/home/abui.../ctrevc3.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💜 CTREVC3 — like, the whole entire manual page 💜

okay so bestie, welcome to /home/abui.../ctrevc3.f(3) from the Library Functions Manual — yes that's the manual name, don't @ me. this is the glow-up of the LAPACK docs for CTREVC3, and honestly? she's iconic. let's get into it ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctrevc3.f

like, that's literally the whole path. she lives right there. periodt.

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine CTREVC3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr,
    mm, m, work, lwork, rwork, lrwork, info)

CTREVC3

👑 Function/Subroutine Documentation 👑

subroutine CTREVC3 (character side, character howmny, logical, dimension( *
) select, integer n, complex, dimension( ldt, * ) t, integer ldt,
complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension(
ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( *
) work, integer lwork, real, dimension( * ) rwork, integer lrwork,
integer info)

CTREVC3

💅 Purpose:

!> !> CTREVC3 computes some or all of the right and/or left eigenvectors of !> a complex upper triangular matrix T. !> Matrices of this type are produced by the Schur factorization of !> a complex general matrix: A = Q*T*QH, as computed by CHSEQR. !> !> The right eigenvector x and the left eigenvector y of T corresponding !> to an eigenvalue w are defined by: !> !> T*x = w*x, (yH)T = w(yH) !> !> where yH denotes the conjugate transpose of the vector y. !> The eigenvalues are not input to this routine, but are read directly !> from the diagonal of T. !> !> This routine returns the matrices X and/or Y of right and left !> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an !> input matrix. If Q is the unitary factor that reduces a matrix A to !> Schur form T, then Q*X and Q*Y are the matrices of right and left !> eigenvectors of A. !> !> This uses a Level 3 BLAS version of the back transformation. !>

so basically: T is that girl (upper triangular, complex), and CTREVC3 is out here finding her eigenvectors. bestie the eigenvalues aren't even passed in — she just reads them straight off the diagonal of T. main character energy, no cap. and oop, the Level 3 BLAS back transformation? we love an efficient queen.

✨ Parameters ✨

🎀 SIDE

!> SIDE is CHARACTER*1 !> = 'R': compute right eigenvectors only; !> = 'L': compute left eigenvectors only; !> = 'B': compute both right and left eigenvectors. !>
  • 'R' → right eigenvectors only, that's it
  • 'L' → left eigenvectors only, we're being selective
  • 'B' → both, because why not have it all 💅

🎀 HOWMNY

!> HOWMNY is CHARACTER*1 !> = 'A': compute all right and/or left eigenvectors; !> = 'B': compute all right and/or left eigenvectors, !> backtransformed using the matrices supplied in !> VR and/or VL; !> = 'S': compute selected right and/or left eigenvectors, !> as indicated by the logical array SELECT. !>
  • 'A' — all the eigenvectors, no picks
  • 'B' — all of them, but backtransformed using the matrices you supplied in VR and/or VL 🌀
  • 'S' — just the selected ones, SELECT decides who gets in (it's giving VIP list)

🎀 SELECT

!> SELECT is LOGICAL array, dimension (N) !> If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed. !> The eigenvector corresponding to the j-th eigenvalue is !> computed if SELECT(j) = .TRUE.. !> Not referenced if HOWMNY = 'A' or 'B'. !>
  • SELECT is LOGICAL, dimension (N)
  • if HOWMNY = 'S', this array is the whole vibe check — the j-th eigenvalue's eigenvector gets computed only if SELECT(j) = .TRUE. ✅
  • lowkey not referenced at all if HOWMNY = 'A' or 'B' — she's off duty 🙈

🎀 N

!> N is INTEGER !> The order of the matrix T. N >= 0. !>

INTEGER, the order of T. N >= 0. fr fr.

🎀 T

!> T is COMPLEX array, dimension (LDT,N) !> The upper triangular matrix T. T is modified, but restored !> on exit. !>
  • COMPLEX, dimension (LDT,N)
  • the upper triangular matrix T herself
  • 💀 heads up bestie: T is modified, but it gets restored on exit. she goes through a phase and comes back exactly the same, we respect it.

🎀 LDT

!> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,N). !>

INTEGER. leading dimension of T. LDT >= max(1,N). remember it.

🎀 VL

!> VL is COMPLEX array, dimension (LDVL,MM) !> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must !> contain an N-by-N matrix Q (usually the unitary matrix Q of !> Schur vectors returned by CHSEQR). !> On exit, if SIDE = 'L' or 'B', VL contains: !> if HOWMNY = 'A', the matrix Y of left eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*Y; !> if HOWMNY = 'S', the left eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VL, in the same order as their !> eigenvalues. !> Not referenced if SIDE = 'R'. !>
  • COMPLEX, dimension (LDVL,MM)
  • on entry: if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR)
  • on exit, if SIDE = 'L' or 'B', VL contains:
    • if HOWMNY = 'A' → the matrix Y of left eigenvectors of T
    • if HOWMNY = 'B' → the matrix Q*Y
    • if HOWMNY = 'S' → the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues
  • not referenced if SIDE = 'R' 🚫

🎀 LDVL

!> LDVL is INTEGER !> The leading dimension of the array VL. !> LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. !>

INTEGER, leading dimension of VL. LDVL >= 1, and if SIDE = 'L' or 'B', then LDVL >= N.

