add vector as pair machine

Physics/MovingParticles.mch

 MACHINE MovingParticles
 // Encoding of an n-body problem in B using the REAL datatype
-INCLUDES Vectors2
+INCLUDES Vectors2 //VectorsAsPairs2 faster; but VisB file needs to be adapted
 DEFINITIONS
   "LibraryReals.def"; "SORT.def"; 
   MASS == FLOAT;

Physics/MovingParticles3.mch

@@ -19,8 +19,8 @@ PROPERTIES
    /*@label "mass_values" */ mass = [5.97e24, 1.989e30, 1.989e30]
     /*@desc "The mass of the 3 objects" */
    &
-   initial_pos =   [ [0.0,0.0]    ,  [0.0,4.5e10],   [0.0,-4.5e10]  ]  &
-   initial_speed = [ [0.05e04,0.0],  [3.0e04,0.0],   [-3.0e04,0.0]  ] 
+   initial_pos =   [ make_vec([0.0,0.0])    ,  make_vec([0.0,4.5e10]),   make_vec([0.0,-4.5e10])  ]  &
+   initial_speed = [ make_vec([0.05e04,0.0]),  make_vec([3.0e04,0.0]),   make_vec([-3.0e04,0.0])  ] 
 
 END
 

Physics/MovingParticles4.mch

@@ -18,8 +18,10 @@ PROPERTIES
    nobjs = 4 & 
    mass = [3.0e28, 3.0e28, 3.0e28, 3.0e28]
    &
-   initial_pos =   [ [-3.5e10,0.0e00], [-1.0e10,0.0e00],   [1.0e10, 0.0e00], [3.5e10, 0.0e00]  ]  &
-   initial_speed = [ [ 0.0e00,1.4e03],  [0.0e00,1.4e03],   [0.0e00,-1.4e03], [0.0e00,-1.4e03]  ] 
+   initial_pos =   [ make_vec([-3.5e10,0.0e00]),  make_vec([-1.0e10,0.0e00]),
+                     make_vec([1.0e10, 0.0e00]),  make_vec([3.5e10, 0.0e00])  ]  &
+   initial_speed = [ make_vec([ 0.0e00,1.4e03]),  make_vec([0.0e00,1.4e03]),
+                     make_vec([0.0e00,-1.4e03]),  make_vec([0.0e00,-1.4e03])  ] 
 
 END
 

Physics/Vectors.mch

@@ -14,7 +14,9 @@ ABSTRACT_CONSTANTS
   
   sigma_reals /*@desc "sum of a numbers of a vector" */,
   add_firstv,
-  sigma_vecs  /*@desc "sum of a sequence of vectors" */
+  sigma_vecs  /*@desc "sum of a sequence of vectors" */,
+  
+  make_vec   /*@desc "construct a vector from a sequence" */
 PROPERTIES
   n:NATURAL1 &
   DIM = (1..n) &
@@ -41,6 +43,8 @@ PROPERTIES
   times_vec = %(k,v1).(k:REAL & v1:VEC | %i.(i:DIM| k*v1(i))) /*@desc "multiply scalar by a vector" */ &
                               
   distance = %(v1,v2).(v1:VEC & v2:VEC | magnitude(delta_vec(v1,v2)))
-    /*@desc "Eucledian distance between two vectors" */
+    /*@desc "Eucledian distance between two vectors" */ &
+
+  make_vec = %v.(v:seq(REAL) & size(v)=n | v )
 
 END
\ No newline at end of file

Physics/Vectors2.mch

@@ -12,7 +12,9 @@ ABSTRACT_CONSTANTS
   times_vec  /*@desc "multiply scalar by a vector" */,
   distance   /*@desc "Eucledian distance between two vectors" */,
   
-  sigma_vecs  /*@desc "sum of a sequence of vectors" */
+  sigma_vecs  /*@desc "sum of a sequence of vectors" */,
+  
+  make_vec   /*@desc "construct a vector from a sequence" */
 PROPERTIES
   n:NATURAL1 & n = 2 &
   DIM = (1..n) &
@@ -39,6 +41,8 @@ PROPERTIES
   times_vec = %(k,v1).(k:REAL & v1:VEC | [k*v1(1),k*v1(2)]) /*@desc "multiply scalar by a vector" */ &
                               
   distance = %(v1,v2).(v1:VEC & v2:VEC | magnitude(delta_vec(v1,v2)))
-    /*@desc "Eucledian distance between two vectors" */
+    /*@desc "Eucledian distance between two vectors" */ &
+
+  make_vec = %v.(v:seq(REAL) & size(v)=2 | v )
 
 END
\ No newline at end of file

Physics/VectorsAsPairs2.mch

+MACHINE VectorsAsPairs2 // an optimized instance of Vectors for n=2 with a pair representation
+DEFINITIONS
+  "LibraryReals.def";
+  p1(r) == prj1(REAL,REAL)(r);
+  p2(r) == prj2(REAL,REAL)(r)
+ABSTRACT_CONSTANTS
+  n,
+  VEC,
+  add_vec     /*@desc "sum of two vectors" */,
+  delta_vec   /*@desc "difference of two vectors" */,
+  dot_product /*@desc "dot product of two vectors" */,
+  magnitude  /*@desc "Magnitude of a vector" */,
+  unit_vec   /*@desc "unit vector of a vector" */,
+  times_vec  /*@desc "multiply scalar by a vector" */,
+  distance   /*@desc "Eucledian distance between two vectors" */,
+  
+  sigma_vecs  /*@desc "sum of a sequence of vectors" */,
+  
+  make_vec   /*@desc "construct a vector from a sequence" */
+PROPERTIES
+  n:NATURAL1 & n = 2 &
+  VEC = (REAL*REAL) &
+  
+  sigma_vecs = %v.(v:seq1(VEC) | ( SIGMA(i).(i:dom(v)|p1(v(i))) , SIGMA(i).(i:dom(v)|p2(v(i))) ) ) 
+               /*@desc "sum of a sequence of vectors" */&
+  
+  add_vec = %(v1,v2).(v1:VEC & v2:VEC | ( p1(v1)+p1(v2) , p2(v1)+p2(v2) )) 
+                /*@desc "sum of two vectors" */ &
+
+  delta_vec = %(v1,v2).(v1:VEC & v2:VEC | ( p1(v1)-p1(v2) , p2(v1)-p2(v2) ) ) 
+                /*@desc "difference of two vectors" */ &
+
+  dot_product = %(v1,v2).(v1:VEC & v2:VEC | p1(v1)*p1(v2) + p2(v1)*p2(v2))
+                /*@desc "dot product of two vectors" */ &
+  
+  magnitude = %v1.(v1:VEC | RSQRT(p1(v1)**2 + p2(v1)**2)) /*@desc "Magnitude of a vector" */ &
+            // alternative: RSQRT(dot_product(v1,v1)))
+  
+  unit_vec = %v1.(v1:VEC | LET m BE m=magnitude(v1) IN
+                              ( p1(v1)/m , p2(v1)/m ) END ) /*@desc "unit vector of a vector" */  &
+                              
+  times_vec = %(k,v1).(k:REAL & v1:VEC | ( k*p1(v1), k*p2(v1) ) ) /*@desc "multiply scalar by a vector" */ &
+                              
+  distance = %(v1,v2).(v1:VEC & v2:VEC | magnitude(delta_vec(v1,v2)))
+    /*@desc "Eucledian distance between two vectors" */ &
+
+
+  make_vec = %v.(v:seq(REAL) & size(v)=2  | ( v(1) , v(2) ) )
+
+END
\ No newline at end of file