LA_GBRPVGRW - 5.2 English - 68552

LA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

   LA_GBRPVGRW computes the reciprocal pivot growth factor
   norm(A)/norm(U). The "max absolute element" norm is used. If this is
   much less than 1, the stability of the LU factorization of the
   (equilibrated) matrix A could be poor. This also means that the
   solution X, estimated condition numbers, and error bounds could be
   unreliable.

Parameters:

• 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.

• NCOLS – [in]

  NCOLS is INTEGER

  The number of columns of the matrix A. NCOLS >= 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.