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: m.transpose().parent() Full MatrixSpace of 3 by 0 dense matrices over Real Double Field zero_at(eps) Returns a copy of the matrix where elements smaller than or equal to eps are replaced with zeroes. For complex matrices, the real and imaginary parts are considered individually. This is useful for modifying output from algorithms which have large relative errors when producing zero elements, e.g. to create reliable doctests. INPUT: •eps - Cutoff value OUTPUT: A modified copy of the matrix. EXAMPLES: sage: a=matrix([[1, 1e-4r, 1+1e-100jr], [1e-8+3j, 0, 1e-58r]]) sage: a [ 1.0 0.0001 1.0 + 1e-100*I] [ 1e-08 + 3.0*I 0.0 1e-58] sage: a.zero_at(1e-50) [ 1.0 0.0001 1.0] [1e-08 + 3.0*I 0.0 0.0] sage: a.zero_at(1e-4) [ 1.0 0.0 1.0] [3.0*I 0.0 0.0] 394 Chapter 19. Dense matrices using a NumPy backend.
CHAPTER TWENTY DENSE MATRICES OVER THE REAL DOUBLE FIELD USING NUMPY Dense matrices over the Real Double Field using NumPy EXAMPLES: sage: b=Mat(RDF,2,3).basis() sage: b[0] [1.0 0.0 0.0] [0.0 0.0 0.0] We deal with the case of zero rows or zero columns: sage: m = MatrixSpace(RDF,0,3) sage: m.zero_matrix() [] TESTS: sage: a = matrix(RDF,2,range(4), sparse=False) sage: TestSuite(a).run() sage: MatrixSpace(RDF,0,0).zero_matrix().inverse() [] AUTHORS: • Jason Grout (2008-09): switch to NumPy backend, factored out the Matrix_double_dense class • Josh Kantor • William Stein: many bug fixes and touch ups. class sage.matrix.matrix_real_double_dense.Matrix_real_double_dense Bases: sage.matrix.matrix_double_dense.Matrix_double_dense Class that implements matrices over the real double field. These are supposed to be fast matrix operations using C doubles. Most operations are implemented using numpy which will call the underlying BLAS on the system. EXAMPLES: sage: m = Matrix(RDF, [[1,2],[3,4]]) sage: m**2 [ 7.0 10.0] [15.0 22.0] sage: n= m^(-1); n 395
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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