density.py 文件源码

def entropy(density):
    """Compute the entropy of a matrix/density object.

    This computes -Tr(density*ln(density)) using the eigenvalue decomposition
    of density, which is given as either a Density instance or a matrix
    (numpy.ndarray, sympy.Matrix or scipy.sparse).

    Parameters
    ==========

    density : density matrix of type Density, sympy matrix,
    scipy.sparse or numpy.ndarray

    Examples
    ========

    >>> from sympy.physics.quantum.density import Density, entropy
    >>> from sympy.physics.quantum.represent import represent
    >>> from sympy.physics.quantum.matrixutils import scipy_sparse_matrix
    >>> from sympy.physics.quantum.spin import JzKet, Jz
    >>> from sympy import S, log
    >>> up = JzKet(S(1)/2,S(1)/2)
    >>> down = JzKet(S(1)/2,-S(1)/2)
    >>> d = Density((up,0.5),(down,0.5))
    >>> entropy(d)
    log(2)/2

    """
    if isinstance(density, Density):
        density = represent(density)  # represent in Matrix

    if isinstance(density, scipy_sparse_matrix):
        density = to_numpy(density)

    if isinstance(density, Matrix):
        eigvals = density.eigenvals().keys()
        return expand(-sum(e*log(e) for e in eigvals))
    elif isinstance(density, numpy_ndarray):
        import numpy as np
        eigvals = np.linalg.eigvals(density)
        return -np.sum(eigvals*np.log(eigvals))
    else:
        raise ValueError(
            "numpy.ndarray, scipy.sparse or sympy matrix expected")