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

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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 is INTEGER
The number of columns of the matrix 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.

[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.

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 is INTEGER
The number of columns of the matrix 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.

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 is INTEGER
The number of columns of the matrix 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

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:

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 is INTEGER
The number of columns of the matrix 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

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.

Author

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