.TH "latdf" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
latdf \- latdf: Dif-estimate with complete pivoting LU, step in tgsen
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclatdf\fP (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)"
.br
.RI "\fBCLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&. "
.ti -1c
.RI "subroutine \fBdlatdf\fP (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)"
.br
.RI "\fBDLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&. "
.ti -1c
.RI "subroutine \fBslatdf\fP (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)"
.br
.RI "\fBSLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&. "
.ti -1c
.RI "subroutine \fBzlatdf\fP (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)"
.br
.RI "\fBZLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBCLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIIJOB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Z\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDA >= max(1, N)\&.
!> 
.fi
.PP
.br
\fIRHS\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIRDSUM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRDSCAL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIJPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4
This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
[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\&.
.RE
.PP
[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\&. 
.PP
Definition at line \fB167\fP of file \fBclatdf\&.f\fP\&.
.SS "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)"

.PP
\fBDLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIIJOB\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Z\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDA >= max(1, N)\&.
!> 
.fi
.PP
.br
\fIRHS\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIRDSUM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRDSCAL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIJPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4
This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. 
.RE
.PP
\fBReferences:\fP
.RS 4

.PP
.nf
!>
!>
!>  [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\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB169\fP of file \fBdlatdf\&.f\fP\&.
.SS "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)"

.PP
\fBSLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIIJOB\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Z\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDA >= max(1, N)\&.
!> 
.fi
.PP
.br
\fIRHS\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIRDSUM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRDSCAL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIJPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4
This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. 
.RE
.PP
\fBReferences:\fP
.RS 4

.PP
.nf
!>
!>
!>  [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\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB169\fP of file \fBslatdf\&.f\fP\&.
.SS "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)"

.PP
\fBZLATDF\fP uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIIJOB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix Z\&.
!> 
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
!>          LDZ is INTEGER
!>          The leading dimension of the array Z\&.  LDA >= max(1, N)\&.
!> 
.fi
.PP
.br
\fIRHS\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIRDSUM\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIRDSCAL\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
.br
\fIJPIV\fP 
.PP
.nf
!>          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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4
This routine is a further developed implementation of algorithm BSOLVE in [1] using complete pivoting in the LU factorization\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
[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\&. 
.br
 [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\&. 
.RE
.PP

.PP
Definition at line \fB167\fP of file \fBzlatdf\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.