Re: [Numpy-discussion] User-defined data-types

2008-07-31 Thread Charles R Harris
On Thu, Jul 31, 2008 at 11:26 PM, Francesc Alted <[EMAIL PROTECTED]>wrote: > Hi, > > We need to make a dtype that needs to be defined in the user's > application space. In the NumPy book there is a section devoted to > this subject, but also warns: > > """ > Adding data-types is one of the less w

Re: [Numpy-discussion] numpy 1.1.rc2: win32 binaries

2008-07-31 Thread David Cournapeau
Bruce Southey wrote: > Hi, > The installation worked on my old Athlon XP running Windows XP and > 'numpy.test(level=1)' gave no errors. > By old, do you mean it does not have at least SSE2 ? If so, the problem would not have happened anyway because the numpy installer does not use ATLAS there,

[Numpy-discussion] User-defined data-types

2008-07-31 Thread Francesc Alted
Hi, We need to make a dtype that needs to be defined in the user's application space. In the NumPy book there is a section devoted to this subject, but also warns: """ Adding data-types is one of the less well-tested areas for NumPy 1.0, so there may be bugs remaining in the approach. """ An

Re: [Numpy-discussion] numpy 1.1.rc2: win32 binaries

2008-07-31 Thread Bruce Southey
Hi, The installation worked on my old Athlon XP running Windows XP and 'numpy.test(level=1)' gave no errors. I did not get an error for the code provided for ticket 844 so I presume this ticket is fixed: 'numpy.inner(F,F)' results in 'array([[ 0.]])' Also, the installer gives this information:

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 11:45, Christopher Barker <[EMAIL PROTECTED]> wrote: > On my OS-X box (10.4.11, python2.5, numpy '1.1.1rc2'), it takes about 7 > seconds to import numpy! Can you try running a Python process that just imports numpy under Shark.app? http://developer.apple.com/tools/shark

Re: [Numpy-discussion] [ANNOUNCE] ETS 3.0.0b1 released!

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 05:48:02PM -0500, Dave Peterson wrote: > easy_install Mayavi Just a precision (I just got caught by that), to install mayavi2, the application, and not just the 3d visualization library that can be used eg in ipython, you need to do: easy_install "Mayavi[ui]" ie the

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Kevin Jacobs <[EMAIL PROTECTED]>
On Thu, Jul 31, 2008 at 7:08 PM, Christopher Burns <[EMAIL PROTECTED]>wrote: > Do you mean add a file on the Wiki or in the source tree somewhere? > Either or both-- so long as there is a convenient place to find them. I suppose a Wiki page would be most flexible, since it could be expanded to

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Stéfan van der Walt
2008/7/31 Andrew Dalke <[EMAIL PROTECTED]>: > I don't see a place to submit patches. Is there a patch manager for > numpy? > > Here's a patch to defer importing 'tempfile' until needed. I > previously mentioned one other place that didn't need tempfile. With > this there is no 'import tempfile'

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Christopher Burns
Kevin, Do you mean add a file on the Wiki or in the source tree somewhere? Chris On Thu, Jul 31, 2008 at 2:14 PM, Kevin Jacobs <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> wrote: > For the help of freeze packages, it would be great if you could add a file > that lists all of the deferred imports that

[Numpy-discussion] [ANNOUNCE] ETS 3.0.0b1 released!

2008-07-31 Thread Dave Peterson
Hello, I am very pleased to announce that ETS 3.0.0b1 has just been tagged and released! All ETS sub-projects, including Traits, Chaco, Mayavi, and Envisage, have been tagged and released in one form or another (alpha, beta, final) as part of this effort. All ETS projects have now been registered

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 16:09, Andrew Dalke <[EMAIL PROTECTED]> wrote: > On Jul 31, 2008, at 10:02 PM, Robert Kern wrote: >> 1) Everything exposed by "from numpy import *" still needs to work. > > Does that include numpy.Tester? I don't mean numpy.test() nor > numpy.bench(). > > Does that include

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Kevin Jacobs <[EMAIL PROTECTED]>
For the help of freeze packages, it would be great if you could add a file that lists all of the deferred imports that you run across. That way, we can add/update recipes more easily for py2app, py2exe, bbfreeze, etc. Thanks, -Kevin On Thu, Jul 31, 2008 at 4:44 PM, Andrew Dalke <[EMAIL PROTECTE

