XMLlab-1.4 Software reference manual

The data entry of the Lotka-Voltera equation parameters is realized in the window illustrated by the following figure :

Figure 2.2. Kinetic parameters data entry

This section contains the following parameters:

The data entry of the initial concentrations of preys and predators per square kilometers is made in the window illustrated by the following figure:

Figure 2.3. Initial concentrations data entry

This section contains the following parameters :

Simulation time entry is done in the window illustrated by the following figure :

Figure 2.4. Siimulation time entry

This section contains the only following parameter :

They are used for the resolution of the differential equation giving the evolution with time of the number of preys and predators :

    <defdomain1d label="time" unit="d">
      <name>Temps</name>

      <interval discretization="linear" steps="1000">
        <initialvalue>0</initialvalue>
        <finalvalue>final_time</finalvalue>
      </interval>
    </defdomain1d>

Definition of the element ode (ordinary differential equation) grouping together the reference to the integration variable time and to its domain of variation, as well as the definition of the states Prey and Predator, with its derivative and its initial value for each one of them:

    <ode label="predation">
      <refdomain1d ref="time" />

      <states>
        <state label="Prey">
          <name lang="french">Concentration en proie (km-2)</name>
          <name lang="french">Prey concentration (km-2)</name>
          <derivative>(r*Prey) - (k*Prey) - (a*Prey*Predator)</derivative>
          <initialcondition>Prey0</initialcondition>
        </state>

        <state label="Predator">
          <name lang="french">Concentration en prédateur (km-2)</name>
          <name lang="french">Predator concentration (km-2)</name>
          <derivative>(b*Prey*Predator) - (q*Predator)</derivative>
          <initialcondition>Predator0</initialcondition>
        </state>
      </states>

    </ode>

It consists of parametric curve x = Prey(t), y = Predator(t) that allows to see the joint evolution of the number of preys and the number of predators :

    <parametriccurve2d label="Prey_vs_predator">
      <name lang="french">Portrait de phase</name>
      <name lang="english">Phase picture</name>

      <x1>
        <value>Prey</value>
      </x1>

      <x2>
        <value>Predator</value>
      </x2>

    </parametriccurve2d>

It is accessible via the menu entry File->Save the results of the simulation for this simulation, thanks to the following lines specifying the default file of saving, as well as the list of the parameters and the results to save :

  <save>
    <file format="csv" href="essai.csv"
          labels="r k a b q time Prey Predator" />
  </save>

Here is the appearance of an example of CSV file obtained , the tag name of each parameter or result preceding its value :

"Growth rate of preys without predator, r (jour-1) : ",2.000000,
"Mortality of prey, without predator, k (jour-1) : ",0.001000,
"Predation rate of prey, per number of predator, a (prédateur-1 jour-1) : ",0.005000,
"Growth rate of predators, per number of eaten prey,
 b (proie-1 jour-1) : ",0.002000,
"Temps : ",0.000000,0.010010,...,10.000000,
"Prey concentratione (km-2) : ",5000.000000,5096.003572,...,3358.727460,
"Predator concentration (km-2) : ",100.000000,100.095849,...,144.851043,

This choice is done in the window illustrated by the following figure :

Figure 3.2. Analyte choice

Actually, it consists of a database containing scalar parameters (here only one, the pKa) for each analyte. For each one of them, a parameter values set is named. For instance, the figure above presents the value set of Hydrochloric acid parameters .

It is also possible to specify that all the value sets can be modified (cf. Section 2.2, « Database tag » for the details of the database tag).

The following lines show the structure of the definition of this whole value sets :

      <database>

        <scalar ... label="database_tag" ...>
          ... definition of the first and sole parameter
        </scalar>

        <record>
          <name lang="english">Hydrochloric acid</name>
          ... definition of the first value set  
          ... for all parameters
        </record>
        ...
        ...
        <record>
          <name lang="english">Salicylic acid</name>
          ... definition of the last value set  
          ... for all parameters
        </record>

      </database>

Let us now examine this structure a little more in detail :

This choice is done in the window illustrated by the following figure :

Figure 3.3. Titrant choice

Once againt, it consists of a database containing a scalar parameter for each titrant.

