geev(3)

📦

version 3.12.1 · 9 versions

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✨ geev — from the Library Functions Manual, like, `geev(3)` ✨

okay bestie, sit down, hydrate, because this one is a whole journey 💖 this is the geev(3) page and it's giving "eigen-everything" energy — no cap.

🌸 NAME 🌸

geev - geev: eig

(yes that's literally it, she's mysterious, she's iconic, she's eig 💅)

🦋 SYNOPSIS 🦋

✨ Functions ✨

subroutine cgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)

subroutine cgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work,
    lwork, rwork, info)

CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices 💖

subroutine dgeev (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)

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 ✨

subroutine sgeev (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)

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 🎀

subroutine zgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)

subroutine zgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work,
    lwork, rwork, info)

ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices 👑

🌈 Detailed Description 🌈

this section is lowkey just a heading in the original — nothing underneath it, and we respect the mystery 🫶 so there's literally nothing else here. moving on, main character energy only.

💅 Function Documentation 💅

💜 subroutine cgeev (character jobvl, character jobvr, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) w, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

subroutine cgeev (character jobvl, character jobvr, integer n, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( * ) w, complex,
    dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr,
    integer ldvr, complex, dimension( * ) work, integer lwork, real,
    dimension( * ) rwork, integer info)

CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices 🔥

🌸 Purpose 🌸

okay so here's the tea, straight from the source:

CGEEV computes for an N-by-N complex 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 — that's the glow-up, periodt 💅

🎀 Parameters 🎀

JOBVL — is CHARACTER*1
- = 'N': left eigenvectors of A are not computed;
- = 'V': left eigenvectors of are computed.
JOBVR — is CHARACTER*1
- = 'N': right eigenvectors of A are not computed;
- = 'V': right eigenvectors of A are computed.
N — is INTEGER. The order of the matrix A. N >= 0. 🦋
A — is COMPLEX array, dimension (LDA,N). On entry, the N-by-N matrix A. On exit, A has been overwritten. (she gets a whole new look, ngl 🙈)
LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
W — is COMPLEX array, dimension (N). W contains the computed eigenvalues ⭐
VL — is COMPLEX 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.
- u(j) = VL(:,j), the j-th column of VL. 💖
LDVL — is INTEGER. The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.
VR — is COMPLEX 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.
- v(j) = VR(:,j), the j-th column of VR. 🌸
LDVR — is INTEGER. The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.
WORK — is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK — is INTEGER. The dimension of the array WORK. LWORK >= max(1,2*N). For good performance, LWORK must generally be larger.

real talk: 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 — is REAL array, dimension (2*N).
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 W contain eigenvalues which have converged.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 178 of file cgeev.f. 📍

💜 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)

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 🌸

the actual wording, because we don't paraphrase the math bestie:

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 — same glow-up rules as her complex sister 💅

🎀 Parameters 🎀

JOBVL — is CHARACTER*1
- = 'N': left eigenvectors of A are not computed;
- = 'V': left eigenvectors of A are computed.
JOBVR — is CHARACTER*1
- = 'N': right eigenvectors of A are not computed;
- = 'V': right eigenvectors of A are computed.
N — is INTEGER. The order of the matrix A. N >= 0. 🦋
A — is DOUBLE PRECISION array, dimension (LDA,N). On entry, the N-by-N matrix A. On exit, A has been overwritten. (she said "new me, who dis" 🙈)
LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
WR — is DOUBLE PRECISION array, dimension (N).
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 — 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 — is INTEGER. The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.
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 — is INTEGER. The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.
WORK — is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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.

okay important, don't skip this: 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 — 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 👑

Univ. of Tennessee

Univ. of California Berkeley

…okay so that's dgeev fully handled, and before we move on, the credits, because we always give credit 💅

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

dgeev is chillin' at Definition at line 190 of file dgeev.f.

