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Titrate:
Structure of Données function, fonction_C and fonction_I
Date:
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Organization (S): EDF-R & D/AMA
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Structures of Données function, fonction_C
and fonction_I

1 General information

The types of concepts function, fonction_C and fonction_I represent functions (with the direction
mathematics of the term) of one, two (or more) variable.

The function have actual values, the fonction_C complex values and the fonction_I
whole values. In the continuation of this document, one will speak only about the functions with actual values
(function) by knowing that all can be transposed to the fonction_C and fonction_I.

A function can be:

· “tabulée”: i.e. that it is known only in certain points. In this case, its evaluation
can require an interpolation or an extrapolation,
· “interpreted”: its representation then contains the mathematical “formula” of the function. (One
also speak about function “formulates”).

Note:

An “interpreted” function (of a variable) can be tabulée (for certain values of its
variable) by command CALC_FONC_INTERP. For such a tabulée function, the evaluation
in a point different from the points of tabulation can be done by interpolation or while calculating
exactly the function formulates having been used for the tabulation (object .FITA).
A formula can have variables as many as necessary. On the other hand, functions
tabulées can have only 0, 1 or 2 variables. One will speak then about “constant function”,
“fonction_1” or “tablecloth”.
The variables of a function (as its result) “are typified”: “TEMP”, “INST”, “EPSI”,
… One will speak then about the name of the variables (or parameters) and the result.
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2 Tree structure


FONCTION (K19)::= record

F
“$VIDE”:
TITER


“.PROL”: OJB
S V K16


| % if the function is interprêtée:
“.ADVA”:
OJB
S
V
I
“.INFX”:
OJB
S
V
I
“.NOVA”:
OJB
S
V
K8
“.POLO”:
OJB
S
V
I


| % if the function is tabulée:



/% if constant function or fonction_1:



“.VALE”
: OJB
S V R




% if tabulée starting from a function formulates:
“.FITA”:
OJB
S

V
K24



/% if tablecloth:
“.PARA”:
OJB
S

V
R
“.VALE”:
OJB
TESTSTEMXÇ
V
R

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3
Contents of the basic objects

3.1 Object
“.PROL”

Object “.PROL” is length 5 for the tabulées functions of 0 or 1 variable and the functions
interpreted. It is length 6 + 2 * nf for the tablecloths, if nf is the number of fonction_1
composing the tablecloth.

· .PROL (1):

Type of the function.

/“CONSTANT”
: constant function
/“FONCTION”
: fonction_1 real
/“FONCT_C'
: fonction_1 complex
/“NAPPE”
: function with 2 variables (tablecloth)
/“INTERPRE”
: interpreted function

· .PROL (2):

Type of interpolation wished between the points of tabulation. Relate to only the functions
tabulées.

/“INTERPRE”:
one uses the exact formula of the function formulates having given rise to the function
tabulée.
/“XXX FFF” where XXX and FFF = “NON” or “LIN” or “LOG”.

XXX relates to the parameter and FFF the function.

“NON”: interpolation is prohibited,
“LIN”: linear interpolation,
“LOG”: interpolation logarithmic curve.

That is to say a function F (X).

One will make a linear interpolation between the 2 points framing the sought point, but for this
linear interpolation, one will use possibly the logarithm of X or F.

For example if “LIN LOG”, one will use X and log (F).

Note:

For a tablecloth, XXX relate to the 2nd parameter of the function.

· .PROL (3):

Name of the last parameter.

/“TOUTPARA” for a constant function,
/name of the only parameter (i.e of the variable) for a fonction_1,
/name of the 2nd parameter for a tablecloth,
/'' for a not tabulée interpreted function.
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· .PROL (4):

/name (or type) of the result of the function,
/“TOUTRESU”.

· .PROL (5):

“prolongation” desired with the function apart from its field of tabulation (extrapolation).
concern that the tabulées functions.

“xy”
where X and y = “E” or “It or “It or “I”.

X:
prolongation “on the left” (for a parameter lower than the smallest parameter of
tabulation),
y:
prolongation “on the right” (for a parameter higher than the greatest parameter of
tabulation).

“E”: excluded prolongation,
“It: constant prolongation,
“It: linear prolongation (starting from the 2 first or of the last 2 points),
“I”: interpreted prolongation (starting from the formula).

Note:

For a tablecloth, these prolongations relate to the 2nd parameter (values of the object
“.PARA”).
There is not prolongation “logarithmic curve”.

· .PROL (6):

For the tablecloths: name of the 1st parameter (name of the parameter of the fonction_1 composing the tablecloth).

