On entry: indicates whether the eigenvalues of  (stored in wr and wi) were found using f08pec (nag_dhseqr).

 The eigenvalues of  were found using f08pec (nag_dhseqr); thus if  has any zero subdiagonal elements (and so is block triangular), then the th eigenvalue can be assumed to be an eigenvalue of the block containing the th row/column. This property allows the function to perform inverse iteration on just one diagonal block.

 No such assumption is made and the function performs inverse iteration using the whole matrix.

Constraint:   "Nag_HSEQRSource" or "Nag_NotKnown". .

On entry: indicates whether you are supplying initial estimates for the selected eigenvectors.

 No initial estimates are supplied.

 Initial estimates are supplied in vl and/or vr.

Constraint:   "Nag_NoVec" or "Nag_UserVec". .

Note: the dimension, dim, of the array select must be at least .

On entry: specifies which eigenvectors are to be computed. To obtain the real eigenvector corresponding to the real eigenvalue ,  must be set true. To select the complex eigenvector corresponding to the complex eigenvalue  with complex conjugate (),  and/or  must be set true; the eigenvector corresponding to the first eigenvalue in the pair is computed.

On exit: if a complex eigenvector was selected as specified above, then  is set to true and  to false.

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: the  by  upper Hessenberg matrix .

Note: the dimension, dim, of the array wr and wi must be at least .

On entry: the real and imaginary parts, respectively, of the eigenvalues of the matrix . Complex conjugate pairs of values must be stored in consecutive elements of the arrays. If , the arrays must be exactly as returned by f08pec (nag_dhseqr).

On exit: some elements of wr may be modified, as close eigenvalues are perturbed slightly in searching for independent eigenvectors.

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: if  and   "Nag_LeftSide" or "Nag_BothSides", vl must contain starting vectors for inverse iteration for the left eigenvectors. Each starting vector must be stored in the same rows or columns as will be used to store the corresponding eigenvector (see below).

If , vl need not be set.

On exit: if   "Nag_LeftSide" or "Nag_BothSides", vl contains the computed left eigenvectors (as specified by select). The eigenvectors are stored consecutively in the rows or columns of the array (depending on the value of storage order), in the same order as their eigenvalues. Corresponding to each selected real eigenvalue is a real eigenvector, occupying one row or column. Corresponding to each selected complex eigenvalue is a complex eigenvector, occupying two rows or columns: the first row or column holds the real part and the second row or column holds the imaginary part.

If , vl is not referenced.

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: if  and   "Nag_RightSide" or "Nag_BothSides", vr must contain starting vectors for inverse iteration for the right eigenvectors. Each starting vector must be stored in the same rows or columns as will be used to store the corresponding eigenvector (see below).

If , vr need not be set.

On exit: if   "Nag_RightSide" or "Nag_BothSides", vr contains the computed right eigenvectors (as specified by select). The eigenvectors are stored consecutively in the rows or columns of the array (depending on the storage order argument), in the same order as their eigenvalues. Corresponding to each selected real eigenvalue is a real eigenvector, occupying one row or column. Corresponding to each selected complex eigenvalue is a complex eigenvector, occupying two rows or columns: the first row or column holds the real part and the second row or column holds the imaginary part.

If , vr is not referenced.

Note: On exit the variable m will have a value of type integer.

On exit: , the number of rows or columns of vl and/or vr required to store the selected eigenvectors.

Note: the dimension, dim, of the array ifaill must be at least

 when   "Nag_LeftSide" or "Nag_BothSides";

 when .

On exit: if   "Nag_LeftSide" or "Nag_BothSides", then  if the selected left eigenvector converged and  if the eigenvector stored in the th row or column of vl (corresponding to the th eigenvalue as held in  failed to converge. If the th and th rows or columns of vl contain a selected complex eigenvector, then  and  are set to the same value.

If , ifaill is not referenced.

Note: the dimension, dim, of the array ifailr must be at least

 when   "Nag_RightSide" or "Nag_BothSides";

 when .

On exit: if   "Nag_RightSide" or "Nag_BothSides", then  if the selected right eigenvector converged and  if the eigenvector stored in the th row or column of vr (corresponding to the th eigenvalue as held in ) failed to converge. If the th and th rows or columns of vr contain a selected complex eigenvector, then  and  are set to the same value.

If , ifailr is not referenced.

Default value: the dimension of the array h.

On entry: , the order of the matrix .

Constraint: . .

Default value: the second dimension of the arrays vl, vr.

On entry: the number of columns in the arrays vl and/or vr if  or the number of rows in the arrays if . The actual number of rows or columns required, , is obtained by counting 1 for each selected real eigenvector and 2 for each selected complex eigenvector (see select); .

Constraint: . .

The NAG error argument, see the documentation for NagError.