Hello,
My name is Zhiqi KANG, I am a 4th year undergraduate of a 5-year engineering institution: Université de Technologie de Compiègne, France. I am interested in the project Linear algebra: Tensor core.Here is the link for the description of project idea. https://github.com/sympy/sympy/wiki/GSoC-2019-Ideas#linear-algebra-tensor-core Even though I am not very familiar with the tensor in the physical field, its principal in the mathematical field is quite interesting. I have precisely looked at the requirement of this project and make sure that I am capable to accomplish most of its task. However, there are still many questions that I would like to discuss with all contributors of SymPy and expecially with the mentor. One urgent problem is that I don't find the name of mentor for this project, so I don't really know who I should CC. Could you please help me to find the mentor for this project? Please review this draft proposal and tell me what to be ameliorated. Thank you! Ø Better Algorithms for sparse array: The idea is to manipulate directly les arrays in the sparse array level. Casting sparse arrays to a dense array and then operating is kind of a redundancy. I have found an example in tomatrix() function of sympy\sympy\tensor\array\sparse_ndim_array.py where we convert the sparse_array to a new dictionay and then cast it to matrix.(Code bellow) But I cannot find more cases in the array/tensor module, it would be great if some one can help me find out where other cases are. from sympy.matrices import SparseMatrix if self.rank() != 2: raise ValueError('Dimensions must be of size of 2') mat_sparse = {} for key, value in self._sparse_array.items(): mat_sparse[self._get_tuple_index(key)] = value return SparseMatrix(self.shape[0], self.shape[1], mat_sparse) Ø NumPy-like operations We have now some operations for arrays in SymPy: ² arrayfy ² tensor product ² derivatives by array ² permute dimension ² contraction For this part of project, I am planning to implement some operations such as: ² sum ² divide/multiply(element wise) ² any ² comparators(greater/less/equal) ² logical operator(and/or/not/xor) ² random Ø lazy operators on arrays lazy evaluation can improve the performance while iterating the array since it creates value only if it is called. To implement lazy operators, I am thinking about two plans: 1. Create a new sub-module named lazy-array (larray) of which most of the operations are lazy evaluated. A standard Array can be cast to a lazy-array by simply calling the constructor of larray and passing it as parameter. By doing so, users can choose whatever they want in the module level, which means that to manipulate a simple array or a lazy array. 1. Create a lazy version for les operators mentioned above. The lazy operators are accessible for a specific purpose. This implementation focusses on a function level for calling lazy evaluated operations, which means to call a simple inverse_matrix function or a lazy one. Besides, I have found in sympy\sympy\tensor\tensor.py a class _TensorDataLazyEvaluator which can be an example for me to implement these functionalities. It has methods like delete item, inverse matrix, etc. Ø code generation for arrays and array operators This part of project should be involved with another GSoC project purely for code generation. I would like to discuss with the mentor of the codegen project to have a better point of view for it. I have had an internship for 6 months in BNP Paribas Securities Services in Paris as developer. During this period, I have similarly worked on code generation task, except that the programming language is C#.( I was using EntityFramework and T4 by Microsoft) I believe that this experience can help me to get familiar with the code generation process in this project. Ø Integration over indexed symbols and arrays Firstly, I would like to talk about integration over arrays: Can we imagine the array as a set of coordinates? Suppose that we have a array A, say 2-dimension as (p, q). We can image two axis x and y so that index i and j are coordinates for the point Pij in axis x and axis y. The value A[pi,qj] should be the coordinate of axis z. By assuming this, we can use a Riemann integral or Lebesgue integral to calculate its integration like summing the column in the 3D space. I don’t know if this idea is correct, I would love to discuss it with you! Secondly, for integration over indexed symbols, I don’t really know what it means. Should the output be an expression rather than a value? It would be great if someone can show me with an example, thanks! Ø Equation solving with indexed symbols. I am not very familiar with this topic either. Should the result be an expression as well? It would be great if someone can show me with an example, thanks! Ø Implement some well-known tensor math If the time permits, I would be glad to do the extra part of this project. But I don’t know very well relativity, electromagnetism, etc. It would take me some time to better understand the principles and start to work on it. However, I do find some math formula that associated with this topic. https://en.wikipedia.org/wiki/Integral Ø Unify the various SymPy module To be done. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/a5ff49d3-63e4-45e5-b87f-4b9d6be30085%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
