I am not aware of a text that defines a minor to be a matrix. Hence I was bit surprised to read
the leading minor of order i is not positive definite
here:
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> > 0: if INFO = i, the leading minor of order i is not |
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*> positive definite, and the factorization could not be |
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*> completed. |
Actually, grep -n SRC/*.f -e "minor" reveals many more instances ...
AFAIK, a minor is a determinant and not a matrix (see, e.g., Aitken, 1944, p. 39; Horn and Johnson, 2013, p. 17; ...), and it is therefore nonsense to consider whether a minor is positive definite. Should the text be globally amended to
the leading principal minor of order i is not positive
or
the leading principal submatrix of order i is not positive definite
depending on context? It would be the former in the case of DPOTRF, at least according to Sylvester's criterion ...
I am not aware of a text that defines a minor to be a matrix. Hence I was bit surprised to read
here:
lapack/SRC/dpotrf.f
Lines 87 to 92 in cea4a63
Actually,
grep -n SRC/*.f -e "minor"reveals many more instances ...AFAIK, a minor is a determinant and not a matrix (see, e.g., Aitken, 1944, p. 39; Horn and Johnson, 2013, p. 17; ...), and it is therefore nonsense to consider whether a minor is positive definite. Should the text be globally amended to
or
depending on context? It would be the former in the case of
DPOTRF, at least according to Sylvester's criterion ...