The structure of the definition of this whole value sets is the same one as previously :

Their entry is done in the window illustrated by the following figure :

Figure 3.4. Titration parameter data entry

It consists of entering the initial concentration of the analyte and the numbers intermediate values used for the calculation :

      <scalar increment="0.000001" label="c_analyte"
              max="1" min="0.000001" unit="mol / L">
        <name lang="french">Concentration de l'espèce à titrer (mol/L)</name>
        <name lang="english">Initial concentration of the analyte (mol/L)</name>
        <value>0.01</value>
      </scalar>

      <scalar increment="10" label="simulation_steps"
              max="1000" min="10" widget="slider">
        <name lang="french">Nombre de valeurs intermédiaires pour le calcul</name>
        <name lang="english">Number of values for the simulation</name>
        <value>100</value>
      </scalar>

Their entering is done in the window illustrated by the following figure :

Figure 3.5. Experimental data entry

It is a matricial-type parameter, whose lines correspond to experimental data (64 maximum) here, and whose the two columns correspond respectively to the abscissa and to the ordinate. It can be saved using the icon in a text file having the extension .dat, downloaded from the same file .dat via the icon , or reseted via the icon .

The part of the XML code corresponding to the definition of this matrix is the following one:

      <matrix clear="yes" cols="2" label="user_curve_mat"
              load="yes" rows="64" save="yes"
              striprow="yes">
        <name/>
        <col>
          <name lang="french">Abscisses</name>
          <name lang="english">X-axis</name>
          <value>0</value>
        </col>
        <col>
          <name lang="french">Ordonnées</name>
          <name lang="english">Y-axis</name>
          <value/>
        </col>
      </matrix>

It is the definition of the domain of the discrete values taken by the variable c_titrant during the titration, the number of these values being fixed by the variable simulation_steps (cf. § Section 2.2.3, « Parameters of the titration ») :

    <defdomain1d label="c_titrant">
      <name lang="french">Concentration du titrant</name>
      <name lang="english">Titrant concentration</name>

      <interval discretization="linear" steps="simulation_steps">
        <initialvalue>0</initialvalue>
        <finalvalue>1.5 * c_analyte</finalvalue>
      </interval>
    </defdomain1d>

It should be precised that the variable c_titrant can also be considered as a vector of all the values taken in its range. It can be involved in the calculations to be realized as a vector.

It consists of using an implicit function defining an application between c_titrant and the pH variable that we try to calculate, through an equation of the form f(c_titrant, pH) = 0 : at each value of c_titrant (cf. § Section 2.3.1, « Definition of the titrant concentration »), The equation admits a unique ph solution.

The following lines represent the structure of the definition of the implicit function ph that also includes :

    <implicitfunction label="ph" method="dichotomic">

      definition of the implicit function variable :
      <refdomain1d ref="c_titrant"/>

      <unknowns>
        definition of the sole unknown pH, where the boundaries 
        and the initial value are precised for each solving of the equation :
        <unknown label="pH">
          <name>pH</name>
          <guess>7</guess>
          <lowerbound>0</lowerbound>
          <upperbound>14</upperbound>
        </unknown>
      </unknowns>

      <equations>

        definition of our sole equation, preceeded by the definition
        of intermediary calculus variables :
        <variable label="Ka_analyte">...</variable>
        ...
        <variable label="titrant_load">...</variable>

        definition of the equation for which the cancelation allows to calculate  
        pH for each value of c_titrant :
        <equation>H - (1e-14)./H - analyte_load + titrant_load</equation>

      </equations>

      <outputs>
        ... definition of the curves function of c_titrant
      </outputs>

    </implicitfunction>

Here is now the detail of the intermediate variables of calculation. It should be noted that certain variables are vectors (as seen for the variable c_titrant), which permits to optimize the calculation of the curves of titration by Scilab.