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Andrew Dalke
On Jul 31, 2008, at 10:02 PM, Robert Kern wrote: > 1) Everything exposed by "from numpy import *" still needs to work. Does that include numpy.Tester? I don't mean numpy.test() nor numpy.bench(). Does that include numpy.PackageLoader? I don't mean numpy.pkgload. > 2) The improvement in impo

Re: [Numpy-discussion] numpy 1.1.rc2: win32 binaries

2008-07-31 Thread Jarrod Millman
On Sun, Jul 27, 2008 at 10:30 PM, David Cournapeau <[EMAIL PROTECTED]> wrote: > http://www.ar.media.kyoto-u.ac.jp/members/david/archives/numpy-1.1.1.dev5559-win32-superpack-python2.5.exe I want to get the final 1.1.1 release out ASAP, but I need some feedback on the windows binaries. Could someon

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread David Cournapeau
On Fri, Aug 1, 2008 at 5:44 AM, Andrew Dalke <[EMAIL PROTECTED]> wrote: > I don't see a place to submit patches. Is there a patch manager for > numpy? > Attaching a patch to numpy trac is the way to go: http://projects.scipy.org/scipy/numpy thanks for the patch, David _

Re: [Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 15:44, Andrew Dalke <[EMAIL PROTECTED]> wrote: > I don't see a place to submit patches. Is there a patch manager for > numpy? http://projects.scipy.org/scipy/numpy -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made t

Re: [Numpy-discussion] Numpy 1.1.1 release notes.

2008-07-31 Thread Charles R Harris
On Thu, Jul 31, 2008 at 12:36 PM, Pierre GM <[EMAIL PROTECTED]> wrote: > Chuck, > Can you remove the entry > "Pierre GM -- masked array, improved support for flexible dtypes." > from "General Improvements" ? > The work was done for 1.2 and not completely backported, so that's not > really > a lot

[Numpy-discussion] patches to reduce import costs

2008-07-31 Thread Andrew Dalke
I don't see a place to submit patches. Is there a patch manager for numpy? Here's a patch to defer importing 'tempfile' until needed. I previously mentioned one other place that didn't need tempfile. With this there is no 'import tempfile' during 'import numpy' This improves startup by a

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
On Fri, Aug 1, 2008 at 5:02 AM, Robert Kern <[EMAIL PROTECTED]> wrote: > > 5) Proxy objects ... I would really like to avoid proxy objects. They > have caused fragility in the past. One recurrent problem around import times optimization is that it is some work to improve it, but it takes one line

Re: [Numpy-discussion] distutils and inplace build: is numpy supposed to work ?

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 09:18, David Cournapeau <[EMAIL PROTECTED]> wrote: > Hi, > >I wanted to know if numpy was supposed to work when built in place > through the -i option of distutils. The reason why I am asking it that I > would like to support it in numscons, and I cannot make it work whe

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 05:43, Andrew Dalke <[EMAIL PROTECTED]> wrote: > On Jul 31, 2008, at 12:03 PM, Robert Kern wrote: >> But you still can't remove them since they are being used inside >> numerictypes. That's why I labeled them "internal utility functions" >> instead of leaving them with mini

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Scott Ransom
On Thu, Jul 31, 2008 at 07:46:20AM -0500, Nathan Bell wrote: > On Thu, Jul 31, 2008 at 7:31 AM, Hanni Ali <[EMAIL PROTECTED]> wrote: > > > > I would just to highlight an alternate use of numpy to interactive use. We > > have a cluster of machines which process tasks on an individual basis where > >

Re: [Numpy-discussion] Numpy 1.1.1 release notes.

2008-07-31 Thread Pierre GM
Chuck, Can you remove the entry "Pierre GM -- masked array, improved support for flexible dtypes." from "General Improvements" ? The work was done for 1.2 and not completely backported, so that's not really a lot of improvements. It will for 1.2, however: when is this one supposed to be released

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 10:12:22AM -0700, Christopher Barker wrote: > I've been wondering about that. > time python -c "import numpy" > real0m8.383s > user0m0.320s > sys 0m7.805s I don't know what is wrong, but this is plain wrong, unless you are on a distant file system, or somethin

Re: [Numpy-discussion] Numpy 1.1.1 release notes.

