/home/abui...RC/sgeev.f(3)

🌸 NAME 🌸

Okay so bestie, this is the manpage for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeev.f — and yes, that whole path is literally the name, no cap. It's part of the Library Functions Manual, and it's the file where SGEEV lives. 💅

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

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine SGEEV (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr,
    work, lwork, info)
     SGEEV computes the eigenvalues and, optionally, the left and/or
    right eigenvectors for GE matrices

So like, SGEEV computes the eigenvalues — and if you want, the left and/or right eigenvectors too — for GE matrices. Iconic behaviour fr fr. 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine SGEEV (character jobvl, character jobvr, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) wr, real,
    dimension( * ) wi, real, dimension( ldvl, * ) vl, integer ldvl, real,
    dimension( ldvr, * ) vr, integer ldvr, real, dimension( * ) work,
    integer lwork, integer info)

SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices. That's the whole vibe. 💖

💫 Purpose 💫

Okay so here's the tea. SGEEV computes, for an N-by-N real nonsymmetric matrix A, the eigenvalues — and, if you ask nicely, the left and/or right eigenvectors. 🫶

The right eigenvector v(j) of A satisfies:

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

where lambda(j) is its eigenvalue. 🌸

The left eigenvector u(j) of A satisfies:

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

where u(j)**H denotes the conjugate-transpose of u(j). (Yes, the **H is doing the heavy lifting there, iykyk.) 🌈

The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real. Slay, normalized, periodt. 💅

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🌟 Parameters 🌟

• JOBVL — is CHARACTER*1. Set it to 'N' and the left eigenvectors of A are not computed; set it to 'V' and the left eigenvectors of A are computed. That's it, that's the whole flag. 💜
• JOBVR — is CHARACTER*1. 'N' means right eigenvectors of A are not computed; 'V' means right eigenvectors of A are computed. Same energy as JOBVL but for the other side. 🎀
• N — is INTEGER. The order of the matrix A. Constraint: N >= 0. (Zero is allowed bestie, don't panic.) ⭐
• A — is REAL array, dimension (LDA,N). On entry, the N-by-N matrix A. On exit… A has been overwritten. 😭 Gone. Replaced. So if you needed the original, copy it first, ngl.
• LDA — is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N). 🔥
• WR — is REAL array, dimension (N). That's the real-parts array, more on it in a sec. ✨
• WI — is REAL array, dimension (N). So WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively, with the eigenvalue having the positive imaginary part first. Order matters, don't shuffle them. 🌸
• VL — is REAL array, dimension (LDVL,N). If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = 'N', VL is not referenced. 👀
  • If the j-th eigenvalue is real, then u(j) = VL(:,j) — the j-th column of VL.
  • If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1). Two columns, one vibe. 🦋
• LDVL — is INTEGER. The leading dimension of the array VL. Constraint: LDVL >= 1; and if JOBVL = 'V', then LDVL >= N. 🫶
• VR — is REAL array, dimension (LDVR,N). If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = 'N', VR is not referenced. 💖
  • If the j-th eigenvalue is real, then v(j) = VR(:,j) — the j-th column of VR.
  • If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1). Mirror image of the VL situation, iconic. 🌈
• LDVR — is INTEGER. The leading dimension of the array VR. Constraint: LDVR >= 1; and if JOBVR = 'V', then LDVR >= N. 💜
• WORK — is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, then WORK(1) returns the optimal LWORK. Little bonus value, we love to see it. 🎁
• LWORK — is INTEGER. The dimension of the array WORK. Constraint: LWORK >= max(1,3*N), and if JOBVL = 'V' or JOBVR = 'V', then LWORK >= 4*N. For good performance, LWORK must generally be larger. ⚡
  • 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. Sneaky little -1, we stan. 🔍
• INFO — is INTEGER. The receipts:
  • = 0: successful exit. 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value. 🙈
  • > 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements i+1:N of WR and WI contain eigenvalues which have converged. Partial results, bestie — handle with care. 💀

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👑 Author 👑

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

Definition at line 190 of file sgeev.f. 📍

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🧚 Author (the meta one) 🧚

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent little doc generator. 🤖✨

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And that's the whole page bestie — every flag, every constraint, every overwritten array. Go forth and diagonalize responsibly. 💅

LAPACK — Version 3.12.0, signed off from /home/abui...RC/sgeev.f(3). Catch you in the next manpage, mwah 🫶💖🎀