Closed
Description
It looks like 45fe8cb has created a regression in Julia's pinv() calculations on SkylakeX. In particular, creating a Hilbert matrix of size 1000 x 100 and asking for the pseudo-inverse now calculates the wrong thing:
using LinearAlgebra
function hilb(T::Type, m::Integer, n::Integer)
a = Matrix{T}(undef, m, n)
for i=1:n
for j=1:m
a[j,i]=one(T)/(i+j-one(T))
end
end
return a
end
hilb(m::Integer, n::Integer) = hilb(Float64,m,n)
a = hilb(1000, 100)
apinv = pinv(a)
Including the SkylakeX kernel gives the following answer:
100×1000 Array{Float64,2}:
2.57526e6 -2.33247e6 2.21848e6 2.19307e6 -4.13046e6 … -4.71439e5 -6.80621e5 -6.56864e5 -8.6676e5 -3.86363e5
-1.22338e11 -2.20992e11 2.36372e11 -1.14835e11 -9.1049e10 1.13475e10 8.51702e9 3.51379e9 1.54455e10 2.8167e8
2.45922e11 3.06366e11 -3.45368e11 6.99788e10 1.34305e11 -2.0333e10 -1.72032e10 -6.35715e9 -3.15537e10 3.42079e9
-1.98151e10 -5.04668e10 6.22131e9 -4.37235e10 -3.29137e9 2.4302e9 3.26304e9 2.4001e9 5.31362e9 1.42072e8
-3.96966e11 1.59586e10 -1.05208e11 -3.27214e11 3.74498e11 5.9171e10 8.17795e10 7.30775e10 1.11105e11 3.58937e10
-1.15417e11 -1.8089e10 3.02927e10 -7.71434e10 6.99771e10 … 1.55784e10 1.9823e10 1.69518e10 2.74274e10 8.50587e9
-7.91383e11 3.19284e11 -5.46209e11 -6.27492e11 1.00493e12 1.26433e11 1.8369e11 1.69215e11 2.44706e11 8.48811e10
-1.12133e11 -3.60367e10 -1.90203e8 -9.61073e10 7.40389e10 1.55288e10 2.07537e10 1.779e10 2.90644e10 7.91371e9
4.19346e11 -2.37896e11 3.70455e11 3.44512e11 -6.0224e11 -6.9822e10 -1.03364e11 -9.66593e10 -1.36339e11 -4.94829e10
-9.51913e9 -1.29776e11 1.82371e11 1.45922e10 -1.32419e11 -3.82507e9 -1.03485e10 -1.22032e10 -1.15361e10 -6.94914e9
2.81647e12 -3.70604e11 9.33114e11 2.35652e12 -2.88098e12 … -4.29963e11 -5.98574e11 -5.4097e11 -8.06547e11 -2.73127e11
2.23042e11 -1.50478e11 1.87991e11 1.81127e11 -3.31279e11 -3.78415e10 -5.5537e10 -5.24234e10 -7.25081e10 -2.8155e10
8.06723e11 -3.62461e11 6.16052e11 6.57412e11 -1.0719e12 -1.30794e11 -1.91569e11 -1.77425e11 -2.54474e11 -8.93792e10
5.53103e10 -1.38396e10 -1.52335e10 3.90026e10 -4.70444e10 -8.49163e9 -1.06612e10 -9.72492e9 -1.3894e10 -6.12903e9
9.43701e11 -5.29597e11 7.95135e11 7.22863e11 -1.31683e12 -1.54868e11 -2.28251e11 -2.12445e11 -3.0164e11 -1.08025e11
-4.21561e11 1.74302e10 -1.05198e11 -3.6234e11 4.02288e11 … 6.38291e10 8.7825e10 7.88592e10 1.18726e11 3.97235e10
⋮ ⋱ ⋮
6.68906e10 -6.53051e9 3.21447e10 4.33472e10 -6.42927e10 -9.61282e9 -1.3713e10 -1.20454e10 -1.88794e10 -5.21562e9
-4.3416e10 9.89228e9 -1.06994e10 -3.73798e10 4.63849e10 … 6.77796e9 9.31398e9 8.54109e9 1.23867e10 4.64291e9
-3.36704e10 -2.19847e10 3.36634e10 -2.54336e10 4.56403e9 4.11065e9 4.50039e9 3.55012e9 6.46187e9 1.91442e9
