add more details about reducedbasis in python #219 #151

/cc @prudhomm

docs/mor/modules/ROOT/nav.adoc

@@ -7,3 +7,4 @@
 ** xref:pbdw.adoc#_using_pbdw[Using PBDW]
 * xref:index.adoc#_cases[Cases]
 ** xref:opusheat:index.adoc[OpusHeat]
+** xref:thermalfin:index.adoc[ThermalFin]

docs/mor/modules/ROOT/pages/index.adoc

@@ -12,3 +12,4 @@ The Parametrized Background Data Weak (xref:pbdw.adoc[PBDW]) method has also bee
 == Cases
 
 - xref:opusheat:index.adoc[OpusHeat]
+- xref:thermalfin:index.adoc[ThermalFin]

docs/mor/modules/thermalfin/nav.adoc

@@ -0,0 +1 @@
+* xref:index.adoc[Thermal fin]

docs/mor/modules/thermalfin/pages/index.adoc

@@ -0,0 +1,3 @@
+= Thermal fin
+
+The redaction of this page is in progress.

docs/user/modules/python/pages/pyfeelppmor/reducedbasis.adoc

@@ -20,19 +20,24 @@ To set the environment, those module also need to be imported :
 [source, python]
 ----
 import sys, os
-from feelpp.toolboxes.heat import *
-import feelpp.toolboxes.core as core
-from feelpp.operators import mass
-import feelpp.mor as mor
+from feelpp.toolboxes.heat import * <1>
+import feelpp.toolboxes.core as core <2>
+from feelpp.operators import mass <3>
+import feelpp.mor as mor <4>
 import feelpp
 ----
 
+<1> The toolbox heat is used to simulate the heat equation on the case studied.
+<2> The module `core` is used to set the environment.
+<3> The `mass` function is needed to create the mass matrix if we work on a time-dependent case.
+<4> The module `mor` is used to get the functions neededd by the toolbox mor.
+
 
 == Set the environment
 
 [source, python]
 ----
-config = feelpp.globalRepository("reducedbasis")
+config = feelpp.localRepository("reducedbasis")
 sys.argv = ["reducedbasis"]
 o = core.toolboxes_options("heat")
 o.add(mor.makeToolboxMorOptions())
@@ -43,22 +48,39 @@ e = feelpp.Environment(sys.argv, opts=o, config=config)
 
 == Set the model
 
+=== Description of the model
+
+In this document, the cases used is `thermal-fin` in 2D, with a stem:[\mathbb{P}_1] discretization and stationnary.
+This model is described in xref:mor:thermalfin:index.adoc[this page].
+
+The usage would be the same for another case.
+
+
+=== Code
+
 Set the parameters nedded to the model :
+
 - `config_file` : path to the cfg file
 - `dim` : the dimension of the case
 - `order` : the order of discretization (`1` for stem:[\mathbb{P}_1], `2` for stem:[\mathbb{P}_2])
-- `time_dependant` : is the case stationnary or transient ? (for now always to `False`)
+- `time_depedent` : is the case stationnary or transient ? (for now always to `False`)
 - `name` : name of the CRB case
 
+
+
 [source,python]
 ----
 config_file = "thermal-fin.cfg"
 dim = 2
 order = 1
-time_dependant = False
+time_depedent = False
 name = "thermalfin-2d"
 ----
 
+The configuration files for this case are available on github : https://raw.githubusercontent.com/feelpp/feelpp/develop/mor/cases/thermal-fin/2d/fin.geo[geometry file], https://raw.githubusercontent.com/feelpp/feelpp/develop/mor/cases/thermal-fin/2d/thermal-fin.cfg[cfg file], and https://raw.githubusercontent.com/feelpp/feelpp/develop/mor/cases/thermal-fin/2d/thermal-fin.json[json file].
+
+Then, we can create the model :
+
 [source,python]
 ----
 cfg = feelpp.readCfg(config_file)
@@ -118,7 +140,7 @@ default_parameter = modelParameters.toParameterValues()
 
 [source, python]
 ----
-model = mor.toolboxmor(name=name, dim=dim, time_dependent=time_dependant)
+model = mor.toolboxmor(name=name, dim=dim, time_dependent=time_depedent)
 model.setFunctionSpaces( Vh=heatBox.spaceTemperature() )
 
 def assembleDEIM(mu):
@@ -305,6 +327,8 @@ rb.computeOfflineErrorRhs()
 rb.computeOfflineError()
 ----
 
+The script `generate_basis.py` run this offline part. See the  xref:pyfeelppmor/reducedbasis_offline.adoc[dedicated page] for more details.
+
 == Online phase
 
 [source, python]
@@ -358,12 +382,3 @@ rb.getSolutionsFE(mu, k=0)
 The two functions `getSolutions` (resp. `getSolutionsFE`) return the solution stem:[u_N(\mu)] (resp. stem:[u(\mu)]) and the value of the output stem:[s_N^k(\mu)] (res. stem:[s^k(\mu)]).
 See xref:pyfeelppmor/parameters.adoc[the dedicated page] for the API of `ParameterSpaceElement`.
 
-
-
-== Offline stage :
-
-See the xref:pyfeelppmor/reducedbasis_offline.adoc[offline stage] page.
-
-== Online stage :
-
-See the xref:pyfeelppmor/reducedbasis_online.adoc[online stage] page.

docs/user/modules/python/pages/pyfeelppmor/toolboxmor.adoc

@@ -2,7 +2,8 @@
 
 = Toolboxmor
 
-For the configuration of the case, and the usage in a C++ application, refer to xref:mor:toolboxmor.adoc[ToolboxMor] documentation.
+For the configuration of the case, and the usage in a C++ application, refer to xref:mor:ROOT:toolboxmor.adoc[ToolboxMor] documentation.
+More details on the functions of the toolbox can be found in xref:pyfeelppmor/reducedbasis.adoc[this page].
 
 == Model
 
@@ -13,7 +14,7 @@ We assume that we have the following decompositions :
 [stem]
 ++++
 \begin{align}
-a(u, v; mu) &= \displaystyle\sum_{q=1}^{Q_a} \beta_A^q(\mu) a^q(u, v) \\
+a(u, v; \mu) &= \displaystyle\sum_{q=1}^{Q_a} \beta_A^q(\mu) a^q(u, v) \\
 f(v; \mu) &= \displaystyle\sum_{p=1}^{Q_f} \beta_F^p(\mu) f^p(v)\\
 l_i(v; \mu) &= \displaystyle\sum_{p=1}^{Q_{l_i}} \beta_{s_i}^p(\mu) l_i^p(v)
 \end{align}
@@ -48,7 +49,7 @@ L_i(\mu) &= \displaystyle\sum_{p=1}^{Q_{l_i}} \beta_{L_i}^p(\mu) L_i^p
 [betaA, betaF] = model.computeBetaQm(mu)
 ----
 
-where `mu` is a `ParameterSpaceElement` (see xref:parameters.adoc[Parameters]).
+where `mu` is a `ParameterSpaceElement` (see xref:pyfeelppmor/parameters.adoc[Parameters]).
 
 * `betaA` is a list of length 1, and `betaA[0]` contains the coefficients of the affine decomposition `betaA[0] = [` stem:[\beta_A^1]`,...,` stem:[\beta_A^{Q_a}] `]`.
 * `betaF` is a list of length  stem:[1 + n_\text{outputs}] contains the coefficients of the affine decompositions of stem:[f], and stem:[s_i] :