hsein(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🌸 NAME 🌸

Okay bestie, welcome to hsein(3) from the Library Functions Manual — the page for hsein, and its whole vibe is hsein: Hessenberg inverse iteration for eigvec. No cap, that's the name. 💖

✨ SYNOPSIS ✨

🎀 Functions 🎀

Here's the cast, copied exactly so you can trust it:

       subroutine chsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl,
           vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
           CHSEIN
       subroutine dhsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl,
           ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
           DHSEIN
       subroutine shsein (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl,
           ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)
           SHSEIN
       subroutine zhsein (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl,
           vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)
           ZHSEIN

💫 Detailed Description 💫

This is the detailed docs zone, bestie. The actual function documentation starts right below. Buckle up. 🦋

🦋 Function Documentation 🦋

💅 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

CHSEIN

🎀 Purpose 🎀

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

For an eigenvalue w, the right eigenvector x and left eigenvector y of H are defined by:

H * x = w * x,     y**h * H = w * y**h

where y**h denotes the conjugate transpose of the vector y. Slay. ✨

🧚 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|. 🎀

Definition at line 242 of file chsein.f. ✨

💜 dhsein 💜

   subroutine dhsein (character side, character eigsrc, character initv,
       logical, dimension( * ) select, integer n, double precision, dimension(
       ldh, * ) h, integer ldh, double precision, dimension( * ) wr, double
       precision, dimension( * ) wi, double precision, dimension( ldvl, * ) vl,
       integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr,
       integer mm, integer m, double precision, dimension( * ) work, integer,
       dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)
       DHSEIN

DHSEIN

🎀 Purpose 🎀

Okay so DHSEIN uses inverse iteration to find the specified right and/or left eigenvectors of a real upper Hessenberg matrix H.

For an eigenvalue w, the right eigenvector x and left eigenvector y of H 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 (WR,WI): = 'Q': the eigenvalues were found using DHSEQR; 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 DHSEIN 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, DHSEIN 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 —
  • SELECT — logical array, dimension (N). This is literally the vibe check for which eigenvectors get computed 💅. To select the real eigenvector for a real eigenvalue WR(j), set SELECT(j) to .TRUE.. To select the complex eigenvector for a complex eigenvalue (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), set either SELECT(j) or SELECT(j+1) or both to .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE.. No cap.
  • N — integer, the order of matrix H. N >= 0.
  • H — double precision array, dimension (LDH,N). The upper Hessenberg matrix H. If a NaN is detected in H, the routine will return with INFO=-6. 🚨 bestie, NaN check is real.
  • LDH — integer, the leading dimension of the array H. LDH >= max(1,N).
  • WR — double precision array, dimension (N).
  • WI — double precision array, dimension (N). On entry, the real and imaginary parts of the eigenvalues of H; a complex conjugate pair of eigenvalues must be stored in consecutive elements of WR and WI. On exit, WR may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors. 🌀
  • VL — double precision 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. 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 — double precision 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. 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; each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns.
  • WORK — double precision array, dimension ((N+2)*N).
  • IFAIL L — integer array, dimension (MM). If SIDE = 'L' or 'B', IFAIL L(i) = j > 0 if the left eigenvector in the i-th column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAIL L(i) = 0 if the eigenvector converged satisfactorily. If the i-th and (i+1)th columns of VL hold a complex eigenvector, then IFAIL L(i) and IFAIL L(i+1) are set to the same value. If SIDE = 'R', IFAIL L is not referenced. 😭 convergence drama.
  • 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 the i-th and (i+1)th columns of VR hold a complex eigenvector, then IFAILR(i) and IFAILR(i+1) are set to the same value. 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 IFAIL L 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 260 of file dhsein.f.

✨ SHSEIN ✨

subroutine shsein (character side, character eigsrc, character initv,
    logical, dimension( * ) select, integer n, real, dimension( ldh, * ) h,
    integer ldh, real, dimension( * ) wr, real, dimension( * ) wi, real,
    dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr,
    integer ldvr, integer mm, integer m, real, dimension( * ) work, integer,
    dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)
    SHSEIN

💖 Purpose 💖

SHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a real 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 — 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 (WR,WI): = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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 real eigenvector corresponding to a real eigenvalue WR(j), SELECT(j) must be set to .TRUE.. To select the complex eigenvector corresponding to a complex eigenvalue (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1) or both must be set to .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE.. 💅
  • N — integer, the order of the matrix H. N >= 0.
  • H — real 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).
  • WR — real array, dimension (N).
  • WI — real array, dimension (N). On entry, the real and imaginary parts of the eigenvalues of H; a complex conjugate pair of eigenvalues must be stored in consecutive elements of WR and WI. On exit, WR may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors. 🌀
  • VL —

VL 💅 — left-eigenvector storage, no cap

  • VL is REAL 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. ✨
  • If SIDE = 'R', VL is not referenced. 💀

LDVL — leading-dimension vibe check

  • LDVL is INTEGER
  • The leading dimension of the array VL.
  • LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

VR 🦋 — right-eigenvector storage era

  • VR is REAL 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(s) 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. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. 🌸
  • If SIDE = 'L', VR is not referenced.

