spectrum.py 文件源码

def spectrum_decomposition(A):
    '''
    compute the spectrum decomposition of matrix A
    '''
    # check if A is a simple matrix
    if isSimple(A) != True:
        raise Exception('non-simple matrix cannot be spectrum-decomposed')

    eigenValues, eigenVectors = la.eig(A)
    invVectors = la.inv(eigenVectors)

    eigenVectors_row = eigenVectors.shape[0]
    eigenVectors_column = eigenVectors.shape[1]
    invVectors_row = invVectors.shape[0]
    invVectors_column = invVectors.shape[1]

    # an array of all distinct eigen values with their associated algebraic multiplicity
    # keys: eigen values
    # values: algebraic multiplicity
    # {eigenValue: algebraicMulti}
    dictValues = {}

    while eigenValues.shape[0] != 0:

        index = np.argwhere(abs(eigenValues - eigenValues[0]) < 0.00001)

        spectrum = eigenVectors[:, index].reshape((eigenVectors_row, len(index))).dot(invVectors[index, :].reshape((len(index), invVectors_column)) )

        dictValues.update({eigenValues[0]: spectrum})
        eigenValues = np.delete(eigenValues, index)
        eigenVectors = np.delete(eigenVectors, index, 1)
        invVectors = np.delete(invVectors, index, 0)

    return dictValues