Dynare++: improvements to comments

[skip ci]

dynare++/kord/dynamic_model.hh

@@ -4,8 +4,10 @@
 
 /* This file only defines a generic interface to a DSGE model. The model
    takes the form:
-   $$E_t\left[f(g^{**}(g^*(y,u_t),u_{t+1}),g(y,u),y,u_t)\right]=0$$
-   The interface is defined via pure virtual class |DynamicModel|. */
+
+    𝔼ₜ(f(g**(g*(y,uₜ),uₜ₊₁),g(y,uₜ),yₜ,uₜ)) = 0
+
+   The interface is defined via pure virtual class DynamicModel. */
 
 #ifndef DYNAMIC_MODEL_H
 #define DYNAMIC_MODEL_H
@@ -32,54 +34,61 @@ public:
   void writeMatIndices(mat_t *fd, const std::string &prefix) const;
 };
 
-/* This is the interface to an information on a generic DSGE
-   model. It is sufficient for calculations of policy rule Taylor
-   approximations at some (not necessarily deterministic) steady state.
-
-   We need to know a partitioning of endogenous variables $y$. We suppose
-   that $y$ is partitioned as
-   $$y=\left[\matrix{\hbox{static}\cr\hbox{pred}\cr\hbox{both}\cr\hbox{forward}}\right]$$
-   of which we define
-   $$y^*=\left[\matrix{\hbox{pred}\cr\hbox{both}}\right]\quad
-   y^{**}=\left[\matrix{\hbox{both}\cr\hbox{forward}}\right]$$
-   where ``static'' are meant those variables, which appear only at time
-   $t$; ``pred'' are meant those variables, which appear only at $t$ and
-   $t-1$; ``both'' are meant those variables, which appear at least at
-   $t-1$ and $t+1$; and ``forward'' are meant those variables, which
-   appear only at $t$ and $t+1$. This partitioning is given by methods
-   |nstat()|, |npred()|, |nboth()|, and |nforw()|. The number of
-   equations |numeq()| must be the same as a number of endogenous
-   variables.
-
-   In order to complete description, we need to know a number of
-   exogenous variables, which is a size of $u$, hence |nexog()| method.
+/* This is the interface to an information on a generic DSGE model. It is
+   sufficient for calculations of policy rule Taylor approximations at some
+   (not necessarily deterministic) steady state.
+
+   We need to know a partitioning of endogenous variables y. We suppose that y
+   is partitioned as:
+
+        ⎡ static⎤
+        ⎢  pred ⎥
+    y = ⎢  both ⎥
+        ⎣forward⎦
+
+   of which we define:
+
+
+         ⎡pred⎤        ⎡  both ⎤
+    y* = ⎣both⎦  y** = ⎣forward⎦
+
+   where “static” are meant those variables, which appear only at time t;
+   “pred” are meant those variables, which appear only at t and t−1; “both” are
+   meant those variables, which appear at least at t−1 and t+1; and “forward”
+   are meant those variables, which appear only at t and t+1. This partitioning
+   is given by methods nstat(), npred(), nboth(), and nforw(). The number of
+   equations numeq() must be the same as a number of endogenous variables.
+
+   In order to complete description, we need to know a number of exogenous
+   variables, which is a size of u, hence nexog() method.
 
    The model contains an information about names of variables, the
-   variance-covariance matrix of the shocks, the derivatives of equations
-   of $f$ at some steady state, and the steady state. These can be
-   retrieved by the corresponding methods.
+   variance-covariance matrix of the shocks, the derivatives of equations of f
+   at some steady state, and the steady state. These can be retrieved by the
+   corresponding methods.
 
    The derivatives of the system are calculated with respect to stacked
-   variables, the stack looks as:
-   $$\left[\matrix{y^{**}_{t+1}\cr y_t\cr y^*_{t-1}\cr u_t}\right].$$
-
-   There are only three operations. The first
-   |solveDeterministicSteady()| solves the deterministic steady steate
-   which can be retrieved by |getSteady()| later. The method
-   |evaluateSystem| calculates $f(y^{**},y,y^*,u)$, where $y$ and $u$ are
-   passed, or $f(y^{**}_{t+1}, y_t, y^*_{t-1}, u)$, where $y^{**}_{t+1}$,
-   $y_t$, $y^*_{t-1}$, $u$ are passed. Finally, the method
-   |calcDerivativesAtSteady()| calculates derivatives of $f$ at the
-   current steady state, and zero shocks. The derivatives can be
-   retrieved with |getModelDerivatives()|. All the derivatives are done
-   up to a given order in the model, which can be retrieved by |order()|.
-
-   The model initialization is done in a constructor of the implementing
-   class. The constructor usually calls a parser, which parses a given
-   file (usually a text file), and retrieves all necessary information
-   about the model, inluding variables, partitioning, variance-covariance
-   matrix, information helpful for calculation of the deterministic
-   steady state, and so on. */
+   variables, the stack looks like:
+
+    ⎡y**ₜ₊₁⎤
+    ⎢  yₜ  ⎥
+    ⎢ y*ₜ₋₁⎥
+    ⎣  uₜ  ⎦
+
+   There are only three operations. The first solveDeterministicSteady() solves
+   the deterministic steady steate which can be retrieved by getSteady() later.
+   The method evaluateSystem() calculates f(y**,y,y*,u), where y and u are
+   passed, or f(y**ₜ₊₁, yₜ, y*ₜ₋₁, u), where y**ₜ₊₁, yₜ, y*ₜ₋₁, u are passed.
+   Finally, the method calcDerivativesAtSteady() calculates derivatives of f at
+   the current steady state, and zero shocks. The derivatives can be retrieved
+   with getModelDerivatives(). All the derivatives are done up to a given order
+   in the model, which can be retrieved by order().
+
+   The model initialization is done in a constructor of the implementing class.
+   The constructor usually calls a parser, which parses a given file (usually a
+   text file), and retrieves all necessary information about the model,
+   inluding variables, partitioning, variance-covariance matrix, information
+   helpful for calculation of the deterministic steady state, and so on. */
 
 class DynamicModel
 {