharp, too. I am convinced I can make use of this later, too, for other approaches for different equations as the equation mentioned is not the only to be dealt with.

So, today I am going to play a little with your solution suggestions.

I just got the message by mail that my problem had been quasi-solved and just wanted to express real quickly my gratitude for and appreciation of your answers. Again, thank you very much.

What still makes me worry, though, is this one observation "5", where the true solution is 17% and not 10,15%. But I guess it is just due to the fact I mindlessly made up the data, the real sample I am dealing with does not contain such extreme values.

Best regards,

Sinistrum

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06-19-2016 04:47 PM

Sinistrum wrote:

What still makes me worry, though, is this one observation "5", where the true solution is 17% and not 10,15%. But I guess it is just due to the fact I mindlessly made up the data, the real sample I am dealing with does not contain such extreme values.

Simple check for obs 5:

p - f(e1, e2, e3; 0.17) = 296.15,

p - f(e1, e2, e3; 0.1015) = 0.0002

PG

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06-20-2016 05:27 AM - edited 06-20-2016 05:32 AM

So, obviously, I am even to clusmy to set up test-data-sets properly for I have made a mistake with discounting e1.

The correct data is

```
data test;
input p e1 e2 e3 r;
datalines;
48.159278738 10 20 30 0.1
79.166666667 20 40 60 0.2
455.28067724 30 45 601 0.15
416.72307808 454 5 5 0.11
4690.7089915 5445 12 45 0.17
0.7513148009 0 0 1 0.1
11.226851852 5 6 5 0.2
2.4078288575 1 2 1 0.3
```

;
run;

With this now corrected data, the estimated "root" matches the "r".

So sorry for this and, once again, thank you very much.

Best regards,

Sinistrum