latdf(3)

NAME
latdf - latdf: Dif-estimate with complete pivoting LU, step in tgsen

SYNOPSIS

  Functions
subroutine clatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)
CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
subroutine dlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)
DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
subroutine slatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)
SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
subroutine zlatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)
ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Detailed Description

Function Documentation

  subroutine clatdf (integer ijob, integer n, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) rhs, real rdsum, real rdscal, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Purpose:

     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.

Parameters
    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).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

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

References:
    [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.

Definition at line 167 of file clatdf.f.

  subroutine dlatdf (integer ijob, integer n, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) rhs, double precision rdsum, double precision rdscal, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

DLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Purpose:

     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.

Parameters
    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).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

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

References:

      [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.

Definition at line 169 of file dlatdf.f.

  subroutine slatdf (integer ijob, integer n, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) rhs, real rdsum, real rdscal, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

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.

Parameters
    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).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

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

References:

      [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.

Definition at line 169 of file slatdf.f.

  subroutine zlatdf (integer ijob, integer n, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) rhs, double precision rdsum, double precision rdscal, integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)

ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Purpose:

     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.

Parameters
    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).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

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

References:
    [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.

Definition at line 167 of file zlatdf.f.

Author

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