topic Re: Solving system of nonlinear equations inside IML in SAS/IML Software and Matrix Computations

Solving system of nonlinear equations inside IML

Salah — Fri, 23 Jul 2021 11:07:59 GMT

Hello ....

I am trying to solve two equations simultaneously. I couldn't find anything for IML. Instead, I found "proc model" and "solve" so I used submit and endsubmit inside my IML. The problem which I am facing now is that I can't export the roots to IML. I would appreciate your help here. Thank you

Re: Solving system of nonlinear equations inside IML

Rick_SAS — Fri, 23 Jul 2021 12:31:09 GMT

1. You can solve a system of nonlinear equations in SAS/IML by using the NLPLM or NLPHQN subroutines. See the article, "Solve a system of nonlinear equations with SAS."

2. I presume you meant to specify the GAMMA function in SAS as part of the nonlinear equations. PROC MODEL is failing because there is not 'GAMA' function in SAS (one M).

3. Don't worry about the color-coding in the editor. The editor gets confused by the SUBMIT/ENDSUBMIT block. When it sees a RUN or QUIT statement, it thinks a procedure has exited. It colors the PRINT statement red because it hasn't seen another 'PROC' statement after the RUN. Of course, if you eliminate the SUBMIT block, that issue will vanish.

Re: Solving system of nonlinear equations inside IML

Salah — Fri, 23 Jul 2021 13:08:10 GMT

Thank you so much for the reply.

Yes, I meant gamma and it was my mistake. I also looked at the link which you sent me but I like to know if the procedure that I used works?

Moreover, after I fixed the spelling I received an error, regarding "n" but I am not using it inside the procedure? please see attached log file.

Thank you again

NOTE: Copyright (c) 2002-2012 by SAS Institute Inc., Cary, NC, USA.
NOTE: SAS (r) Proprietary Software 9.4 (TS1M2)
Licensed to UNIVERSITY OF JORDAN, Site 70235184.
NOTE: This session is executing on the X64_8PRO platform.

NOTE: Updated analytical products:

SAS/STAT 13.2
SAS/ETS 13.2
SAS/OR 13.2
SAS/IML 13.2
SAS/QC 13.2

NOTE: Additional host information:

X64_8PRO WIN 6.2.9200 Workstation

NOTE: SAS initialization used:
real time 0.92 seconds
cpu time 0.62 seconds

1 /*Solve system of non linear equations */
2
3 title1 'Solving a Simultaneous System';
4 data test;
5 input a b @@;
6 datalines;

NOTE: SAS went to a new line when INPUT statement reached past the end of a line.
NOTE: The data set WORK.TEST has 3 observations and 2 variables.
NOTE: DATA statement used (Total process time):
real time 0.09 seconds
cpu time 0.00 seconds

8 ;
9
NOTE: Writing HTML Body file: sashtml.htm
10 proc model data=test;
11 eq.sqrt = sqrt(x) - y;
12 eq.hyperbola = a + b / x - y;

13 solve x y / solveprint;
14 id a b;
15 run;

NOTE: PROCEDURE MODEL used (Total process time):
real time 28:52.50
cpu time 14.54 seconds

17 proc iml;
NOTE: IML Ready
18
19 seed=12345;
19 ! k=1;
20
21 alpha=2;
21 ! lambda=2;
22
23
24 n=100;
24 ! m=n;
24 ! R=J(m,1,0);
25
26 print alpha lambda;
27
28
29
30 W=J(m,1,0);
30 ! V=J(m,1,0);
30 ! X_p=J(m,1,0);
30 ! X_A=J(m,1,0);
30 ! U=J(m,1,0);
31
32 X=J(m,1,0);
33
34 do i=1 to m;
35 W[i]=Uniform(seed);
36 end;
37
38 S=1+R[m];
39 V[1]=W[1]**(1/S);
40
41 do i=2 to m;
42 S=S+(1+R[m-i+1]);
43 V[i]=W[i]**(1/S);
44 end;
45
46 do i=1 to m;
47
48 U[i]=1-prod( V[ m:( m-i+1)] );
48 ! ** the U's are the required progressively type II from U(0,1);
49
50 END;
51
52
53 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
54
55
56 print X;
57
58 quit;
NOTE: Exiting IML.
NOTE: PROCEDURE IML used (Total process time):
real time 0.06 seconds
cpu time 0.06 seconds

59
60 proc iml;
NOTE: IML Ready
61
62 seed=12345;
62 ! k=1;
63
64 alpha=2;
64 ! lambda=2;
65
66
67 n=10;
67 ! m=n;
67 ! R=J(m,1,0);
68
69 print alpha lambda;
70
71
72
73 W=J(m,1,0);
73 ! V=J(m,1,0);
73 ! X_p=J(m,1,0);
73 ! X_A=J(m,1,0);
73 ! U=J(m,1,0);
74
75 X=J(m,1,0);
76
77 do i=1 to m;
78 W[i]=Uniform(seed);
79 end;
80
81 S=1+R[m];
82 V[1]=W[1]**(1/S);
83
84 do i=2 to m;
85 S=S+(1+R[m-i+1]);
86 V[i]=W[i]**(1/S);
87 end;
88
89 do i=1 to m;
90
91 U[i]=1-prod( V[ m:( m-i+1)] );
91 ! ** the U's are the required progressively type II from U(0,1);
92
93 END;
94
95
96 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
97
98
99 print X;
100
101 quit;
NOTE: Exiting IML.
NOTE: PROCEDURE IML used (Total process time):
real time 0.03 seconds
cpu time 0.03 seconds

