Verification of qr-pullback with pytorch

pytorch_qr_pullback.py

import torch 

def f1(A):
    q, r = torch.qr(A)
    return q.sum()

def f2(A):
    q, r = torch.qr(A)
    return r.sum()
    
V1 = torch.tensor([[0.0107703 , 0.2082,    0.257278 ,  0.509395],
                   [0.886279,   0.29217,   0.579832,   0.470256],
                   [0.693459,   0.594034,  0.0419015,  0.0499426],
                   [0.225352,   0.481055,  0.0644581,  0.961967]], requires_grad=True)

V2 = torch.tensor([[  0.502334,    0.110096,    1.1055,     -0.602707],
                   [ -0.516984,   -0.251176,   -1.10673,    -1.27967],
                   [ -0.560501,    0.369714,   -3.21136,     0.997317],
                   [ -0.0192918,   0.0721164,  -0.0740145,   0.302423],
                   [ 0.128064,   -1.50343,     0.150976,   -0.036446],
                   [  1.85278,     1.56417 ,    0.769278,    0.141974],
                   [ -0.827763,   -1.39674,    -0.310153,    0.521273]], requires_grad=True)

V3 = torch.tensor([[  0.896748  , -1.09122 ,   0.165837,  -0.541716,   2.41747  ,  -0.987177,   0.447358,   2.06353 ,  -1.58492 ,   0.259671,  -1.15533],
                   [ -0.51353   , -0.580517,  -0.408438,  -0.686494,  -0.307974 ,   1.48217 ,  -0.396211,  -1.41453 ,  -1.975   ,  -1.04861 ,   0.81871],
                   [ -0.764799  , -0.315437,  -1.00978 ,  -0.712932,   1.2453   ,  -0.522772,   0.366773,   0.134475,   0.076418,   0.199609,   0.15131],
                   [ -1.54143   , -1.36145 ,  -0.543805,  -0.327059,  -0.0499502,  -1.5807  ,   0.621673,  -0.750421,   0.799335,  -0.80678 ,   1.24723],
                   [ -0.0801625 , -0.114457,  -1.22672 ,   0.514836,  -1.05478  ,   0.131842,   0.182588,   0.170778,  -0.734161,   0.197804,  -0.981132]], requires_grad=True)
                   
def test_f(fun, V):
    V_input = V.clone().detach().requires_grad_(True)
    result = fun(V_input)
    result.backward()
    print(V_input.grad)


test_f(f1, V1)
test_f(f1, V2)
test_f(f1, V3)

test_f(f2, V1)
test_f(f2, V2)
test_f(f2, V3)