!>
!> 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.