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 chosen as either +1 or


              -1.  Default.

N

          N is INTEGER


          The number of columns of the matrix Z.

Z

          Z is COMPLEX 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 COMPLEX 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.

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.

 DLATDF uses the LU factorization of the n-by-n matrix Z computed by


 DGETC2 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 DGETC2 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 DGECON, 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 chosen as either +1 or -1 (Default).

N

          N is INTEGER


          The number of columns of the matrix Z.

Z

          Z is DOUBLE PRECISION array, dimension (LDZ, N)


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


          matrix Z computed by DGETC2:  Z = P * L * U * Q

LDZ

          LDZ is INTEGER


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

RHS

          RHS is DOUBLE PRECISION 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 DOUBLE PRECISION


          On entry, the sum of squares of computed contributions to


          the Dif-estimate under computation by DTGSYL, 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 DTGSY2 is called by STGSYL.

RDSCAL

          RDSCAL is DOUBLE PRECISION


          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 DTGSY2 is called by


                DTGSYL.

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.

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.


  [2] Peter Poromaa,


      On Efficient and Robust Estimators for the Separation


      between two Regular Matrix Pairs with Applications in


      Condition Estimation. Report IMINF-95.05, Departement of


      Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

 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.

IJOB

          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 chosen 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 SGETC2:  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 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

          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

          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.

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.


  [2] Peter Poromaa,


      On Efficient and Robust Estimators for the Separation


      between two Regular Matrix Pairs with Applications in


      Condition Estimation. Report IMINF-95.05, Departement of


      Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

 ZLATDF 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 ZGETC2. On entry RHS = f holds the


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


 The factorization of Z returned by ZGETC2 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 ZGECON, 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 chosen as either +1 or


              -1.  Default.

N

          N is INTEGER


          The number of columns of the matrix Z.

Z

          Z is COMPLEX*16 array, dimension (LDZ, N)


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


          matrix Z computed by ZGETC2:  Z = P * L * U * Q

LDZ

          LDZ is INTEGER


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

RHS

          RHS is COMPLEX*16 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 DOUBLE PRECISION


          On entry, the sum of squares of computed contributions to


          the Dif-estimate under computation by ZTGSYL, 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 ZTGSY2 is called by CTGSYL.

RDSCAL

          RDSCAL is DOUBLE PRECISION


          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 ZTGSY2 is called by


          ZTGSYL.

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.

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.
[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report UMINF-95.05, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.