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tutorial_subsystem [2014/07/12 08:00]
guillaume [Transformations involving subsystems]
tutorial_subsystem [2017/04/19 13:31] (current)
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 Let us assume that we want to compute the mean of the values of a vector. It is feasible through the following Alpha system: Let us assume that we want to compute the mean of the values of a vector. It is feasible through the following Alpha system:
-<sxh alphabets; gutter:false>+<sxh alphabets; gutter:true>
 affine mean {N | N>0} affine mean {N | N>0}
 input input
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 </​sxh>​ </​sxh>​
  
-However, let us assume that you already have another Alpha system which computes the sum of the elements of a vector. It is possible to use this affine system (instead of rewriting its equation in the main system), by calling it through a "use equation"+However, let us assume that you already have another Alpha system which computes the sum of the elements of a vector. It is possible to use this affine system (instead of rewriting its equation in the main system), by calling it through a **use equation**
-<sxh alphabets; gutter:false>+<sxh alphabets; gutter:true>
 affine sum {P| P>0} // Computes the sum of the elements of a vector of size P affine sum {P| P>0} // Computes the sum of the elements of a vector of size P
 input input
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 In general, the syntax of a use equation is the following: In general, the syntax of a use equation is the following:
-<sxh alphabets; gutter:false>+<sxh alphabets; gutter:true>
 use subsystem_name[list of parameters] (list of input expressions) returns (list of output variables); use subsystem_name[list of parameters] (list of input expressions) returns (list of output variables);
 </​sxh>​ </​sxh>​
  
-If your subsystem ​have several parameters/​inputs/​outputs,​ you have to provide them in the order in which they are declared.+If your subsystem ​has several parameters/​inputs/​outputs,​ you have to provide them in the order in which they are declared.
  
  
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-Let us assume that you have a system which computes a dot product ​between ​two vectors: +Let us assume that you have a system which computes a dot product ​of two vectors: 
-<sxh alphabets; gutter:false>+<sxh alphabets; gutter:true>
 affine dotProduct {N | N>0} affine dotProduct {N | N>0}
 input input
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 </​sxh>​ </​sxh>​
  
-If you want to compute a matrix vector multiplication using this affine system, you will need to call it once per rows of the matrix. Thus, you will need a parametrised number of call to the "​dotProduct"​ system.+If you want to compute a matrix vector multiplication using this affine system, you will need to instanciate ​it once per rows of the matrix. Thus, you will need a parametrised number of call to the "​dotProduct"​ system.
  
 It is possible to do it by using an extension domain: It is possible to do it by using an extension domain:
-<sxh alphabets; gutter:false>+<sxh alphabets; gutter:true>
 affine dotProduct {N | N>0} affine dotProduct {N | N>0}
 input input
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  float vectRes {i | 0<​=i<​R};​  float vectRes {i | 0<​=i<​R};​
 let let
- use {k | 0<​=k<​R} dotProduct[R] ( (k,​j->​k,​j)@mat, (k,​j->​j)@vect) returns (vectRes);+ use {k | 0<​=k<​R} dotProduct[R] ( mat, (k,​j->​j)@vect) returns (vectRes);
 . .
 </​sxh>​ </​sxh>​
  
-The set "{k | 0<=k<​R}"​ before the subsystem name is called ​an extension domain. We are calling the system "​dotProduct"​ once, for each instance of "​k"​ in the extension domain. We can use the indexes of the extension domain to parametrize the parameters, inputs given to the subsystem and the outputs computed by the subsystem:+The set "{k | 0k<​R}"​ before the subsystem name is called ​the **extension domain**. We are calling the system "​dotProduct"​ once, for each instance of "​k"​ in the extension domain. We can use the indexes of the extension domain to parametrize the parameters, inputs given to the subsystem and the outputs computed by the subsystem:
   - the indexes can be used to specify the parameters (ex: "​R+k"​)   - the indexes can be used to specify the parameters (ex: "​R+k"​)
-  - the first dimensions of the input expressions correspond to the dimensions of the extension domain. For a given subsystem call kInstthe corresponding input sent is the one where the first dimensions are set to "​kInst" ​(ex: in the previous example, the third call to "​dotProduct"​ will obtain ​"​(j->​3,​j)@mat"​ and "​(j->​j)@vect"​ as inputs).+  - the first dimensions of the input expressions correspond to the dimensions of the extension domain. For exampleeach row of "​mat"​ will be sent to a different instance of the subsystem ​(ex: in the previous example, the third instance of "​dotProduct"​ will receive ​"​(j->​3,​j)@mat"​ and "​(j->​j)@vect"​ as inputs).
   - the first dimensions of the output variables correspond to the dimensions of the extension domain. All the results from every subsystem call are gathered inside common variables (ex: "​vectRes[3]"​ is the output of the third instance of "​dotProduct"​)   - the first dimensions of the output variables correspond to the dimensions of the extension domain. All the results from every subsystem call are gathered inside common variables (ex: "​vectRes[3]"​ is the output of the third instance of "​dotProduct"​)
  
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 **InlineSubSystem:​** Inline the equations of a subsystem inside the affine system calling it. The use equation of the main system is replaced by the equations of the subsystem (which are adapted), and new local variables are added. **InlineSubSystem:​** Inline the equations of a subsystem inside the affine system calling it. The use equation of the main system is replaced by the equations of the subsystem (which are adapted), and new local variables are added.
 +
 +The command is: ''​void InlineSubSystem(Program program, String systemName, String label)''​ where ''​label''​ is the label of the inlined use equation.
 +
  
 **OutlineSubSystem:​** Given a list of equations of an affine systemm, outline them inside a new system and replace these equation by a use equation. The current version (July 2014) do not allow to specify an extension domain, however this is a work in progress. **OutlineSubSystem:​** Given a list of equations of an affine systemm, outline them inside a new system and replace these equation by a use equation. The current version (July 2014) do not allow to specify an extension domain, however this is a work in progress.
 +
 +The command is ''​void OutlineSubSystem(Program program, String system, String listEquations)''​ where ''​listEquations''​ is the list of label of the equations to be outlined.
tutorial_subsystem.1405173626.txt.gz · Last modified: 2014/07/12 08:00 by guillaume