Expression Matching with USE

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Introduction

It is possible to match user defined expressions with the USE_MACRO keyword. The general input structure for a match command is the following:

MATCH,USE_MACRO;
... VARY statements ...
USE_MACRO, NAME=macro1;
     or
macro1: MACRO={ ... madx statements};
CONSTRAINT, expr=  "lhs1 < | = | > rhs1";
CONSTRAINT, expr=  "lhs2 < | = | > rhs2";
...  CONSTRAINT statements ...
MACRO 2 definition
... CONSTRAINT statements ...
MACRO n definition
... CONSTRAINT statements ...
... METHODS statements ...
ENDMATCH;

The algorithm for evaluating the penalty function is the following:

execute the first macro,
evaluate and compute the difference between the lhs and the rhs the first set of expressions,
in case of other macros, evaluates in order the macro and the expressions
the set of differences are minimized by the selected method using the variables defined in the VARY statements.

Initiating the Matching Module with USE_MACRO

With:

   MATCH,USE_MACRO;

the 'match' command can be used for matching any expression which can be defined through expression. It requires a slightly different syntax.

VARY statements

In the USE_MACRO mode the vary statement follows the same rules of the other modes explained in the section Define Variable Parameter

Macro definitions

The macro to be used in the matching routine can be defined in two ways:

using USE_MACRO statement:
```
 USE_MACRO, NAME=macro1;
  
```

macros

After a macro definition is necessary to define a set of constraints exclusively with the following syntax:

 CONSTRAINT, expr=  "lhs = rhs";

 CONSTRAINT, expr=  "lhs < rhs";

 CONSTRAINT, expr=  "lhs > rhs";

where "lhs" and "rhs" are well defined MadX expressions. Other set of macro and constraints can be defined afterwards.

Examples

The following example the USE_MACRO mode can emulate a matching script which uses the normal syntax.
Normal syntax:

MATCH,SEQUENCE=LHCB1,LHCB2;
    VARY, NAME=KSF.B1, STEP=0.00001;
    VARY, NAME=KSD.B1, STEP=0.00001;
    VARY, NAME=KSF.B2, STEP=0.00001;
    VARY, NAME=KSD.B2, STEP=0.00001;
    GLOBAL,SEQUENCE=LHCB1,DQ1=QPRIME;
    GLOBAL,SEQUENCE=LHCB1,DQ2=QPRIME;
    GLOBAL,SEQUENCE=LHCB2,DQ1=QPRIME;
    GLOBAL,SEQUENCE=LHCB2,DQ2=QPRIME;
    LMDIF, CALLS=10, TOLERANCE=1.0E-21;
ENDMATCH;

USE_MACRO syntax:

MATCH,USE_MACRO;
    VARY, NAME=KSF.B1, STEP=0.00001;
    VARY, NAME=KSD.B1, STEP=0.00001;
    VARY, NAME=KSF.B2, STEP=0.00001;
    VARY, NAME=KSD.B2, STEP=0.00001;
    M1: MACRO={ TWISS,SEQUENCE=LHCB1; };
    CONSTRAINT, EXPR= "TABLE(SUMM,DQ1)=QPRIME";
    CONSTRAINT, EXPR= "TABLE(SUMM,DQ2)=QPRIME";
    M2: MACRO={ TWISS,SEQUENCE=LHCB2; };
    CONSTRAINT, EXPR= "TABLE(SUMM,DQ1)=QPRIME";
    CONSTRAINT, EXPR= "TABLE(SUMM,DQ2)=QPRIME";
    LMDIF, CALLS=10, TOLERANCE=1.0E-21;
ENDMATCH;

Oliver Brüning, October, 2003; Riccardo de Maria, February, 2006.