I suddenly get the HEAD version of libgpuarray works
I found that if I increase the size of the matrix, the error will appear.
The first few rows of the matrix are correct, and then there will be errors
for the remaining rows.
I guess there is a synchronization or memory bug.
$ python3 cho.py
row #0: err=0 (max=0)
row #1: err=0 (max=0)
row #2: err=0 (max=0)
row #3: err=1.77636e-15 (max=1.77636e-15)
row #4: err=0 (max=0)
row #5: err=1.77982e-15 (max=1.77636e-15)
row #6: err=1.14439e-16 (max=1.11022e-16)
row #7: err=6.245e-17 (max=5.55112e-17)
row #8: err=1.79104e-15 (max=1.77636e-15)
row #9: err=1.84778e-15 (max=1.77636e-15)
row #10: err=1.83628e-15 (max=1.77636e-15)
row #11: err=7.13054e-16 (max=6.66134e-16)
row #12: err=8.55484e-17 (max=8.32667e-17)
row #13: err=7.19641e-16 (max=4.44089e-16)
row #14: err=2.30555e-16 (max=1.11022e-16)
row #15: err=1.93574e-15 (max=1.77636e-15)
row #16: err=3.61888e-16 (max=2.22045e-16)
row #17: err=1.94548e-15 (max=1.77636e-15)
row #18: err=1.81003e-15 (max=1.77636e-15)
row #19: err=1.85793e-15 (max=1.77636e-15)
row #20: err=1.93489e-15 (max=1.77636e-15)
row #21: err=2.10577e-15 (max=1.77636e-15)
row #22: err=9.14588e-16 (max=4.44089e-16)
row #23: err=7.63657e-16 (max=4.44089e-16)
row #24: err=1.42114e-15 (max=8.88178e-16)
row #25: err=3.80154e-15 (max=3.55271e-15)
row #26: err=3.66222e-15 (max=3.55271e-15)
row #27: err=1.06328e-15 (max=8.88178e-16)
row #28: err=2.31959e-15 (max=1.77636e-15)
row #29: err=3.65102e-15 (max=3.55271e-15)
row #30: err=9.84652e-16 (max=4.44089e-16)
row #31: err=1.98222e-15 (max=1.33227e-15)
row #32: err=1.69428e-15 (max=8.88178e-16)
row #33: err=2.39616e-15 (max=1.77636e-15)
row #34: err=1.29213e-15 (max=8.88178e-16)
row #35: err=1.04169e-15 (max=4.44089e-16)
row #36: err=2.56552e-15 (max=1.77636e-15)
row #37: err=1.92892e-15 (max=8.88178e-16)
row #38: err=2.20448e-15 (max=1.77636e-15)
row #39: err=1.49001e-15 (max=6.66134e-16)
row #40: err=1.17059e-15 (max=5.55112e-16)
row #41: err=1.77533e-15 (max=8.88178e-16)
row #42: err=2.27739e-15 (max=1.77636e-15)
row #43: err=1.47627e-15 (max=6.66134e-16)
row #44: err=2.09264e-15 (max=1.33227e-15)
row #45: err=1.81502e-15 (max=8.88178e-16)
row #46: err=1.84387e-15 (max=8.88178e-16)
row #47: err=1.06552e-15 (max=4.44089e-16)
row #48: err=2.76471e-15 (max=1.77636e-15)
row #49: err=2.18163e-15 (max=1.33227e-15)
row #50: err=3.22704e-15 (max=1.77636e-15)
row #51: err=3.64846e-15 (max=1.77636e-15)
row #52: err=1.66905e-15 (max=6.66134e-16)
row #53: err=1.81576e-15 (max=1.11022e-15)
row #54: err=2.41371e-15 (max=1.77636e-15)
row #55: err=3.9903e-15 (max=3.55271e-15)
row #56: err=3.00212e-15 (max=1.77636e-15)
row #57: err=3.06269e-15 (max=1.77636e-15)
row #58: err=2.50664e-15 (max=1.77636e-15)
row #59: err=3.85325e-15 (max=3.55271e-15)
row #60: err=3.55556e-15 (max=1.77636e-15)
row #61: err=2.1962e-15 (max=8.88178e-16)
row #62: err=3.49413e-15 (max=1.77636e-15)
row #63: err=3.29766e-15 (max=1.77636e-15)
