Automatic Derivatives

The NLIN Procedure

Automatic Derivatives

Depending on the optimization method you select, analytical first- and second-order derivatives are computed automatically. Derivatives can still be supplied using the DER.parm syntax. These DER.parm derivatives are not verified by the differentiator. If any needed derivatives are not supplied, they are computed and added to the program statements. To view the computed derivatives, use the LISTDER or LIST option.

The following model is solved using Newton's method. Analytical first- and second-order derivatives are automatically computed.

   proc nlin data=Enzyme method=newton list;
      parms x1=4 x2=2 ;
      model Velocity = x1 * exp (x2 * Concentration);
   run;

The NLIN Procedure

Listing of Compiled Program Code
Stmt	Line:Col	Statement as Parsed
1	471:74	MODEL.Velocity = x1 * EXP(x2 * Concentration);
1	471:74	@MODEL.Velocity/@x1 = EXP(x2 * Concentration);
1	471:74	@MODEL.Velocity/@x2 = x1 * Concentration * EXP(x2 * Concentration);
1	471:74	@@MODEL.Velocity/@x1/@x2 = Concentration * EXP(x2 * Concentration);
1	471:74	@@MODEL.Velocity/@x2/@x1 = Concentration * EXP(x2 * Concentration);
1	471:74	@@MODEL.Velocity/@x2/@x2 = x1 * Concentration * Concentration * EXP(x2 * Concentration);

Figure 45.5: Model and Derivative Code Output

Note that all the derivatives require the evaluation of EXP(X2 * Concentration). If you specify the LISTCODE option in the PROC NLIN statement, the actual machine level code produced is as follows.

The NLIN Procedure

Code Listing

1 Stmt MODEL	line 328 column 78. (1) arg=MODEL.Velocity argsave=MODEL.Velocity
	Source Text:	model Velocity = x1 * exp (x2 * Concentration);
Oper *	at 328:108 (30,0,2).	* : #temp1 <- x2 Concentration
Oper EXP	at 328:104 (103,0,1).	EXP : #temp2 <- #temp1
Oper *	at 328:98 (30,0,2).	* : MODEL.Velocity <- x1 #temp2
Oper eeocf	at 328:104 (18,0,1).	eeocf : _DER_ <- _DER_
Oper *	at 328:104 (30,0,2).	* : @1dt1_1 <- Concentration #temp2
Oper =	at 328:98 (1,0,1).	= : @MODEL.Velocity/@x1 <- #temp2
Oper *	at 328:98 (30,0,2).	* : @MODEL.Velocity/@x2 <- x1 @1dt1_1
Oper *	at 328:104 (30,0,2).	* : @2dt1_1 <- Concentration @1dt1_1
Oper =	at 328:98 (1,0,1).	= : @@MODEL.Velocity/@x1/@x2 <- @1dt1_1
Oper =	at 328:98 (1,0,1).	= : @@MODEL.Velocity/@x2/@x1 <- @1dt1_1
Oper *	at 328:98 (30,0,2).	* : @@MODEL.Velocity/@x2/@x2 <- x1 @2dt1_1

Figure 45.6: LISTCODE Output

Note that, in the generated code, only one exponentiation is performed. The generated code reuses previous operations to be more efficient.

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