3. Operands#
3.1. Operand NOM_PARA#
♦ NOM_PARA = no
Refers to the name of the table parameter (second variable) as an example in [§4.1].
The allowed values listed are the same as in DEFI_FONCTION [U4.31.02].
3.2. Operand NOM_RESU#
◊ NOM_RESU = nr
Name of the result, of the values of the table. It must be identical to NOM_RESU for each of the functions making up the tablecloth.
In fact, this operand is not always used for consistency checks in code execution. These consistency checks are done by the CALC_FONCTION [U4.32.04] command.
3.3. Operand PARA#
♦ PARA = lp
List of values of the characteristic parameter of the tablecloth: para1, para2,… The cardinal of this list must be equal to the number of functions defined next.
3.4. Operands PROL_DROITE and PROL_GAUCHE#
◊ PROL_DROITE and PROL_GAUCHE =
Define the type of extension to the right (left) of the variable’s domain of definition:
“CONSTANT” |
for an extension with the last (or first) value of the table, |
“LINEAIRE” |
for an extension along the first defined segment (PROL_GAUCHE) or the last defined segment (PROL_DROITE), this extension does not take into account a possible logarithmic interpolation, |
“EXCLU” |
if extrapolation of values outside the domain of definition of the parameter np is forbidden (in this case if a calculation requires a value of the function outside the domain of definition, the code will stop in a fatal error). |
3.5. Operand INTERPOL#
◊ INTERPOL =
Type of interpolation of the table: one type for the interpolation of the second variable and one for the interpolation between two functions. This is obtained by providing a list of 2 texts from:
“LIN”: |
linear, |
“LOG”: |
logarithmic, |
Note:
If only one value is specified, it is taken into account by both the interpolation of the parameter and the function. INTERPOL = “LOG” is equivalent to (“LOG”, “LOG”) .
3.6. Operand INFO#
◊ INFO =
Specify the options for printing on the message file (unit 6).
1: |
no printing (option by default) |
2: |
Print the parameters plus the list of the first 10 values of each function in ascending order of the first 10 parameters |
3.7. Operand VERIF#
◊ VERIF =
The DEFI_NAPPE operator reorders the values of the nP parameters in ascending order. If VERIF is set to “Ascending” the operator stops execution if the values of the pn parameter have not been given in this order.
3.8. Definition of the functions of the tablecloth#
Two ways of defining the tablecloth are possible:
from a list of existing functions [§3.8.1],
by directly defining the various functions of the tablecloth [§3.8.2].
3.8.1. Operand FONCTION#
FONCTION = lf
List of function-type concepts created by DEFI_Fonction [U4.31.02], DEFI_CONSTANTE [U4.31.01], CALC_FONC_INTERP [U4.32.01],… commands created by commands [],…
lf is the list of function concept names corresponding to the values of the parameter.
All functions in the list must have the same variable name (NOM_PARA from DEFI_FONCTION, which we’ll call npf) and have the same nr for the result name.
nf is a tablecloth of the name variable NP and the name variable NPF and whose value is of the name nr.
3.8.2. Direct definition of functions#
3.8.2.1. Operand NOM_PARA_FONC#
Name of the characteristic parameter of the functions constituting the table.
The allowed values listed are the same as for NOM_PARA.
3.8.2.2. Keyword DEFI_FONCTION#
Direct definition of the functions constituting the tablecloth.
3.8.2.3. Operand VALE#
lv is the list of values (x1, y1,…, xn, yn) with in order:
x1, y1 (the first value of the parameter and the corresponding value of the result),
…
xn, yn (the last value of the parameter and the corresponding value of the result).
3.8.2.4. Operands PROL_DROITE and PROL_GAUCHE#
Define the type of extension to the right (left) of the variable’s domain of definition:
“CONSTANT” |
for an extension with the last (or first) value of the function, |
“LINEAIRE” |
for an extension along the first defined segment (PROL_GAUCHE) or the last defined segment (PROL_DROITE), |
“EXCLU” |
if extrapolation of values outside the domain of definition of the npfparameter is forbidden (in this case if a calculation requires a value of the function outside the domain of definition, the code will stop in a fatal error). |
3.8.2.5. Operand INTERPOL#
◊ INTERPOL =
Type of interpolation of the function between values in the domain of definition of the function: one type for interpolation of the abscissa and one for the interpolation of the ordinates of the function. This is achieved by providing a list of texts from:
“LIN”: |
linear, |
“LOG”: |
logarithmic, |
“NON”: |
we do not interpolate (and therefore the program will stop if we ask for the value of the function for a value of the parameter where it has not been defined). |
Note:
If only one value is specified, it is taken into account by both the interpolation of the parameter and the function. INTERPOL = “LOG” is equivalent to (“LOG”, “LOG”) .
3.9. Operand TITRE#
◊ TITRE = you
Title attached to the concept produced by this operator [U4.03.01].
3.10. Assessment of a tablecloth#
Let’s say a \(N\) sheet whose parameter is NOM_PARA = \(y\) and composed of functions including NOM_PARA_FONC = \(x\), of values NOM_RESU = \(z\mathrm{=}f(x)\).
To rate \(N(x,y)\):
We’re looking for \(i\) such as \({y}_{i}\mathrm{\le }y<{y}_{i+1}\),
The two functions \({f}_{i}\) and \({f}_{i+1}\) are evaluated in \(x\). To do this, we use the extensions and the interpolation types of each function (defined in the DEFI_FONCTION command or under the keyword DEFI_FONCTION factor of DEFI_NAPPE).
We then evaluate \(N(x,y)\) by interpolating using values \(({y}_{i},{y}_{i+1})\) and \(({f}_{i}(x),{f}_{i+1}(x))\). The extensions and types of interpolation defined by the simple keywords PROL_GAUCHE, PROL_DROITE, INTERPOL of DEFI_NAPPE are then used.
One would write:
tablecloth = DEFI_NAPPE (NOM_PARA = “y”,
NOM_RESU = “z”,
NOM_PARA_FONC = “x”,
INTERPOL = (a, b),
DEFI_FONCTION = (_F (VALE = … ,
INTERPOL = (c, d),),
other functions…),)
The types of interpolation used are:
c between two values x,
d when we evaluate the functions in x,
has between two values of y,
b between two different functions (evaluated in x).