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255. BIORTH: Subroutine for Matrix Biorthogonalization
by F. Prosser, Computer Science Department, and S.
Hagstrom, Department of Chemistry, Indiana University,
Bloomington, Indiana 47405
This routine performs biorthogonalization of a real
matrix 'W' of dimensions 'NROWX' by 'NCOLX'. As
defined here, biorthogonalization involves determining
left or right transformation matrices 'L' and 'R' such
that
L W R = D
where 'L' is a lower triangular matrix of dimension
'NROWX' by 'NROWX' with unit diagonal (and zero upper
triangular part) and 'R' is a corresponding upper
triangular matrix of dimension 'NCOLX' by 'NCOLX' with
unit diagonal (and zero lower triangular diagonal).
Reference should be made to the paper "On the Rapid
Computation of Matrix Elements," Int. J. Quantum
Chemistry, 2, 89-99 (1968) for further details about
the algorithm and its use in the evaluation of quantum
mechanical matrix elements between non-orthogonal
determinental wave functions, in particular the
evaluation of co-factors of singular overlap matrices.
Note that if 'W' is a metric (i.e., symmetric and
positive definite), biorthogonalization reduces to
Choleski decomposition, thus BIORTH includes Schmidt
orthogonalization as a special case.
FORTRAN IV
Lines of Code: 283
Recommended Citation: F. Prosser and S. Hagstrom, QCPE
11, 255 (1974).
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