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tutorial_subsystem [2014/07/07 11:51] yun created |
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- | In this tutorial, we will show how to write structured alpha programs with subsystems. | + | ======SubSystem in Alpha====== |
+ | |||
+ | In this tutorial, we will present | ||
+ | |||
+ | |||
+ | ====Syntax of Use Equation (without extension domain)==== | ||
+ | |||
+ | 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: | ||
+ | affine mean {N | N>0} | ||
+ | input | ||
+ | float A {k | 0< | ||
+ | output | ||
+ | float C {|}; | ||
+ | local | ||
+ | float temp {|}; | ||
+ | let | ||
+ | temp = reduce(+, [k], A[k]); | ||
+ | C = temp / N; | ||
+ | . | ||
+ | </ | ||
+ | |||
+ | 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: | ||
+ | affine sum {P| P>0} // Computes the sum of the elements of a vector of size P | ||
+ | input | ||
+ | float vect {i | 0< | ||
+ | output | ||
+ | float Res; | ||
+ | let | ||
+ | Res = reduce(+, [k], vect[k]); | ||
+ | . | ||
+ | |||
+ | affine mean {N | N>0} | ||
+ | input | ||
+ | float A {k | 0< | ||
+ | output | ||
+ | float C {|}; | ||
+ | local | ||
+ | float temp {|}; | ||
+ | let | ||
+ | use sum[N] (A) returns (temp); // Compute " | ||
+ | C = temp / N; | ||
+ | . | ||
+ | </ | ||
+ | |||
+ | The system " | ||
+ | |||
+ | |||
+ | In general, the syntax of a use equation is the following: | ||
+ | <sxh alphabets; gutter: | ||
+ | use subsystem_name[list of parameters] (list of input expressions) returns (list of output variables); | ||
+ | </ | ||
+ | |||
+ | If your subsystem has several parameters/ | ||
+ | |||
+ | |||
+ | |||
+ | ====Extension domain==== | ||
+ | |||
+ | |||
+ | Let us assume that you have a system which computes a dot product of two vectors: | ||
+ | <sxh alphabets; gutter: | ||
+ | affine dotProduct {N | N>0} | ||
+ | input | ||
+ | float v1 {k | 0< | ||
+ | float v2 {k | 0< | ||
+ | output | ||
+ | float Res {|}; | ||
+ | let | ||
+ | Res = reduce(+, [k], v1[k]*v2[k]); | ||
+ | . | ||
+ | </ | ||
+ | |||
+ | 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 " | ||
+ | |||
+ | It is possible to do it by using an extension domain: | ||
+ | <sxh alphabets; gutter: | ||
+ | affine dotProduct {N | N>0} | ||
+ | input | ||
+ | float v1 {k | 0< | ||
+ | float v2 {k | 0< | ||
+ | output | ||
+ | float Res {|}; | ||
+ | let | ||
+ | Res = reduce(+, [k], v1[k]*v2[k]); | ||
+ | . | ||
+ | |||
+ | affine matrixVectorProduct {R,S | (R, | ||
+ | input | ||
+ | float mat {i,j | 0< | ||
+ | float vect {j | 0< | ||
+ | output | ||
+ | float vectRes {i | 0< | ||
+ | let | ||
+ | use {k | 0< | ||
+ | . | ||
+ | </ | ||
+ | |||
+ | The set "{k | 0≤k< | ||
+ | - the indexes can be used to specify the parameters (ex: " | ||
+ | - the first dimensions of the input expressions correspond to the dimensions of the extension domain. For example, each row of " | ||
+ | - 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: " | ||
+ | |||
+ | |||
+ | Apart from the compatibility of dimensions, the input expressions must be defined at least on the points asked by the subsystem, and the output variable must be defined on a subset of the domain of the subsystem output. | ||
+ | |||
+ | |||
+ | ====Transformations involving subsystems==== | ||
+ | |||
+ | **InlineSubSystem: | ||
+ | |||
+ | The command is: '' | ||
+ | |||
+ | |||
+ | **OutlineSubSystem: | ||
+ | |||
+ | The command is '' |