row #64: err=2.4585e-15 (max=1.33227e-15)
row #65: err=2.12112e-15 (max=8.88178e-16)
row #66: err=3.71809e-15 (max=1.77636e-15)
row #67: err=2.7659e-15 (max=8.88178e-16)
row #68: err=3.32757e-15 (max=1.77636e-15)
row #69: err=2.41245e-15 (max=8.60423e-16)
row #70: err=3.99688e-15 (max=1.9984e-15)
row #71: err=2.52257e-15 (max=8.88178e-16)
row #72: err=3.55973e-15 (max=1.55431e-15)
row #73: err=2.7763e-15 (max=8.88178e-16)
row #74: err=4.40704e-15 (max=3.55271e-15)
row #75: err=3.55809e-15 (max=1.77636e-15)
row #76: err=3.04663e-15 (max=1.77636e-15)
row #77: err=2.85651e-15 (max=1.11022e-15)
row #78: err=4.05814e-15 (max=1.77636e-15)
row #79: err=3.33612e-15 (max=1.32533e-15)
row #80: err=3.20748e-15 (max=1.77636e-15)
row #81: err=3.8984e-15 (max=1.77636e-15)
row #82: err=3.5669e-15 (max=1.22125e-15)
row #83: err=4.28332e-15 (max=2.22045e-15)
row #84: err=3.64221e-15 (max=1.33227e-15)
row #85: err=4.83762e-15 (max=3.55271e-15)
row #86: err=4.0986e-15 (max=1.77636e-15)
row #87: err=3.60163e-15 (max=1.77636e-15)
row #88: err=5.06272e-15 (max=3.55271e-15)
row #89: err=3.68688e-15 (max=1.77636e-15)
row #90: err=7.07646e-15 (max=5.32907e-15)
row #91: err=3.83584e-15 (max=1.05471e-15)
row #92: err=4.50821e-15 (max=1.77636e-15)
row #93: err=5.47632e-15 (max=1.77636e-15)
row #94: err=4.46046e-15 (max=1.44329e-15)
row #95: err=5.61405e-15 (max=3.55271e-15)
row #96: err=5.06176e-15 (max=2.22045e-15)
row #97: err=3.81964e-15 (max=1.55431e-15)
row #98: err=4.37526e-15 (max=1.77636e-15)
row #99: err=3.98392e-15 (max=1.55431e-15)
row #100: err=4.91222e-15 (max=1.77636e-15)
row #101: err=3.35853e-15 (max=1.22125e-15)
row #102: err=4.78829e-15 (max=2.22045e-15)
row #103: err=4.60413e-15 (max=1.33227e-15)
row #104: err=4.5791e-15 (max=1.38778e-15)
row #105: err=5.45668e-15 (max=1.9984e-15)
row #106: err=7.5096e-15 (max=3.55271e-15)
row #107: err=4.63925e-15 (max=1.33227e-15)
row #108: err=5.44862e-15 (max=2.44249e-15)
row #109: err=4.83685e-15 (max=2.22045e-15)
row #110: err=4.11954e-15 (max=1.55431e-15)
row #111: err=5.48967e-15 (max=1.9984e-15)
row #112: err=4.78231e-15 (max=1.77636e-15)
row #113: err=6.65255e-15 (max=2.22045e-15)
row #114: err=6.33143e-15 (max=3.55271e-15)
row #115: err=7.17902e-15 (max=3.21965e-15)
row #116: err=6.00826e-15 (max=1.83187e-15)
row #117: err=6.52156e-15 (max=2.22045e-15)
row #118: err=4.56739e-15 (max=1.55431e-15)
row #119: err=5.78508e-15 (max=2.22045e-15)
row #120: err=6.4643e-15 (max=2.08167e-15)
row #121: err=4.31762e-15 (max=1.33227e-15)
row #122: err=7.30575e-15 (max=3.55271e-15)
row #123: err=5.16371e-15 (max=1.55431e-15)
row #124: err=6.8954e-15 (max=2.66454e-15)
row #125: err=6.68844e-15 (max=1.9984e-15)
row #126: err=6.36886e-15 (max=2.10942e-15)
row #127: err=8.18275e-15 (max=3.10862e-15)
row #128: err=7.58721e-15 (max=2.9976e-15)
row #129: err=8.76019e-15 (max=2.44249e-15)
row #130: err=8.60251e-15 (max=4.16334e-15)
row #131: err=7.45057e-15 (max=1.88738e-15)
row #132: err=7.273e-15 (max=1.9984e-15)
