# dla_gbrcond.f - Man Page

SRC/dla_gbrcond.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### double precision function dla_gbrcond (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)

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

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.```
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 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

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

AFB

```          AFB is 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

```          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 DGBTRF; 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 167 of file dla_gbrcond.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dla_gbrcond(3) is an alias of dla_gbrcond.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK