def softmax(x):
## TODO: Implement the softmax function here
#print("torch.exp(x)=",torch.exp(x))
s = torch.sum(torch.exp(x),dim=1)
print("s.size=",s.size())
print("s.view(-1,1)=",s.view(-1,1).size())
#有問題的return （torch.exp(x)/s).view(-1,1)
return torch.exp(x)/(s.view(-1,1))
"""
def softmax(x):
print("x.shape=",x.shape)
return torch.exp(x)/torch.sum(torch.exp(x), dim=1).view(-1, 1)
"""
# Here, out should be the output of the network in the previous excercise with shape (64,10)
#print("out=",out)
print("out.shape=",out.shape)
probabilities = softmax(out)
print("probabilities=",probabilities)
# Does it have the right shape? Should be (64, 10)
#print(probabilities.shape)
# Does it sum to 1?
#print(probabilities)
print(probabilities.sum(dim=1))
#result
out.shape= torch.Size([64, 10])
s.size= torch.Size([64])
s.view(-1,1)= torch.Size([64, 1])
probabilities= tensor([[ 3.0988e-16, 1.0000e+00, 1.8007e-11, 1.4650e-11, 8.8916e-09,
5.3950e-17, 4.7416e-09, 8.0687e-19, 3.1054e-09, 2.2082e-10],
[ 7.2884e-18, 9.9896e-01, 4.5583e-08, 1.2075e-05, 2.1988e-09,
1.5377e-13, 1.0279e-03, 2.0932e-10, 2.9357e-07, 4.3231e-11],
[ 5.2138e-16, 4.6368e-02, 8.9821e-14, 3.0514e-09, 3.1598e-09,
1.3639e-17, 9.5363e-01, 6.5663e-15, 1.2519e-09, 1.5230e-12],
[ 1.5445e-11, 9.9793e-01, 2.8143e-08, 1.2875e-04, 1.2082e-04,
9.7656e-14, 3.9710e-05, 7.6168e-09, 1.7803e-03, 1.4417e-08],
[ 1.0958e-13, 9.6759e-01, 2.2564e-12, 1.9013e-11, 1.9647e-11,
1.8859e-12, 3.2378e-02, 5.4169e-08, 2.7937e-05, 3.2464e-13],
[ 8.1973e-11, 6.9379e-01, 5.9974e-09, 8.5656e-06, 5.1688e-03,
2.4149e-17, 2.3638e-02, 4.3271e-12, 4.1039e-05, 2.7735e-01],
[ 3.7563e-10, 9.9727e-01, 2.4940e-06, 8.8124e-04, 3.5414e-05,
1.8617e-11, 2.0491e-04, 1.7631e-11, 1.6052e-03, 1.5836e-10],
[ 9.4069e-17, 9.9962e-01, 5.0893e-13, 2.1499e-11, 2.3957e-06,
3.5678e-20, 3.8035e-04, 1.4381e-14, 7.2088e-07, 2.4388e-08],
[ 3.5989e-12, 9.9864e-01, 1.6160e-06, 2.3764e-04, 1.2289e-06,
6.1952e-12, 2.6893e-07, 1.1190e-06, 1.1140e-03, 1.5123e-07],
[ 7.6218e-18, 9.5789e-01, 2.4285e-11, 1.9727e-09, 4.4734e-13,
1.1504e-13, 4.2112e-02, 5.4719e-12, 1.1318e-07, 4.2207e-14],
[ 6.9200e-18, 9.9999e-01, 3.3765e-11, 3.0676e-09, 6.6521e-10,
1.9209e-17, 9.4535e-06, 1.0995e-13, 1.4980e-07, 1.1143e-08],
