CGEGS(3)

💅 CGEGS(3) — the deprecated girlies' guide 🎀

okay so first things first, bestie: this whole page lives at cgegs.f, and the manual name up top is literally just that path — /home/abui...TED/cgegs.f(3) — because Doxygen was feeling lazy. anyway. sit down, hydrate, and let me tell you about a Fortran subroutine that is lowkey iconic and also highkey deprecated 😭

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✨ NAME ✨

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

that's it. that's the name. she's just a file path. main character energy, zero branding 💀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CGEGS (jobvsl, jobvsr, n, a, lda, b, ldb, alpha, beta, vsl,
    ldvsl, vsr, ldvsr, work, lwork, rwork, info)

CGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B) 🦋

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🦋 Function/Subroutine Documentation 🦋

subroutine CGEGS (character jobvsl, character jobvsr, integer n, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( * ) alpha, complex, dimension( * )
    beta, complex, dimension( ldvsl, * ) vsl, integer ldvsl, complex,
    dimension( ldvsr, * ) vsr, integer ldvsr, complex, dimension( * ) work,
    integer lwork, real, dimension( * ) rwork, integer info)

CGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B) ⭐

💖 Purpose 💖

This routine is deprecated and has been replaced by routine CGGES.

like, she's retired but still showing up to the group chat. respect 🫶

CGEGS computes the eigenvalues, Schur form, and, optionally, the left and or/right Schur vectors of a complex matrix pair (A,B). Given two square matrices A and B, the generalized Schur factorization has the form

A = Q*S*Z**H,  B = Q*T*Z**H

where Q and Z are unitary matrices and S and T are upper triangular. The columns of Q are the left Schur vectors and the columns of Z are the right Schur vectors. 👑

If only the eigenvalues of (A,B) are needed, the driver routine CGEGV should be used instead. See CGEGV for a description of the eigenvalues of the generalized nonsymmetric eigenvalue problem (GNEP). iykyk ✨

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🎀 Parameters 🎀

• JOBVSL — is CHARACTER*1. = 'N': do not compute the left Schur vectors; = 'V': compute the left Schur vectors (returned in VSL). pick your fighter 💅
• JOBVSR — is CHARACTER*1. = 'N': do not compute the right Schur vectors; = 'V': compute the right Schur vectors (returned in VSR). same energy, other side 🦋
• N — is INTEGER. The order of the matrices A, B, VSL, and VSR. N >= 0. no negative girlies allowed 🙈
• A — is COMPLEX array, dimension (LDA, N). On entry, the matrix A. On exit, the upper triangular matrix S from the generalized Schur factorization. she goes in as A and comes out as S, a true glow-up 💖
• LDA — is INTEGER. The leading dimension of A. LDA >= max(1,N). don't skimp on her ⭐
• B — is COMPLEX array, dimension (LDB, N). On entry, the matrix B. On exit, the upper triangular matrix T from the generalized Schur factorization. same deal, B becomes T ✨
• LDB — is INTEGER. The leading dimension of B. LDB >= max(1,N). periodt 🌸
• ALPHA — is COMPLEX array, dimension (N). The complex scalars alpha that define the eigenvalues of GNEP. ALPHA(j) = S(j,j), the diagonal element of the Schur form of A. she's literally the diagonal, no cap 🔥
• BETA — is COMPLEX array, dimension (N). The non-negative real scalars beta that define the eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element of the triangular factor T.

Together, the quantities alpha = ALPHA(j) and beta = BETA(j) represent the j-th eigenvalue of the matrix pair (A,B), in one of the forms lambda = alpha/beta or mu = beta/alpha. Since either lambda or mu may overflow, they should not, in general, be computed. ⚠️ like do NOT compute these casually, that's an overflow jump scare

• VSL — is COMPLEX array, dimension (LDVSL,N). If JOBVSL = 'V', the matrix of left Schur vectors Q. Not referenced if JOBVSL = 'N'. she simply isn't invited to that party 🫶
• LDVSL — is INTEGER. The leading dimension of the matrix VSL. LDVSL >= 1, and if JOBVSL = 'V', LDVSL >= N. read the fine print bestie 💅
• VSR — is COMPLEX array, dimension (LDVSR,N). If JOBVSR = 'V', the matrix of right Schur vectors Z. Not referenced if JOBVSR = 'N'. 🌈
• LDVSR — is INTEGER. The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >= N. 🎀
• WORK — is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. she's a workspace, she works 💪
• LWORK — is INTEGER. The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must generally be larger. To compute the optimal value of LWORK, call ILAENV to get blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; the optimal LWORK is N*(NB+1). math girlie behaviour ngl 🧚

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. the -1 hack, a classic 😭

• RWORK — is REAL array, dimension (3*N). and that's the whole description. she's mysterious 💜
• INFO — is INTEGER. the vibe check, and she's got opinions:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. you did a whoopsie 🫠
  • =1,...,N: The QZ iteration failed. (A,B) are not in Schur form, but ALPHA(j) and BETA(j) should be correct for j=INFO+1,...,N. partial slay, the rest is in shambles 😔
  • > N: errors that usually indicate LAPACK problems:
    • =N+1: error return from CGGBAL
    • =N+2: error return from CGEQRF
    • =N+3: error return from CUNMQR
    • =N+4: error return from CUNGQR
    • =N+5: error return from CGGHRD
    • =N+6: error return from CHGEQZ (other than failed iteration)
    • =N+7: error return from CGGBAK (computing VSL)
    • =N+8: error return from CGGBAK (computing VSR)
    • =N+9: error return from CLASCL (various places)

fr fr, if INFO comes back > N it's not you, it's the library. but still, screenshot it and send it to the group chat 💀

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👑 Author 👑

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

the whole squad, credited, as they should be 🫶

Definition at line 222 of file cgegs.f.

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⭐ Author (again, but the Doxygen one) ⭐

Generated automatically by Doxygen for LAPACK from the source code. so she was born from a script, we love a nepo baby 💅

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and that's the page, bestie!! 🎀 no cap, every single flag, every INFO value, every author and every line number is right there. love that for us 💖

— written up from LAPACK, Version 3.12.0, dated /home/abui...TED/cgegs.f(3) 🌸 mwah, go compute something ✨