Input

• A - S3L array handle describing a real or complex parallel array. On entry, A contains one or more two-dimensional Hermitian matrices, b, each of which is assumed to be dense and square. The axes of b are identified by the arguments axis1 and axis2.

• axis1 - Integer variable denoting the axis of A that contains the rows of each Hermitian matrix, b.

• axis2 - Integer variable denoting the axis of A that contains the columns of each Hermitian matrix, b. axis2 must be greater than axis1.

• job - Integer variable indicating whether or not eigenvectors are to be computed. A value of 0 indicates that only eigenvalues are desired. Otherwise, both eigenvalues and eigenvectors are calculated.

• range - Integer variable indicating the range of eigenvalues to be computed, as follows:

  • 0 - Return all eigenvalues.

  • 1 - Compute all eigenvalues within the specified interval.

  • 2 - Return a range of eigenvalue indices (when eigenvalues are sorted in ascending order).

• limits - Defines the eigenvalue interval when the value of range is 1 or 2. Specifically, when range equals:

  • 0 - limits is not used.

  • 1 - limits must be a scalar real vector of length 2. Its values bracket the interval in which eigenvalues are requested--that is, all eigenvalues in the interval [limits(1), limits(2)] will be found.

  • 2 - limits must be a scalar integer vector of length 2. For eigenvalues sorted in ascending order, eigenvalues corresponding to limits(1) through limits(2) will be found.

• tolerances - Real vector of length 2. Its precision must match that of A. That is, if A is of type S3L_float or S3L_complex, tolerances must be single-precision. If A is of type S3L_double or S3L_double_complex, tolerances must be double-precision.

tolerances(1) gives the absolute error tolerance for the eigenvalues. If tolerances(1) is less than or equal to zero, the value eps * norm(b) will be used in its place, where eps is the machine tolerance and norm(b) is the 1-norm of the tridiagonal matrix obtained by reducing b to tridiagonal form.

tolerances(2) controls the reorthogonalization of eigenvectors. Eigenvectors corresponding to eigenvalues that are within tolerances(2) * norm(b) of each other will be reorthogonalized. If tolerances(1) is less than or equal to zero, the value 1.0e-03 will be used in its place.