la_gels.doc - Purpose = LA_GELS solves overdetermined or underdetermined real linear systems involving an m-by-n matrix A or its transpose using a QR or

# la_gels.doc - Purpose = LA_GELS solves overdetermined or...

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!----------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_GELS solves overdetermined or underdetermined real linear systems ! involving an m-by-n matrix A, or its transpose, using a QR or LQ ! factorization of A. It is assumed that A has full rank. ! The following options are provided: ! 1. If TRANS = 'N' and m >= n: find the least squares solution of ! an overdetermined system, i.e., solve the least squares problem ! minimize || B - A*X ||. ! 2. If TRANS = 'N' and m < n: find the minimum norm solution of ! an underdetermined system A * X = B. ! 3. If TRANS = 'T' and m >= n: find the minimum norm solution of ! an undetermined system A**T * X = B. ! 4. If TRANS = 'T' and m < n: find the least squares solution of ! an overdetermined system, i.e., solve the least squares problem ! minimize || B - A**T * X ||. ! Several right hand side vectors b and solution vectors x can be ! handled in a single call; they are stored as the columns of the ! m-by-nrhs right hand side matrix B and the n-by-nrhs solution ! matrix X. ! ! Arguments ! ========= ! ! SUBROUTINE LA_GELS( A, B, TRANS, INFO ) ! <type>(<wp>), INTENT( INOUT ) :: A( :, : ), <rhs> ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: TRANS !  #### You've reached the end of your free preview.

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