Estimates the Skeel condition number for a general banded matrix.
call sla_gbrcond( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork )
call dla_gbrcond( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork )
The function estimates the Skeel condition number of
op(A) * op2(C)
the cmode parameter determines
op2 as follows:
The Skeel condition number
cond(A) = norminf(|inv(A)||A|)
is computed by computing scaling factors R such that
is row equilibrated and by computing the standard infinity-norm condition number.
CHARACTER*1. Must be 'N' or 'T' or 'C'.
Specifies the form of the system of equations:
trans = 'N', the system has the form A*X = B.
trans = 'T', the system has the form AT*X = B.
trans = 'C', the system has the form AH*X = B.
INTEGER. The number of linear equations, that is, the order of the matrix A; n ≥ 0.
INTEGER. The number of subdiagonals within the band of A; kl ≥ 0.
INTEGER. The number of superdiagonals within the band of A; ku ≥ 0.
- ab, afb, c, work
REAL for sla_gbrcond
DOUBLE PRECISION for dla_gbrcond
ab(ldab,*) contains the original band matrix A 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)
max(1,j-ku) ≤ i ≤ min(n,j+kl)
afb(ldafb,*) 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+kusuperdiagonals in rows 1 to
kl+ku+1, and the multipliers used during the factorization are stored in rows
c, DIMENSION n. The vector
Cin the formula
op(A) * op2(C).
work is a workspace array of DIMENSION (5*n).
The second dimension of ab and afb must be at least
INTEGER. The leading dimension of the array ab. ldab ≥
INTEGER. The leading dimension of afb. ldafb ≥
Array with DIMENSION n. The pivot indices from the factorization
A = P*L*Uas computed by ?gbtrf. Row i of the matrix was interchanged with row
op2(C)in the formula
op(A) * op2(C)as follows:
cmode = 1,
cmode = 0,
cmode = -1,
INTEGER. Workspace array with DIMENSION n.