[ 1.1968e-10, 9.9062e-01, 8.3010e-10, 1.9934e-03, 2.6987e-08,
6.7082e-12, 5.9127e-05, 5.9065e-06, 7.3257e-03, 3.9619e-08],
[ 2.6697e-20, 1.0000e+00, 6.1491e-14, 5.5949e-13, 3.8020e-12,
4.6593e-19, 1.3082e-07, 1.8616e-14, 8.4002e-11, 8.4461e-15],
[ 2.4753e-17, 1.0000e+00, 5.8076e-12, 1.6527e-07, 1.4076e-10,
3.4725e-13, 8.1565e-07, 2.1852e-11, 2.3215e-07, 4.4056e-12],
[ 4.7344e-17, 1.0000e+00, 3.3414e-11, 3.1781e-10, 8.6068e-12,
2.3071e-15, 2.8367e-10, 2.3826e-12, 1.7079e-07, 3.1149e-11],
[ 4.4352e-11, 9.9746e-01, 2.8773e-09, 7.2385e-11, 3.6884e-08,
4.4588e-15, 9.4779e-08, 1.2648e-13, 2.5424e-03, 7.2419e-13],
[ 1.1315e-14, 4.7640e-01, 4.4058e-08, 5.7084e-13, 6.0529e-09,
7.8344e-15, 5.2360e-01, 6.2813e-09, 5.5826e-14, 3.6299e-14],
[ 7.4028e-14, 9.7872e-01, 3.0862e-10, 1.8337e-07, 1.6125e-06,
4.8351e-14, 2.1259e-02, 7.2829e-11, 1.4334e-05, 1.3491e-09],
[ 1.3201e-13, 9.9998e-01, 1.2696e-10, 1.9295e-08, 4.1318e-11,
7.8015e-12, 1.6925e-05, 3.8119e-15, 6.8226e-07, 1.3916e-11],
[ 1.4418e-18, 8.1829e-01, 1.2666e-11, 5.9709e-13, 1.2443e-06,
2.1665e-16, 1.8171e-01, 6.2544e-13, 3.6078e-13, 9.4016e-15],
[ 2.1567e-10, 9.6855e-01, 3.3647e-10, 5.3065e-07, 2.0691e-06,
2.1863e-20, 2.8312e-02, 1.0761e-07, 2.8217e-03, 3.0837e-04],
[ 7.6143e-12, 9.8924e-01, 2.0398e-06, 8.3411e-06, 1.1166e-03,
6.4356e-08, 9.6115e-03, 3.7792e-08, 1.4629e-05, 2.7286e-06],
[ 1.0694e-19, 1.0000e+00, 1.6696e-11, 9.9358e-11, 3.0807e-15,
1.4382e-16, 4.7081e-09, 6.2134e-14, 8.9735e-11, 4.8432e-13],
[ 1.6541e-16, 9.0249e-01, 9.2298e-12, 8.2350e-06, 1.0797e-10,
2.7196e-13, 9.7506e-02, 2.3810e-09, 1.0474e-07, 1.2539e-13],
[ 3.7895e-15, 9.9998e-01, 3.1908e-08, 4.6845e-15, 6.6953e-07,
1.8835e-17, 2.2061e-05, 3.7345e-11, 5.3391e-10, 9.8172e-13],
[ 2.2465e-13, 9.9520e-01, 3.3508e-10, 2.0350e-07, 1.6494e-05,
1.1619e-11, 1.7151e-05, 2.1420e-09, 4.7628e-03, 4.6928e-13],
[ 6.8133e-13, 9.9846e-01, 1.0881e-06, 6.1678e-10, 7.9566e-07,
1.2640e-13, 1.0096e-05, 2.6806e-10, 5.2880e-09, 1.5275e-03],
[ 4.0346e-06, 9.9922e-01, 5.6760e-14, 5.1681e-04, 2.7113e-10,
1.9770e-15, 3.4958e-08, 4.6642e-09, 2.5622e-04, 3.5541e-06],
[ 2.3558e-15, 9.9996e-01, 1.5141e-10, 9.6498e-08, 3.9098e-05,
1.0603e-15, 1.3403e-08, 4.2760e-15, 1.1000e-09, 4.5716e-11],