1.00752e11 -9.78859e10 1.5892e11 7.5809e10 -1.8612e11 -1.78414e10 -2.82659e10 -2.68784e10 -3.70109e10 -1.31011e10
-6.24935e11 1.72017e11 -3.18826e11 -5.14607e11 7.21608e11 9.79871e10 1.39412e11 1.27482e11 1.86508e11 6.45552e10
-3.56138e11 4.75922e10 -1.07088e11 -2.96353e11 3.60894e11 5.43011e10 7.52645e10 6.80322e10 1.01325e11 3.46671e10
1.41477e11 -1.55157e11 2.42801e11 1.08982e11 -2.78805e11 … -2.57232e10 -4.11459e10 -3.94458e10 -5.35713e10 -1.95093e10
-1.71703e11 6.41864e9 -2.29926e10 -1.45472e11 1.56983e11 2.57486e10 3.4882e10 3.13021e10 4.71032e10 1.62219e10
-1.57418e11 -2.50531e10 1.42196e10 -1.16675e11 1.07792e11 2.18507e10 2.86411e10 2.47383e10 3.9572e10 1.19948e10
-5.09849e11 1.45783e11 -2.73511e11 -3.97073e11 5.85682e11 7.9147e10 1.13045e11 1.02973e11 1.5164e11 5.11554e10
-2.01401e11 9.45476e10 -1.55585e11 -1.48556e11 2.6349e11 3.21347e10 4.71454e10 4.34308e10 6.28048e10 2.14634e10
6.55703e11 -1.91764e11 3.65181e11 5.46763e11 -7.75768e11 … -1.03493e11 -1.481e11 -1.35717e11 -1.97988e11 -6.84949e10
4.39019e11 -7.20111e10 1.66746e11 3.76386e11 -4.6781e11 -6.78667e10 -9.50602e10 -8.63599e10 -1.27719e11 -4.38774e10
-1.35314e11 1.43088e11 -2.17464e11 -8.70376e10 2.51535e11 2.36837e10 3.76675e10 3.57591e10 4.93057e10 1.72898e10
2.95696e10 5.86712e10 -7.47343e10 2.73326e10 3.03537e10 -2.52465e9 -1.2501e9 -4.13464e7 -2.64329e9 3.99575e7
-7.70318e10 -3.93945e10 4.41432e10 -8.97948e10 4.01424e10 1.12653e10 1.37315e10 1.20607e10 1.87392e10 7.00317e9
Excluding the SkylakeX kernel (e.g. reverting to 544b069) gives the result:
100×1000 Array{Float64,2}:
112.527 -6192.3 1.06925e5 -8.28373e5 3.21394e6 -6.01292e6 … -2.99287e5 -3.02032e5 -3.04795e5 -3.07576e5
-6305.8 4.64899e5 -9.07773e6 7.54681e7 -3.07426e8 5.99356e8 3.28027e7 3.31027e7 3.34047e7 3.37085e7
1.1309e5 -9.42656e6 1.9735e8 -1.71896e9 7.25526e9 -1.46068e10 -8.71604e8 -8.79551e8 -8.8755e8 -8.95596e8
-9.32272e5 8.33527e7 -1.82785e9 1.64741e10 -7.1497e10 1.47819e11 9.57181e9 9.65882e9 9.74639e9 9.83447e9
3.98657e6 -3.73868e8 8.48896e9 -7.86389e10 3.49436e11 -7.39605e11 -5.19571e10 -5.24279e10 -5.29016e10 -5.33781e10
-8.8007e6 8.57783e8 -2.00715e10 1.90643e11 -8.66324e11 1.8764e12 … 1.44167e11 1.45468e11 1.46778e11 1.48094e11
7.90418e6 -8.06081e8 1.95704e10 -1.91875e11 8.97794e11 -2.00535e12 -1.75621e11 -1.77197e11 -1.78783e11 -1.80377e11
2.40961e6 -2.157e8 4.61896e9 -3.98835e10 1.62513e11 -3.0448e11 -1.76662e9 -1.79326e9 -1.82037e9 -1.84804e9
-5.54279e6 5.75778e8 -1.41936e10 1.40992e11 -6.67618e11 1.50955e12 1.37796e11 1.39031e11 1.40274e11 1.41523e11
-4.00904e6 3.9166e8 -9.13369e9 8.60798e10 -3.86441e11 8.21383e11 5.04267e10 5.08898e10 5.13561e10 5.18251e10
1.63339e6 -1.8959e8 5.10176e9 -5.45604e10 2.76223e11 -6.69193e11 … -8.18735e10 -8.25983e10 -8.33273e10 -8.40596e10