LDVR — more leading-dimension realness

  • LDVR is INTEGER
  • The leading dimension of the array VR.
  • LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.

MM — column count, literally

  • MM is INTEGER
  • The number of columns in the arrays VL and/or VR. MM >= M.

M — how many columns we actually need

  • M is INTEGER
  • The number of columns in the arrays VL and/or VR required to store the eigenvectors; each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns.

WORK — the workspace bestie

  • WORK is REAL array, dimension ((N+2)*N)

IFAIL — convergence receipts for the left side

  • IFAIL is INTEGER array, dimension (MM)
  • If SIDE = 'L' or 'B', IFAIL(i) = j > 0 if the left eigenvector in the i-th column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAIL(i) = 0 if the eigenvector converged satisfactorily.
  • If the i-th and (i+1)th columns of VL hold a complex eigenvector, then IFAIL(i) and IFAIL(i+1) are set to the same value.
  • If SIDE = 'R', IFAIL is not referenced.

IFAILR — convergence receipts for the right side

  • 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 the i-th and (i+1)th columns of VR hold a complex eigenvector, then IFAILR(i) and IFAILR(i+1) are set to the same value.
  • If SIDE = 'L', IFAILR is not referenced.

INFO — the final status tea ☕

  • 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 IFAIL 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 260 of file shsein.f.

zhsein — the complex cousin 🦋

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 — pick a side, bestie

  • SIDE is CHARACTER*1
  • = 'R': compute right eigenvectors only.
  • = 'L': compute left eigenvectors only.
  • = 'B': compute both right and left eigenvectors. 💅

EIGSRC — where the eigenvalues came from

  • 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 — do we already have starting vectors?

  • 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 — choose your eigenvectors

  • 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 — matrix order

  • N is INTEGER
  • The order of the matrix H. N >= 0.

H — the complex upper Hessenberg icon

  • 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 — leading dimension of H

  • LDH is INTEGER
  • The leading dimension of the array H. LDH >= max(1,N).

W — eigenvalues, but make it slightly mutable

  • 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 — left eigenvectors for the complex case

  • 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 — leading dimension of VL

  • LDVL is INTEGER
  • The leading dimension of the array VL.
  • LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.

VR — right eigenvectors for the complex case

  • 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 — leading dimension of VR

  • LDVR is INTEGER
  • The leading dimension of the array VR.
  • LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.

MM — columns available

  • MM is INTEGER
  • The number of columns in the arrays VL and/or VR. MM >= M.

M — columns needed

  • 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 — complex workspace

  • WORK is COMPLEX*16 array, dimension (N*N)

RWORK — real workspace

  • RWORK is DOUBLE PRECISION array, dimension (N)

IFAIL — left-side convergence receipts, complex edition

  • IFAIL is INTEGER array, dimension (MM)
  • If SIDE = 'L' or 'B', IFAIL(i) = j > 0 if the left eigenvector in the i-th column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAIL(i) = 0 if the eigenvector converged satisfactorily.
  • If SIDE = 'R', IFAIL is not referenced.

IFAILR

  • IFAILR — INTEGER array, dimension (MM). Okay bestie, here’s the tea ☕: if SIDE = 'R' or 'B', then IFAILR(i) = j > 0 means the right eigenvector in the i-th column of VR (the one corresponding to the eigenvalue w(j)) failed to converge 😭, and IFAILR(i) = 0 means that eigenvector converged satisfactorily ✨. If SIDE = 'L', IFAILR is not referenced — she’s off duty 💅.
  • INFO — INTEGER, the official vibe check 👑:
    • = 0: successful exit, we love a happy ending 💖
    • < 0: if INFO = -i, the i-th argument had an illegal value 🚨
    • > 0: if INFO = i, then 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, no cap 🧚✨.

Definition at line 242 of file zhsein.f.

🎀 Author — auto-generated edition 🎀

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