row #133: err=8.46628e-15 (max=2.44249e-15)
row #134: err=6.03992e-15 (max=1.9984e-15)
row #135: err=8.54499e-15 (max=3.55271e-15)
row #136: err=7.33755e-15 (max=3.10862e-15)
row #137: err=1.32453e-14 (max=7.10543e-15)
row #138: err=9.21473e-15 (max=2.88658e-15)
row #139: err=1.38584e-14 (max=8.21565e-15)
row #140: err=9.92134e-15 (max=4.77396e-15)
row #141: err=8.12191e-15 (max=3.55271e-15)
row #142: err=8.54742e-15 (max=3.05311e-15)
row #143: err=1.1525e-14 (max=3.9968e-15)
row #144: err=9.56483e-15 (max=3.55271e-15)
row #145: err=7.57599e-15 (max=2.16493e-15)
row #146: err=9.08358e-15 (max=3.77476e-15)
row #147: err=1.261e-14 (max=4.16334e-15)
row #148: err=1.04084e-14 (max=3.88578e-15)
row #149: err=1.52547e-14 (max=6.21725e-15)
row #150: err=1.34445e-14 (max=6.21725e-15)
row #151: err=1.28415e-14 (max=5.32907e-15)
row #152: err=1.37001e-14 (max=4.88498e-15)
row #153: err=104.091 (max=38.2524)
row #154: err=90.9855 (max=28.555)
row #155: err=114.057 (max=35.5966)
row #156: err=90.1876 (max=34.3175)
row #157: err=114.274 (max=41.0308)
row #158: err=68.7615 (max=29.8493)
row #159: err=102.592 (max=45.7777)
row #160: err=88.559 (max=39.3841)
row #161: err=102.897 (max=37.4962)
row #162: err=89.7443 (max=39.1052)
row #163: err=91.8647 (max=40.6695)
row #164: err=92.5436 (max=39.478)
row #165: err=67.0603 (max=22.3479)
row #166: err=97.741 (max=35.374)
row #167: err=88.4444 (max=33.1283)
row #168: err=66.4308 (max=29.6943)
row #169: err=76.6372 (max=40.7606)
row #170: err=68.7239 (max=28.0245)
row #171: err=91.2993 (max=48.1353)
row #172: err=94.0889 (max=48.0026)
row #173: err=76.6705 (max=33.9253)
row #174: err=78.756 (max=39.5833)
row #175: err=51.6685 (max=29.4995)
row #176: err=74.8719 (max=28.4035)
row #177: err=82.6127 (max=35.2276)
row #178: err=43.8165 (max=20.9576)
row #179: err=67.3553 (max=27.4942)
row #180: err=74.5054 (max=39.5853)
row #181: err=52.8585 (max=29.805)
row #182: err=54.6962 (max=22.4845)
row #183: err=49.1812 (max=26.9341)
row #184: err=79.5791 (max=37.3105)
row #185: err=36.5226 (max=22.6301)
row #186: err=54.368 (max=37.7491)
row #187: err=31.9472 (max=16.7787)
row #188: err=59.4599 (max=33.4338)
row #189: err=67.0638 (max=49.7558)
row #190: err=54.539 (max=42.0158)
row #191: err=29.0013 (max=17.6628)
row #192: err=55.0378 (max=27.5013)
row #193: err=36.5066 (max=33.2416)
row #194: err=22.4157 (max=13.6764)
row #195: err=36.426 (max=29.0035)
row #196: err=24.4191 (max=22.5652)
row #197: err=27.3912 (max=25.9949)
row #198: err=0.915223 (max=0.915223)
row #199: err=3.60679e-13 (max=2.98261e-13)
494.5201252308407 49.755829752019224
494.5201252308407 49.755829752019224
I attached my test code in this message.
Wong Hang <wongh...@gmail.com> 於 2020年2月7日 週五 下午10:49寫道：
> Hi all,
>
> I found that the cholesky factorization unit test no longer works.
> The value returned are completely wrong. It looks like a memory error.
> I checked if I skip tril call, the value returned by cuSOLVER is correct.