[ 7.2170e-17, 9.9850e-01, 1.0450e-11, 4.0275e-07, 1.7123e-09,
5.7820e-12, 1.5023e-03, 3.4995e-12, 9.2998e-09, 1.2087e-11],
[ 7.0592e-17, 9.9999e-01, 3.2517e-09, 2.0088e-13, 2.8803e-12,
7.7315e-18, 3.9520e-06, 3.0273e-11, 1.4446e-06, 7.1642e-14],
[ 1.9605e-14, 9.9196e-01, 2.2681e-07, 1.8784e-05, 4.0640e-07,
2.9341e-11, 1.3631e-03, 1.0106e-06, 6.6461e-03, 1.3264e-05],
[ 2.0659e-11, 9.9777e-01, 1.1538e-11, 9.0129e-06, 3.1849e-05,
2.0640e-11, 2.0553e-03, 1.6242e-07, 1.3015e-04, 4.3597e-10],
[ 4.0858e-13, 9.9590e-01, 7.0598e-13, 4.0908e-03, 1.4616e-06,
2.7791e-13, 1.0953e-05, 2.4548e-09, 2.6244e-07, 8.3998e-11],
[ 2.4086e-11, 9.9991e-01, 1.3949e-10, 5.7709e-05, 3.4177e-07,
9.4874e-16, 7.1716e-06, 7.3639e-13, 2.9284e-05, 6.0737e-13],
[ 6.1061e-14, 9.3933e-01, 2.6500e-10, 3.2538e-07, 4.3397e-07,
9.8440e-16, 4.2918e-05, 6.4921e-13, 6.0628e-02, 8.5904e-13],
[ 4.5025e-17, 1.0000e+00, 1.1380e-15, 1.2371e-17, 3.1707e-15,
1.0971e-22, 5.5156e-11, 3.0394e-16, 2.0227e-13, 2.7100e-13],
[ 8.6031e-14, 9.9975e-01, 1.5011e-06, 5.5593e-05, 2.7639e-08,
4.2199e-15, 3.8121e-07, 1.6479e-04, 2.6434e-05, 7.3974e-10],
[ 7.8388e-10, 9.9906e-01, 3.6027e-09, 1.8897e-04, 5.1720e-10,
5.0279e-11, 7.4521e-04, 1.6138e-06, 5.0832e-12, 1.4910e-07],
[ 8.1989e-15, 9.9968e-01, 3.4793e-14, 2.9727e-04, 9.1857e-11,
5.3726e-14, 2.2063e-05, 3.3956e-08, 5.2318e-08, 1.4547e-08],
[ 2.9552e-11, 9.9901e-01, 1.8481e-04, 5.5410e-05, 2.9475e-07,
3.4597e-12, 7.4382e-04, 4.2870e-09, 7.1338e-06, 1.2287e-08],
[ 1.4819e-11, 2.0494e-01, 2.6659e-12, 4.1191e-09, 1.4334e-06,
1.6648e-16, 7.9506e-01, 4.5270e-11, 1.4956e-07, 1.4043e-08],
[ 4.1190e-11, 9.7229e-01, 3.6178e-04, 1.7179e-02, 8.1722e-08,
5.6448e-15, 2.3135e-05, 1.6037e-06, 1.0142e-02, 1.6100e-08],
[ 7.3725e-11, 7.0134e-01, 1.7235e-07, 1.5593e-04, 2.1137e-07,
4.9391e-15, 2.9849e-01, 1.3844e-06, 8.7998e-06, 3.4835e-06],
[ 1.4538e-16, 9.9962e-01, 1.0699e-14, 2.9652e-06, 3.3357e-08,
5.2820e-13, 3.7365e-04, 1.6186e-13, 1.0933e-07, 2.0106e-10],
[ 2.5675e-18, 1.0000e+00, 6.6527e-11, 3.2654e-10, 6.1968e-11,
1.0783e-16, 4.2726e-06, 5.4559e-14, 5.1654e-08, 4.5689e-09],
[ 3.8212e-13, 9.9232e-01, 2.4962e-07, 1.1517e-08, 1.8197e-05,
5.6938e-10, 6.1286e-08, 8.9154e-11, 7.6590e-03, 8.1098e-07],