🦋 `sgeev` — the real nonsymmetric one (eigenvalues + optional left/right eigenvectors)

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 ✨

💜 Purpose

Okay so here's the tea, bestie: 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. Iconic.

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. No cap.

🌸 Parameters

JOBVL — CHARACTER*1
- = 'N': left eigenvectors of A are not computed;
- = 'V': left eigenvectors of A are computed.
JOBVR — CHARACTER*1
- = 'N': right eigenvectors of A are not computed;
- = 'V': right eigenvectors of A are computed.
N — INTEGER
- The order of the matrix A. N >= 0.
A — REAL array, dimension (LDA,N)
- On entry, the N-by-N matrix A.
- On exit, A has been overwritten. (she's gone, she's not coming back 💀)
LDA — INTEGER
- The leading dimension of the array A. LDA >= max(1,N).
WR — REAL array, dimension (N)
WI — REAL 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 — 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).
LDVL — INTEGER
- The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.
VR — 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).
LDVR — INTEGER
- The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.
WORK — REAL 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(1,3*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 — 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

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

sgeev is posted up at Definition at line 190 of file sgeev.f.

🧚 `zgeev` — the complex*16 sibling, living her best life

subroutine zgeev (character jobvl, character jobvr, integer n, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( * ) w,
    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)

ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices ✨

💜 Purpose

ZGEEV computes, for an N-by-N complex 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. Same energy as her real sister, honestly. 🫶

🌸 Parameters

JOBVL — CHARACTER*1
- = 'N': left eigenvectors of A are not computed;
- = 'V': left eigenvectors of are computed.
JOBVR — CHARACTER*1
- = 'N': right eigenvectors of A are not computed;
- = 'V': right eigenvectors of A are computed.
N — INTEGER
- The order of the matrix A. N >= 0.
A — COMPLEX*16 array, dimension (LDA,N)
- On entry, the N-by-N matrix A.
- On exit, A has been overwritten. bye bestie 💀
LDA — INTEGER
- The leading dimension of the array A. LDA >= max(1,N).
W — COMPLEX*16 array, dimension (N)
- W contains the computed eigenvalues. 💖
VL — COMPLEX*16 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.
- u(j) = VL(:,j), the j-th column of VL.
LDVL — INTEGER
- The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.
VR — COMPLEX*16 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.
- v(j) = VR(:,j), the j-th column of VR.
LDVR — INTEGER
- The leading dimension of the array VR. LDVR >= 1; 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. LWORK >= max(1,2*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.
RWORK — DOUBLE PRECISION array, dimension (2*N)
INFO — 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 W contain eigenvalues which have converged.

🌈 Author

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

zgeev is serving at Definition at line 178 of file zgeev.f.

💅 Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🎀)

And that's the whole page, bestie — you ate that. 💖 This one's LAPACK, Version 3.12.0, churned out by Doxygen straight from the source code, and it's signed off on the geev(3) page. Go forth and diagonalize responsibly. 🦋✨👑

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

geev(3)

✨ geev — from the Library Functions Manual, like, geev(3) ✨

🌸 NAME 🌸

🦋 SYNOPSIS 🦋

✨ Functions ✨

🌈 Detailed Description 🌈

💅 Function Documentation 💅

🌸 Purpose 🌸

🎀 Parameters 🎀

👑 Author 👑

🌸 Purpose 🌸

🎀 Parameters 🎀

👑 Author 👑

🦋 sgeev — the real nonsymmetric one (eigenvalues + optional left/right eigenvectors)

💜 Purpose

🌸 Parameters

🌈 Author

🧚 zgeev — the complex*16 sibling, living her best life

💜 Purpose

🌸 Parameters

🌈 Author

💅 Author

✨ geev — from the Library Functions Manual, like, `geev(3)` ✨

🦋 `sgeev` — the real nonsymmetric one (eigenvalues + optional left/right eigenvectors)

🧚 `zgeev` — the complex*16 sibling, living her best life