GBRCOND - 5.2 English - 68552

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

Purpose:

 LA_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 – [in]

  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 – [in]

  N is INTEGER

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

• KL – [in]

  KL is INTEGER

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

• KU – [in]

  KU is INTEGER

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

• AB – [in]

  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 fla_max(1,j-KU)<=i<=min(N,j+kl)

• LDAB – [in]

  LDAB is INTEGER

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

• AFB – [in]

  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 – [in]

  LDAFB is INTEGER

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

• IPIV – [in]

  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 – [in]

  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 – [in]

  C is REAL array, dimension (N)

  The vector C in the formula op(A) * op2(C).

• INFO – [out]

  INFO is INTEGER

  = 0: Successful exit.

  i > 0: The ith argument is invalid.

• WORK – [out]

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

  Workspace.

• IWORK – [out]

  IWORK is INTEGER array, dimension (N).

  Workspace.