STREVC(3)

💖 STREVC(3) — Library Functions Manual 💖

okay so bestie, this is the STREVC(3) page from the Library Functions Manual, and the file it’s documenting is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strevc.f. Yes, that’s the whole path — it’s giving build-server realness 😭.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strevc.f — that’s the file this page is about, bestie. STREVC is the main character here.

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🧚 SYNOPSIS 🧚

Functions/Subroutines

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

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✨ Function/Subroutine Documentation ✨

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

🎯 Purpose

STREVC computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by SHSEQR.

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 y.

The eigenvalues are not input to this routine, but are read directly from the diagonal blocks 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 orthogonal 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. math slay ✨

🧸 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 by the matrices 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.
  • If w(j) is a real eigenvalue, the corresponding real eigenvector is computed if SELECT(j) is .TRUE..
  • If w(j) and w(j+1) are the real and imaginary parts of a complex eigenvalue, the corresponding complex eigenvector is computed if either SELECT(j) or SELECT(j+1) is .TRUE., and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to .FALSE..
  • Not referenced if HOWMNY = 'A' or 'B'.

N

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

T

• T is REAL array, dimension (LDT,N).
  • The upper quasi-triangular matrix T in Schur canonical form.

LDT

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

VL

• VL is REAL 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 orthogonal matrix Q of Schur vectors returned by SHSEQR).
  • 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.
  • 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.
  • 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 REAL 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 orthogonal matrix Q of Schur vectors returned by SHSEQR).
  • 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.
  • 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.
  • 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.

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 real eigenvector occupies one column and each selected complex eigenvector occupies two columns.

WORK

• WORK is REAL array, dimension (3*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|. normalization ate, no crumbs 💅

Definition at line 220 of file strevc.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Footer sign-off, bestie: LAPACK Version 3.12.0, path /home/abui...RC/strevc.f(3) — no date in that footer line, so I’m not making one up. periodt 🫶