CTREVC(3)

💖 CTREVC(3) — LAPACK’s complex upper-triangular eigenvector bestie 💖

okay so this is the <pink>CTREVC(3)</pink> manual page, and it is <highkey>literally</highkey> the LAPACK routine for computing some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. We are in our numerical linear algebra era, and it’s giving iconic. 💅

✨ NAME ✨

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

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💅 SYNOPSIS 💅

🎀 Functions/Subroutines 🎀

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

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🦋 Function/Subroutine Documentation 🦋

subroutine CTREVC (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, real,
    dimension( * ) rwork, integer info)

CTREVC

💖 Purpose 💖

Bestie, here’s the whole point: CTREVC 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*Q**H, 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,     (y**H)*T = w*(y**H)

where y**H 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. ate, no cap. 🌈

🌸 Parameters 🌸

🌟 SIDE

SIDE is CHARACTER*1.

• 'R' — compute right eigenvectors only.
• 'L' — compute left eigenvectors only.
• 'B' — compute both right and left eigenvectors.

🦋 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.

🎀 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'. 💖

✨ N

N is INTEGER.

The order of the matrix T. N >= 0.

💜 T

T is COMPLEX array, dimension (LDT,N).

The upper triangular matrix T. T is modified, but restored on exit. yes, it comes back, bestie. 🫶

🍓 LDT

LDT is INTEGER.

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

🧚 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'.

🌈 LDVL

LDVL is INTEGER.

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

🔥 LDVR

LDVR is INTEGER.

The leading dimension of the array VR. LDVR >= 1, and if SIDE = 'R' or 'B'; LDVR >= N. semicolon came through with its original baggage, keeping it real.

👑 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 actually used to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N. Each selected eigenvector occupies one column. one eigenvector, one column, periodt. 💅

🫶 WORK

WORK is COMPLEX array, dimension (2*N).

🌸 RWORK

RWORK is REAL array, dimension (N).

🦋 INFO

INFO is INTEGER.

• = 0: successful exit.
• < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🔥 Further Details 🔥

The algorithm used in this program is basically backward (forward) substitution, with scaling to make 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|. that’s the normalization lore, bestie. ✨

Definition at line 216 of file ctrevc.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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sign-off tea 🫶: this page is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/ctrevc.f(3). That’s the source/version/date-ish goodnight kiss. 💋✨