/home/abui.../strevc3.f(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strevc3.f

Okay so this is the Library Functions Manual page for that file, bestie — and the star of the show is STREVC3. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine STREVC3 (side, howmny, select, n, t, ldt, vl, ldvl, vr, ldvr,
    mm, m, work, lwork, info)

STREVC3 — iconic name, no notes. ✨

🦋 Function/Subroutine Documentation 🦋

subroutine STREVC3 (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
    lwork, integer info)

STREVC3 — yes queen. 👑

🎀 Purpose 🎀

Okay so STREVC3 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. Slay. 💅

The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by:

T*x = w*x,     (y**T)*T = w*(y**T)

where y**T denotes the transpose of the vector y. The eigenvalues are not input to this routine — they’re read directly from the diagonal blocks of T. The way that works is lowkey iconic. 👑

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. No cap.

This uses a Level 3 BLAS version of the back transformation. Glow-up confirmed. ✨

🌸 Parameters 🌸

• SIDE — is CHARACTER*1. = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. 💅
• 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 — 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 — is INTEGER. The order of the matrix T. N >= 0. 🫶
• T — is REAL array, dimension (LDT,N). The upper quasi-triangular matrix T in Schur canonical form. 👑
• LDT — is INTEGER. The leading dimension of the array T. LDT >= max(1,N). 🌸
• 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 — is INTEGER. The leading dimension of the array VL. LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. 🦋
• 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 — is INTEGER. The leading dimension of the array VR. LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. 🦋
• MM — is INTEGER. The number of columns in the arrays VL and/or VR. MM >= 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 — is REAL array, dimension (MAX(1,LWORK)). 🫶
• LWORK — is INTEGER. The dimension of array WORK. LWORK >= max(1,3*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. 🔥
• 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.

Academic royalty, honestly. 👑

✨ Further Details ✨

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

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|. Math girlie behavior. 🧮✨

📌 Definition at line 235 of file strevc3.f. 📌

💜 Author — generated note 💜

Generated automatically by Doxygen for LAPACK from the source code.

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💖 And that’s the whole page, bestie! Source/version energy: LAPACK, Version 3.12.0, and the source path /home/abui.../strevc3.f(3). Bye, mwah! 🎀