LAPACK
3.8.0
LAPACK: Linear Algebra PACKage

real function sla_gbrpvgrw  (  integer  N, 
integer  KL,  
integer  KU,  
integer  NCOLS,  
real, dimension( ldab, * )  AB,  
integer  LDAB,  
real, dimension( ldafb, * )  AFB,  
integer  LDAFB  
) 
SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
Download SLA_GBRPVGRW + dependencies [TGZ] [ZIP] [TXT]
SLA_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.
[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]  NCOLS  NCOLS is INTEGER The number of columns of the matrix A. NCOLS >= 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 jth column of A is stored in the jth column of the array AB as follows: AB(KU+1+ij,j) = A(i,j) for max(1,jKU)<=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. 
Definition at line 119 of file sla_gbrpvgrw.f.