2008-07-31 Thread Charles R Harris
On Thu, Jul 31, 2008 at 12:23 PM, Pauli Virtanen <[EMAIL PROTECTED]> wrote: > Thu, 31 Jul 2008 12:12:54 -0600, Charles R Harris wrote: > > > Hi All, > > > > I've attached draft release notes for Numpy 1.1.1. If you have anything > > to add or correct, let me know. > [clip] > > Bug fixes > > #854,

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
> > hot -- it takes about 10 cold. > > I've been wondering about that. > > time python -c "import numpy" > > real0m8.383s > user0m0.320s > sys 0m7.805s > > and similar results if run multiple times in a row. What does python -c "import sys; print sys.path" say ? > Any idea what could

Re: [Numpy-discussion] Numpy 1.1.1 release notes.

2008-07-31 Thread Pauli Virtanen
Thu, 31 Jul 2008 12:12:54 -0600, Charles R Harris wrote: > Hi All, > > I've attached draft release notes for Numpy 1.1.1. If you have anything > to add or correct, let me know. [clip] > Bug fixes #854, r5456? -- Pauli Virtanen ___ Numpy-discussion m

Re: [Numpy-discussion] distutils and inplace build: is numpy supposed to work ?

2008-07-31 Thread Charles R Harris
On Thu, Jul 31, 2008 at 8:18 AM, David Cournapeau < [EMAIL PROTECTED]> wrote: > Hi, > >I wanted to know if numpy was supposed to work when built in place > through the -i option of distutils. The reason why I am asking it that I > would like to support it in numscons, and I cannot make it work

Re: [Numpy-discussion] The date/time dtype and the casting issue

2008-07-31 Thread Francesc Alted
A Thursday 31 July 2008, Alan G Isaac escrigué: > > A Thursday 31 July 2008, Matt Knox escrigué: > >> While on the topic of FAME... being a financial analyst, I really > >> am quite fond of the multitude of quarterly frequencies we have in > >> the timeseries package (with different year end points

[Numpy-discussion] Numpy 1.1.1 release notes.

2008-07-31 Thread Charles R Harris
Hi All, I've attached draft release notes for Numpy 1.1.1. If you have anything to add or correct, let me know. Chuck Numpy 1.1.1 is a bug fix release featuring major improvements in Python 2.3.x compatibility and masked arrays. Python 2.3.x fixes Robert Kern -- remove developement bran

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Huard
On Thu, Jul 31, 2008 at 1:12 PM, Christopher Barker <[EMAIL PROTECTED]>wrote: > David Cournapeau wrote: > > Christopher Barker wrote: > >> On my OS-X box (10.4.11, python2.5, numpy '1.1.1rc2'), it takes about 7 > >> seconds to import numpy! > > > > Hot or cold ? If hot, there is something horribly

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Nils Wagner
On Thu, 31 Jul 2008 10:12:22 -0700 Christopher Barker <[EMAIL PROTECTED]> wrote: > David Cournapeau wrote: >> Christopher Barker wrote: >>> On my OS-X box (10.4.11, python2.5, numpy '1.1.1rc2'), >>>it takes about 7 >>> seconds to import numpy! >> >> Hot or cold ? If hot, there is something hor

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Christopher Barker
David Cournapeau wrote: > Christopher Barker wrote: >> On my OS-X box (10.4.11, python2.5, numpy '1.1.1rc2'), it takes about 7 >> seconds to import numpy! > > Hot or cold ? If hot, there is something horribly wrong with your setup. hot -- it takes about 10 cold. I've been wondering about that.

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Christopher Barker
Stéfan van der Walt wrote: > No one is *waiting* for NumPy to start. I am, and probably 10 times, a day, yes. And it's a major issue for CGI, though maybe no one's using that anymore anyway. > Just by answering this > e-mail I could have (and maybe should have) started NumPy three > hundred

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
Christopher Barker wrote: > On my OS-X box (10.4.11, python2.5, numpy '1.1.1rc2'), it takes about 7 > seconds to import numpy! > > Hot or cold ? If hot, there is something horribly wrong with your setup. On my macbook, it takes ~ 180 ms to to python -c "import numpy", and ~ 100 ms on linux (sa

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Christopher Barker
Andrew Dalke wrote: > If I had my way, remove things like (in numpy/__init__.py) > > import linalg > import fft > import random > import ctypeslib > import ma as a side benefit, this might help folks using py2exe, py2app and friends -- as it stands all those sub-modules