· .PROL (7):

Type of interpolation wanted for the 1ère fonction_1 composing the tablecloth


(“FLAX LOG”, “LOG LOG”,…) (see .PROL (2)).

· .PROL (8):

Type of prolongation wanted for the 1ère fonction_1 composing the tablecloth


(“EL”, “DC”,…) (see .PROL (5)).

· .PROL (9):

Type of interpolation wanted for the 2nd fonction_1 composing the tablecloth

· .PROL (10)…

3.2 Object
“.PARA”

This object contains the values of the “2nd” variable of the tablecloth. With each value of this 2nd
variable corresponds an object of the collection “.VALE” which contains the values of the fonction_1
associated this variable.
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3.3 Object
“.VALE”

1) For a fonction_1, this object contains the numerical values of the points of tabulation.
That is to say N: the number of points of tabulation,

V (1,…, N)
:
X-coordinates

points,
V (n+1,…, 2 * N)
:
values of the function at the points.

Note:

If the function is with complex values, 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,





V (3 * N): imaginary part of the function at the last point.

The number of points of discretization (N) can be obtained by division by 2 (or 3) of the attribute
“LONMAX” of object” .VALE ".

2) For a tablecloth, this object is a contiguous numbered collection. Each object I of collection
with the same structure as object “.VALE” of the fonction_1 (above). It describes the attached function
with the ième value of the 2nd variable of the tablecloth.

3.4 Object
“.FITA”

When the fonction_1 was obtained by CALC_FONC_INTERP, this object contains the name of the function
“formula” which was used for calculation of the values of the tabulée function. The name of the function formulates initial
is necessary if the interpolation for the tabulée function is worth: “INT (erprete)”.

3.5 Object
“.NOVA”

This object contains the name of the variables of the function “formulates”.

3.6 Objects
“.ADVA”,” .INFX ", “.POLO”

These objects contain “pointers” towards objects “supervisor” (“&&SYS FI.ARITE”, '&&SYS
FI.CLASSE, '&&SYS FI.NOM,…) who are not currently documented. Us them
will thus not comment on here.
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4 Examples

4.1
Constant function: f1

f1=defi_constante (vale:1.2 nom_resu:“nom_res1”);
impr_co (Co:f1);

====> IMPR_CO OF THE STRUCTURE OF DATA: F1
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F1 .PROL <
1 - >CONSTANT<>LIN LIN <>TOUTPARA<>NOM_RES1<>CC <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F1 .TITR <
1 - >ASTER 3.07.02 F1 CONCEPT CALCULATES THE 20/08/96 A 09:36:57 OF FUNCTION TYPE <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F1 .VALE <
1 - 1.00000E+00 1.20000E+00

4.2
Tabulée real function: f2

lpara=defi_list_reel (beginning: 3. interval:(jusqu_a:6. numbers:3));
lfonc=defi_list_reel (beginning: 3.2 interval:(jusqu_a:6.2 a number:3));
f2=defi_fonction (
titrate: “this is my title”
Interpol:“not” will nom_para:“DX” nom_resu:“mom_res2”
prol_gauche:“excluded” prol_droit:“constant”
will vale_para: vale_fonc will lpara: lfonc
);
impr_co (Co:f2);

====> IMPR_CO OF THE STRUCTURE OF DATA: F2
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F2 .PROL <
1 - >FONCTION<>NON NON <>DX <>MOM_RES2<>EC <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F2 .TITR <
1 - >ceci is my title <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F2 .VALE <
1 - 3.00000E+00 4.00000E+00 5.00000E+00 6.00000E+00 3.20000E+00
6 - 4.20000E+00 5.20000E+00 6.20000E+00
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4.3
Tabulée complex function: f3

f3=defi_fonction (
Interpol:(“flax”, “log”) will nom_para:“INST” nom_resu:“mom_res3”
prol_gauche:“linear” prol_droit:“constant”
vale_c: (0. 1.2.2.2 1. 3.7.4.7 2. 5.6.6.6 3. 3.5.4.5)
);
impr_co (Co:f3);

====> IMPR_CO OF THE STRUCTURE OF DATA: F3
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F3 .PROL <
1 - >FONCT_C <>LIN LOG <>INST <>MOM_RES3<>LC <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F3 .TITR <
1 - >ASTER 3.07.02 F3 CONCEPT CALCULATES THE 20/08/96 A 09:36:57 OF TYPE FONCTION_C <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >F3 .VALE <
1 - 0.00000E+00 1.00000E+00 2.00000E+00 3.00000E+00 1.20000E+00
6 - 2.20000E+00 3.70000E+00 4.70000E+00 5.60000E+00 6.60000E+00
11 - 3.50000E+00 4.50000E+00