[ 1.0655e-15, 9.9801e-01, 8.3258e-07, 2.4878e-09, 7.7644e-07,
1.6196e-12, 1.9839e-03, 3.1300e-10, 7.4616e-09, 5.4257e-14],
[ 4.8779e-16, 9.9999e-01, 8.2279e-12, 7.2976e-11, 4.4960e-13,
6.2256e-13, 1.3462e-05, 8.8224e-12, 3.6317e-11, 1.3092e-11],
[ 7.8841e-19, 9.9997e-01, 5.5566e-11, 4.0056e-10, 9.2204e-11,
1.1939e-11, 2.6435e-05, 2.1659e-09, 9.7906e-08, 2.7225e-17],
[ 2.9075e-11, 9.9067e-01, 4.3553e-09, 3.9526e-09, 5.5092e-08,
1.6082e-14, 9.3325e-03, 1.3082e-08, 3.2009e-07, 1.7811e-09],
[ 6.3138e-09, 9.9999e-01, 4.1571e-07, 2.6991e-07, 3.8994e-06,
4.2260e-14, 3.8578e-06, 7.5499e-12, 1.2526e-07, 1.3982e-10],
[ 5.6722e-16, 8.2703e-01, 4.3730e-14, 2.1261e-07, 1.2086e-10,
9.9402e-16, 1.7297e-01, 3.5612e-12, 2.2576e-08, 4.4894e-11],
[ 6.6159e-14, 1.0000e+00, 2.1189e-07, 2.3230e-06, 7.5754e-09,
8.0700e-11, 1.8903e-06, 4.0510e-10, 3.2011e-09, 6.0312e-08],
[ 5.6496e-13, 9.9997e-01, 7.0953e-10, 7.8982e-06, 7.9838e-07,
5.1995e-17, 1.3731e-05, 1.6974e-13, 3.9789e-06, 3.2110e-07],
[ 3.3208e-07, 9.5613e-01, 2.8434e-09, 4.1989e-07, 7.8602e-07,
6.8962e-14, 2.7200e-04, 1.1510e-09, 4.3544e-02, 5.3730e-05],
[ 1.8417e-13, 9.9728e-01, 3.9895e-07, 3.4604e-05, 6.7489e-09,
2.1293e-11, 2.1081e-03, 8.0648e-09, 3.0386e-07, 5.8137e-04],
[ 3.7823e-12, 1.0000e+00, 3.2145e-10, 2.3663e-10, 4.1574e-07,
1.8841e-12, 5.5345e-07, 6.2556e-13, 1.5828e-10, 3.6763e-14],
[ 2.4093e-17, 1.0000e+00, 7.4625e-15, 2.2570e-13, 5.3833e-09,
7.0629e-20, 3.6674e-10, 2.6192e-16, 1.0119e-09, 1.5468e-21],
[ 8.6024e-15, 2.1488e-01, 3.2251e-10, 1.0990e-06, 1.4385e-06,
6.2122e-13, 7.8512e-01, 1.5255e-08, 1.1232e-06, 1.2307e-08],
[ 3.4641e-09, 9.9518e-01, 5.8583e-10, 1.6316e-04, 1.2406e-03,
4.2527e-15, 3.3174e-03, 1.1678e-06, 9.8092e-05, 8.7550e-07],
[ 9.6422e-15, 1.0000e+00, 2.1577e-12, 4.3397e-13, 2.8023e-09,
1.4402e-18, 2.1583e-07, 1.4629e-14, 1.1131e-10, 5.5922e-12],
[ 1.4889e-13, 9.9998e-01, 1.3683e-08, 2.6725e-11, 7.6360e-12,
2.5601e-14, 1.5277e-05, 1.4099e-10, 2.0855e-09, 1.5405e-15],
[ 2.0768e-16, 9.9753e-01, 5.2618e-07, 2.0046e-06, 6.0347e-07,
2.9689e-13, 2.4702e-03, 3.1447e-09, 5.1434e-09, 4.9742e-10]])
tensor([ 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000,
1.0000])
#問題原因爲 s爲1維的，來除torch.exp(x)（64x10）時候，維數不對應,需要將s也要轉換爲2維的即維數爲（64x1）,纔可以廣播按行對應相除