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Update README.markdown to reflect changes in an earlier commit. #31

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Jan 12, 2014
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Update README.markdown to reflect changes in an earlier commit. #31

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8 changes: 4 additions & 4 deletions README.markdown
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Original file line number Diff line number Diff line change
Expand Up @@ -65,22 +65,22 @@ inspect lazily. Somewhat more intuitive answers can be obtained by converting th

The answer:

Prelude Numeric.AD> headJet $ tensors $ grads (\[x,y] -> exp (x * y)) [1,2]
Prelude Numeric.AD Numeric.AD.Types> headJet $ jet $ grads (\[x,y] -> exp (x * y)) [1,2]
7.38905609893065

The gradient:

Prelude Numeric.AD> headJet $ tailJet $ tensors $ grads (\[x,y] -> exp (x * y)) [1,2]
Prelude Numeric.AD Numeric.AD.Types> headJet $ tailJet $ jet $ grads (\[x,y] -> exp (x * y)) [1,2]
[14.7781121978613,7.38905609893065]

The hessian (n * n matrix of 2nd derivatives)

Prelude Numeric.AD> headJet $ tailJet $ tailJet $ tensors $ grads (\[x,y] -> exp (x * y)) [1,2]
Prelude Numeric.AD Numeric.AD.Types> headJet $ tailJet $ tailJet $ jet $ grads (\[x,y] -> exp (x * y)) [1,2]
[[29.5562243957226,22.16716829679195],[22.16716829679195,7.38905609893065]]

Or even higher order tensors of derivatives.

Prelude Numeric.AD> headJet $ tailJet $ tailJet $ tailJet $ tensors $ grads (\[x,y] -> exp (x * y)) [1,2]
Prelude Numeric.AD Numeric.AD.Types> headJet $ tailJet $ tailJet $ tailJet $ jet $ grads (\[x,y] -> exp (x * y)) [1,2]
[[[59.1124487914452,44.3343365935839],[44.3343365935839,14.7781121978613]],[[44.3343365935839,14.7781121978613],[14.7781121978613,7.38905609893065]]]

Note the redundant values caused by the various symmetries in the tensors. The `ad` library is careful to compute
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