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tutorial_subsystem [2014/07/12 07:33] guillaume [Extension domain] |
tutorial_subsystem [2017/04/19 13:31] |
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- | ======SubSystem in Alpha====== | ||
- | In this tutorial, we will present how to write structured alpha programs with subsystems, and we will present the associated transformations. | ||
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- | ====Syntax of Use Equation (without extension domain)==== | ||
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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: | ||
- | <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; | ||
- | . | ||
- | </ | ||
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- | 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]); | ||
- | . | ||
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- | 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; | ||
- | . | ||
- | </ | ||
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- | The system " | ||
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- | 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); | ||
- | </ | ||
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- | If your subsystem have several parameters/ | ||
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- | ====Extension domain==== | ||
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- | Let us assume that you have a system which computes a dot product between 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]); | ||
- | . | ||
- | </ | ||
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- | 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 " | ||
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- | 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]); | ||
- | . | ||
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- | affine matrixVectorProduct {R,S | (R,S)>0} | ||
- | input | ||
- | float mat {i,j | 0< | ||
- | float vect {j | 0< | ||
- | output | ||
- | float vectRes {i | 0< | ||
- | let | ||
- | use {k | 0< | ||
- | . | ||
- | </ | ||
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- | The set "{k | 0< | ||
- | - 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 a given subsystem call kInst, the corresponding input sent is the one where the first dimensions are set to " | ||
- | - 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: " | ||
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- | 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. | ||
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- | ====Transformations involving subsystems==== | ||
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- | (incoming, after the previous incoming) |