For this reason, certain particular Scilab operator must be specified (v, v1 and v2 are vector, k an scalar) :

These operators are used in our case, certain manipulated variables being vectors (calculation of the pH, the coefficients of partitions, analyte, titrand and media charges), whereas other variables are positive scalars. The table below allows to distinguish the two types of variables in the following code :

        <variable label="Ka_analyte">10^(-pKa_analyte)</variable>
        <variable label="Ka_titrant">10^(-pKa_titrant)</variable>
        <variable label="H">10.^(-pH)</variable>        
        <variable label="alpha1_analyte">H./(H + Ka_analyte)</variable>
        <variable label="alpha0_analyte">Ka_analyte./(H + Ka_analyte)</variable>
        <variable label="charge_analyte">c_analyte.*alpha0_analyte</variable>
        <variable label="alpha1_titrant">H./(H + Ka_titrant)</variable>
        <variable label="alpha0_titrant">Ka_titrant./(H + Ka_titrant)</variable>
        <variable label="charge_titrant">c_titrant.*alpha1_titrant</variable>

Here is now the detail of the curves function of c_titrant that are defined :

        <output label="alpha1">
          <name>HA</name>
          <value>alpha1_analyte</value>
        </output>

        <output label="alpha0">
          <name>A-</name>
          <value>alpha0_analyte</value>
        </output>

It is a pseudo parametric curve, whose X-coordinates and ordinates are given by the columns of the user_curve_mat matrix described in § Section 2.2.4, « Experimental data » :

    <parametriccurve2d label="user_curve">
      <name lang="french">Points expérimentaux</name>
      <name lang="english">Experimental data</name>
      <x1>
        <name/>
        <value>user_curve_mat(:,1)</value>
                 -> first column of user_curve_mat
      </x1>
      <x2>
        <name/>
        <value>user_curve_mat(:,2)</value>
                 -> second column of user_curve_mat
      </x2>
    </parametriccurve2d>

The saving session, it's available for all the simulation from the menu entry File->Save the session, consists of saving the whole parameters of the simulation in a file, under the form of a code file Tcl whose execution will later allow to restore their values, this through the entry of the menu "load a session". Here is an example of such a file for our simulation:

set  {$}
set pKa_analyte {-7}
set  {$}
set pKa_titrant {14.8}
set c_analyte {0.01}
set simulation_steps {100}
array set user_curve_mat {
  39,0 39 40,0 40 5,0 5 23,0 23 5,1 0.008 5,2 2.8 61,0 61 44,0 44 9,0 9 27,
  0 27 11,0 11 48,0 48 32,0 32 15,0 15 53,0 53 36,0 36 2,0 2 19,0 19 20,
  0 20 2,1 0.002 2,2 2.4 57,0 57 41,0 41 6,0 6 24,0 24 6,1 0.010 6,2 8 62,
  0 62 45,0 45 28,0 28 12,0 12 50,0 50 49,0 49 33,0 33 16,0 16 54,0 54 37,
  0 37 3,0 3 21,0 21 3,1 0.004 3,2 2.6 58,0 58 42,0 42 7,0 7 25,0 25 7,
  1 0.012 active Abscisses 7,2 11.4 63,0 63 46,0 46 29,0 29 30,0 30 13,
  0 13 51,0 51 34,0 34 17,0 17 0,1 Abscisses 0,2 Ordonnées 55,0 55 38,
  0 38 4,0 4 22,0 22 4,1 0.006 4,2 2.7 60,0 60 59,0 59 43,0 43 8,0 8 26,
  0 26 8,1 0.014 10,0 10 8,2 11.7 64,0 64 47,0 47 31,0 31 14,0 14 52,
  0 52 35,0 35 1,0 1 18,0 18 1,1 0 1,2 2.2 56,0 56
}

It is accessible from the entry menu File->Saving simulation results as soon as it was defined via the tag save in the XML file of the simulation. The choice of the default file of saving and its format, as well as the list of the parameters and the results to be saved is determined by the following lines :

  <save>
    <file format="csv" href="essai.csv"
          labels="pKa_analyte c_analyte pKa_titrant c_titrant pH" />
  </save>

The following window allow to choose the name of the file which will be saved here with the format CSV :

Figure 3.7. Saving simulation results  

Here is the appearance of an example of a file obtained, the tag name of each parameter or result preceeding its value:

"pKa : ",-7.000000,
"Analyte concentration (mol/L) : ",0.010000,
"pKa : ",14.800000,
"Titrant concentration : ",0.000000,0.000152,...,0.015000,
"pH : ",2.000006,2.006628,...,11.697931,

Their data entry is done in the previously seen window.

