EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Real Expressions

An expression is built from a combination of operator and operand, and it may contain random generators.

Operators in Arithmetic Expressions

Arithmetic operators

• + Addition,
• - Subtraction,
• * Multiplication,
• / Division,
• ^ Exponentiation.

Ordinary functions

• sqrt(x) square root,
• log(x) natural logarithm,
• log10(x) logarithm base 10,
• exp(x) exponential,
• sin(x) trigonometric sine,
• cos(x) trigonometric cosine,
• tan(x) trigonometric tangent,
• asin(x) arc sine,
• acos(x) arc cosine,
• atan(x) arc tangent,
• sinh(x) hyperbolic sine,
• cosh(x) hyperbolic cosine,
• tanh(x) hyperbolic tangent,
• abs(x) absolute value;

random number generators

• ranf() random number, uniformly distributed in [0,1],
• gauss() random number, gaussian distribution with unit standard deviation,
• tgauss(x) random number, gaussian distribution with unit standard deviation, truncated at x standard deviations;

table access functions

• table(x,z): accesses value of the named table column "z" of table "x"; example: table(summ,q1) returns the hor. tune of the Twiss summary table "summ".
• table(x,y,z): accesses value of the named table column "z" for element "y" (first table row with that name) of table "x"; example: table(twiss,mb.12,betx) returns the beta_x at element mb.12 from the Twiss table "twiss". When the element is called with its proper name, as in the example above, the value is returned at the first occurrence of the element of this name. If the value is needed at a occurrence number: NNN, then "[NNN]" has to be appended to the name, e.g. in the above example one obtains the betx of the 23th occurrence of the element "mb.12" by changing the example to: "table(twiss,mb.12[23],betx)". Mind you that the old, but little known, form: "table(twiss,mb.12->23,betx)" continues to work. Lastly, if NNN exceeds the maximum occurrence number the return value is arbitrarily small.

  Beware:

• Unnamed Drifts are not included in the table name database, so as to speed up the search for "real" elements. Therefore, those unnamed drifts cannot be found. However, named drifts can be searched for.
• Due to the importance of finding elements in the table for a proper functioning of the MAD-X runs, the programs throws a "fatal_error" if an element cannot be found in the table.

  There is a second option of this function with 3 entries

• table(x,z,N_row): accesses the value of the named table column "z" at the "N_row" number of rows of table "x" (row numbers start at 1); example: table(twiss,betx,370) returns the beta_x at row number "370" of the Twiss table "twiss". The return value is zero if "N_row" is outside of the allowed range.

  Note that "N_row" has to be a number and not a variable. However, the Macro facility in MAD-X allows one to use a variable instead.

  A typical example could look like this, in fact the square root of betx (user defined variable myvar) is added to the twiss table:

  myvar := sqrt(table(twiss,betx));
  select,flag=twiss,column=name,s,myvar,betx;
  twiss,file;
  

  Or another arbitrary test case of adding k1l taken from the Twiss table:

  Define macro:

  mycrap(xx,yy,zz): macro = {myval = table(xx,yy,zz);};
  

  Use macro in loop:

  i = 0;
  incval = 0;
  while (i < 100) {
  value,i;
  exec,mycrap(twiss,k1l,$i);
  incval = incval + myval;
  value,i,myval,incval;                
  i = i + 1;
  }
  

  Features as of Version 3_03_50

• FILL,TABLE=t,ROW=n;

  fill a table row with the present variable values. If ROW is negative or missing a new row is created. If ROW is greater than the number of rows, the last row is selected without creating a new row.

• SETVARS,TABLE=t,ROW=n;

  set variables according to the column names of the given table and the values of the given row. if ROW is negative, missing or greater than the number of rows, the last row is selected.

• An example can be found at: Special Features

• The length of a table can be determined by using the attribute "tablelength" via table("your_table_name", tablelength). This is useful when creating a table from existing ones. See an example at: user table II

Operands in Arithmetic Expressions

Literal constants

Examples:

1, 10.35, 5E3, 314.1592E-2

Symbolic constants

Additional symbolic constants may be defined to simplify their repeated use in statements and expressions.

CONST name=constant-expression;

Example:

const in = 0.0254;

Table 1: Predefined Symbolic Constants in MAD

mad name	symbol	value used	unit
pi	pi	4 * atan(1)	1
twopi	2 pi	2 * pi	1
degrad	180/pi	180 / pi	deg/rad
raddeg	pi/180	180 / pi	rad/deg
e	e	exp(1)	1
emass	m_e	.510998902*10(-3)	GeV
pmass	m_p	.938271998	GeV
mumass	m_mu	.1056583568	GeV
clight	c	2.99792458*10**8	m/s
qelect	elem. charge	1.602176462e-19	As

Parameter labels

x = a;

x = x + 1;

x := a;

x := x + 1;

x = 0.1;
x := 0.1;

When such a parameter is used in an expression, MAD uses the current value of the parameter if the expression is deferred:

Example:

x:=1.0;
d1: drift,l = x;
d2: drift,l := 2.0 - x;

Element or command attributes

element-name->attribute-name
command-name->attribute-name

Example:

D1: DRIFT,L=1.0;
D2: DRIFT,L=2.0-D1->L;

Expressions and Random Values

Example:

a := 3*ranf();

error:  ealign,range,dx:=sigma*gauss();