SRC/zhsein.f(3)

✨ SRC/zhsein.f — Library Functions Manual ✨

💖 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

ZHSEIN is the main character here, obviously. 👑

🦋 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 🎀

Okay so ZHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. Slay. ✨

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 — CHARACTER*1
  • = 'R': compute right eigenvectors only;
  • = 'L': compute left eigenvectors only;
  • = 'B': compute both right and left eigenvectors.
• EIGSRC — 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 — CHARACTER*1
  • = 'N': no initial vectors are supplied;
  • = 'U': user-supplied initial vectors are stored in the arrays VL and/or VR.
• SELECT — 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 — INTEGER. The order of the matrix H. N >= 0.
• H — 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 — INTEGER. The leading dimension of the array H. LDH >= max(1,N).
• W — 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 — 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 — INTEGER. The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
• VR — 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 — INTEGER. The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
• MM — INTEGER. The number of columns in the arrays VL and/or VR. MM >= M.
• M — 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 — COMPLEX*16 array, dimension (N*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• IFAILL — INTEGER array, dimension (MM). If SIDE = 'L' or 'B', IFAIL L? no bestie, it's IFAIL L? okay deep breath: it's 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 — 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 — 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.

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Sign-off bestie: it's LAPACK, Version 3.12.0, SRC/zhsein.f(3) — mwah! 💅💖