ZGGEV3(3)

✨ NAME ✨

Welcome to ZGGEV3(3) from the Library Functions Manual, bestie! 💖 This page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zggev3.f — yes, that whole path, no cap. It's the ZGGEV3 routine, and she's iconic.

🌸 SYNOPSIS 🌸

🦋 Functions/Subroutines 🦋

       subroutine ZGGEV3 (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl,
           ldvl, vr, ldvr, work, lwork, rwork, info)
            ZGGEV3 computes the eigenvalues and, optionally, the left and/or
           right eigenvectors for GE matrices (blocked algorithm)

Okay so ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices, and it does it with the blocked algorithm. Slay. 💅

💖 Function/Subroutine Documentation 💖

🎀 subroutine ZGGEV3 🎀

Here's the full signature, verbatim, because we do not play with specs:

   subroutine ZGGEV3 (character jobvl, character jobvr, integer n, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
       integer ldb, complex*16, dimension( * ) alpha, complex*16, dimension( *
       ) beta, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16,
       dimension( ldvr, * ) vr, integer ldvr, complex*16, dimension( * ) work,
       integer lwork, double precision, dimension( * ) rwork, integer info)

And what does she do? ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm). Main character energy, fr fr. 👑

🌈 Purpose 🌈

Okay so picture a pair of N-by-N complex nonsymmetric matrices (A,B). ZGGEV3 computes the generalized eigenvalues for that pair, and optionally the left and/or right generalized eigenvectors. Obsessed. 💜

A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), because there is a reasonable interpretation for beta=0, and even for both being zero. No cap.

The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies

A * v(j) = lambda(j) * B * v(j).

The left generalized eigenvector u(j) corresponding to the generalized eigenvalues lambda(j) of (A,B) satisfies

u(j)**H * A = lambda(j) * u(j)**H * B

where u(j)**H is the conjugate-transpose of u(j). Periodt. 💅

🎀 Parameters 🎀

• JOBVL — CHARACTER*1. = 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors. 🦋
• JOBVR — CHARACTER*1. = 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors. 🦋
• N — INTEGER. The order of the matrices A, B, VL, and VR. N >= 0. ✨
• A — COMPLEX*16 array, dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten. (So don't expect your original A back, bestie. 💀)
• LDA — INTEGER. The leading dimension of A. LDA >= max(1,N). 🌸
• B — COMPLEX*16 array, dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten. 💀
• LDB — INTEGER. The leading dimension of B. LDB >= max(1,N). 🌸
• ALPHA — COMPLEX*16 array, dimension (N). 🍓
• BETA — COMPLEX*16 array, dimension (N). On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized eigenvalues. ⚠️ Note: the quotients ALPHA(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, ALPHA will be always less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B).
• VL — COMPLEX*16 array, dimension (LDVL,N). If JOBVL = 'V', the left generalized eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. Each eigenvector is scaled so the largest component has abs(real part) + abs(imag. part) = 1. Not referenced if JOBVL = 'N'. 🦋
• LDVL — INTEGER. The leading dimension of the matrix VL. LDVL >= 1, and if JOBVL = 'V', LDVL >= N. ✨
• VR — COMPLEX*16 array, dimension (LDVR,N). If JOBVR = 'V', the right generalized eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. Each eigenvector is scaled so the largest component has abs(real part) + abs(imag. part) = 1. Not referenced if JOBVR = 'N'. 🦋
• LDVR — INTEGER. The leading dimension of the matrix VR. LDVR >= 1, and if JOBVR = 'V', LDVR >= N. ✨
• WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 🔥
• LWORK — INTEGER. The dimension of the array WORK. 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 — DOUBLE PRECISION array, dimension (8*N). 💜
• INFO — INTEGER.
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • =1,...,N: The QZ iteration failed. No eigenvectors have been calculated, but ALPHA(j) and BETA(j) should be correct for j=INFO+1,...,N.
  • > N: =N+1: other then QZ iteration failed in ZHGEQZ, =N+2: error return from ZTGEVC. 😭

👑 Author 👑

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

Definition at line 214 of file zggev3.f. 📌

💌 Author 💌

Generated automatically by Doxygen for LAPACK from the source code. 🤖

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Big kiss from LAPACK, Version 3.12.0 — this page lives at /home/abui...RC/zggev3.f(3) 💖✨