This section contains the following parameters :

This variable is used to discretize Γ1 and Γ2 with n points :

    <defdomain1d label="thetain">
      <interval discretization="linear" steps="n">
        <initialvalue>0</initialvalue>
        <finalvalue>2*%pi</finalvalue>
      </interval>
    </defdomain1d>

We also illustrates the possibility of using Scilab constants , here %pi.

This variable is used to discretize Γ0 with 2n points :

    <defdomain1d label="thetaout">
      <interval discretization="linear" steps="2*n">
        <initialvalue>0</initialvalue>
        <finalvalue>2*%pi</finalvalue>
      </interval>
    </defdomain1d>

Its boundary is Γ = Γ0 ∪ Γ1 ∪ Γ2. Its definition (tag defdomain2d) is composed of the description of its boundaries Γ0, Γ1 and Γ2, each of them being described by a 2D parametric curve (tag parametriccurve2d) depending on the variables thetain and thetaout, the tag refdomain1d indicating the variable (domain1d) in dependance :

    <defdomain2d dependencies="n" label="omega">
      <border>
        <parametriccurve2d label="gamma_0">
          <refdomain1d ref="thetaout"/>
          <x1>
            <value>cos(thetaout)</value>
          </x1>
          <x2>
            <value>sin(thetaout)</value>
          </x2>
        </parametriccurve2d>
        <parametriccurve2d label="gamma_1">
          <refdomain1d ref="thetain"/>
          <x1>
            <value>0.4+0.2*cos(thetain)</value>
          </x1>
          <x2>
            <value>0.2*sin(-thetain)</value>
          </x2>
        </parametriccurve2d>
        <parametriccurve2d label="gamma_2">
          <refdomain1d ref="thetain"/>
          <x1>
            <value>-0.4+0.25*cos(thetain)</value>
          </x1>
          <x2>
            <value>0.25*sin(-thetain)</value>
          </x2>
        </parametriccurve2d>
      </border>
    </defdomain2d>

The attribute dependencies="n" allows to indicate that the triangulation of the domain, which is an expensive operation, must only be done when it changes, thus when n changes of value.

It is contained in the following code, the correspondences being as follows :

    <stationary-pde label="pde1">
      <refdomain2d ref="omega"/>
      <pdestate label="u">
        <name lang="french">Tension</name>
        <name lang="english">Voltage</name>
        <inside dependencies="n d">
          <diffusion>[10 0;0 d]</diffusion>
          <proportional>0</proportional>
          <source>0</source>
        </inside>
        <boundary>
          <condition bdy="gamma_0">
            <dirichlet>0</dirichlet>
          </condition>
          <condition bdy="gamma_1">
            <dirichlet>a</dirichlet>
          </condition>
          <condition bdy="gamma_2">
            <dirichlet>b</dirichlet>
          </condition>
        </boundary>
      </pdestate>
    </stationary-pde>

Here also, we use the attribute dependencies of the inside tag to calculate only what is necessary when the parameters change. Thus, the assembly of the problem in the domain is redone only if n or d changes, allowing to vary the boundary conditions without doing aganin large useless calculations.

Their data entry is done in the window illustrated by the following figure :

Figure 5.4. System parameters data entry

This section contains the following parameters:

Their data entry is done in the window illustrated by the following figure :

Figure 5.5. Solving parameters data entry

This section contains the following parameters :

It is the integration variable used for the solution of our differential equation, the discretization interval being cut out in 1000 steps :

    <defdomain1d label="t" unit="s">
      <name>Time</name>
      <discretization interval="linear" steps="1000">
        <initialvalue>0</initialvalue>
        <finalvalue>jf*24*3600</finalvalue>
      </interval>
    </defdomain1d>

Definition of the ode element (ordinary differential equation) grouping together :

    <ode label="terre_lune">
      <refdomain1d ref="t"/>

      <states>
        <variable label="r3">norm(xT-xL)^3</variable>

        <state label="xT" size="2">
          <name>Earth position</name>
          <derivative>vT</derivative>
          <initialcondition>[0;0]</initialcondition>
        </state>