> There should be something wrong in libgpuarray
>
> ======================================================================
> ERROR: test_dense_chol_lower
> (theano.gpuarray.tests.test_linalg.TestGpuCholesky64)
> ----------------------------------------------------------------------
> Traceback (most recent call last):
> File
> "/home/wonghang/github/Theano/theano/gpuarray/tests/test_linalg.py", line
> 327, in test_dense_chol_lower
> self.compare_gpu_cholesky_to_np(A_val, lower=lower, inplace=inplace)
> File
> "/home/wonghang/github/Theano/theano/gpuarray/tests/test_linalg.py", line
> 280, in compare_gpu_cholesky_to_np
> utt.assert_allclose(chol_A_res, chol_A_val)
> File "/home/wonghang/github/Theano/theano/tests/unittest_tools.py", line
> 358, in assert_allclose
> raise WrongValue(expected, value, rtol, atol)
> theano.tests.unittest_tools.WrongValue: WrongValue
> : shape, dtype, strides, min, max, n_inf, n_nan:
> Expected : (3, 3) float64 (24, 8) 1.078578362e-314 1.0548793676823098 0
> 0
> Value : (3, 3) float64 (24, 8) 0.0 1.5121774155893968 0 0
> expected : [[2.00683310e-314 3.46328020e-001 1.07857836e-314]
> [2.29026158e-001 1.05487937e+000 4.86725043e-001]
> [2.07913268e-001 4.16263205e-001 1.04157477e+000]]
> value : [[1.51217742 0. 0. ]
> [0.22902616 1.05487937 0. ]
> [0.20791327 0.41626321 1.04157477]]
> Max Abs Diff: 1.5121774155893968
> Mean Abs Diff: 0.2605811643516005
> Median Abs Diff: 1.078578362e-314
> Std Abs Diff: 0.4752077922970366
> Max Rel Diff: inf
> Mean Rel Diff: inf
> Median Rel Diff: 1.3335589252099037e-16
> Std Rel Diff: nan
>
> rtol, atol: 1e-05 1e-08
>
>
> ======================================================================
> ERROR: test_diag_chol (theano.gpuarray.tests.test_linalg.TestGpuCholesky64)
> ----------------------------------------------------------------------
> Traceback (most recent call last):
> File
> "/home/wonghang/github/Theano/theano/gpuarray/tests/test_linalg.py", line
> 317, in test_diag_chol
> self.compare_gpu_cholesky_to_np(A_val, lower=lower, inplace=inplace)
> File
> "/home/wonghang/github/Theano/theano/gpuarray/tests/test_linalg.py", line
> 280, in compare_gpu_cholesky_to_np
> utt.assert_allclose(chol_A_res, chol_A_val)
> File "/home/wonghang/github/Theano/theano/tests/unittest_tools.py", line
> 358, in assert_allclose
> raise WrongValue(expected, value, rtol, atol)
> theano.tests.unittest_tools.WrongValue: WrongValue
> : shape, dtype, strides, min, max, n_inf, n_nan:
> Expected : (5, 5) float64 (40, 8) 0.0 1.3969459393428005 0 0
> Value : (5, 5) float64 (40, 8) 0.0 1.3969459393428005 0 0
> expected : [[1.26525335e-314 0.00000000e+000 0.00000000e+000
> 0.00000000e+000
> 0.00000000e+000]
> [0.00000000e+000 2.01543086e-314 0.00000000e+000 0.00000000e+000
> 0.00000000e+000]
> [0.00000000e+000 0.00000000e+000 1.29480282e+000 0.00000000e+000
> 0.00000000e+000]
> [0.00000000e+000 0.00000000e+000 0.00000000e+000 1.31448015e+000
> 0.00000000e+000]
> [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000
> 1.39694594e+000]]
> value : [[1.3040081 0. 0. 0. 0. ]
> [0. 1.35800834 0. 0. 0. ]
> [0. 0. 1.29480282 0. 0. ]
> [0. 0. 0. 1.31448015 0. ]
> [0. 0. 0. 0. 1.39694594]]
> Max Abs Diff: 1.3580083368118308
> Mean Abs Diff: 0.106480657426342
> Median Abs Diff: 0.0
> Std Abs Diff: 0.361174224138967
> Max Rel Diff: nan
> Mean Rel Diff: nan
> Median Rel Diff: nan
> Std Rel Diff: nan
>
> rtol, atol: 1e-05 1e-08
>
>
> ----------------------------------------------------------------------
> Ran 40 tests in 12.218s
>
> FAILED (errors=2, skipped=16)
>
> Please use the revision 07cd4ad56054c279442ee28413b26939f4c03632 of
> libgpuarray
>
> Use the following command to install an old version of libgpuarray:
>
> $ git clone https://github.com/Theano/libgpuarray.git
> $ cd libgpuarray
> $ git checkout 07cd4ad56054c279442ee28413b26939f4c03632 .
