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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sla_gbrcond.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sla_gbrcond.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/sla_gbrcond.f

SYNOPSIS

Functions/Subroutines


real function SLA_GBRCOND (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)
SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Function/Subroutine Documentation

real function SLA_GBRCOND (character trans, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

!>
!>    SLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
!>    where op2 is determined by CMODE as follows
!>    CMODE =  1    op2(C) = C
!>    CMODE =  0    op2(C) = I
!>    CMODE = -1    op2(C) = inv(C)
!>    The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
!>    is computed by computing scaling factors R such that
!>    diag(R)*A*op2(C) is row equilibrated and computing the standard
!>    infinity-norm condition number.
!> 

Parameters

TRANS

!>          TRANS is CHARACTER*1
!>     Specifies the form of the system of equations:
!>       = 'N':  A * X = B     (No transpose)
!>       = 'T':  A**T * X = B  (Transpose)
!>       = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
!> 

N

!>          N is INTEGER
!>     The number of linear equations, i.e., the order of the
!>     matrix A.  N >= 0.
!> 

KL

!>          KL is INTEGER
!>     The number of subdiagonals within the band of A.  KL >= 0.
!> 

KU

!>          KU is INTEGER
!>     The number of superdiagonals within the band of A.  KU >= 0.
!> 

AB

!>          AB is REAL array, dimension (LDAB,N)
!>     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
!>     The j-th column of A is stored in the j-th column of the
!>     array AB as follows:
!>     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
!> 

LDAB

!>          LDAB is INTEGER
!>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
!> 

AFB

!>          AFB is REAL array, dimension (LDAFB,N)
!>     Details of the LU factorization of the band matrix A, as
!>     computed by SGBTRF.  U is stored as an upper triangular
!>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
!>     and the multipliers used during the factorization are stored
!>     in rows KL+KU+2 to 2*KL+KU+1.
!> 

LDAFB

!>          LDAFB is INTEGER
!>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
!> 

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>     The pivot indices from the factorization A = P*L*U
!>     as computed by SGBTRF; row i of the matrix was interchanged
!>     with row IPIV(i).
!> 

CMODE

!>          CMODE is INTEGER
!>     Determines op2(C) in the formula op(A) * op2(C) as follows:
!>     CMODE =  1    op2(C) = C
!>     CMODE =  0    op2(C) = I
!>     CMODE = -1    op2(C) = inv(C)
!> 

C

!>          C is REAL array, dimension (N)
!>     The vector C in the formula op(A) * op2(C).
!> 

INFO

!>          INFO is INTEGER
!>       = 0:  Successful exit.
!>     i > 0:  The ith argument is invalid.
!> 

WORK

!>          WORK is REAL array, dimension (5*N).
!>     Workspace.
!> 

IWORK

!>          IWORK is INTEGER array, dimension (N).
!>     Workspace.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file sla_gbrcond.f.

Author

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Version 3.12.0 LAPACK