        <state label="vT" size="2">
          <name>Earth speed</name>
          <derivative>6.67e-11*mL*1e24*(xL-xT)/r3</derivative>
          <initialcondition>[0;0]</initialcondition>
        </state>

        <state label="xL" size="2">
          <name>Moon position</name>
          <derivative>vL</derivative>
          <initialcondition>[3.84402e8;0]</initialcondition>
        </state>

        <state label="vL" size="2">
          <name>Moon speed</name>
          <derivative>6.67e-11*mT*1e24*(xT-xL)/r3</derivative>
          <initialcondition>
            vL0*[cos(%pi*theta/180);sin(%pi*theta/180)]
          </initialcondition>
        </state>
      </states>

      <outputs>
        <output label="xG">
          <name>Gravity centre</name>
          <value>(xL*mL+xT*mT)/(mL+mT)</value>
        </output>
      </outputs>
    </ode>

It consists in the earth position relative to the centre of gravity of the Earth-Moon system :

    <parametriccurve2d label="traj_terre">
      <name>Earth</name>
      <refdomain1d ref="t"/>
      <x1>
        <value>xT(:,1)-xG(:,1)</value>
      </x1>
      <x2>
        <value>xT(:,2)-xG(:,2)</value>
      </x2>
    </parametriccurve2d>

It consists in the moon position relative to the centre of gravity of the Earth-Moon system :

    <parametriccurve2d label="traj_lune">
      <name>Moon</name>
      <refdomain1d ref="t"/>
      <x1>
        <value>xL(:,1)-xG(:,1)</value>
      </x1>
      <x2>
        <value>xL(:,2)-xG(:,2)</value>
      </x2>
    </parametriccurve2d>

It allows to define a system of differential equations (ordinary differential equation) :

    <ode label="id_ode"
         dependencies="param_list_label">
           -> the list separator is the space ;
              that indicate that this calculation element depends  
              only on the listed parameters, that avoid useless recalculations
      ...
    </ode>

It gathers the following elements :

For examples of the ode tag, use refer to the following simulations:

It is supposed that we have an equation f( x , y ) = 0. If for each value of x , this equation admits a single solution in y , the application that associates x to y is called implicit function ( of y as a function of x ). Exemple : whether the equation f( x , y ) = x 2 + y 2 - 1 = 0. For each value of x of the interval [0,1], the equation admits a unique solution y = 1 − x 2 . However, it is not possible in general to express y as a function of x .

The role of the implicit function tag is actually to define a system of implicit functions :

    <implicitfunction label="implicit_function_id"
                      method="newton|dichotomic"
                        -> method used for the equation resolutions in each value of the variable in dependence
                           méthode utilisée pour la résolution des équations  en chaque valeur de la variable en dépendance
    >
      ...
    </implicitfunction>

It gathers the following elements:

For an example of implicit function tag use, refer to the acido-basic simulation of titration in aqueous medium, § Section 2.3.2, «  pH calculation using the dichotomic method ».

It aims at describing the following Laplace equation:

with two types of boundary conditions :

knowing that the domain Ω have as boundary Γ = Γ0 ∪ Γ1 ∪ ... Γi ∪ ... Γn.

This tag has the following aspect, knowing that the definition of the 2d domain corresponding to Ω to which it refers, must include the definitions of Γ0, Γ1, ... Γi, ... Γn via a border tag containing a parametriccurve2d tag for each Γi. The convention being that the interior of the domain is always on the left curve when its parameter increases, which allows to build domains containing holes :

    <stationary-pde label="stationary_pde_id">

      once and only once :
      <refdomain2d ref="domaine2d_ref_id">...(cf. § Section 4.2.2, « Defdomain2d and
          refdomain2d Tag»)

      once and only once :
      <pdestate label="variable_u_id">

        one or several times :
        <name lang="french|english|german|spanish">
          variable name as displayed in the simulation save file
        </name>

        <inside>...equation definition

        <boundary>...boundary conditions definition 

      </pdestate>

    </stationary-pde>

Here is the detail of the elements concerning the equation and the boundary conditions :

Caution: when the coefficients are functions, one must absolutely use x and y to handle the X-coordinate and the ordinate (whatever the labels used in the parametriccurve2d in the border).

