This is very good discussion. Thank you all for replying. I can see the fundamental difference is that I always think/talk/read/write a 3D image as I(x, y, z), not (plane, row, column) . I am coming from MRI (magnetic resonance imaging) research, and I can assure you that the entire MRI community is using (x, y, z), including books, journal papers, conference abstracts, presentations, everything. We even talk about what we called "logical x/y/z" and "physical x/y/z", and the rotation matrix that converts the two coordinate systems. The radiologists are also used to (x, y, z). For example, we always say "my image is 256 by 256 by 20 slices", and we never say "20 by 256 by 256".
So, basically, at least in MRI, we always talk about an image as I(x, y, z), and we always assume that "x" is the fastest changing index. That's why I prefer column-major (because it is more natural). Of course, I can totally get my work done by using row-major, I just have to always remind myself "write last dimension index first" when coding. I actually have done this before, and I found it would be so much easier if just using column-major. Kang On 08/02/15, Juan Nunez-Iglesias <jni.s...@gmail.com> wrote: > Hi Kang, > > Feel free to come chat about your application on the scikit-image list [1]! > I'll note that we've been through the array order discussion many times there > and even have a doc page about it [2]. > > The short version is that you'll save yourself a lot of pain by starting to > think of your images as (plane, row, column) instead of (x, y, z). The syntax > actually becomes friendlier too. For example, to do something to each slice > of data, you do: > > for plane in image: > plane += foo > > > instead of > > > for z in image.shape[2]: > image[:, :, z] += foo > > > for example. > > > Juan. > > > [1] scikit-im...@googlegroups.com > [2] > http://scikit-image.org/docs/dev/user_guide/numpy_images.html#coordinate-conventions > > > PS: As to the renamed Fortran-ordered numpy, may I suggest "funpy". The F is > for Fortran and the fun is for all the fun you'll have maintaining it. =P > > On Mon, 3 Aug 2015 at 6:28 am Daniel Sank <sank.dan...@gmail.com> wrote: > > > > Kang, > > > > Thank you for explaining your motivation. It's clear from your last note, > > as you said, that your desire for column-first indexing has nothing to do > > with in-memory data layout. That being the case, I strongly urge you to > > just use bare numpy and do not use the "fortran_zeros" function I > > recommended before. Changing the in-memory layout via the "order" keyword > > in numpy.zeros will not change the way indexing works at all. You gain > > absolutely nothing by changing the in-memory order unless you are writing > > some C or Fortran code which will interact with the data in memory. > > > > > > To see what I mean, consider the following examples: > > > > > > x = np.array([1, 2, 3], [4, 5, 6]]) > > x.shape > > >>> (2, 3) > > > > > > and > > > > > > x = np.array([1, 2, 3], [4, 5, 6]], order='F') > > x.shape > > >>> (2, 3) > > > > > > > > You see that changing the in-memory order has nothing whatsoever to do with > > the array's shape or how you access it. > > > > > > > > > You will see run time error. Depending on environment, you may get useful > > > error message > > > (i.e. index out of range), but sometimes you just get bad image results. > > > > > > > > Could you give a very simple example of what you mean? I can't think of how > > this could ever happen and your fear here makes me think there's a > > fundamental misunderstanding about how array operations in numpy and other > > programming languages work. As an example, iteration in numpy goes through > > the first index: > > > > > > x = np.array([[1, 2, 3], [4, 5, 6]]) > > for foo in x: > > ... > > > > > > Inside the for loop, foo takes on the values [1, 2, 3] on the first > > iteration and [4, 5, 6] on the second. If you want to iterate through the > > columns just do this instead > > > > > > x = np.array([[1, 2, 3], [4, 5, 6]]) > > for foo in x.T: > > ... > > > > > > > > If your complaint is that you want np.array([[1, 2, 3], [4, 5, 6]]) to > > produce an array with shape (3, 2) then you should own up to the fact that > > the array constructor expects it the other way around and do this > > > > > > > > x = np.array([[1, 2, 3], [4, 5, 6]]).T > > > > > > > > instead. This is infinity times better than trying to write a shim function > > or patch numpy because with .T you're using (fast) built-in functionality > > which other people your code will understand. > > > > The real message here is that whether the first index runs over rows or > > columns is actually meaningless. The only places the row versus column > > issue has any meaning is when doing input/output (in which case you should > > use the transpose if you actually need it), or when doing iteration. One > > thing that would make sense if you're reading from a binary file format > > which uses column-major format would be to write your own reader function: > > > > > > > > def read_fortran_style_binary_file(file): > > return np.fromfile(file).T > > > > > > Note that if you do this then you already have a column major array in > > numpy and you don't have to worry about any other transposes (except, > > again, when doing more I/O or passing to something like a plotting > > function). > > > > > > > > > > > > > > > > > > > > > > On Sun, Aug 2, 2015 at 7:16 PM, Kang Wang <kwan...