🎀 VR

!> VR is COMPLEX array, dimension (LDVR,MM) !> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must !> contain an N-by-N matrix Q (usually the unitary matrix Q of !> Schur vectors returned by CHSEQR). !> On exit, if SIDE = 'R' or 'B', VR contains: !> if HOWMNY = 'A', the matrix X of right eigenvectors of T; !> if HOWMNY = 'B', the matrix Q*X; !> if HOWMNY = 'S', the right eigenvectors of T specified by !> SELECT, stored consecutively in the columns !> of VR, in the same order as their !> eigenvalues. !> Not referenced if SIDE = 'L'. !>
  • COMPLEX, dimension (LDVR,MM)
  • on entry: if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the unitary matrix Q of Schur vectors returned by CHSEQR)
  • on exit, if SIDE = 'R' or 'B', VR contains:
    • if HOWMNY = 'A' → the matrix X of right eigenvectors of T
    • if HOWMNY = 'B' → the matrix Q*X
    • if HOWMNY = 'S' → the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues
  • not referenced if SIDE = 'L' 🚫

(literally twins with VL, just right-side flavored 💖)

🎀 LDVR

!> LDVR is INTEGER !> The leading dimension of the array VR. !> LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. !>

INTEGER, leading dimension of VR. LDVR >= 1, and if SIDE = 'R' or 'B', then LDVR >= N.

🎀 MM

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

INTEGER. the number of columns in VL and/or VR. MM >= M. the ceiling of the situation, basically.

🎀 M

!> M is INTEGER !> The number of columns in the arrays VL and/or VR actually !> used to store the eigenvectors. !> If HOWMNY = 'A' or 'B', M is set to N. !> Each selected eigenvector occupies one column. !>
  • INTEGER
  • the number of columns in VL and/or VR actually used to store the eigenvectors (the real ones who showed up)
  • if HOWMNY = 'A' or 'B', M is set to N
  • each selected eigenvector occupies exactly one column. one icon per row, iykyk.

🎀 WORK

!> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !>

COMPLEX array, dimension (MAX(1,LWORK)). the workspace. she works hard so you don't have to 🫶

🎀 LWORK

!> LWORK is INTEGER !> The dimension of array WORK. LWORK >= max(1,2*N). !> For optimum performance, LWORK >= N + 2*N*NB, where NB is !> the optimal blocksize. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !>
  • INTEGER, the dimension of WORK
  • minimum: LWORK >= max(1,2*N)
  • for optimum performance tho? LWORK >= N + 2*N*NB, where NB is the optimal blocksize 🔥
  • if LWORK = -1, it's a workspace query — the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and XERBLA issues no error message related to LWORK. so you can ask "how much do you need babe" without getting yelled at 🥺

🎀 RWORK

!> RWORK is REAL array, dimension (LRWORK) !>

REAL array, dimension (LRWORK).

🎀 LRWORK

!> LRWORK is INTEGER !> The dimension of array RWORK. LRWORK >= max(1,N). !> !> If LRWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the RWORK array, returns !> this value as the first entry of the RWORK array, and no error !> message related to LRWORK is issued by XERBLA. !>
  • INTEGER, the dimension of RWORK
  • LRWORK >= max(1,N)
  • if LRWORK = -1, same workspace-query deal: the routine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and XERBLA issues no error message related to LRWORK 💅

🎀 INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>
  • INTEGER
  • = 0 → successful exit, we ate and left no crumbs ✅
  • < 0 → if INFO = -i, the i-th argument had an illegal value 💀 (go check argument number i, bestie)

🌈 Author 🌈

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

like, the whole squad. academic royalty 👑

⭐ Further Details: ⭐

!> !> The algorithm used in this program is basically backward (forward) !> substitution, with scaling to make the the code robust against !> possible overflow. !> !> 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|. !>

so the algorithm is basically backward (forward) substitution, with scaling to make the code robust against possible overflow 🛡️ (and yes, the original really does say "the the" — we don't gatekeep typos here, it's camp)

and every eigenvector is normalized so the element of largest magnitude has magnitude 1. and for a complex number (x,y)? magnitude is taken to be |x| + |y|. noted. memorized. tattooed. 🦋

🎀 Definition 🎀

Definition at line 242 of file ctrevc3.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote the original. she still slays.)

okay that's the whole page bestie, hope you took notes 📝💖

LAPACK — Version 3.12.0 · /home/abui.../ctrevc3.f(3)

mwah, ily, go compute some eigenvectors 🫶✨🎀

📦 where this page comes from