For an example of stationary-pde tag use, refers to simulation via finite elements of the Poisson's equation, § Section 2.3.4, « Definition of the stationary partial derivatives ».

It deals with a curve defined by a function y = f(x). It contains the domain of variation of x and the definition of f :

    <nonparametriccurve2d label="curve_id">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.1, « Drawcurve2d Tag»)
      </name>

X definition :
      once and only once :
      (cf. § Section 4.2.1, « Defdomain1d and
          refdomain1d Tag»)
      <defdomain1d>...
        OR
      <refdomain1d>...

Y definition y = f(x) :
      once and only once :
      <x2 label="Y_data_id" unit="Y data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          Y data name (not used at present)
        </name>
        once and only once :
        <value>
          f(x)
        </value>
      </x2>

    </nonparametriccurve2d>

For an example of nonparametriccurve2d Tag use, refer to the file Math/tangente.xml in the subdirectory examples of the XMLlab installation directory .

It consists of a parametric curve x = f(t), y = g(t). It contains the domain of variation of t and the definitions of f and g :

    <parametriccurve2d label="curve_id">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.1, « Drawcurve2d Tag»)
      </name>

T definition :
      once and only once :
      (cf. § Section 4.2.1, « Defdomain1d and
          refdomain1d Tag»)
      <defdomain1d>...
        OR
      <refdomain1d>...

X definition x = f(t) :
      once and only once :
      <x1 label="X_data_id" unit="X data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          X data name (not used at present)
        </name>
        once and only once :
        <value>
          f(t)
        </value>
      </x1>

Y definition  y = g(t) :
      once and only once :
      <x2 label="Y_data_id" unit="Y data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          Y data name (not used at present)
        </name>
        once and only once :
        <value>
          g(t)
        </value>
      </x2>

    </parametriccurve2d>

For example of parametriccurve2d tag use, refers to the following simulations :

It consists of a parametric curve x = f(t), y = g(t), z = h(t). It contains the domain of variation of t and the definitions of f, g and h :

    <parametriccurve3d label="curve_id">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.3, « Drawsurface Tag »)
      </name>

      none or several times :
      (cf. § Section 4.2.1, « Defdomain1d and
          refdomain1d Tag »)
      <defdomain1d>...
        OR
      <refdomain1d>...

      once and only once :
      <x1 label="X_data_id" unit="X data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          X data name  (not used at present)
        </name>
        once and only once :
        <value>
          f(t)
        </value>
      </x1>

      once and only once :
      <x2 label="Y_data_id" unit="Y data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          Y data name (not used at present)
        </name>
         once and only once :
        <value>
          g(t)
        </value>
      </x2>

      once and only once :
      <x3 label=" z_id" unit="z unit">
        none or several times :
        <name lang="french|english|german|spanish">
          z name (not used at present)
        </name>
        once and only once :
        <value>
          h(t)
        </value>
      </x3>

    </parametriccurve3d>

For an exemple of parametriccurve3d tag use , refers to the file Math/helice.xml in the subdirectory examples of the XMLlab installation directory .

It deals with a non parametric surface z = h(x, y). Its contains the 2D domain of the variation of (x, y) and the definition of h :

    <nonparametricsurface label="surface_id">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.3, « Balise drawsurface »)
      </name>

      once and only once :
      (cf. § Section 4.2.2, « Defdomain2d and
          refdomain2d Tag»)
      <defdomain2d>...
        OR
      <refdomain2d>...

      once and only once :
      <x3 label=" z_id" unit="z unit">
        none or several times :
        <name lang="french|english|german|spanish">
          z name (not used at present)
        </name>
        once and only once :
        <value>
          h(x,y)
            -> X and y being labels identifying the x and y coordinates 
               of 2D domaine points, namely as this one contains one :
               - <rectangle> : x and y are the 2 domains 1D labels
                               defined or in reference,
               - <border>    : x and y are the <x1> and <x2> tags labels of
                               <parametriccurve2d> defining the 2D domain.
        </value>
      </x3>

    </nonparametricsurface>

For an exemple of nonparametricsurface tag use, refers to the Math/gauss.xml file in the subdirectory examples of the XMLlab installation directory .

