doc: small tutorial for the GF's

doc/tutorials/c++/contents.rst

@@ -10,5 +10,6 @@ C++ libraries
 
    array_tutorial
    det_manip_tutorial
+   gfs_tutorial
 
 ..

doc/tutorials/c++/gfs_tutorial.rst

@@ -0,0 +1,129 @@
+Green function cookbook
+=======================
+
+.. highlight:: c
+
+.. toctree::
+   :maxdepth: 1
+
+The gfs class of TRIQS contains objects representing Green functions over real or imaginary times, rela or imaginary frequencies...  that can be easily manipulated. 
+(see  :doc:`here  <../../reference/c++/gf/contents>`). 
+Here are a couple of simple examples showing the basic use of this class.
+
+Creation of a real time GF
+-----------------------------
+
+Here we create a GF define on the time interval from tmin to tmax. 
+If we want the value of the GF at any time to be a scalar, we use:
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+
+    int main() {
+      double tmin=0, tmax=10; // the time interval
+      int n_times=100;        // we will have 100 points
+      auto g = gf<retime, scalar_valued>{ {tmin, tmax, n_times}};
+    }
+
+If we need a matrix of size n by m, we use:
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+
+    int main() {
+      double tmin = 0, tmax = 10;    // the time interval
+      const int n=2, m=2, n_times = 100;   // we will have 100 points
+      auto g = gf<retime, matrix_valued>{ {tmin, tmax, n_times} , {n, m} };
+    }
+    
+Or a tensor !
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+
+    int main() {
+      double tmin = 0, tmax = 10;    // the time interval
+      double beta=1;
+      int n_times = 100;   // we will have 100 pointspoints
+      auto g =gf<cartesian_product<retime,imtime>, tensor_valued<3>>{ 
+        { {tmin, tmax, n_times}, {beta, Fermion, n_times} }, {2,2,2}};
+    }
+
+    
+Creation of other simple GF's
+-------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+
+    int main() {
+      double beta=10; // the time interval
+      int n_times=100;        // we will have 100 
+      auto g = gf<imtime, scalar_valued>{ {beta, Fermion, n_times}};
+    }
+
+Creation of a two real time GF
+--------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+    int main(){
+     double tmin = 0, tmax = 1.0;
+     int nt = 100;
+     auto g = gf< cartesian_product<retime,retime>,scalar_valued>{{{tmin,tmax,nt},{tmin,tmax,nt}}};
+    }
+
+
+How to fill a GF with placeholders
+-----------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+    int main(){
+     double tmin = 0, tmax = 1.0;
+     int nt = 100;
+     auto g = gf< cartesian_product<retime,retime>,scalar_valued>{{{tmin,tmax,nt},{tmin,tmax,nt}}};
+     triqs::clef::placeholder<0> t1_;
+     triqs::clef::placeholder<1> t2_;
+     g( t1_, t2_) << 2*t1_;
+    }
+
+
+How to interpolate the GF value at a point of the domain
+---------------------------------------------------------
+
+You simply have to call the GF with the coordinates of the point: 
+
+.. compileblock:: 
+
+    #include <triqs/gfs.hpp>
+    using namespace triqs::gfs;
+    int main(){
+     double tmin = 0, tmax = 1.0;
+     int nt = 100;
+     auto g = gf< cartesian_product<retime, retime>, scalar_valued >{ 
+     { {tmin, tmax, nt}, {tmin, tmax, nt} } };
+     triqs::clef::placeholder<0> t1_;
+     triqs::clef::placeholder<1> t2_;
+     g( t1_, t2_) << 2.*t1_;
+     std::cout << g(0.24, 0.36) << std::endl;
+    }
+    
+    
+
+
+Learn more in the full reference, see :ref:`gf`
+
+