Dense matrices over the Real Double Field using NumPy


sage: b = Mat(RDF,2,3).basis()
sage: b[0,0]
[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()


  • 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.


sage: m = Matrix(RDF, [[1,2],[3,4]])
sage: m**2
[ 7.0 10.0]
[15.0 22.0]
sage: n = m^(-1); n     # rel tol 1e-15
[-1.9999999999999996  0.9999999999999998]
[ 1.4999999999999998 -0.4999999999999999]

To compute eigenvalues the use the functions left_eigenvectors or right_eigenvectors

sage: p,e = m.right_eigenvectors()

the result of eigen is a pair (p,e), where p is a list of eigenvalues and the e is a matrix whose columns are the eigenvectors.

To solve a linear system Ax = b where A = [[1,2],[3,4]] and b = [5,6].

sage: b = vector(RDF,[5,6])
sage: m.solve_right(b)  # rel tol 1e-15
(-3.9999999999999987, 4.499999999999999)

See the commands qr, lu, and svd for QR, LU, and singular value decomposition.