It deals wtih a parametric surface x = f(θ, φ), y = g(θ, φ), z = h(θ, φ). Its contains the 2D domain of variation of (θ, φ) and the definition of f, g and h :

    <nonparametricsurface label="id_surface">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.3, « Balise drawsurface »)
      </name>

      once and only once :
      (cf. § Section 4.2.2, « Defdomain2d and
          refdomain2d Tag»)
      <defdomain2d>...
        OR
      <refdomain2d>...

      once and only once :
      <x1 label="X_data_id" unit="X data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          X data name (not used at present)
        </name>
        once and only once :
        <value>
          f(θ,φ)
        </value>
      </x1>

      once and only once :
      <x2 label="Y_data_id" unit="Y data unit">
        none or several times :
        <name lang="french|english|german|spanish">
          Y data name  (not used at present)
        </name>
        once and only once :
        <value>
          g(θ,φ)
        </value>
      </x2>

      once and only once :
      <x3 label="z_id" unit="z unit">
        none or several times :
        <name lang="french|english|german|spanish">
          z name  (not used at present)
        </name>
        once and only once :
        <value>
          h(θ,φ)
        </value>
      </x3>

    </nonparametricsurface>

For an exemple of the parametricsurface tag use, refers to the file Math/sphere.xml in the subdirectory examples of the XMLlab installation directory.

It deals with a 2D or 3D multiline curve defined by a set of points (vertex tag) of segments composing it :

    <polyline label="id_courbe">

      none or several times :
      <name lang="french|english|german|spanish">
        possible curve name as displayed in its plot (cf. § Section 5.2.1, «Drawcurve2d Tag»)
      </name>

      one or several times :
      <vertex x1="x" x2="y" x3="z">

        none or several times :
        <name lang="french|english|german|spanish">
          possible curve name as displayed in its plot
        </name>

      </vertex>

    </polyline>

For an exemple of the polyline tag use, refers tothe file Math/gauss.xml provided in the subdirectory examples of the XMLlab installation directory.

It consists of a 2D axes system contained in a window or a part of a window, and for which we define:

      <axis2d type="cartesian|polar"
              position="left|right|center|origin"
                -> - "left" or "right" : puts the y axis at left or at right
                   - "center" : always puts the axes crossing in the center of the graphic window 
                   - "origin" : puts the axis crossing if possible at (0,0)
              xmin="x_min" xmax="x_max"
              ymin="y_min" ymax="y_max"
              iso="yes|no"
                -> indicate if, whatever is the system of axis size  
                   (via the recutting of the window which contains it),
                   the scales of X, and Y are identical
              cmin="z_min" cmax="z_max"
              colorbar="on|off|top|left|right|bot"
                -> position of the possible legend "color(z)"  
                   ("on" is equivalent to "left")
      >

        one or several times :
        <drawcurve2d |
         drawsurface |
         drawpoints>... cf. § Section 5.2, « Curves and surfaces »

      </axis2d>

For examples of the axis2d tag use, refers to the following simulations :

It deals whith a 3D system of axes contained in a window or a part of window, and for which we define :

      <axis3d xmin="x_min" xmax="x_max"
              ymin="y_min" ymax="y_max"
              zmin="z_min" zmax="z_max"
              elevation="3D view elevation (default number 45)" -> in degree
              azimuth="3D view azimuth (default number -45)"    -> in degree
              iso="yes|no"
                -> indicate if, whatever is the system of axis size  
                   (via the recutting of the window which contains it),
                   the scales of X, Y and Z are identical 
              cmin="min_z_or_illumination" cmax="max_z_or_illumination"
              colorbar="off|top|left|right|bot"
                -> position of the possible legend 
                   "color (Z or illumination)"   
      >

        one or several times :
        <drawsurface |
         drawcurve3d>... cf. § Section 5.2, « Curves and surfaces »

      </axis3d>

For examples of axis3d tag use, refers to the simulation via finite elements of the Poisson's equation, § Section 2.4, « Results display ».

