2. Basic object content#

2.1. Purpose. PROL#

The object ». PROL » is 6 in length for tabulated functions with 0 or 1 variable and formulas. It is \(7+2\mathrm{\ast }\mathit{nf}\) in length for tablecloths, if \(\mathit{nf}\) is the number of functions composing the tablecloth.

. PROL (1)

Type of function.

“CONSTANT”

: constant function

“FONCTION”

: real function_1

“FONCT_C”

: function_1 complex

“NAPPE”

: function with 2 variables (table)

“INTERPRE”

: interpreted function (formula)

. PROL (2) = “XXX FFF “

The type of interpolation you want between tab points. Only applies to tabulated functions. XXXconcerne the parameter and FFF the function. The possibilities are:

  • “LIN”: linear interpolation,

  • “LOG”: logarithmic interpolation.

Let’s be a \(f(x)\) function.

We will do a linear interpolation between the two points surrounding the point sought, but for this linear interpolation, we will possibly use the logarithm of \(x\) or \(f\).

For example if “LIN LOG”, we’ll use \(x\) and \(\mathrm{log}(f)\).

Note:

For a tablecloth, XXXconcerne is also the second parameter of the function.

. PROL (3)

Parameter name.

  • “TOUTPARA” for a constant function,

  • name of the parameter (i.e. the variable) for a function,

  • name of the second parameter for a tablecloth,

  • “”(empty) for a formula.

. PROL (4)

  • name (or type) of the result of the function,

  • TOUTRESU “.

. PROL (5)

Desired « extension » to the function outside of its tabulation domain (extrapolation). Only applies to tabulated functions.

“xy” where x and y = “E” or “L” or “C”.

x: extension « to the left » (for a parameter less than the smallest parameter of the tab),

y: extension « to the right » (for a parameter greater than the largest parameter in the tab).

“E”: extension excluded, “C”: constant extension, “L”: linear extension (from the first two or the last two points).

For a tablecloth, these extensions concern the second parameter (values of the object). PARA).

There is no « logarithmic » extension.

. PROL (6)

Name of the function or tablecloth. This is used for the purposes of code to clarify error or alarm messages when we no longer have access to the user’s functional concept (case of coded material).

. PROL (7)

Only for tablecloths: name of the parameter of the functions composing the tablecloth (NOM_PARA_FONC of DEFI_NAPPE).

. PROL (8)

Type of interpolation wanted for the first function composing the array (“LIN LOG”, “LOGLOG”,…) (see ». PROL (2) »).

. PROL (9)

Type of extension required for the first function composing the cable (“EL”, “CC”,…) (see ». PROL (5) »).

. PROL (10)

Type of interpolation required for the second function composing the array… and next.

2.2. Subject ». PARA »#

This object contains the values of the second variable in the table. Each value of this second variable corresponds to an object from the collection ». VALE « which contains the values of the function associated with this variable.

2.3. Subject ». VALE »#

2.3.1. Case of a function#

For a function, this object contains the numerical values of the tab points.

Let \(n\): the number of tab points,

  • \(V(\mathrm{1,}\mathrm{...},n)\): x-axis of points,

  • \(V(n+\mathrm{1,}\mathrm{...}\mathrm{,2}\mathrm{\ast }n)\): values of the function at the points.

Note: If the function has complex values, the storage is as follows:

  • \(V(n+1)\): real part of the function at the 1st point,

  • \(V(n+2)\): imaginary part of the function at the 1st point,

  • \(V(n+3)\): real part of the function at the 2nd point,

  • \(V(n+4)\): imaginary part of the function at the 2nd point,

  • \(\mathrm{...}\)

  • \(V(3\mathrm{\ast }n)\): imaginary part of the function at the last point.

The number of discretization points \((n)\) can be obtained by dividing the « LONMAX » attribute of the object by 2 (or 3). » VALE »

2.3.2. Case of a tablecloth#

For a tablecloth, this object is a contiguous numbered collection. Each \(i\) collector’s item has the same structure as the object. » VALE « functions (above). It describes the function attached to the \(i\) value of the second table variable.

2.4. Subject ». NOVA »#

This object contains the names of the variables in the « formula » function.