Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - DLA_GBRCOND Estimate 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

```

#### SYNOPSIS

```       DOUBLE PRECISION FUNCTION  DLA_GBRCOND(  TRANS,  N,  KL,  KU,  AB, LDAB, AFB, LDAFB, IPIV,
CMODE, C, INFO, WORK, IWORK )

IMPLICIT     NONE

CHARACTER    TRANS

INTEGER      N, LDAB, LDAFB, INFO, KL, KU, CMODE

INTEGER      IWORK( * ), IPIV( * )

DOUBLE       PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), C( * )

```

#### PURPOSE

```          DLA_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.

```

#### ARGUMENTS

```        TRANS   (input) 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       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

AB      (input) DOUBLE PRECISION 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.

AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by DGBTRF.  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   (input) INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

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

CMODE   (input) 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       (input) DOUBLE PRECISION array, dimension (N)
The vector C in the formula op(A) * op2(C).

INFO    (output) INTEGER
= 0:  Successful exit.
i > 0:  The ith argument is invalid.

WORK    (input) DOUBLE PRECISION array, dimension (5*N).
Workspace.

IWORK   (input) INTEGER array, dimension (N).
Workspace.

LAPACK routine (version 3.2.2)          April 2011                       DLA_GBRCOND(3lapack)
```