Computes the reciprocal pivot growth factor norm(A)/norm(U) for a general band matrix.
FORTRAN 77:
call sla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )
call dla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )
call cla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )
call zla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )
The ?la_gbrpvgrw routine 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.
n |
INTEGER. The number of linear equations, the order of the matrix A; n ≥ 0. |
kl |
INTEGER. The number of subdiagonals within the band of A; kl ≥ 0. |
ku |
INTEGER. The number of superdiagonals within the band of A; ku ≥ 0. |
ncols |
INTEGER. The number of columns of the matrix A; ncols ≥ 0. |
ab, afb |
REAL for sla_gbrpvgrw DOUBLE PRECISION for dla_gbrpvgrw COMPLEX for cla_gbrpvgrw DOUBLE COMPLEX for zla_gbrpvgrw. Arrays: ab(ldab,*), afb(ldafb,*). ab contains the original band matrix A (see Matrix Storage Schemes) stored in rows from 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) afb contains details of the LU factorization of the band matrix A, as returned by ?gbtrf. 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. |
ldab |
INTEGER. The leading dimension of ab; ldab ≥ kl+ku+1. |
ldafb |
INTEGER. The leading dimension of afb; ldafb ≥ 2*kl+ku+1. |