SRC/DEPRECATED/cgegs.f(3)

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version 3.12.1 · 2 versions
, in arch rolling

🌸 NAME 🌸

SRC/DEPRECATED/cgegs.f — hii bestie, this is the Library Functions Manual page for SRC/DEPRECATED/cgegs.f(3), aka the cgegs routine 💖. It’s the deprecated one, so keep that in mind, okay? 🫶

✨ 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) ✨.

💅 Function/Subroutine Documentation 💅

🧚 subroutine cgegs — the whole glowing signature 🧚

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) — periodt 💅.

Purpose: 🌟

⚠️ This routine is deprecated and has been replaced by routine CGGES.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

Okay so 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). ✨

Parameters 🎀

  • JOBVSL — CHARACTER*1. 'N': do not compute the left Schur vectors; 'V': compute the left Schur vectors (returned in VSL). 💖
  • JOBVSR — CHARACTER*1. 'N': do not compute the right Schur vectors; 'V': compute the right Schur vectors (returned in VSR). 🌸
  • N — INTEGER. The order of the matrices A, B, VSL, and VSR. N >= 0. 🫶
  • A — COMPLEX array, dimension (LDA, N). On entry, the matrix A. On exit, the upper triangular matrix S from the generalized Schur factorization. 💅
  • LDA — INTEGER. The leading dimension of A. LDA >= max(1,N). 🎀
  • B — COMPLEX array, dimension (LDB, N). On entry, the matrix B. On exit, the upper triangular matrix T from the generalized Schur factorization. 💜
  • LDB — INTEGER. The leading dimension of B. LDB >= max(1,N). 🌈
  • ALPHA — 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. 🔥
  • BETA — 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. 😭

  • VSL — COMPLEX array, dimension (LDVSL,N). If JOBVSL = 'V', the matrix of left Schur vectors Q. Not referenced if JOBVSL = 'N'. 🦋
  • LDVSL — INTEGER. The leading dimension of the matrix VSL. LDVSL >= 1, and if JOBVSL = 'V', LDVSL >= N. ✨
  • VSR — COMPLEX array, dimension (LDVSR,N). If JOBVSR = 'V', the matrix of right Schur vectors Z. Not referenced if JOBVSR = 'N'. 🌸
  • LDVSR — INTEGER. The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >= N. 💖
  • WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🔥
  • LWORK — 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).

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. 💀

  • RWORK — REAL array, dimension (3*N). 🍓
  • INFO — INTEGER. Behold the receipts:
    • = 0: successful exit 👑
    • < 0: if INFO = -i, the i-th argument had an illegal value. 🙈
    • =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. 😭
    • > 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) 💅

Author 🌈

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

Definition at line 222 of file cgegs.f.

👑 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

okay bestie, that’s the whole cgegs saga — from LAPACK, Version 3.12.0, for SRC/DEPRECATED/cgegs.f(3). Go forth and maybe use CGGES instead 💅✨

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