CLATDF computes the contribution to the reciprocal Dif-estimate


 by solving for x in Z * x = b, where b is chosen such that the norm


 of x is as large as possible. It is assumed that LU decomposition


 of Z has been computed by CGETC2. On entry RHS = f holds the


 contribution from earlier solved sub-systems, and on return RHS = x.


 The factorization of Z returned by CGETC2 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.

IJOB

          IJOB is INTEGER


          IJOB = 2: First compute an approximative null-vector e


              of Z using CGECON, 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

          N is INTEGER


          The number of columns of the matrix Z.

Z

          Z is REAL array, dimension (LDZ, N)


          On entry, the LU part of the factorization of the n-by-n


          matrix Z computed by CGETC2:  Z = P * L * U * Q

LDZ

          LDZ is INTEGER


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

RHS

          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 according to the value of IJOB (see above).

RDSUM

          RDSUM is REAL


          On entry, the sum of squares of computed contributions to


          the Dif-estimate under computation by CTGSYL, 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 CTGSY2 is called by CTGSYL.

RDSCAL

          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 CTGSY2 is called by


          CTGSYL.

IPIV

          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

          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).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization.

Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.

[1] Bo Kagstrom and Lars Westin, Generalized Schur Methods with Condition Estimators for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.