[Numpy-discussion] PyMatrix: Announcement

Colin J. Williams cjw at sympatico.ca
Wed Dec 10 05:32:01 CST 2003


Sebastian Haase wrote:

>Hi Colin,
>We are interested in using your PyMatrix packages (It' numarray not Numeric,
>right?).
>
That is correct.  Testing so far is with numarray 0.7.  Please remember 
to also install the version 0.7 addons.  When version 0.8 arrives, all 
will be included in one package.

The package is intended for comment and review.  There is at least one 
problem in numarray, which we hope will be resolved in version 0.8.  For 
example, for some functions, upon the first call, the function returns 
an instance of the M class (matrix), on the second call, it returns an 
instance of the NumArray class.

> First though, someone in my lab had the following concern:
>What if I actually need the element-wise multiplication ?
>(In other words: The Matlab .* operator) [1] <%5B1%5D>
>
>I understand that python does not allow to invent new operator symbols.
>
Yes.  This issue was discussed in PEP 225 
<http://www.python.org/peps/pep-0225.html>.

>How about multiplying a Matrix with a Numarray ?
>
Please see [2] <#2>.

>Is it possible to have a 'numarray view' of a Matrix object ? (I'm thinking
>of two differently typed objects sharing one "value-memory space", so that
>essentially the type determines which multiplication is being used ...)
>
There is a need to think through the copy/view approach in PyMatrix.  
Currently, most cases are copies.

I'm inclined to deprecate the dual view approach, but I would appreciate 
comments.

Let me know if you have any questions or comments.

Colin W.

>Thanks,
>Sebastian Haase
>
>
>----- Original Message ----- 
>From: "Colin J. Williams" <cjw at sympatico.ca>
>Newsgroups: comp.lang.python,comp.lang.python.announce
>To: "numpy-discussion" <numpy-discussion at lists.sourceforge.net>; "SciPy
>Discussion List" <scipy-user at scipy.net>
>Cc: "Huaiyu Zhu" <hzhu at users.sourceforge.net>
>Sent: Monday, November 24, 2003 5:17 AM
>Subject: [Numpy-discussion] PyMatrix: Announcement
>
>
>  
>
>>PyMatrix is available for test and review.
>>     http://www3.sympatico.ca/cjw
>>
>>PyMatrix provides access to basic matrix arithmetic, using Python and
>>numarray.
>>
>>Examples:
>>          A * B                   =>               the product of
>>matrices A and B
>>          A.I                       =>               the inverse of matrix
>>    
>>
>A
>  
>
>>          A.EVectors           =>               the eigenvectors of A
>>          A.var(0)               =>               the variances of the
>>columns of A
>>          (a.T*a).I * a.T*b  =>               the solution (x) for a *
>>x  =  b,
>>                                                        where a is a
>>matrix and b a column vector
>>
>>This package was developed on a Windows XP.  I would appreciate
>>comments, particularly with respect to usage on other systems.
>>
>>Colin W.
>>
>>
>>
>>
>>
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Notes:

    [1] Elementwise Multiplication
    The thinking here is that, for most matrix usage, the elementwise
    multiplication is less frequently required.
    Thus, a more complex expression can be tolerated.  See the example
    below:

          a= mRange(9, shape=(3, 3))
          b= mRange((9, 18), shape= (3, 3))
          print 'Matrixwise multiplation:'
          print 'a * b (prettyprinted):', pp(a * b)
          print 'Elementwise multiplation:'
          print 'a * b (prettyprinted):', pp(M(a.A * b.A)))

    In the last case, we use the array mechanism.
    The output is:

        Matrixwise multiplation:
        a * b (prettyprinted):matrix([[ 42,  45,  48],
               [150, 162, 174],
               [258, 279, 300]])
         None
        Elementwise multiplation:
        a * b (prettyprinted):matrix([[  0,  10,  22],
               [ 36,  52,  70],
               [ 90, 112, 136]])
         None

    [2] Multiplication of a matrix by an array or nested list
    When an compatible array or list is juxtapositioned with a matrix,
    it is in effect coerced to the higher class.

          a= mRange(9, shape=(3, 3)
          c= N.arange(9, shape=(3, 3))
          print 'A matrix multiplied by an array:'
          print 'a * c (prettyprinted):', pp(a * c)
          print 'A matrix multiplied by a list:'
          lst= [[0, 1, 2],
                [3, 4, 5],
                [6, 7, 8]]
          print 'a * lst (prettyprinted):', pp(a * lst)

    The output is:

        A matrix multiplied by an array:
        a * c (prettyprinted):matrix([[ 15,  18,  21],
               [ 42,  54,  66],
               [ 69,  90, 111]])
         None
        A matrix multiplied by a list:
        a * lst (prettyprinted):matrix([[ 15,  18,  21],
               [ 42,  54,  66],
               [ 69,  90, 111]])
         None






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