--- name: "zhsein.f" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/zhsein.f" --- # zhsein.f(3) ## NAME SRC/zhsein.f ## SYNOPSIS ### Functions/Subroutines subroutine **zhsein** (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)\ **ZHSEIN** ## Function/Subroutine Documentation ### subroutine zhsein (character side, character eigsrc, character initv, logical, dimension( \* ) select, integer n, complex\*16, dimension( ldh, \* ) h, integer ldh, complex\*16, dimension( \* ) w, complex\*16, dimension( ldvl, \* ) vl, integer ldvl, complex\*16, dimension( ldvr, \* ) vr, integer ldvr, integer mm, integer m, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork, integer, dimension( \* ) ifaill, integer, dimension( \* ) ifailr, integer info) **ZHSEIN** **Purpose:** ``` !> !> ZHSEIN uses inverse iteration to find specified right and/or left !> eigenvectors of a complex upper Hessenberg matrix H. !> !> The right eigenvector x and the left eigenvector y of the matrix H !> corresponding to an eigenvalue w are defined by: !> !> H * x = w * x, y**h * H = w * y**h !> !> where y**h denotes the conjugate transpose of the vector y. !> ``` **Parameters** *SIDE* ``` !> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors. !> ``` *EIGSRC* ``` !> EIGSRC is CHARACTER*1 !> Specifies the source of eigenvalues supplied in W: !> = 'Q': the eigenvalues were found using ZHSEQR; thus, if !> H has zero subdiagonal elements, and so is !> block-triangular, then the j-th eigenvalue can be !> assumed to be an eigenvalue of the block containing !> the j-th row/column. This property allows ZHSEIN to !> perform inverse iteration on just one diagonal block. !> = 'N': no assumptions are made on the correspondence !> between eigenvalues and diagonal blocks. In this !> case, ZHSEIN must always perform inverse iteration !> using the whole matrix H. !> ``` *INITV* ``` !> INITV is CHARACTER*1 !> = 'N': no initial vectors are supplied; !> = 'U': user-supplied initial vectors are stored in the arrays !> VL and/or VR. !> ``` *SELECT* ``` !> SELECT is LOGICAL array, dimension (N) !> Specifies the eigenvectors to be computed. To select the !> eigenvector corresponding to the eigenvalue W(j), !> SELECT(j) must be set to .TRUE.. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix H. N >= 0. !> ``` *H* ``` !> H is COMPLEX*16 array, dimension (LDH,N) !> The upper Hessenberg matrix H. !> If a NaN is detected in H, the routine will return with INFO=-6. !> ``` *LDH* ``` !> LDH is INTEGER !> The leading dimension of the array H. LDH >= max(1,N). !> ``` *W* ``` !> W is COMPLEX*16 array, dimension (N) !> On entry, the eigenvalues of H. !> On exit, the real parts of W may have been altered since !> close eigenvalues are perturbed slightly in searching for !> independent eigenvectors. !> ``` *VL* ``` !> VL is COMPLEX*16 array, dimension (LDVL,MM) !> On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must !> contain starting vectors for the inverse iteration for the !> left eigenvectors; the starting vector for each eigenvector !> must be in the same column in which the eigenvector will be !> stored. !> On exit, if SIDE = 'L' or 'B', the left eigenvectors !> specified by SELECT will be stored consecutively in the !> columns of VL, in the same order as their eigenvalues. !> If SIDE = 'R', VL is not referenced. !> ``` *LDVL* ``` !> LDVL is INTEGER !> The leading dimension of the array VL. !> LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. !> ``` *VR* ``` !> VR is COMPLEX*16 array, dimension (LDVR,MM) !> On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must !> contain starting vectors for the inverse iteration for the !> right eigenvectors; the starting vector for each eigenvector !> must be in the same column in which the eigenvector will be !> stored. !> On exit, if SIDE = 'R' or 'B', the right eigenvectors !> specified by SELECT will be stored consecutively in the !> columns of VR, in the same order as their eigenvalues. !> If SIDE = 'L', VR is not referenced. !> ``` *LDVR* ``` !> LDVR is INTEGER !> The leading dimension of the array VR. !> LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. !> ``` *MM* ``` !> MM is INTEGER !> The number of columns in the arrays VL and/or VR. MM >= M. !> ``` *M* ``` !> M is INTEGER !> The number of columns in the arrays VL and/or VR required to !> store the eigenvectors (= the number of .TRUE. elements in !> SELECT). !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (N*N) !> ``` *RWORK* ``` !> RWORK is DOUBLE PRECISION array, dimension (N) !> ``` *IFAILL* ``` !> IFAILL is INTEGER array, dimension (MM) !> If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left !> eigenvector in the i-th column of VL (corresponding to the !> eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the !> eigenvector converged satisfactorily. !> If SIDE = 'R', IFAILL is not referenced. !> ``` *IFAILR* ``` !> IFAILR is INTEGER array, dimension (MM) !> If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right !> eigenvector in the i-th column of VR (corresponding to the !> eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the !> eigenvector converged satisfactorily. !> If SIDE = 'L', IFAILR is not referenced. !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, i is the number of eigenvectors which !> failed to converge; see IFAILL and IFAILR for further !> details. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. **Further Details:** ``` !> !> Each eigenvector is normalized so that the element of largest !> magnitude has magnitude 1; here the magnitude of a complex number !> (x,y) is taken to be |x|+|y|. !> ``` Definition at line **242** of file **zhsein.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.