4.4
Real tablecloth defined by functions: nap1

f21=defi_fonction (nom_resu:“bid1” will nom_para:“temp”
Interpol:(“flax”, “flax”) prol_droit:“linear”
vale: (1.2 3.7.4.2.6.7));
f22=defi_fonction (nom_resu:“bid2” will nom_para:“inst”
Interpol:(“log”, “log”) prol_droit:“constant”
vale: (10.2 30.7 40.2 60.7));
f23=defi_fonction (nom_resu:“bid2” will nom_para:“inst”
Interpol:(“log”, “flax”) prol_gauche:“linear”
vale: (11.2 31.7 41.2 61.7));
nap1=defi_nappe (
Interpol:(“flax”, “log”) will nom_para:“PULS” nom_resu:“mom_nap1”
prol_gauche:“excluded” prol_droit:“constant”
para: (8.9 12.9 17.9)
function: (f21 f22 f23)
);
impr_co (Co:nap1);

====> IMPR_CO OF THE STRUCTURE OF DATA: NAP1
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP1 .PARA <
1 - 8.90000E+00 1.29000E+01 1.79000E+01
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP1 .PROL <
1 - >NAPPE <>LIN LOG <>PULS <>MOM_NAP1<>EC <>TEMP <>LIN FLAX <
8 - >EL <>LOG LOG <>EC <>LOG FLAX <>LE <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP1 .TITR <
1 - >ASTER 3.07.02 CONCEPT NAP1 CALCULATES THE 20/08/96 A 09:36:58 OF FUNCTION TYPE <
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: NAP1 .VALE
OBJECT IMPRESSION OF COLLECTION CONTIGUE>NAP1 .VALE< OC: 1
1 - 1.20000E+00 4.20000E+00 3.70000E+00 6.70000E+00
OBJECT IMPRESSION OF COLLECTION CONTIGUE>NAP1 .VALE< OC: 2
1 - 1.02000E+01 4.02000E+01 3.07000E+01 6.07000E+01
OBJECT IMPRESSION OF COLLECTION CONTIGUE>NAP1 .VALE< OC: 3
1 - 1.12000E+01 4.12000E+01 3.17000E+01 6.17000E+01
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4.5
Definite real tablecloth completion: nap2

nap2=defi_nappe (
Interpol:(“flax”, “log”) will nom_para:“PULS” nom_resu:“mom_nap2”
prol_gauche:“excluded” prol_droit:“constant”
para: (8.9 12.9)
nom_para_fonc:“EPSI”
defi_fonction:(prol_droit:“linear”
vale: (1.2 3.5.2.2.4.5 3.2.6.5))
defi_fonction:(prol_gauche:“constant”
vale: (1.2 3.7.4.2.6.7))
);
impr_co (Co:nap2);

====> IMPR_CO OF THE STRUCTURE OF DATA: NAP2
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP2 .PARA <
1 - 8.90000E+00 1.29000E+01
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP2 .PROL <
1 - >NAPPE <>LIN LOG <>PULS <>MOM_NAP2<>EC <>EPSI <>LIN FLAX <
8 - >EL <>LIN LIN <>CE <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >NAP2 .TITR <
1 - >ASTER 3.07.02 CONCEPT NAP2 CALCULATES THE 20/08/96 A 09:36:58 OF FUNCTION TYPE <
--------------------------------------------------------------------------------
IMPRESSION OF THE COLLECTION: NAP2 .VALE
OBJECT IMPRESSION OF COLLECTION CONTIGUE>NAP2 .VALE< OC: 1
1 - 1.20000E+00 2.20000E+00 3.20000E+00 3.50000E+00 4.50000E+00
6 - 6.50000E+00
OBJECT IMPRESSION OF COLLECTION CONTIGUE>NAP2 .VALE< OC: 2
1 - 1.20000E+00 4.20000E+00 3.70000E+00 6.70000E+00

4.6
Function formulates to 1 variable: ff1

!formulate (real:(ff1 (real:inst) =
2.3 * (cos (3.2+sqrt (inst))) - heavysid (inst - pi)
));
impr_co (Co:ff1);