@wisc.edu> wrote: > > > > > > > > > Thank you all for replying and providing useful insights and suggestions. > > > > > > The reasons I really want to use column-major are: > > > > > > I am image-oriented user (not matrix-oriented, as explained in > > > http://docs.scipy.org/doc/numpy/reference/internals.html#multidimensional-array-indexing-order-issues) > > > I am so used to read/write "I(x, y, z)" in textbook and code, and it is > > > very likely that if the environment (row-major environment) forces me to > > > write I(z, y, x), I will write a bug if I am not 100% focused. When this > > > happens, it is difficult to debug, because everything compile and build > > > fine. You will see run time error. Depending on environment, you may get > > > useful error message (i.e. index out of range), but sometimes you just > > > get bad image results. > > > It actually has not too much to do with the actual data layout in > > > memory. In imaging processing, especially medical imaging where I am > > > working in, if you have a 3D image, everyone will agree that in memory, > > > the X index is the fasted changing index, and the Z dimension (we often > > > call it the "slice" dimension) has the largest stride in memory. So, if > > > data layout is like this in memory, and image-oriented users are so used > > > to read/write "I(x,y,z)", the only storage order that makes sense is > > > column-major > > > I also write code in MATLAB and C/C++. In MATLAB, matrix is > > > column-major array. In C/C++, we often use ITK, which is also > > > column-major (http://www.itk.org/Doxygen/html/classitk_1_1Image.html). I > > > really prefer always read/write column-major code to minimize coding bugs > > > related to storage order. > > > I also prefer index to be 0-based; however, there is nothing I can do > > > about it for MATLAB (which is 1-based). > > > > > > I can see that my original thought about "modifying NumPy source and > > > re-compile" is probably a bad idea. The suggestions about using > > > "fortran_zeros = partial(np.zeros(order='F'))" is probably the best way > > > so far, in my opinion, and I am going to give it a try. > > > > > > > > > Again, thank you all for replying. > > > > > > > > > Kang > > > > > > On 08/02/15, Nathaniel Smith <n...@pobox.com> wrote: > > > > > > > > On Aug 2, 2015 7:30 AM, "Sturla Molden" <sturla.mol...@gmail.com> wrote: > > > > > > > > > > > > > > > > > > On 02/08/15 15:55, Kang Wang wrote: > > > > > > > > > > > > > > > > > > > Can anyone provide any insight/help? > > > > > > > > > > > > > > > > > > There is no "default order". There was before, but now all operators > > > > > > > > > control the order of their return arrays from the order of their input > > > > > > > > > array. > > > > > > > > This is... overoptimistic. I would not rely on this in code that I > > > > wrote. > > > > > > > > It's true that many numpy operations do preserve the input order. But > > > > there are also many operations that don't. And which are which often > > > > changes between releases. (Not on purpose usually, but it's an easy bug > > > > to introduce. And sometimes it is done intentionally, e.g. to make > > > > functions faster. It sucks to have to make a function slower for > > > > everyone because someone somewhere is depending on memory layout > > > > default details.) And there are operations where it's not even clear > > > > what preserving order means (indexing a C array with a Fortran array, > > > > add(C, fortran), ...), and even lots of operations that intrinsically > > > > break contiguity/ordering (transpose, diagonal, slicing, swapaxes, > > > > ...), so you will end up with mixed orderings one way or another in any > > > > non-trivial program. > > > > > > > > Instead, it's better to explicitly specify order= just at the places > > > > where you care. That way your code is *locally* correct (you can check > > > > it will work by just reading the one function). The alternative is to > > > > try and enforce a *global* property on your program ("everyone > > > > everywhere is very careful to only use contiguity-preserving > > > > operations", where "everyone" includes third party libraries like numpy > > > > and others). In software design, local invariants invariants are always > > > > better than global invariants -- the most well known example is local > > > > variables versus global variables, but the principle is much broader. > > > > > > > > -n > > > > > > > > > > > > > > > > > -- > > > Kang Wang, Ph.D. > > > 1111 Highland Ave., Room 1113 > > > Madison, WI 53705-2275 > > > ---------------------------------------- > > > > > > > > > _______________________________________________ > > > > > > NumPy-Discussion mailing list > > > > > > NumPy-Discussion@scipy.org > > > > > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > > > > > > > > > > > > > > > > > > > > -- > > Daniel Sank > > > > > > > > > > > > > > > > > > _______________________________________________ > > > > NumPy-Discussion mailing list > > > > NumPy-Discussion@scipy.org > > > > http://mail.scipy.org/mailman/listinfo/numpy-discussion > > > > > > > > > -- Kang Wang, Ph.D. 1111 Highland Ave., Room 1113 Madison, WI 53705-2275 ----------------------------------------
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