[Numpy-discussion] RFC: A (second) proposal for implementing some date/time types in NumPy
Ivan Vilata i Balaguer
ivan@selidor....
Fri Jul 18 09:42:47 CDT 2008
Francesc Alted (el 2008-07-16 a les 18:44:36 +0200) va dir::
> After tons of excellent feedback received for our first proposal about
> the date/time types in NumPy Ivan and me have had another brainstorming
> session and ended with a new proposal for your consideration.
After re-reading the proposal, Francesc and me found some points that
needed small corrections and some clarifications or enhancements. Here
you have a new version of the proposal. The changes aren't fundamental:
* Reference to POSIX-like treatment of leap seconds.
* Notes on default resolutions.
* Meaning of the stored values.
* Usage examples for scalar constructor.
* Using an ISO 8601 string as a date value.
* Fixed str() and repr() representations.
* Note on operations with mixed resolutions.
* Other small corrections.
Thanks for the feedback!
----
====================================================================
A (second) proposal for implementing some date/time types in NumPy
====================================================================
:Author: Francesc Alted i Abad
:Contact: faltet@pytables.com
:Author: Ivan Vilata i Balaguer
:Contact: ivan@selidor.net
:Date: 2008-07-18
Executive summary
=================
A date/time mark is something very handy to have in many fields where
one has to deal with data sets. While Python has several modules that
define a date/time type (like the integrated ``datetime`` [1]_ or
``mx.DateTime`` [2]_), NumPy has a lack of them.
In this document, we are proposing the addition of a series of date/time
types to fill this gap. The requirements for the proposed types are
two-folded: 1) they have to be fast to operate with and 2) they have to
be as compatible as possible with the existing ``datetime`` module that
comes with Python.
Types proposed
==============
To start with, it is virtually impossible to come up with a single
date/time type that fills the needs of every case of use. So, after
pondering about different possibilities, we have stuck with *two*
different types, namely ``datetime64`` and ``timedelta64`` (these names
are preliminary and can be changed), that can have different resolutions
so as to cover different needs.
.. Important:: the resolution is conceived here as metadata that
*complements* a date/time dtype, *without changing the base type*. It
provides information about the *meaning* of the stored numbers, not
about their *structure*.
Now follows a detailed description of the proposed types.
``datetime64``
--------------
It represents a time that is absolute (i.e. not relative). It is
implemented internally as an ``int64`` type. The internal epoch is the
POSIX epoch (see [3]_). Like POSIX, the representation of a date
doesn't take leap seconds into account.
Resolution
~~~~~~~~~~
It accepts different resolutions, each of them implying a different time
span. The table below describes the resolutions supported with their
corresponding time spans.
======== =============== ==========================
Resolution Time span (years)
------------------------ --------------------------
Code Meaning
======== =============== ==========================
Y year [9.2e18 BC, 9.2e18 AC]
Q quarter [3.0e18 BC, 3.0e18 AC]
M month [7.6e17 BC, 7.6e17 AC]
W week [1.7e17 BC, 1.7e17 AC]
d day [2.5e16 BC, 2.5e16 AC]
h hour [1.0e15 BC, 1.0e15 AC]
m minute [1.7e13 BC, 1.7e13 AC]
s second [ 2.9e9 BC, 2.9e9 AC]
ms millisecond [ 2.9e6 BC, 2.9e6 AC]
us microsecond [290301 BC, 294241 AC]
ns nanosecond [ 1678 AC, 2262 AC]
======== =============== ==========================
When a resolution is not provided, the default resolution of
microseconds is used.
The value of an absolute date is thus *an integer number of units of the
chosen resolution* passed since the internal epoch.
Building a ``datetime64`` dtype
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The proposed way to specify the resolution in the dtype constructor
is:
Using parameters in the constructor::
dtype('datetime64', res="us") # the default res. is microseconds
Using the long string notation::
dtype('datetime64[us]') # equivalent to dtype('datetime64')
Using the short string notation::
dtype('T8[us]') # equivalent to dtype('T8')
Compatibility issues
~~~~~~~~~~~~~~~~~~~~
This will be fully compatible with the ``datetime`` class of the
``datetime`` module of Python only when using a resolution of
microseconds. For other resolutions, the conversion process will loose
precision or will overflow as needed. The conversion from/to a
``datetime`` object doesn't take leap seconds into account.