Re: [Numpy-discussion] [ANNOUNCE] Traits 3.0 has been released

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 10:38:42AM -0400, Kevin Jacobs <[EMAIL PROTECTED]> wrote: >All of the URLs on PyPi to Enthought seem to be broken (e.g., >[2]http://code.enthought.com/traits). Can you give an example showing how >traits work? I'm mildly intrigued, but too lazy to dig beyond t

Re: [Numpy-discussion] [ANNOUNCE] Traits 3.0 has been released

2008-07-31 Thread Kevin Jacobs <[EMAIL PROTECTED]>
On Wed, Jul 30, 2008 at 9:25 PM, Dave Peterson <[EMAIL PROTECTED]>wrote: > Hello, > > I am very pleased to announce that Traits 3.0 has just been released! > > All of the URLs on PyPi to Enthought seem to be broken (e.g., http://code.enthought.com/traits). Can you give an example showing how trai

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 10:34:04AM -0400, Kevin Jacobs <[EMAIL PROTECTED]> wrote: >The morale of this discussion, for me, is that just because _you_ don't >care about a particular aspect or feature, doesn't mean that others don't >or shouldn't. Your workarounds may not be viable for m

[Numpy-discussion] distutils and inplace build: is numpy supposed to work ?

2008-07-31 Thread David Cournapeau
Hi, I wanted to know if numpy was supposed to work when built in place through the -i option of distutils. The reason why I am asking it that I would like to support it in numscons, and I cannot make it work when using distutils. Importing numpy works in the source tree, but most tests fail be

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 11:16:12PM +0900, David Cournapeau wrote: > Gael Varoquaux wrote: > > Obviously, the build part has to be well-tuned for the machinery to work, > > but there is a lot of value here. > Ah yes, setuptools does have this. But this is specific to setuptools, > bare distutils d

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Kevin Jacobs <[EMAIL PROTECTED]>
On Thu, Jul 31, 2008 at 10:14 AM, Gael Varoquaux < [EMAIL PROTECTED]> wrote: > On Thu, Jul 31, 2008 at 12:43:17PM +0200, Andrew Dalke wrote: > > Startup performance has not been a numpy concern. It a concern for > > me, and it has been (for other packages) a concern for some of my > > clients. >

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
Gael Varoquaux wrote: > Obviously, the build part has to be well-tuned for the machinery to work, > but there is a lot of value here. > Ah yes, setuptools does have this. But this is specific to setuptools, bare distutils does not have this test command, right ? cheers, David

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 11:05:33PM +0900, David Cournapeau wrote: > Gael Varoquaux wrote: > > That's why distutils have a test target. You can do "python setup.py > > test", and if you have setup you setup.py properly it should work > > (obviously it is easy to make this statement, and harder to g

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
Gael Varoquaux wrote: > > That's why distutils have a test target. You can do "python setup.py > test", and if you have setup you setup.py properly it should work > (obviously it is easy to make this statement, and harder to get the thing > working). > I have already seen some discussion about

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Alan McIntyre
On Thu, Jul 31, 2008 at 2:12 AM, Andrew Dalke <[EMAIL PROTECTED]> wrote: > Hmm. And it looks like testing/nosetester.py (which implements the > 'test' function above) is meant to make it easier to run nose, except > my feeling is the extra level of wrapping makes things more > complicated. The nos

Re: [Numpy-discussion] Example of numpy cov() not correct?

2008-07-31 Thread Keith Goodman
On Thu, Jul 31, 2008 at 1:14 AM, Pauli Virtanen <[EMAIL PROTECTED]> wrote: > Yes, the example on > >http://www.scipy.org/Numpy_Example_List_With_Doc#cov > > is wrong; cov(T,P) indeed returns a matrix. And it would be nice if > someone fixed this, you can simply register a wiki account and f

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 12:43:17PM +0200, Andrew Dalke wrote: > Startup performance has not been a numpy concern. It a concern for > me, and it has been (for other packages) a concern for some of my > clients. I am curious, if startup performance is a problem, I guess it is because you are ru

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Gael Varoquaux
On Thu, Jul 31, 2008 at 03:41:15PM +0900, David Cournapeau wrote: > Yes. Nothing that an easy make file cannot solve, nonetheless (I am sure > I am not the only one with a makefile/script which automates the above, > to test a new svn updated numpy in one command). That's why distutils have a test