4.57405e6 -4.75446e8 1.17311e10 -1.16639e11 5.52734e11 -1.25049e12 -1.12594e11 -1.13605e11 -1.14622e11 -1.15644e11
3.29825e6 -3.27272e8 7.73331e9 -7.3721e10 3.34416e11 -7.18287e11 -4.43866e10 -4.47954e10 -4.52068e10 -4.56208e10
-37289.1 2.26601e7 -9.77279e8 1.3636e10 -8.32615e10 2.3651e11 4.70926e10 4.75026e10 4.79148e10 4.83286e10
-2.81123e6 3.03789e8 -7.75788e9 7.96192e10 -3.89208e11 9.11377e11 9.80715e10 9.89445e10 9.98226e10 1.00705e11
-3.65969e6 3.80616e8 -9.39927e9 9.35385e10 -4.43642e11 1.00441e12 … 8.90641e10 8.98655e10 9.06717e10 9.14823e10
⋮ ⋮ ⋱
-5.52909e5 6.12481e7 -1.61047e9 1.70918e10 -8.69055e10 2.14183e11 3.86899e10 3.90212e10 3.93541e10 3.96884e10
-992608.0 1.08145e8 -2.79998e9 2.92745e10 -1.46579e11 3.54876e11 … 5.63476e10 5.68342e10 5.73232e10 5.78142e10
-1.35946e6 1.47079e8 -3.78272e9 3.92898e10 -1.95373e11 4.69163e11 6.97768e10 7.03821e10 7.09905e10 7.16015e10
-1.59876e6 1.72258e8 -4.41282e9 4.56535e10 -2.26067e11 5.40144e11 7.69398e10 7.76094e10 7.82824e10 7.89583e10
-1.68423e6 1.80867e8 -4.61853e9 4.76281e10 -2.35036e11 5.59247e11 7.6759e10 7.74288e10 7.81023e10 7.87786e10
-1.5861e6 1.69768e8 -4.32122e9 4.44178e10 -2.18431e11 5.17537e11 6.82601e10 6.88577e10 6.94585e10 7.0062e10
-1.28093e6 1.36538e8 -3.46127e9 3.54304e10 -1.73446e11 4.08663e11 … 5.09162e10 5.13641e10 5.18145e10 5.2267e10
-7.85551e5 8.29992e7 -2.08563e9 2.1155e10 -1.02525e11 2.38529e11 2.56914e10 2.59206e10 2.61511e10 2.63827e10
-1.22319e5 1.1641e7 -2.59973e8 2.29043e9 -9.22435e9 1.59028e10 -5.87688e9 -5.92236e9 -5.96796e9 -6.01363e9
6.34345e5 -6.95395e7 1.8113e9 -1.90533e10 9.60279e10 -2.3435e11 -4.02598e10 -4.06052e10 -4.09522e10 -4.13007e10
1.37734e6 -1.49026e8 3.83373e9 -3.98355e10 1.98204e11 -4.76404e11 -7.24162e10 -7.30427e10 -7.36725e10 -7.43049e10
1.94231e6 -2.09213e8 5.35875e9 -5.54398e10 2.74569e11 -6.56287e11 … -9.49885e10 -9.58134e10 -9.66426e10 -9.74753e10
2.11244e6 -2.26877e8 5.79482e9 -5.97807e10 2.95167e11 -7.02918e11 -9.83543e10 -9.92107e10 -1.00072e11 -1.00936e11
1.59804e6 -1.71043e8 4.3541e9 -4.47652e10 2.20217e11 -5.22078e11 -6.99398e10 -7.0551e10 -7.11654e10 -7.17825e10
23549.4 -1.60268e6 1.77704e7 5.98452e7 -1.59272e9 7.57578e9 6.25708e9 6.3078e9 6.35871e9 6.40975e9
-3.07648e6 3.31117e8 -8.47524e9 8.76252e10 -4.33698e11 1.03595e12 1.49876e11 1.51177e11 1.52485e11 1.53798e11
Note that the pinv() definition is using SVD internally, so this is turning into an LAPACK.gesdd() call, which is itself giving very different answers, so this should be easy to reproduce locally by passing a Hilbert matrix of the above dimensions in through whichever interface you wish to dgesdd.
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