``timedelta64``
---------------
It represents a time that is relative (i.e. not absolute). It is
implemented internally as an ``int64`` type.
Resolution
~~~~~~~~~~
It accepts different resolutions, each of them implying a different time
span. The table below describes the resolutions supported with their
corresponding time spans.
======== =============== ==========================
Resolution Time span
------------------------ --------------------------
Code Meaning
======== =============== ==========================
W week +- 1.7e17 years
d day +- 2.5e16 years
h hour +- 1.0e15 years
m minute +- 1.7e13 years
s second +- 2.9e12 years
ms millisecond +- 2.9e9 years
us microsecond +- 2.9e6 years
ns nanosecond +- 292 years
ps picosecond +- 106 days
fs femtosecond +- 2.6 hours
as attosecond +- 9.2 seconds
======== =============== ==========================
When a resolution is not provided, the default resolution of
microseconds is used.
The value of a time delta is thus *an integer number of units of the
chosen resolution*.
Building a ``timedelta64`` dtype
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The proposed way to specify the resolution in the dtype constructor
is:
Using parameters in the constructor::
dtype('timedelta64', res="us") # the default res. is microseconds
Using the long string notation::
dtype('timedelta64[us]') # equivalent to dtype('timedelta64')
Using the short string notation::
dtype('t8[us]') # equivalent to dtype('t8')
Compatibility issues
~~~~~~~~~~~~~~~~~~~~
This will be fully compatible with the ``timedelta`` class of the
``datetime`` module of Python only when using a resolution of
microseconds. For other resolutions, the conversion process will
loose precision or will overflow as needed.
Example of use
==============
Here it is an example of use for the ``datetime64``::
In [5]: numpy.datetime64(42) # use default resolution of "us"
Out[5]: datetime64(42, 'us')
In [6]: print numpy.datetime64(42) # use default resolution of "us"
1970-01-01T00:00:00.000042 # representation in ISO 8601 format
In [7]: print numpy.datetime64(367.7, 'D') # decimal part is lost
1971-01-02 # still ISO 8601 format
In [8]: numpy.datetime('2008-07-18T12:23:18', 'm') # from ISO 8601
Out[8]: datetime64(20273063, 'm')
In [9]: print numpy.datetime('2008-07-18T12:23:18', 'm')
Out[9]: 2008-07-18T12:23
In [10]: t = numpy.zeros(5, dtype="datetime64[ms]")
In [11]: t[0] = datetime.datetime.now() # setter in action
In [12]: print t
[2008-07-16T13:39:25.315 1970-01-01T00:00:00.000
1970-01-01T00:00:00.000 1970-01-01T00:00:00.000
1970-01-01T00:00:00.000]
In [13]: t[0].item() # getter in action
Out[13]: datetime.datetime(2008, 7, 16, 13, 39, 25, 315000)
In [14]: print t.dtype
dtype('datetime64[ms]')
And here it goes an example of use for the ``timedelta64``::
In [5]: numpy.timedelta64(10) # use default resolution of "us"
Out[5]: timedelta64(10, 'us')
In [6]: print numpy.timedelta64(10) # use default resolution of "us"
0:00:00.010
In [7]: print numpy.timedelta64(3600.2, 'm') # decimal part is lost
2 days, 12:00
In [8]: t1 = numpy.zeros(5, dtype="datetime64[ms]")
In [9]: t2 = numpy.ones(5, dtype="datetime64[ms]")
In [10]: t = t2 - t1
In [11]: t[0] = datetime.timedelta(0, 24) # setter in action
In [12]: print t
[0:00:24.000 0:00:01.000 0:00:01.000 0:00:01.000 0:00:01.000]
In [13]: t[0].item() # getter in action
Out[13]: datetime.timedelta(0, 24)
In [14]: print t.dtype
dtype('timedelta64[s]')
Operating with date/time arrays
===============================
``datetime64`` vs ``datetime64``
--------------------------------
The only arithmetic operation allowed between absolute dates is the
subtraction::
In [10]: numpy.ones(5, "T8") - numpy.zeros(5, "T8")
Out[10]: array([1, 1, 1, 1, 1], dtype=timedelta64[us])
But not other operations::
In [11]: numpy.ones(5, "T8") + numpy.zeros(5, "T8")
TypeError: unsupported operand type(s) for +: 'numpy.ndarray' and 'numpy.ndarray'
Comparisons between absolute dates are allowed.
