Computes the LU factorization of a general band matrix using the unblocked version of the algorithm.
call sgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )
call dgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )
call cgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )
call zgbtf2( m, n, kl, ku, ab, ldab, ipiv, info )
The routine forms the LU factorization of a general real/complex m-by-n band matrix A with kl sub-diagonals and ku super-diagonals. The routine uses partial pivoting with row interchanges and implements the unblocked version of the algorithm, calling Level 2 BLAS. See also ?gbtrf.
INTEGER. The number of rows of the matrix A (m≥ 0).
INTEGER. The number of columns in A (n≥ 0).
INTEGER. The number of sub-diagonals within the band of A (kl≥ 0).
INTEGER. The number of super-diagonals within the band of A (ku≥ 0).
REAL for sgbtf2
DOUBLE PRECISION for dgbtf2
COMPLEX for cgbtf2
DOUBLE COMPLEX for zgbtf2.
Array, DIMENSION (ldab,*).
The array ab contains the matrix A in band storage (see Matrix Arguments).
The second dimension of ab must be at least max(1, n).
INTEGER. The leading dimension of the array ab.
(ldab≥ 2kl + ku +1)
Overwritten by details of the factorization. The diagonal and kl + ku super-diagonals of U are stored in the first 1 + kl + ku rows of ab. The multipliers used during the factorization are stored in the next kl rows.
Array, DIMENSION at least max(1,min(m,n)).
The pivot indices: row i was interchanged with row ipiv(i).
INTEGER. If info =0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info = i, uii is 0. The factorization has been completed, but U is exactly singular. Division by 0 will occur if you use the factor U for solving a system of linear equations.