[Numpy-discussion] design issues - octave 'incompatibilities'

[Chris Barker]

Soeren Sonnenburg wrote:
> -- why do vectors have no 'orientation', i.e. there are only row but no
> column vectors (or why do you treat matrices/vectors differently, i.e.
> have vectors at all as a separate type)

I think the key to understanding this is that NumPy uses a 
fundamentally different data type that MATLAB ans it's derivatives. 
MATLAB was originally just what it is called: a "Matrix" laboratory. The 
basic data type of Matlab is a 2-d matrix. Even a scalar is really a 1X! 
matrix. Matlab has a few tricks that can make these look like row and 
column vectors, etc, but they are really always matrices.

On the other hand, NumPy arrays are N-dimensional, where N is 
theoretically unlimited. In practice, I think the max N is defined and 
compiled in, but you could change it and re-compile if you wanted. In 
any case, many of us frequently use 3-d and higher arrays, and they can 
be very useful. When thought  of this way, you can see why there is no 
such thing as a column vs. a row vector. A vector is a one-dimensional 
array: it has no orientation.

However, NumPy does support NX1 and 1XN 2-d arrays which can be very handy:
 >>> import numarray as N
 >>> a = N.arange(5)
 >>> a.shape = (1,-1)
 >>> a
array([[0, 1, 2, 3, 4]])
 >>> b = N.arange(5)
 >>> b.shape = (-1,1)
 >>> a
array([0, 1, 2, 3, 4])
 >>> b
array([[0],
        [1],
        [2],
        [3],
        [4]])

So a is a row vector and b is a column vector. If you multiply them, you 
get "array broadcasting":
 >>> a * b
array([[ 0,  0,  0,  0,  0],
        [ 0,  1,  2,  3,  4],
        [ 0,  2,  4,  6,  8],
        [ 0,  3,  6,  9, 12],
        [ 0,  4,  8, 12, 16]])

This eliminates a LOT of extra duplicate arrays that you have to make in 
Matlab with meshgrid.

When you index into an array, you reduce its rank (number of dimensions) 
by 1:
 >>> a = N.arange(27)
 >>> a.shape = (3,3,3)
 >>> a
array([[[ 0,  1,  2],
         [ 3,  4,  5],
         [ 6,  7,  8]],

        [[ 9, 10, 11],
         [12, 13, 14],
         [15, 16, 17]],

        [[18, 19, 20],
         [21, 22, 23],
         [24, 25, 26]]])
 >>> a.shape
(3, 3, 3)
 >>> a[1].shape
(3, 3)
 >>> a[1][1].shape
(3,)

When you slice, you keep the rank the same:

 >>> a[1:2].shape
(1, 3, 3)

This creates a way to make row and column "vectors" from your 2-d array 
(matrix)
 >>> a = N.arange(25)
 >>> a.shape = (5,5)
 >>> a
array([[ 0,  1,  2,  3,  4],
        [ 5,  6,  7,  8,  9],
        [10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19],
        [20, 21, 22, 23, 24]])

To make a "row vector" (really a 1XN matrix)
 >>> a[0:1,:]
array([[0, 1, 2, 3, 4]])


To make a "column vector" (really a NX1 matrix)
 >>> a[:,0:1]
array([[ 0],
        [ 5],
        [10],
        [15],
        [20]])


I hope that helps:
-Chris



-- 
Christopher Barker, Ph.D.
Oceanographer
                                     		
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