``datetime64`` vs ``timedelta64``
---------------------------------
It will be possible to add and subtract relative times from absolute
dates::
In [10]: numpy.zeros(5, "T8[Y]") + numpy.ones(5, "t8[Y]")
Out[10]: array([1971, 1971, 1971, 1971, 1971], dtype=datetime64[Y])
In [11]: numpy.ones(5, "T8[Y]") - 2 * numpy.ones(5, "t8[Y]")
Out[11]: array([1969, 1969, 1969, 1969, 1969], dtype=datetime64[Y])
But not other operations::
In [12]: numpy.ones(5, "T8[Y]") * numpy.ones(5, "t8[Y]")
TypeError: unsupported operand type(s) for *: 'numpy.ndarray' and 'numpy.ndarray'
``timedelta64`` vs anything
---------------------------
Finally, it will be possible to operate with relative times as if they
were regular int64 dtypes *as long as* the result can be converted back
into a ``timedelta64``::
In [10]: numpy.ones(5, 't8')
Out[10]: array([1, 1, 1, 1, 1], dtype=timedelta64[us])
In [11]: (numpy.ones(5, 't8[M]') + 2) ** 3
Out[11]: array([27, 27, 27, 27, 27], dtype=timedelta64[M])
But::
In [12]: numpy.ones(5, 't8') + 1j
TypeError: the result cannot be converted into a ``timedelta64``
dtype/resolution conversions
============================
For changing the date/time dtype of an existing array, we propose to use
the ``.astype()`` method. This will be mainly useful for changing
resolutions.
For example, for absolute dates::
In[10]: t1 = numpy.zeros(5, dtype="datetime64[s]")
In[11]: print t1
[1970-01-01T00:00:00 1970-01-01T00:00:00 1970-01-01T00:00:00
1970-01-01T00:00:00 1970-01-01T00:00:00]
In[12]: print t1.astype('datetime64[d]')
[1970-01-01 1970-01-01 1970-01-01 1970-01-01 1970-01-01]
For relative times::
In[10]: t1 = numpy.ones(5, dtype="timedelta64[s]")
In[11]: print t1
[1 1 1 1 1]
In[12]: print t1.astype('timedelta64[ms]')
[1000 1000 1000 1000 1000]
Changing directly from/to relative to/from absolute dtypes will not be
supported::
In[13]: numpy.zeros(5, dtype="datetime64[s]").astype('timedelta64')
TypeError: data type cannot be converted to the desired type
Final considerations
====================
Why the ``origin`` metadata disappeared
---------------------------------------
During the discussion of the date/time dtypes in the NumPy list, the
idea of having an ``origin`` metadata that complemented the definition
of the absolute ``datetime64`` was initially found to be useful.
However, after thinking more about this, we found that the combination
of an absolute ``datetime64`` with a relative ``timedelta64`` does offer
the same functionality while removing the need for the additional
``origin`` metadata. This is why we have removed it from this proposal.
Operations with mixed resolutions
---------------------------------
Whenever an operation between two time values of the same dtype with the
same resolution is accepted, the same operation with time values of
different resolutions should be possible (e.g. adding a time delta in
seconds and one in microseconds), resulting in an adequate resolution.
The exact semantics of this kind of operations is yet to be defined,
though.
Resolution and dtype issues
---------------------------
The date/time dtype's resolution metadata cannot be used in general as
part of typical dtype usage. For example, in::
numpy.zeros(5, dtype=numpy.datetime64)
we have yet to find a sensible way to pass the resolution. At any rate,
one can explicitly create a dtype::
numpy.zeros(5, dtype=numpy.dtype('datetime64', res='Y'))
BTW, prior to all of this, one should also elucidate whether::
numpy.dtype('datetime64', res='Y')
or::
numpy.dtype('datetime64[Y]')
numpy.dtype('T8[Y]')
numpy.dtype('T[Y]')
would be a consistent way to instantiate a dtype in NumPy. We do really
think that could be a good way, but we would need to hear the opinion of
the expert. Travis?
