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File Content: misc.cpython-35.opt-1.pyc

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    Matrix or vector norm.

This function is able to return one of seven different matrix norms,
    or one of an infinite number of vector norms (described below), depending
    on the value of the ``ord`` parameter.

Parameters
    ----------
    a : (M,) or (M, N) array_like
        Input array.  If `axis` is None, `a` must be 1-D or 2-D.
    ord : {non-zero int, inf, -inf, 'fro'}, optional
        Order of the norm (see table under ``Notes``). inf means numpy's
        `inf` object
    axis : {int, 2-tuple of ints, None}, optional
        If `axis` is an integer, it specifies the axis of `a` along which to
        compute the vector norms.  If `axis` is a 2-tuple, it specifies the
        axes that hold 2-D matrices, and the matrix norms of these matrices
        are computed.  If `axis` is None then either a vector norm (when `a`
        is 1-D) or a matrix norm (when `a` is 2-D) is returned.
    keepdims : bool, optional
        If this is set to True, the axes which are normed over are left in the
        result as dimensions with size one.  With this option the result will
        broadcast correctly against the original `a`.

Returns
    -------
    n : float or ndarray
        Norm of the matrix or vector(s).

Notes
    -----
    For values of ``ord <= 0``, the result is, strictly speaking, not a
    mathematical 'norm', but it may still be useful for various numerical
    purposes.

The following norms can be calculated:

=====  ============================  ==========================
    ord    norm for matrices             norm for vectors
    =====  ============================  ==========================
    None   Frobenius norm                2-norm
    'fro'  Frobenius norm                --
    inf    max(sum(abs(x), axis=1))      max(abs(x))
    -inf   min(sum(abs(x), axis=1))      min(abs(x))
    0      --                            sum(x != 0)
    1      max(sum(abs(x), axis=0))      as below
    -1     min(sum(abs(x), axis=0))      as below
    2      2-norm (largest sing. value)  as below
    -2     smallest singular value       as below
    other  --                            sum(abs(x)**ord)**(1./ord)
    =====  ============================  ==========================

The Frobenius norm is given by [1]_:

:math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}`

The ``axis`` and ``keepdims`` arguments are passed directly to
    ``numpy.linalg.norm`` and are only usable if they are supported
    by the version of numpy in use.

References
    ----------
    .. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
           Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15

Examples
    --------
    >>> from scipy.linalg import norm
    >>> a = np.arange(9) - 4.0
    >>> a
    array([-4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])
    >>> b = a.reshape((3, 3))
    >>> b
    array([[-4., -3., -2.],
           [-1.,  0.,  1.],
           [ 2.,  3.,  4.]])

>>> norm(a)
    7.745966692414834
    >>> norm(b)
    7.745966692414834
    >>> norm(b, 'fro')
    7.745966692414834
    >>> norm(a, np.inf)
    4
    >>> norm(b, np.inf)
    9
    >>> norm(a, -np.inf)
    0
    >>> norm(b, -np.inf)
    2

>>> norm(a, 1)
    20
    >>> norm(b, 1)
    7
    >>> norm(a, -1)
    -4.6566128774142013e-010
    >>> norm(b, -1)
    6
    >>> norm(a, 2)
    7.745966692414834
    >>> norm(b, 2)
    7.3484692283495345

>>> norm(a, -2)
    0
    >>> norm(b, -2)
    1.8570331885190563e-016
    >>> norm(a, 3)
    5.8480354764257312
    >>> norm(a, -3)
    0

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    Strict check for `arr` not sharing any data with `original`,
    under the assumption that arr = asarray(original)

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isinstancer���Zndarray�hasattr�base)ZarrZoriginalr���r���r����_datacopied����s
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__init__.cpython-35.pyc	6592 bytes	0644
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basic.cpython-35.opt-1.pyc	33967 bytes	0644
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flinalg.cpython-35.opt-1.pyc	1376 bytes	0644
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matfuncs.cpython-35.pyc	20010 bytes	0644
misc.cpython-35.opt-1.pyc	5150 bytes	0644
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