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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/matrix/matrix_complex_double_dense.pyx
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"""

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Dense matrices over the Complex Double Field using NumPy

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EXAMPLES::

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    sage: b=Mat(CDF,2,3).basis()

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    sage: b[0]

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    [1.0 0.0 0.0]

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    [0.0 0.0 0.0]

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

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    sage: m = MatrixSpace(CDF,0,3)

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    sage: m.zero_matrix()

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    []

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TESTS::

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    sage: a = matrix(CDF,2,[i+(4-i)*I for i in range(4)], sparse=False)

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    sage: TestSuite(a).run()

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    sage: Mat(CDF,0,0).zero_matrix().inverse()

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    []

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AUTHORS:

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- Jason Grout (2008-09): switch to NumPy backend

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- Josh Kantor

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- William Stein: many bug fixes and touch ups.

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"""

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##############################################################################

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#       Copyright (C) 2004,2005,2006 Joshua Kantor <[email protected]>

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#  Distributed under the terms of the GNU General Public License (GPL)

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#  The full text of the GPL is available at:

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#                  http://www.gnu.org/licenses/

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##############################################################################

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import matrix_double_dense

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from sage.rings.complex_double import CDF

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cimport numpy as cnumpy

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numpy=None

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cdef class Matrix_complex_double_dense(matrix_double_dense.Matrix_double_dense):

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    """

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    Class that implements matrices over the real double field. These

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    are supposed to be fast matrix operations using C doubles. Most

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    operations are implemented using numpy which will call the

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    underlying BLAS on the system.

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    EXAMPLES::

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        sage: m = Matrix(CDF, [[1,2*I],[3+I,4]])

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        sage: m**2

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        [-1.0 + 6.0*I       10.0*I]

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        [15.0 + 5.0*I 14.0 + 6.0*I]

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        sage: n= m^(-1); n

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        [  0.333333333333 + 0.333333333333*I   0.166666666667 - 0.166666666667*I]

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        [ -0.166666666667 - 0.333333333333*I 0.0833333333333 + 0.0833333333333*I]

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    To compute eigenvalues the use the functions left_eigenvectors or

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    right_eigenvectors

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    ::

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        sage: p,e = m.right_eigenvectors()

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    the result of eigen is a pair (p,e), where p is a list of

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    eigenvalues and the e is a matrix whose columns are the

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    eigenvectors.

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

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    [3,4]]

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    ::

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        sage: b = vector(CDF,[5,6])

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        sage: m.solve_right(b)

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        (2.66666666667 + 0.666666666667*I, -0.333333333333 - 1.16666666667*I)

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

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    decomposition.

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    """

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    ########################################################################

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    # LEVEL 1 functionality

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    #   * __cinit__  

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    #   * __dealloc__   

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    #   * __init__      

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    #   * set_unsafe

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    #   * get_unsafe

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    #   * __richcmp__    -- always the same

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    #   * __hash__       -- always simple

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    ########################################################################

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    def __cinit__(self, parent, entries, copy, coerce):

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        global numpy

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        if numpy is None:

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            import numpy

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        self._numpy_dtype = numpy.dtype('complex128')

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        self._python_dtype = complex

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        self._numpy_dtypeint = cnumpy.NPY_CDOUBLE

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        # TODO: Make ComplexDoubleElement instead of CDF for speed

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        self._sage_dtype = CDF

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        self.__create_matrix__()

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        return

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