.. [1] http://docs.python.org/lib/module-datetime.html
.. [2] http://www.egenix.com/products/python/mxBase/mxDateTime
.. [3] http://en.wikipedia.org/wiki/Unix_time
.. Local Variables:
.. mode: rst
.. coding: utf-8
.. fill-column: 72
.. End:
----
::
Ivan Vilata i Balaguer @ Welcome to the European Banana Republic! @
http://www.selidor.net/ @ http://www.nosoftwarepatents.com/ @
-------------- next part --------------
====================================================================
A (second) proposal for implementing some date/time types in NumPy
====================================================================
:Author: Francesc Alted i Abad
:Contact: faltet@pytables.com
:Author: Ivan Vilata i Balaguer
:Contact: ivan@selidor.net
:Date: 2008-07-18
Executive summary
=================
A date/time mark is something very handy to have in many fields where
one has to deal with data sets. While Python has several modules that
define a date/time type (like the integrated ``datetime`` [1]_ or
``mx.DateTime`` [2]_), NumPy has a lack of them.
In this document, we are proposing the addition of a series of date/time
types to fill this gap. The requirements for the proposed types are
two-folded: 1) they have to be fast to operate with and 2) they have to
be as compatible as possible with the existing ``datetime`` module that
comes with Python.
Types proposed
==============
To start with, it is virtually impossible to come up with a single
date/time type that fills the needs of every case of use. So, after
pondering about different possibilities, we have stuck with *two*
different types, namely ``datetime64`` and ``timedelta64`` (these names
are preliminary and can be changed), that can have different resolutions
so as to cover different needs.
.. Important:: the resolution is conceived here as metadata that
*complements* a date/time dtype, *without changing the base type*. It
provides information about the *meaning* of the stored numbers, not
about their *structure*.
Now follows a detailed description of the proposed types.
``datetime64``
--------------
It represents a time that is absolute (i.e. not relative). It is
implemented internally as an ``int64`` type. The internal epoch is the
POSIX epoch (see [3]_). Like POSIX, the representation of a date
doesn't take leap seconds into account.
Resolution
~~~~~~~~~~
It accepts different resolutions, each of them implying a different time
span. The table below describes the resolutions supported with their
corresponding time spans.
======== =============== ==========================
Resolution Time span (years)
------------------------ --------------------------
Code Meaning
======== =============== ==========================
Y year [9.2e18 BC, 9.2e18 AC]
Q quarter [3.0e18 BC, 3.0e18 AC]
M month [7.6e17 BC, 7.6e17 AC]
W week [1.7e17 BC, 1.7e17 AC]
d day [2.5e16 BC, 2.5e16 AC]
h hour [1.0e15 BC, 1.0e15 AC]
m minute [1.7e13 BC, 1.7e13 AC]
s second [ 2.9e9 BC, 2.9e9 AC]
ms millisecond [ 2.9e6 BC, 2.9e6 AC]
us microsecond [290301 BC, 294241 AC]
ns nanosecond [ 1678 AC, 2262 AC]
======== =============== ==========================
When a resolution is not provided, the default resolution of
microseconds is used.
The value of an absolute date is thus *an integer number of units of the
chosen resolution* passed since the internal epoch.
Building a ``datetime64`` dtype
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The proposed way to specify the resolution in the dtype constructor
is:
Using parameters in the constructor::
dtype('datetime64', res="us") # the default res. is microseconds
Using the long string notation::
dtype('datetime64[us]') # equivalent to dtype('datetime64')
Using the short string notation::
dtype('T8[us]') # equivalent to dtype('T8')
Compatibility issues
~~~~~~~~~~~~~~~~~~~~
This will be fully compatible with the ``datetime`` class of the
``datetime`` module of Python only when using a resolution of
microseconds. For other resolutions, the conversion process will loose
precision or will overflow as needed. The conversion from/to a
``datetime`` object doesn't take leap seconds into account.
``timedelta64``
---------------
It represents a time that is relative (i.e. not absolute). It is
implemented internally as an ``int64`` type.
Resolution
~~~~~~~~~~
It accepts different resolutions, each of them implying a different time
span. The table below describes the resolutions supported with their
corresponding time spans.
