Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: A[0,0] = 5 sage: A.determinant() 1 sage: A.set_immutable() sage: A[0,0] = 5 Traceback (most recent call last): ... ValueError: matrix is immutable; please change a copy instead (i.e., use copy(M) to change a copy of 3.1.1 Implementation and Design Class Diagram (an x means that class is currently supported): x Matrix x Matrix_sparse x Matrix_generic_sparse x Matrix_integer_sparse x Matrix_rational_sparse Matrix_cyclo_sparse x Matrix_modn_sparse Matrix_RR_sparse Matrix_CC_sparse Matrix_RDF_sparse Matrix_CDF_sparse x x x x x x x Matrix_dense Matrix_generic_dense Matrix_integer_dense Matrix_integer_2x2_dense Matrix_rational_dense Matrix_cyclo_dense -- idea: restrict scalars to QQ, compute charpoly there, then factor Matrix_modn_dense Matrix_RR_dense Matrix_CC_dense Matrix_real_double_dense Matrix_complex_double_dense The corresponding files in the sage/matrix library code directory are named [matrix] [base ring] [dense or sparse]. See the files matrix_template.pxd and matrix_template.pyx. New matrices types can only be implemented in Cython. *********** LEVEL 1 ********** NON-OPTIONAL For each base field it is *absolutely* essential to completely implement the following functionality for that base ring: * set_unsafe(self, size_t i, size_t j, x) -- doesn’t do bounds or any other checks; assumes x is i * __cinit__ -- should use sage_malloc from ext/stdsage.pxi (only needed if allocate memory) * __init__ -- this signature: ’def __init__(self, parent, entries, copy, coerce)’ * __dealloc__ -- use sage_free (only needed if allocate memory) * get_unsafe(self, size_t i, size_t j) -- doesn’t do checks * __richcmp__ -- always the same (I don’t know why its needed -- bug in PYREX). 64 Chapter 3. Matrices over an arbitrary ring
Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 Note that the __init__ function must construct the all zero matrix if ‘‘entries == None‘‘. *********** LEVEL 2 ********** IMPORTANT (and *highly* recommended): After getting the special class with all level 1 functionality to work, implement all of the following (they should not change functionality, except speed (always faster!) in any way): * def _pickle(self): return data, version * def _unpickle(self, data, int version) reconstruct matrix from given data and version; may assume _parent, _nrows, and _ncols are Use version numbers >= 0 so if you change the pickle strategy then old objects still unpickle. * cdef _list -- list of underlying elements (need not be a copy) * cdef _dict -- sparse dictionary of underlying elements * cdef _add_ -- add two matrices with identical parents * _matrix_times_matrix_c_impl -- multiply two matrices with compatible dimensions and identical base rings (both sparse or both dense) * cdef _cmp_c_impl -- compare two matrices with identical parents * cdef _lmul_c_impl -- multiply this matrix on the right by a scalar, i.e., self * scalar * cdef _rmul_c_impl -- multiply this matrix on the left by a scalar, i.e., scalar * self * __copy__ * __neg__ The list and dict returned by _list and _dict will *not* be changed by any internal algorithms and are not accessible to the user. *********** LEVEL 3 ********** OPTIONAL: * cdef _sub_ * __invert__ * _multiply_classical * __deepcopy__ Further special support: * Matrix windows -- to support Strassen multiplication for a given base ring. * Other functions, e.g., transpose, for which knowing the specific representation can be helpful. .. note:: - For caching, use self.fetch and self.cache. - Any method that can change the matrix should call ‘‘check_mutability()‘‘ first. There are also many fast cdef’d bounds checking methods. - Kernels of matrices Implement only a left_kernel() or right_kernel() method, whichever requires the least overhead (usually meaning little or no transposing). Let the methods in the matrix2 class handle left, right, generic kernel distinctions. 3.1. Indexing 65
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