def norm(a, ord=None):
<EOL>a = np.asarray_chkfinite(a)<EOL>if ord in (None, <NUM_LIT:2>) and (a.ndim == <NUM_LIT:1>) and (a.dtype.char in '<STR_LIT>'):<EOL><INDENT>func_name = _nrm2_prefix.get(a.dtype.char, '<STR_LIT:d>') + '<STR_LIT>'<EOL>nrm2 = getattr(blas, func_name)<EOL>return nrm2(a)<EOL><DEDENT>return np.linalg.norm(a, ord=ord)<EOL>
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
----------
x : (M,) or (M, N) array_like
    Input array.
ord : {non-zero int, inf, -inf, 'fro'}, optional
    Order of the norm (see table under ``Notes``). inf means numpy's
    `inf` object.

Returns
-------
norm : float
    Norm of the matrix or vector.

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}`

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