====> IMPR_CO OF THE STRUCTURE OF DATA: FF1
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF1 .ADVA <
1 - 53 0 0 0 0
6 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF1 .INFX <
1 - 54 26 23 12 23
6 - 55 24 7 23 53
11 - 40 40 40 25 21
16 - 23 53 25 43 40
21 - 42 0 0 0 0
26 - 0 0 0 0 0
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF1 .NOVA <
1 - >INST <> <> <> <> <> <> <
8 - > <> <> <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF1 .POLO <
1 - 54 55 53 7 24
6 - 12 26 53 43 25
11 - 21 25 40 25 21
16 - 23 53 25 43 40
21 - 42 0 0 0 0
26 - 0 0 0 0 0
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF1 .PROL <
1 - >INTERPRE<>INTERPRE<> <>TOUTRESU<>II <
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4.7
Function formulates with 2 variables: ff2

!formulate (real:(ff2 (real:X, reality:y) =
2.3 * (cos (3.2+sqrt (X))) - (ff1 (y) +3.4 * f2 (X))
));
impr_co (Co:ff2);

====> IMPR_CO OF THE STRUCTURE OF DATA: FF2
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF2 .ADVA <
1 - 57 58 0 0 0
6 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF2 .INFX <
1 - 54 26 23 12 23
6 - 55 24 7 23 57
11 - 40 40 40 25 23
16 - 20 52 23 58 40
21 - 24 59 26 22 60
26 - 23 57 40 40 42
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF2 .NOVA <
1 - >X <>Y <> <> <> <> <> <
8 - > <> <> <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF2 .POLO <
1 - 54 55 57 7 24
6 - 12 26 58 52 20
11 - 59 57 60 22 26
16 - 24 25 23 58 40
21 - 24 59 26 22 60
26 - 23 57 40 40 42
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF2 .PROL <
1 - >INTERPRE<>INTERPRE<> <>TOUTRESU<>II <
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4.8
Function formulates to 1 variable: ff3 tabulée thereafter

!formulate (real:(ff3 (real:X) =sqrt (X)));
&ff3=calc_fonc_interp (
function: ff3
Interpol:“int” prol_droit: “linear”
vale_r:(1. 4. 9. 16.)
);
impr_co (Co:ff3);

====> IMPR_CO OF THE STRUCTURE OF DATA: FF3
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .ADVA <
1 - 62 0 0 0 0
6 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .FITA <
1 - >FF3 <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .INFX <
1 - 7 23 62 40 42
6 - 0 0 0 0 0
11 - 0 0 0 0 0
16 - 0 0 0 0 0
21 - 0 0 0 0 0
26 - 0 0 0 0 0
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .NOVA <
1 - >X <> <> <> <> <> <> <
8 - > <> <> <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .POLO <
1 - 62 7 62 40 42
6 - 0 0 0 0 0
11 - 0 0 0 0 0
16 - 0 0 0 0 0
21 - 0 0 0 0 0
26 - 0 0 0 0 0
31 - 0 0 0 0 0
36 - 0 0 0 0 0
41 - 0 0 0 0 0
46 - 0 0 0 0 0
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .PROL <
1 - >FONCTION<>INT INT <>X <>TOUTRESU<>EL <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .TITR <
1 - >ASTER 3.07.02 CONCEPT FF3 CALCULATES THE 20/08/96 A 09:36:58 OF FUNCTION TYPE <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF3 .VALE <
1 - 1.00000E+00 4.00000E+00 9.00000E+00 1.60000E+01 1.00000E+00
6 - 2.00000E+00 3.00000E+00 4.00000E+00
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4.9
Function tabulée starting from another function

!formulate (real:(ff41 (real:X) =sqrt (X)));
!formulate (real:(ff42 (real:X) =2.* ff41 (X) * sqrt (X)));
ff4=calc_fonc_interp (
function: ff42 nom_resu: “nom_res4”
Interpol:(“log”, “flax”)
prol_droit: “excluded” prol_gauche: “interpre”
vale_r:(1.6 2.6.3.6.4.6)
);
impr_co (Co:ff4);

====> IMPR_CO OF THE STRUCTURE OF DATA: FF4
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF4 .FITA <
1 - >FF42 <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF4 .PROL <
1 - >FONCTION<>LOG LIN <>X <>NOM_RES4<>IE <> <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF4 .TITR <
1 - >ASTER 3.07.02 CONCEPT FF4 CALCULATES THE 20/08/96 A 09:36:58 OF FUNCTION TYPE <
--------------------------------------------------------------------------------
SEGMENT IMPRESSION OF VALUES >FF4 .VALE <
1 - 1.60000E+00 2.60000E+00 3.60000E+00 4.60000E+00 3.20000E+00
6 - 5.20000E+00 7.20000E+00 9.20000E+00

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