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

okay bestie, this is the manual page for /home/abui...RC/dgeev.f(3) from the Library Functions Manual — and it's literally about the LAPACK subroutine DGEEV. no cap, it's giving main-character linear algebra energy. 💅✨

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🌸 NAME 🌸

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

✨ SYNOPSIS ✨

Functions/Subroutines

bestie, the synopsis is serving exactly one subroutine. here it is, untouched:

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

💅 Function/Subroutine Documentation 💅

and here's the full function/subroutine documentation vibe — signature first, because she's iconic:

   subroutine DGEEV (character jobvl, character jobvr, integer n, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( * ) wr, double precision, dimension( * ) wi, double
       precision, dimension( ldvl, * ) vl, integer ldvl, double precision,
       dimension( ldvr, * ) vr, integer ldvr, double precision, dimension( * )
       work, integer lwork, integer info)
        DGEEV computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for GE matrices

🎯 Purpose 🎯

okay so DGEEV computes, for an N-by-N real nonsymmetric matrix A, the eigenvalues and — optionally — 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).

the computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real. periodt. 💖

🧸 Parameters 🧸

bestie, here's every parameter, no skips:

JOBVL

JOBVL is CHARACTER*1 ✨

• = 'N': left eigenvectors of A are not computed;
• = 'V': left eigenvectors of A are computed.

JOBVR

JOBVR is CHARACTER*1 ✨

• = 'N': right eigenvectors of A are not computed;
• = 'V': right eigenvectors of A are computed.

N

N is INTEGER. the order of the matrix A. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N). on entry, the N-by-N matrix A. on exit, A has been overwritten.

bestie, yes: on exit, A has been overwritten. 💀

LDA

LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).

WR

WR is DOUBLE PRECISION array, dimension (N).

WI

WI is DOUBLE PRECISION array, dimension (N). 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. 🌀

VL

VL is DOUBLE PRECISION 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).

LDVL

LDVL is INTEGER. the leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.

VR

VR is DOUBLE PRECISION 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).

LDVR

LDVR is INTEGER. the leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER. the dimension of the array WORK. LWORK >= max(1,3*N), and if JOBVL = 'V' or JOBVR = 'V', 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. 👑

INFO

INFO is INTEGER.

• = 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.

🫶 Author 🫶

shoutout to the authors:

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

Definition at line 190 of file dgeev.f.

🫶 Author 🫶

and this page itself was:

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. mwah 💋 — source/version vibes are LAPACK Version 3.12.0, and the manual path is /home/abui...RC/dgeev.f(3). 🎀✨