======== =============== ==========================
Resolution Time span
------------------------ --------------------------
Code Meaning
======== =============== ==========================
W week +- 1.7e17 years
d day +- 2.5e16 years
h hour +- 1.0e15 years
m minute +- 1.7e13 years
s second +- 2.9e12 years
ms millisecond +- 2.9e9 years
us microsecond +- 2.9e6 years
ns nanosecond +- 292 years
ps picosecond +- 106 days
fs femtosecond +- 2.6 hours
as attosecond +- 9.2 seconds
======== =============== ==========================
When a resolution is not provided, the default resolution of
microseconds is used.
The value of a time delta is thus *an integer number of units of the
chosen resolution*.
Building a ``timedelta64`` dtype
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The proposed way to specify the resolution in the dtype constructor
is:
Using parameters in the constructor::
dtype('timedelta64', res="us") # the default res. is microseconds
Using the long string notation::
dtype('timedelta64[us]') # equivalent to dtype('timedelta64')
Using the short string notation::
dtype('t8[us]') # equivalent to dtype('t8')
Compatibility issues
~~~~~~~~~~~~~~~~~~~~
This will be fully compatible with the ``timedelta`` class of the
``datetime`` module of Python only when using a resolution of
microseconds. For other resolutions, the conversion process will
loose precision or will overflow as needed.
Example of use
==============
Here it is an example of use for the ``datetime64``::
In [5]: numpy.datetime64(42) # use default resolution of "us"
Out[5]: datetime64(42, 'us')
In [6]: print numpy.datetime64(42) # use default resolution of "us"
1970-01-01T00:00:00.000042 # representation in ISO 8601 format
In [7]: print numpy.datetime64(367.7, 'D') # decimal part is lost
1971-01-02 # still ISO 8601 format
In [8]: numpy.datetime('2008-07-18T12:23:18', 'm') # from ISO 8601
Out[8]: datetime64(20273063, 'm')
In [9]: print numpy.datetime('2008-07-18T12:23:18', 'm')
Out[9]: 2008-07-18T12:23
In [10]: t = numpy.zeros(5, dtype="datetime64[ms]")
In [11]: t[0] = datetime.datetime.now() # setter in action
In [12]: print t
[2008-07-16T13:39:25.315 1970-01-01T00:00:00.000
1970-01-01T00:00:00.000 1970-01-01T00:00:00.000
1970-01-01T00:00:00.000]
In [13]: t[0].item() # getter in action
Out[13]: datetime.datetime(2008, 7, 16, 13, 39, 25, 315000)
In [14]: print t.dtype
dtype('datetime64[ms]')
And here it goes an example of use for the ``timedelta64``::
In [5]: numpy.timedelta64(10) # use default resolution of "us"
Out[5]: timedelta64(10, 'us')
In [6]: print numpy.timedelta64(10) # use default resolution of "us"
0:00:00.010
In [7]: print numpy.timedelta64(3600.2, 'm') # decimal part is lost
2 days, 12:00
In [8]: t1 = numpy.zeros(5, dtype="datetime64[ms]")
In [9]: t2 = numpy.ones(5, dtype="datetime64[ms]")
In [10]: t = t2 - t1
In [11]: t[0] = datetime.timedelta(0, 24) # setter in action
In [12]: print t
[0:00:24.000 0:00:01.000 0:00:01.000 0:00:01.000 0:00:01.000]
In [13]: t[0].item() # getter in action
Out[13]: datetime.timedelta(0, 24)
In [14]: print t.dtype
dtype('timedelta64[s]')
Operating with date/time arrays
===============================
``datetime64`` vs ``datetime64``
--------------------------------
The only arithmetic operation allowed between absolute dates is the
subtraction::
In [10]: numpy.ones(5, "T8") - numpy.zeros(5, "T8")
Out[10]: array([1, 1, 1, 1, 1], dtype=timedelta64[us])
But not other operations::
In [11]: numpy.ones(5, "T8") + numpy.zeros(5, "T8")
TypeError: unsupported operand type(s) for +: 'numpy.ndarray' and 'numpy.ndarray'
Comparisons between absolute dates are allowed.