Re: [Numpy-discussion] The date/time dtype and the casting issue

2008-07-31 Thread Alan G Isaac
> A Thursday 31 July 2008, Matt Knox escrigué: >> While on the topic of FAME... being a financial analyst, I really am >> quite fond of the multitude of quarterly frequencies we have in the >> timeseries package (with different year end points) because they are >> very useful when doing things l

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Nathan Bell
On Thu, Jul 31, 2008 at 5:36 AM, Andrew Dalke <[EMAIL PROTECTED]> wrote: > > The user base for numpy might be .. 10,000 people? 100,000 people? > Let's go with the latter, and assume that with command-line scripts, > CGI scripts, and the other programs that people write in order to > help do resea

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread David Cournapeau
Nathan Bell wrote: > > There are other components of NumPy/SciPy that are more worthy of > optimization. Given that programmer time is a scarce resource, it's > more sensible to direct our efforts towards making the other 98.5% of > the computation faster. > To be fair, when I took a look at t

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Nathan Bell
On Thu, Jul 31, 2008 at 7:31 AM, Hanni Ali <[EMAIL PROTECTED]> wrote: > > I would just to highlight an alternate use of numpy to interactive use. We > have a cluster of machines which process tasks on an individual basis where > a master tasks may spawn 600 slave tasks to be processed. These tasks

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Hanni Ali
Hi All, I've been reading this discussion with interest. I would just to highlight an alternate use of numpy to interactive use. We have a cluster of machines which process tasks on an individual basis where a master tasks may spawn 600 slave tasks to be processed. These tasks are spread across t

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Stéfan van der Walt
2008/7/31 Andrew Dalke <[EMAIL PROTECTED]>: > The user base for numpy might be .. 10,000 people? 100,000 people? > Let's go with the latter, and assume that with command-line scripts, > CGI scripts, and the other programs that people write in order to > help do research means that numpy is started

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Andrew Dalke
On Jul 31, 2008, at 12:03 PM, Robert Kern wrote: > That said, the reason those particular docstrings are verbose is > because I wanted people to know why those functions exist there (e.g. > "This is an internal utility function"). Err, umm, you mean that first line of the second paragraph in t

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Andrew Dalke
On Jul 31, 2008, at 11:42 AM, Stéfan van der Walt wrote: > Maybe when we're convinced that there is a lot to be gained from > making such a change. From my perspective, it doesn't look good: > > I) Major code breakage > II) Confused users > III) More difficult function discovery for beginners I'm

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Robert Kern
On Thu, Jul 31, 2008 at 04:42, Stéfan van der Walt <[EMAIL PROTECTED]> wrote: > 2008/7/31 Andrew Dalke <[EMAIL PROTECTED]>: >> I wrote that I don't know the reasons for why the design was as it >> is. Are those functions ("english_upper", "english_lower", >> "english_capitalize") expected as part

Re: [Numpy-discussion] "import numpy" is slow

2008-07-31 Thread Stéfan van der Walt
2008/7/31 Andrew Dalke <[EMAIL PROTECTED]>: >> Numpy has a very flat namespace, for better or worse, which implies >> many imports. > > I don't get the feeling that numpy is flat. Python's stdlib is flat. > Numpy has many 2- and 3-level modules. With 500+ functions in the root namespace, I'd call

[Numpy-discussion] Sorry!, please disregard (Re: NumPy won't work with distutils loaded?)

2008-07-31 Thread Dag Sverre Seljebotn
Dag Sverre Seljebotn wrote: > While developing a testcase for NumPy in Cython, I had the problem > demonstrated below. Essentially this means that I couldn't run testcases > in our Cython testing framework (though I will work around it). Is this > some known restriction in how NumPy can be used,

[Numpy-discussion] NumPy won't work with distutils loaded?

2008-07-31 Thread Dag Sverre Seljebotn
While developing a testcase for NumPy in Cython, I had the problem demonstrated below. Essentially this means that I couldn't run testcases in our Cython testing framework (though I will work around it). Is this some known restriction in how NumPy can be used, is it work in progress, a problem

Re: [Numpy-discussion] Example of numpy cov() not correct?

2008-07-31 Thread Pauli Virtanen
Wed, 30 Jul 2008 18:49:10 +0300, Nadav Horesh wrote: > If you read the cov function documentation you'll see that if a second > vector is given, it joins the 2 into one matrix and calculate the > covariance of it. In your case, you are looking for the off-diagonal > elements. So the final answer