SRC/chsein.f(3)

💖 SRC/chsein.f 💖

okay bestie, welcome to the Library Functions Manual glow-up for SRC/chsein.f — this is the page where CHSEIN lives, and she is lowkey iconic. no cap. 🫶

✨ NAME ✨

SRC/chsein.f — literally the source file for the CHSEIN subroutine. slay.

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🦋 SYNOPSIS 🦋

💅 Functions/Subroutines

subroutine chsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl,
    vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
CHSEIN

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🌸 Function/Subroutine Documentation 🌸

🎀 subroutine chsein 🎀

subroutine chsein (character side, character eigsrc, character initv,
    logical, dimension( * ) select, integer n, complex, dimension( ldh, * )
    h, integer ldh, complex, dimension( * ) w, complex, dimension( ldvl, * )
    vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr,
    integer mm, integer m, complex, dimension( * ) work, real, dimension( *
    ) rwork, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr,
    integer info)
CHSEIN

💖 Purpose 💖

okay so CHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. the way that it does this is genuinely giving main character energy. ✨

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. periodt. 💅

🎀 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 CHSEQR; 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 CHSEIN 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, CHSEIN 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 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 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 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 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 array, dimension (N*N)
• RWORK — REAL array, dimension (N)
• IFAILL — 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 — 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|. that's the whole rule, bestie. no extra lore. 💜

📍 Definition at line 242 of file chsein.f 📍

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. iykyk.

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signed off by LAPACK Version 3.12.0 and the SRC/chsein.f(3) source page — no separate date is listed in that footer, so that's the whole vibe. 💅✨🎀