[Minuit2] Document why covariance transform omits 2nd-derivative term#22720
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[Minuit2] Document why covariance transform omits 2nd-derivative term#22720guitargeek wants to merge 1 commit into
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Int2extCovariance/Ext2intCovariance transform the error matrix between internal and external coordinates using only the first-order Jacobian (dPext/dPint), even on the diagonal. This is intentional and contrasts with the Hessian/G2 transformation in AnalyticalGradientCalculator, which carries an extra diagonal term d^2Pext/dPint^2 * gradient. The Hessian needs that non-tensorial term because it is evaluated at arbitrary, non-stationary points where the external gradient is nonzero. The covariance matrix is the inverse Hessian evaluated at the minimum, where the gradient vanishes; the term is then identically zero and the covariance transforms as a genuine (2,0) tensor with the Jacobian alone. Adding it would also break the exact round-trip between Int2extCovariance and Ext2intCovariance.
Test Results 23 files 23 suites 3d 17h 20m 53s ⏱️ For more details on these failures, see this check. Results for commit 3ae4b52. |
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Int2extCovariance/Ext2intCovariance transform the error matrix between internal and external coordinates using only the first-order Jacobian (dPext/dPint), even on the diagonal. This is intentional and contrasts with the Hessian/G2 transformation in
AnalyticalGradientCalculator, which carries an extra diagonal term d^2Pext/dPint^2 * gradient.
The Hessian needs that non-tensorial term because it is evaluated at arbitrary, non-stationary points where the external gradient is nonzero. The covariance matrix is the inverse Hessian evaluated at the minimum, where the gradient vanishes; the term is then identically zero and the covariance transforms as a genuine (2,0) tensor with the Jacobian alone. Adding it would also break the exact round-trip between Int2extCovariance and Ext2intCovariance.
FYI @lmoneta, this is to preempt questions like you had in #22700 (review)