Arguments

AB

(input/output) REAL or COMPLEX rectangular array, shape $(:,:)$ with $size({\bf AB},1) = 2 kl+ku+1$ and $size({\bf AB},2) = n$, where $kl$ and $ku$ are, respectively, the numbers of subdiagonals and superdiagonals in the band of $A$, and $n$ is the order of $A$.
On entry, the matrix $A$ in band storage. The $(kl+ku+1)$ diagonals of $A$ are stored in rows $(kl+1)$ to $(2 kl+ku+1)$ of AB, so that the $j^{th}$ column of $A$ is stored in the $j^{th}$ column of AB as follows:

$$\begin{array}{c\vert c} A_{i,j} & i,j \\ \hline {\bf AB}_{k... ...(n,j+kl) \\ 1 \leq j \leq n \end{array} \\ \hline \end{array}$$

The remaining elements in ${\bf AB}$ need not be set.
On exit, details of the factorization. $U$ is an upper triangular band matrix with $(kl+ku+1)$ diagonals. These are stored in the first $(kl+ku+1)$ rows of ${\bf AB}$. The multipliers that arise during the factorization are stored in the remaining rows.

B

(input/output) REAL or COMPLEX array, shape $(:,:)$ with $size({\bf B},1) = n$ or shape $(:)$ with $size({\bf B}) = n$.
On entry, the matrix $B$.
On exit, the solution matrix $X$.

KL

Optional (input) INTEGER.
The number of subdiagonals in the band of $A$ (${\bf KL} = kl$).
The number of superdiagonals in the band is given by $ku = size({\bf AB},1) - 2\,kl -1$.
Default value: $(size({\bf AB},1)-1)/3$.

IPIV

Optional (output) INTEGER array, shape $(:)$ with $size({\bf IPIV})=n$.
The pivot indices that define the row interchanges; row $i$ of the matrix was interchanged with row ${\bf IPIV}_i\:$.

INFO

Optional (output) INTEGER


If ${\bf INFO}$ is not present and an error occurs, then the program is terminated with an error message.

References: [1] and [17,9,20].