> $ mkdir cmake
> $ cd cmake
> $ cmake ..
> $ make
> $ sudo make install
> $ sudo ldconfig
> $ cd ..
> $ python3 setup.py install
>
> and then run your theano code again. I think it would work now.
> I will check the code in libgpuarray later. Let me raise an issue first.
>
> Best,
> wonghang
>
> Paul Baggenstoss <p.m.baggenst...@ieee.org> 於 2020年2月7日 週五 下午9:49寫道：
>
>> Hi wonghang, Sorry to pester you with emails, but I have some
>> interesting timing information.
>> I ran a process using different processors and ways of computing
>> Cholesky()
>> The results are surprising.
>>
>> GpuMagmaCholesky() 9.0 sec
>> slinalg.Cholesky(uses cusolver) 2.9 sec
>> CPU 1.9 sec
>>
>> It looks like it pays to just use the CPU!
>>
>> Doesn't make any sense!
>> Paul
>>
>>
>> On Thursday, February 6, 2020 at 2:53:55 PM UTC+1, Paul Baggenstoss wrote:
>>>
>>>
>>> Hello again.
>>> So I added 64-bit support to
>>> theano/gpuarray/c_code/magma_cholesky.c and to theano/gpuarray/linalg.py in
>>> the function GpuMagmaCholesky(). I attached the files.
>>> It works now for 32 and 64 bit and has gradient. The numerical problem
>>> is gone.
>>> But (and this is a big BUT) it iseems to be a factor of at least 2
>>> times slower than the CPU. Any thoughts on this?
>>> Paul
>>>
>>>
>>> On Thursday, February 6, 2020 at 10:28:08 AM UTC+1, Paul Baggenstoss
>>> wrote:
>>>>
>>>> Simon,
>>>> I did more digging and have some more information. I tested
>>>> theano.gpuarray.linalg.GpuMagmaCholesky(), on float32 and it looks good.
>>>> The result is exactly the same as for CPU.
>>>> So the problem seems to be in CUsolver. The problem is that
>>>> theano.gpuarray.linalg.GpuMagmaCholesky()(Cll) does not define a gradient
>>>> and works only for
>>>> float32. I installed the latest magma-2.5.2 and it has support for
>>>> double precision Cholesky (dpotrf) but Theano seems to use it's own copy of
>>>> the MAGMA source.
>>>> Not sure how that works. Can I force Theano to use magma-2.5.2 ? If
>>>> not, it seems feasible to borrow the gradient from
>>>> theano.gpuarray.linalg.GpuCholesky()
>>>> and add support for float64 as well. Thoughts?
>>>> Paul
>>>>
>>>>
>>>> On Wednesday, February 5, 2020 at 5:32:43 PM UTC+1, Paul Baggenstoss
>>>> wrote:
>>>>>
>>>>> Hi Simon, I forgot to mention that I use the gradient of Cholesky, and
>>>>> this has even more error than the Cholesky decomo, but I assume that this
>>>>> is because
>>>>> of a bug in Cholesky itself.
>>>>> Paul
>>>>>
>>>>>
>>>>> On Wednesday, February 5, 2020 at 5:30:10 PM UTC+1, Paul Baggenstoss
>>>>> wrote:
>>>>>>
>>>>>> Hi Simon,I have uploaded the MATLAB format file with the matrix Cll,
>>>>>> which is the original matrix, and R_cpu which was produced using CPU by
>>>>>> slinalg.Cholesky( ), and R_cuda which
>>>>>> was produced by the same function, but with GPU ( I think it uses
>>>>>> theano.gpuarray.linalg.GpuCholesky() ) Both used the same precision
>>>>>> (float32) so should give the same results.
>>>>>> But you can see that at the end of the diagonal, the values go wild.
>>>>>> It appears to be numericla errors.
>>>>>> Thanks in advance!
>>>>>> Paul
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Wednesday, February 5, 2020 at 4:56:14 PM UTC+1, Wong Hang wrote:
>>>>>>>
>>>>>>>
>>>>>>> Hi,
>>>>>>>
>>>>>>> The GPU cholesky decomposition relies on cuSOLVER or Magma. I
>>>>>>> believe nvidia knows their hardware well and cuSOLVER should provide the
>>>>>>> best efficient result.
