Arguments

AB

(input/output) REAL or COMPLEX array, shape $(:,:)$ with $size$(AB,1) $= kd+1$ and $size$(AB,2) $= n$, where $kd$ is the number of subdiagonals or superdiagonals in the band and $n$ is the order of $A$.
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') triangle of matrix $A$ in band storage. The $kd+1$ diagonals of $A$ are stored in the rows of AB so that the $j^{th}$ column of $A$ is stored in the $j^{th}$ column of ${\bf AB}$ as follows:

$$\begin{array}{c\vert c\vert c} A_{i,j} & i,j & {\bf UPLO} ... ...1 \leq j \leq n \end{array} & \mbox{'L'} \\ \hline \end{array}$$

On exit, ${\bf AB}$ is overwritten by values generated during the reduction of $A$ to a tridiagonal matrix $T$. If ${\bf UPLO} =$ 'U', the first superdiagonal and the diagonal of $T$ are returned in rows $kd$ and $kd+1$ of ${\bf AB}$. If ${\bf UPLO} =$ 'L', the diagonal and first subdiagonal of $T$ are returned in the first two rows of ${\bf AB}$.

W

(output) REAL array, shape $(:)$ with $size$(W) $= n$.
The eigenvalues in ascending order.

UPLO

Optional (input) CHARACTER(LEN=1).


Default value: 'U'.

Z

Optional (output) REAL or COMPLEX square array, shape $(:,:)$ with $size$(Z,1) $= n$.
The columns of Z contain the orthonormal eigenvectors of $A$ in the order of the eigenvalues.

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].