SLATDF(3)      LAPACK routine of NEC Numeric Library Collection      SLATDF(3)



NAME
       SLATDF

SYNOPSIS
       SUBROUTINE SLATDF (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)



PURPOSE
            SLATDF uses the LU factorization of the n-by-n matrix Z computed by
            SGETC2 and computes a contribution to the reciprocal Dif-estimate
            by solving Z * x = b for x, and choosing the r.h.s. b such that
            the norm of x is as large as possible. On entry RHS = b holds the
            contribution from earlier solved sub-systems, and on return RHS = x.

            The factorization of Z returned by SGETC2 has the form Z = P*L*U*Q,
            where P and Q are permutation matrices. L is lower triangular with
            unit diagonal elements and U is upper triangular.




ARGUMENTS
           IJOB      (input)
                     IJOB is INTEGER
                     IJOB = 2: First compute an approximative null-vector e
                         of Z using SGECON, e is normalized and solve for
                         Zx = +-e - f with the sign giving the greater value
                         of 2-norm(x). About 5 times as expensive as Default.
                     IJOB .ne. 2: Local look ahead strategy where all entries of
                         the r.h.s. b is choosen as either +1 or -1 (Default).

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix Z.

           Z         (input)
                     Z is REAL array, dimension (LDZ, N)
                     On entry, the LU part of the factorization of the n-by-n
                     matrix Z computed by SGETC2:  Z = P * L * U * Q

           LDZ       (input)
                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDA >= max(1, N).

           RHS       (input/output)
                     RHS is REAL array, dimension N.
                     On entry, RHS contains contributions from other subsystems.
                     On exit, RHS contains the solution of the subsystem with
                     entries acoording to the value of IJOB (see above).

           RDSUM     (input/output)
                     RDSUM is REAL
                     On entry, the sum of squares of computed contributions to
                     the Dif-estimate under computation by STGSYL, where the
                     scaling factor RDSCAL (see below) has been factored out.
                     On exit, the corresponding sum of squares updated with the
                     contributions from the current sub-system.
                     If TRANS = 'T' RDSUM is not touched.
                     NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.

           RDSCAL    (input/output)
                     RDSCAL is REAL
                     On entry, scaling factor used to prevent overflow in RDSUM.
                     On exit, RDSCAL is updated w.r.t. the current contributions
                     in RDSUM.
                     If TRANS = 'T', RDSCAL is not touched.
                     NOTE: RDSCAL only makes sense when STGSY2 is called by
                           STGSYL.

           IPIV      (input)
                     IPIV is INTEGER array, dimension (N).
                     The pivot indices; for 1 <= i <= N, row i of the
                     matrix has been interchanged with row IPIV(i).

           JPIV      (input)
                     JPIV is INTEGER array, dimension (N).
                     The pivot indices; for 1 <= j <= N, column j of the
                     matrix has been interchanged with column JPIV(j).



LAPACK routine                  31 October 2017                      SLATDF(3)