[lang] Support matrix initialization with a list of vectors

[KLozes]

Related issue = #810

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[yuanming-hu]

Thanks for implementing this! I think this is a very useful feature. Two thoughts:

• Maybe we can use a syntax like ti.Matrix(rows=[a, b, c])/ti.Matrix(cols=[a, b, c]) so that the matrix composition is clearer? I was unsure if the vectors are rows or columns at the first glance. This also prevents ti.Matrix(...) from being too smart.
• Let's briefly document this fancy matrix creation approach in https://github.com/taichi-dev/taichi/blob/master/docs/linalg.rst#matrices so that users know what you have done here :-)

[KLozes]

I think the rows/cols is a good idea. Should we make it mandatory? And should it also be used for list of list style initialization?

[yuanming-hu]

I think the rows/cols is a good idea. Should we make it mandatory? And should it also be used for list of list style initialization?

Yeah I think we can make it mandatory for making matrices from vectors. For list of list, let's keep the old style, since changing that might break some code.

Btw, I had to do a force-push just now to fix a PR merging issue on the master branch - could you update your local master branch, and rebase (or cherrypick) commit 919bfdb based on it, and then (force-)update your vec_to_matrix branch? Sorry about the trouble...
I fixed that. Please simply git fetch and then git reset --hard 95c55bce3410386037c53a27e0837fbf937e8950 on your branch. Sorry about that!

[archibate]

Sorry about the confusing commits! To remove them:

git checkout master
git reset --hard origin/master
git pull --set-upstream origin master
git reset --hard origin/master
git checkout vector_to_matrix
git rebase -i master

Then you'll see:

pick xxx [glsl] xxx # delete this line!
pick xxx [glsl] yyy # delete this line!
pick xxx [lang] zzz
pick xxx [lang] www

Please delete those lines that are not related to this PR, then save and quit (:wq).

[yuanming-hu]

Sorry about the confusing commits!

That was my fault - when merging #785 I accidentally chose Create a merge commit instead of Squash and merge. Then I had to use a force push to fix that, leading to the divergence here.

To prevent this from happening again, I have disabled Create a merge commit and Rebase and merge in this repo...

[KLozes]

oh no. lots and lots of test failing, not just test_ad_atomic

test_ad_atomic.py F                                                                                                 [100%]

======================================================== FAILURES =========================================================
_____________________________________________________ test_ad_reduce ______________________________________________________

>   ???

/home/klozes/Documents/software/taichi/tests/python/test_ad_atomic.py:27: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
../../python/taichi/lang/kernel.py:484: in wrapped
    primal(*args, **kwargs)
../../python/taichi/lang/kernel.py:414: in __call__
    self.materialize(key=key, args=args, arg_features=arg_features)
../../python/taichi/lang/kernel.py:232: in materialize
    src = remove_indent(inspect.getsource(self.func))
/usr/lib/python3.6/inspect.py:973: in getsource
    lines, lnum = getsourcelines(object)
/usr/lib/python3.6/inspect.py:955: in getsourcelines
    lines, lnum = findsource(object)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

object = <function test_ad_reduce.<locals>.func at 0x7f50f83bdb70>

    def findsource(object):
        """Return the entire source file and starting line number for an object.
    
        The argument may be a module, class, method, function, traceback, frame,
        or code object.  The source code is returned as a list of all the lines
        in the file and the line number indexes a line in that list.  An OSError
        is raised if the source code cannot be retrieved."""
    
        file = getsourcefile(object)
        if file:
            # Invalidate cache if needed.
            linecache.checkcache(file)
        else:
            file = getfile(object)
            # Allow filenames in form of "<something>" to pass through.
            # `doctest` monkeypatches `linecache` module to enable
            # inspection, so let `linecache.getlines` to be called.
            if not (file.startswith('<') and file.endswith('>')):
                raise OSError('source code not available')
    
        module = getmodule(object, file)
        if module:
            lines = linecache.getlines(file, module.__dict__)
        else:
            lines = linecache.getlines(file)
        if not lines:
>           raise OSError('could not get source code')
E           OSError: could not get source code

/usr/lib/python3.6/inspect.py:786: OSError

[KLozes]

oh wait I see why its failing. for some reason the path to the test.py is wrong. but not for all tests

[yuanming-hu]

Thank you so much! Now it LGTM except for a few minor nits.

Thanks for improving the documentation of both linalg (which should more or less be renamed matrix now...) and vector! This feature will be very useful.

[KLozes]

bug fixed. all test seem to be running fine. I just had to delete the pycache in the test directory. I change the local repo name last week and I guess the cached files remembered the old name.

[yuanming-hu]

Everything LGTM! Thanks!