real function cla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.
Purpose:
CLA_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 is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
KL
KL is INTEGER
The number of subdiagonals within the band of A. KL >= 0.
KU
KU is INTEGER
The number of superdiagonals within the band of A. KU >= 0.
NCOLS
NCOLS is INTEGER
The number of columns of the matrix A. NCOLS >= 0.
AB
AB is COMPLEX 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)
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB
AFB is COMPLEX array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by CGBTRF. 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
LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 119 of file cla_gbrpvgrw.f.
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