94 lines
2.2 KiB
Python
94 lines
2.2 KiB
Python
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import numpy as np
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import theano
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import theano.tensor as T
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# normal gradient
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x = T.dscalar('x')
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z = T.dscalar('z')
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y = x ** 3 + z ** 2
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gy = T.grad(y, [x, z])
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f = theano.function([x, z], gy)
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# print(theano.pp(f.maker.fgraph.outputs[0]))
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# print(theano.pp(f.maker.fgraph.outputs[1]))
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print(f(4, 8))
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# logistic gradient
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x = T.dmatrix('x')
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l = T.sum(1 / (1 + T.exp(-x)))
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gl = T.grad(l, x)
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f_lg = theano.function([x], gl)
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print(f_lg([[0, 1], [-1, -2]]))
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# np.matrix([[1, 2], [3, 4]])
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# jacobian matrix
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print('jacobian matrix1')
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x = T.dvector('x')
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y = x ** 2
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J, updates = theano.scan(lambda i, y, x : T.grad(y[i], x), sequences=T.arange(y.shape[0]), non_sequences=[y, x])
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f = theano.function([x], J, updates=updates)
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print(f([1, 2, 3, 4, 5]))
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# already implemented jacobian matrix
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# W, V = T.dmatrices('W', 'V')
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J = theano.gradient.jacobian(y, x)
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f2 = theano.function([x], J)
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print(f2([1, 2, 3, 4, 5]))
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# jacobian matrix with matrix :)
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W, V = T.dmatrices('W', 'V')
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x = T.dvector('x')
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y = T.dot(x, W)
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J = theano.gradient.jacobian(y, W)
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f2 = theano.function([W, x], J)
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print(f2(np.array([[1, 1], [1, 1]]), np.array([0, 1])))
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JV2 = T.dot(J, V)
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f2 = theano.function([W, V, x], JV2)
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print(f2(np.array([[1, 1], [1, 1]]), np.array([[2, 2], [2, 2]]), np.array([0, 1])))
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print('jacobian matrix2')
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x = T.dvector('x')
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z = T.dvector('z')
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y = x ** 2 + z ** 2
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J, updates = theano.scan(lambda i, y, x, z: T.grad(y[i], [x, z]), sequences=T.arange(y.shape[0]), non_sequences=[y,x,z])
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f = theano.function([x, z], J, updates=updates)
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test = T.arange(y.shape[0])
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t_f = theano.function([x, z], test)
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print(f([4, 4], [1, 1]))
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print(t_f([4, 4], [1, 1]))
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# hessian matrix
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x = T.dvector('x')
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y = x ** 3
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cost = y.sum()
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gy = T.grad(cost, x)
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H, updates = theano.scan(lambda i, gy, x : T.grad(gy[i], x), sequences=T.arange(gy.shape[0]), non_sequences=[gy, x])
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f = theano.function([x], H, updates=updates)
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print(f([4, 4]))
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# jacobian times vector
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# R-operator
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W = T.dmatrix('W')
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V = T.dmatrix('V')
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x = T.dvector('x')
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y = T.dot(x, W)
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JV = T.Rop(y, W, V)
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f = theano.function([W, V, x], JV)
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print(f([[1, 1], [1, 1]], [[2, 2], [2, 2]], [0,1]))
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# L-operator
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W = T.dmatrix('W')
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v = T.dvector('v')
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x = T.dvector('x')
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y = T.dot(x, W)
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VJ = T.Lop(y, W, v)
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f = theano.function([v,x], VJ)
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print(f([2, 2], [0, 1]))
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