``datetime64`` vs ``timedelta64``
---------------------------------
It will be possible to add and subtract relative times from absolute
dates::
In [10]: numpy.zeros(5, "T8[Y]") + numpy.ones(5, "t8[Y]")
Out[10]: array([1971, 1971, 1971, 1971, 1971], dtype=datetime64[Y])
In [11]: numpy.ones(5, "T8[Y]") - 2 * numpy.ones(5, "t8[Y]")
Out[11]: array([1969, 1969, 1969, 1969, 1969], dtype=datetime64[Y])
But not other operations::
In [12]: numpy.ones(5, "T8[Y]") * numpy.ones(5, "t8[Y]")
TypeError: unsupported operand type(s) for *: 'numpy.ndarray' and 'numpy.ndarray'
``timedelta64`` vs anything
---------------------------
Finally, it will be possible to operate with relative times as if they
were regular int64 dtypes *as long as* the result can be converted back
into a ``timedelta64``::
In [10]: numpy.ones(5, 't8')
Out[10]: array([1, 1, 1, 1, 1], dtype=timedelta64[us])
In [11]: (numpy.ones(5, 't8[M]') + 2) ** 3
Out[11]: array([27, 27, 27, 27, 27], dtype=timedelta64[M])
But::
In [12]: numpy.ones(5, 't8') + 1j
TypeError: the result cannot be converted into a ``timedelta64``
dtype/resolution conversions
============================
For changing the date/time dtype of an existing array, we propose to use
the ``.astype()`` method. This will be mainly useful for changing
resolutions.
For example, for absolute dates::
In[10]: t1 = numpy.zeros(5, dtype="datetime64[s]")
In[11]: print t1
[1970-01-01T00:00:00 1970-01-01T00:00:00 1970-01-01T00:00:00
1970-01-01T00:00:00 1970-01-01T00:00:00]
In[12]: print t1.astype('datetime64[d]')
[1970-01-01 1970-01-01 1970-01-01 1970-01-01 1970-01-01]
For relative times::
In[10]: t1 = numpy.ones(5, dtype="timedelta64[s]")
In[11]: print t1
[1 1 1 1 1]
In[12]: print t1.astype('timedelta64[ms]')
[1000 1000 1000 1000 1000]
Changing directly from/to relative to/from absolute dtypes will not be
supported::
In[13]: numpy.zeros(5, dtype="datetime64[s]").astype('timedelta64')
TypeError: data type cannot be converted to the desired type
Final considerations
====================
Why the ``origin`` metadata disappeared
---------------------------------------
During the discussion of the date/time dtypes in the NumPy list, the
idea of having an ``origin`` metadata that complemented the definition
of the absolute ``datetime64`` was initially found to be useful.
However, after thinking more about this, we found that the combination
of an absolute ``datetime64`` with a relative ``timedelta64`` does offer
the same functionality while removing the need for the additional
``origin`` metadata. This is why we have removed it from this proposal.
Operations with mixed resolutions
---------------------------------
Whenever an operation between two time values of the same dtype with the
same resolution is accepted, the same operation with time values of
different resolutions should be possible (e.g. adding a time delta in
seconds and one in microseconds), resulting in an adequate resolution.
The exact semantics of this kind of operations is yet to be defined,
though.
Resolution and dtype issues
---------------------------
The date/time dtype's resolution metadata cannot be used in general as
part of typical dtype usage. For example, in::
numpy.zeros(5, dtype=numpy.datetime64)
we have yet to find a sensible way to pass the resolution. At any rate,
one can explicitly create a dtype::
numpy.zeros(5, dtype=numpy.dtype('datetime64', res='Y'))
BTW, prior to all of this, one should also elucidate whether::
numpy.dtype('datetime64', res='Y')
or::
numpy.dtype('datetime64[Y]')
numpy.dtype('T8[Y]')
numpy.dtype('T[Y]')
would be a consistent way to instantiate a dtype in NumPy. We do really
think that could be a good way, but we would need to hear the opinion of
the expert. Travis?
.. [1] http://docs.python.org/lib/module-datetime.html
.. [2] http://www.egenix.com/products/python/mxBase/mxDateTime
.. [3] http://en.wikipedia.org/wiki/Unix_time
.. Local Variables:
.. mode: rst
.. coding: utf-8
.. fill-column: 72
.. End:
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 307 bytes
Desc: Digital signature
Url : http://projects.scipy.org/pipermail/numpy-discussion/attachments/20080718/07b67134/attachment-0001.bin
More information about the Numpy-discussion
mailing list