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## sla_gbrcond()

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.

Download SLA_GBRCOND + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  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)
      !>

  [in]

  N

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

  [in]

  KL

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

  [in]

  KU

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

  [in]

  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)
      !>

  [in]

  LDAB

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

  [in]

  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.
      !>

  [in]

  LDAFB

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

  [in]

  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).
      !>

  [in]

  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)
      !>

  [in]

  C

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

  [out]

  INFO

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

  [out]

  WORK

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

  [out]

  IWORK

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

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.