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derivative calculation: midpoint rule
author Jeff Hammel <k0scist@gmail.com>
date Sun, 17 Dec 2017 13:51:13 -0800
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2 X = [x1 x2 ...xm] = A0
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5 Z1 = w'X + b1
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7 A1 = sigmoid(Z1)
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9 Z2 = W2 A1 + b2
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11 [---]
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12 W1 = [---]
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13 [---]
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15 `W1x1` gives some column vector, where `x1`
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16 is the first training example.
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18 Y = [ y1 y2 ... ym]
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20 For a two-layer network:
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22 dZ2 = A2 - Y
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24 dW = (1/m) dZ2 A1'
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26 db2 = (1./m)*np.sum(dZ2, axis=1, keepdims=True)
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28 dZ1 = W2' dZ2 * g1 ( Z1 )
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29 : W2' dZ2 : an (n1, m) matrix
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30 : * : element-wise product
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32 dW1 = (1/m) dZ1 X'
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34 db1 = (1/m) np.sum(dZ1, axis=1, keepdims=True)