Dense matrices over the Complex Double Field using NumPy

EXAMPLES:

sage: b=Mat(CDF,2,3).basis()
sage: b[0]
[1.0   0   0]
[  0   0   0]

We deal with the case of zero rows or zero columns:

sage: m = MatrixSpace(CDF,0,3)
sage: m.zero_matrix()
[]

TESTS:

sage: a = matrix(CDF,2,[i+(4-i)*I for i in range(4)], sparse=False)
sage: TestSuite(a).run()
sage: Mat(CDF,0,0).zero_matrix().inverse()
[]

AUTHORS:

• Jason Grout (2008-09): switch to NumPy backend
• Josh Kantor
• William Stein: many bug fixes and touch ups.

class sage.matrix.matrix_complex_double_dense.Matrix_complex_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(CDF, [[1,2*I],[3+I,4]])
sage: m**2
[-1.0 + 6.0*I       10.0*I]
[15.0 + 5.0*I 14.0 + 6.0*I]
sage: n= m^(-1); n
[  0.333333333333 + 0.333333333333*I   0.166666666667 - 0.166666666667*I]
[ -0.166666666667 - 0.333333333333*I 0.0833333333333 + 0.0833333333333*I]

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] and b = [5,6] [3,4]]

sage: b = vector(CDF,[5,6])
sage: m.solve_left(b)
(2.66666666667 + 0.666666666667*I, -0.333333333333 - 1.16666666667*I)

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