>>>>>>>
>>>>>>> Although cholesky decomposition is very numerical stable, when I
>>>>>>> write the test case, I find that I will get trouble for relatively small
>>>>>>> matrix if I use single-precision.
>>>>>>>
>>>>>>> Are you using single-precision on a big matrix?
>>>>>>> If not, try to compute the condition number of the matrix to see if
>>>>>>> it is too big.
>>>>>>>
>>>>>>> If it is not too big, then it may be a bug. I also need to use the
>>>>>>> cholesky operator, Please send me the matrix and I am willing to fix it.
>>>>>>>
>>>>>>> Best,
>>>>>>>
>>>>>>> 2020年2月6日(木) 0:34 Paul Baggenstoss <p.m.ba...@ieee.org>:
>>>>>>>
>>>>>>>> HI Simon, I was wondering if you got anywhere with the faster
>>>>>>>> Cholesky for Theano. I also use it a lot and have found it to be
>>>>>>>> unstable
>>>>>>>> on the GPU.
>>>>>>>> Paul
>>>>>>>>
>>>>>>>> On Saturday, March 7, 2015 at 11:45:36 AM UTC+1, Simon Ebner wrote:
>>>>>>>>>
>>>>>>>>> Hi all,
>>>>>>>>>
>>>>>>>>> I want to do computations where I rely heavily on the Cholesky
>>>>>>>>> decomposition. Writing a small benchmark for tensor.slinalg.Cholesky,
>>>>>>>>> I
>>>>>>>>> noticed that the implementation is not as fast as I hoped. As far as
>>>>>>>>> I can
>>>>>>>>> tell it is not optimized for GPUs yet but relies on the scipy
>>>>>>>>> implementation?
>>>>>>>>> Doing a bit of a google seach I found several cuda implementations
>>>>>>>>> for fast Cholesky decompositions on the GPU. Before I try to include
>>>>>>>>> that
>>>>>>>>> code into my theano environment, could you let me know whether you
>>>>>>>>> decided
>>>>>>>>> not to implement fast Cholesky decomposition on the GPU on purpose?
>>>>>>>>> Furthermore, since I'm fairly new to theano I'm not completely
>>>>>>>>> confident
>>>>>>>>> how to incorporate cuda code best into my existing theano code. Is the
>>>>>>>>> sensible to create a custom OP with optimized C-Code?
>>>>>>>>>
>>>>>>>>> Best,
>>>>>>>>> Simon
>>>>>>>>>
>>>>>>>> --
>>>>>>>>
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>>>>>>>> https://groups.google.com/d/msgid/theano-users/aca41c35-ec36-4055-bac7-e53aced30ea7%40googlegroups.com
>>>>>>>> <https://groups.google.com/d/msgid/theano-users/aca41c35-ec36-4055-bac7-e53aced30ea7%40googlegroups.com?utm_medium=email&utm_source=footer>
>>>>>>>> .
>>>>>>>>
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>>
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import numpy as np
from numpy import linalg
from scipy.io import loadmat
import theano
import theano.tensor as T
import theano.tensor.slinalg as Tla
#data = loadmat("test.mat")
#cpu_X32 = data['Cll']
#cpu_X64 = cpu_X32.astype(np.float64)
np.random.seed(11111)
N = 200
L = np.random.normal(size=(N,N))
X = L@L.T
cpu_X32 = X.astype(np.float64)
cpu_X64 = X
gpu_X32 = theano.shared(cpu_X32)
gpu_X64 = theano.shared(cpu_X64)
gpu_compute32 = theano.function(inputs=[],outputs=Tla.cholesky(gpu_X32))
gpu_compute64 = theano.function(inputs=[],outputs=Tla.cholesky(gpu_X64))
cpu_L = linalg.cholesky(cpu_X64)
gpu_X32_L = gpu_compute32()
gpu_X64_L = gpu_compute64()
for k in range(N):
err = gpu_X64_L[k] - cpu_L[k]
print("row #%d: err=%g (max=%g)" % (k,linalg.norm(err),np.max(np.abs(err))))
err = gpu_X32_L - cpu_L
print(linalg.norm(err),np.max(np.abs(err)))
err = gpu_X64_L - cpu_L
print(linalg.norm(err),np.max(np.abs(err)))