It consists of a 2D curve displayed in a 2D system of axes, and for which we defines :

        <drawcurve2d ref="curve label to draw"
                       -> could be the label of one of the following tags :
                          - <state> of one <ode>
                          - <unknown> of one <implicitfunction>
                          - <nonparametriccurve2d>
                          - <parametriccurve2d>
                          - <polyline>
                     color="auto|blue|green|red|cyan|magenta|black|yellow"
                       -> "auto" : colors follow a cycle from a curve 
                          to the other one among the curves of the same <axis2d>
                          (there are two possible cycles as the  
                           <window> background is rather "clear" or "dark")
                     linetype="solid|dashed|dashdot|none"
                       -> - "solid" : continuous line
                          - "dashed" : dashed line
                          - "dashdot" : alternation of points and lines
                          - "none" : has sense only if marker is defined:
                                     there is even in that case a line
                                     which connects points, except if linetype="none"
                     thickness="1|2|3|4|5"  -> line thickness
                     marker="point|circle|trefoil|plus|star|diamond|
                             filled-diamond|triangle-up|triangle-down"
                       -> point, circle, trefoil, plus sign, star, 
                          diamond, filled diamond, triangle point in top, 
                          triangle points in bottom
        />

For examples of the drawcurve2d tag use , refers to the following simulations:

It deals with 3D curves displayed in a 3D system of axes, and for which we define:

        <drawcurve3d ref="curve label to draw"
                       -> could be the label of one of the following tags :
                          - <state> of one <ode>o
                          - <pdestate> of one <stationary-pde>
                          - <parametriccurve3d>
                          - <polyline>
                     color="auto|blue|green|red|cyan|magenta|black|yellow"
                       -> "auto" : colors follow a cycle from a curve 
                          to the other one among the curves of the same <axis2d>
                          (there are two possible cycles as the  
                           <window> background is rather "clear" or "dark")
                     linetype="solid|dashed|dashdot|none"
                       -> - "solid" : continuous line
                          - "dashed" : dashed line
                          - "dashdot" : alternation of points and lines
                          - "none" : has sense only if marker is defined:
                                     there is even in that case a line
                                     which connects points, except if linetype="none"
 
                     thickness="1|2|3|4|5"  -> line thickness
                     marker="point|circle|trefoil|plus|star|diamond|
                             filled-diamond|triangle-up|triangle-down"
                       -> point, circle, trefoil, plus sign, star, 
                          diamond, filled diamond, triangle point in top, 
                          triangle points in bottom
        />

For examples of the drawcurve3d tag use, refers to the file Math/helice.xml located in the subdirectory examples of the installation directory of XMLlab.

It consists a displayed surface in a 2D or 3D axes system, and for which we defines :

        <drawsurface ref="surface label to draw"
                       -> could be the label of one of the following tags :
                          - <pdestate> of one <stationary-pde>
                          - <parametriccurve3d>
                          - <nonparametricsurface>
                          - <parametricsurface>
                          - <polyline>
                     mode="level|light|wireframe"
                       -> - level : surface filled, color aiming 
                                    towards the black when Z decreases,
                          - light : surface filled, shade calculated 
                                    in function to a source of light,
                          - wireframe : wire representation.
                     shading="flat|interp|faceted"
                       -> shadow depiction, only taken into account 
                          if mode <> "wireframe" :
                          - flat : plain on each facet,
                          - interp : continue, by interpolation on each facet,
                          - faceted : flat + white wire around each facet in superpositionf
                     hidden="off"  -> not used at present
        />

For examples of the drawsurface tag use, refers to the simulation via finite elements of the Poisson's equation, § Section 2.4, « Results display ».

It deals with a list of 2D or 3D points displayed in a 2D or 3D system of axes, each point being illustrated by a cross accompanied by its co-ordinates :

        <drawpoints ref="points_labels_list"
                      -> list, separated by spaces,
                         <point> labels to draw
        />

Moreover, the position of each 2D point listed is manipulable from the constraints defined on it remain respected : click on the cross, the coordinates of the point is displayed then in a different color. Move then the cursor to modify its position. All the calculations resulting from the modification of this parameter are then realized in real time and curves in dependence are displayed again. Once obtained the wished value, click again the cross to fix its position.

For examples of the drawpoints tag use, refers to the simulation of the pendulum in the document Getting started XMLlab.