102
103 proc iml;
NOTE: IML Ready
104
105 seed=12345;
105! k=1;
106
107 alpha=2;
107! lambda=2;
108
109
110 n=10;
110! m=n;
110! R=J(m,1,0);
111
112 print alpha lambda;
113
114
115
116 W=J(m,1,0);
116! V=J(m,1,0);
116! X_p=J(m,1,0);
116! X_A=J(m,1,0);
116! U=J(m,1,0);
117
118 X=J(m,1,0);
119
120 do i=1 to m;
121 W[i]=Uniform(seed);
122 end;
123
124 S=1+R[m];
125 V[1]=W[1]**(1/S);
126
127 do i=2 to m;
128 S=S+(1+R[m-i+1]);
129 V[i]=W[i]**(1/S);
130 end;
131
132 do i=1 to m;
133
134 U[i]=1-prod( V[ m:( m-i+1)] );
134! ** the U's are the required progressively type II from U(0,1);
135
136 END;
137
138
139 X=( 1-(1-U)##(1/alpha) )##(1/lambda);
140
141
142 *******************************************************************************;
143 *** MLE for the Kumaraswamy using Type II Adaptive progressive censoring ***** ;
144 *******************************************************************************;
145
146 start MLE_func(y) global (n,m,X,R);
147
148 func=0;
149
150 alpha=y[1];
151 lambda=y[2];
152
153
154 Sum_log=J(m,1,0);
155 Sum_log=log(x);
156
157 Sum_log_1=J(m,1,0);
158 Sum_log_1=log(1-X##lambda);
159
160
161 func=func + m*log(alpha*lambda)+(lambda-1)* Sum_log[+] + (alpha-1) * Sum_log_1[+] ;
162
163 Return(func);
164
165 finish;
NOTE: Module MLE_FUNC defined.
166
167
168
169
170 ************* Constrain MLE ***********************;
171
172 con={0.01 0.01 , . .};
173 x0={0.05, 0.05};
174 tc={10000 14000};
175
176 *************** MLE *********************;
177
178
179 call nlpnra(rc, MLE_ret, "MLE_func", x0, opt, con,tc);
ERROR: (execution) Matrix has not been set to a value.

operation : NLPNRA at line 179 column 1
operands : *LIT1049, x0, opt, con, tc

*LIT1049 1 row 1 col (character, size 😎

MLE_func

x0 2 rows 1 col (numeric)

0.05
0.05

opt 0 row 0 col (type ?, size 0)

con 2 rows 2 cols (numeric)

0.01 0.01
. .

tc 1 row 2 cols (numeric)

10000 14000

statement : CALL at line 179 column 1
180
181 alpha_mle =MLE_ret[1];
ERROR: (execution) Matrix has not been set to a value.

operation : [ at line 181 column 19
operands : MLE_ret, *LIT1050

MLE_ret 0 row 0 col (type ?, size 0)

*LIT1050 1 row 1 col (numeric)

statement : ASSIGN at line 181 column 1
182 lambda_mle=MLE_ret[2];
ERROR: (execution) Matrix has not been set to a value.

operation : [ at line 182 column 19
operands : MLE_ret, *LIT1051

MLE_ret 0 row 0 col (type ?, size 0)

*LIT1051 1 row 1 col (numeric)

statement : ASSIGN at line 182 column 1
183
184
185 print alpha_mle lambda_mle;
ERROR: Matrix alpha_mle has not been set to a value.

statement : PRINT at line 185 column 1
186
187
188
189
190 quit;
NOTE: Exiting IML.
NOTE: The SAS System stopped processing this step because of errors.
NOTE: PROCEDURE IML used (Total process time):
real time 0.08 seconds
cpu time 0.03 seconds

Re: Solving system of nonlinear equations inside IML

Rick_SAS — Fri, 23 Jul 2021 13:06:58 GMT

The log file tells you exactly what is wrong: You are using the variable OPT but you have not set it to a value:

179 call nlpnra(rc, MLE_ret, "MLE_func", x0, opt, con,tc);
ERROR: (execution) Matrix has not been set to a value.

operation : NLPNRA at line 179 column 1
operands : *LIT1049, x0, opt, con, tc

opt 0 row 0 col (type ?, size 0)

In general, search the log for the FIRST error. Fix that error. Then re-run and repeat the process until there are no errors.

You might also want to read the article, "Ten tips before you run an optimization."

Re: Solving system of nonlinear equations inside IML

Salah — Fri, 23 Jul 2021 18:53:48 GMT

It seems that I sent the old log file. The error due to opt was fixed. The error which I am referring to it is the one below.

Moreover, You suggested to me to use the procedure in the https://blogs.sas.com/content/iml/2018/02/28/solve-system-nonlinear-equations-sas.html

does that mean that the one that I am using in my code is not correct or may not work in my case?

Thank you

Re: Solving system of nonlinear equations inside IML

Rick_SAS — Fri, 23 Jul 2021 19:49:07 GMT

The third paragraph of that article says

In SAS/ETS software, you can use the SOLVE statement in PROC MODEL to solve the system

so, yes, you can do it that way. It is not as efficient as solving the system in SAS/IML, but it'll work.

I suggest that you debug the PROC MODEL statement outside of the SUBMIT block and the IML loop. That is what is causing the errors. Your second equation is

eq.Xsqr = Xsqr/n-alpha1*gamma(alpha1)*gamma(2/lambda1+1)/gamma(alpha1+2/lambda1+1);
and the error message is telling you that n has not been defined.