ggev3(3)

📦

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✨ `ggev3(3)` — Library Functions Manual, but make it cute ✨

bestie, welcome to the ggev3 glow-up 💅 this is the generalized eigenvalue/eigenvector saga for GE matrices, blocked-algorithm edition, and it's honestly giving main character energy. 🦋

🌸 NAME 🌸

ggev3 — ggev3: eig — aka the whole generalized eig friend group: cggev3, dggev3, sggev3, and zggev3. They compute eigenvalues and, optionally, left and/or right eigenvectors for GE matrices using the blocked algorithm. Periodt. 💖

🦋 SYNOPSIS 🦋

✨ Functions ✨

cggev3 — CGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

subroutine cggev3 (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl,
    ldvl, vr, ldvr, work, lwork, rwork, info)

dggev3 — DGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

subroutine dggev3 (jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai,
    beta, vl, ldvl, vr, ldvr, work, lwork, info)

sggev3 — SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

subroutine sggev3 (jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai,
    beta, vl, ldvl, vr, ldvr, work, lwork, info)

zggev3 — ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)

subroutine zggev3 (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl,
    ldvl, vr, ldvr, work, lwork, rwork, info)

💖 DETAILED DESCRIPTION 💖

okay so this is where the ggev3 family actually spills the tea. It's the blocked-algorithm version of generalized eig for GE matrices, and the full deets live right below. Grab a strawberry 🍓 and let's get into it.

🎀 FUNCTION DOCUMENTATION 🎀

🦋 subroutine cggev3 🦋

subroutine cggev3 (character jobvl, character jobvr, integer n, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( * ) alpha, complex, dimension( * )
    beta, complex, dimension( ldvl, * ) vl, integer ldvl, complex,
    dimension( ldvr, * ) vr, integer ldvr, complex, dimension( * ) work,
    integer lwork, real, dimension( * ) rwork, integer info)

CGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm). slay. ✨

🌟 Purpose 🌟

CGGEV3 computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. no cap, that's the whole vibe.

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), as there is a reasonable interpretation for beta=0, and even for both being zero.

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). iykyk 💜

🌟 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 array, dimension (LDA, N); on entry, the matrix A in the pair (A,B). On exit, A has been overwritten. she's changed, bestie. 🍑
LDA — INTEGER; the leading dimension of A. LDA >= max(1,N). ✨
B — COMPLEX array, dimension (LDB, N); on entry, the matrix B in the pair (A,B). On exit, B has been overwritten. also changed, lowkey. 🍑
LDB — INTEGER; the leading dimension of B. LDB >= max(1,N). ✨
ALPHA — COMPLEX array, dimension (N). 💖
BETA — COMPLEX array, dimension (N); on exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized eigenvalues.

bestie, listen: 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). do not just divide and pray, okay? 😭

VL — COMPLEX 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 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 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.

workspace query tea: 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. so don't panic, it's just asking, not doing. 💚

RWORK — REAL 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 CHGEQZ, =N+2: error return from CTGEVC. not the slay we wanted, but at least the receipts are clear. 💀

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📌 Definition at line 215 of file cggev3.f. 📌

🦋 subroutine dggev3 🦋

subroutine dggev3 (character jobvl, character jobvr, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * )
    alphar, double precision, dimension( * ) alphai, double precision,
    dimension( * ) beta, double precision, dimension( ldvl, * ) vl, integer
    ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, double
    precision, dimension( * ) work, integer lwork, integer info)

DGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm). real nonsymmetric edition, let's goooo. 🔥

🌟 Purpose 🌟

DGGEV3 computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors.

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

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

The left eigenvector u(j) corresponding to the eigenvalue 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). same energy, real arithmetic. 💜

🌟 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 — DOUBLE PRECISION array, dimension (LDA, N); on entry, the matrix A in the pair (A,B). On exit, A has been overwritten. again, she's not the same matrix after. 🍑
LDA — INTEGER; the leading dimension of A. LDA >= max(1,N). ✨
B — DOUBLE PRECISION array, dimension (LDB, N); on entry, the matrix B in the pair (A,B). On exit, B has been overwritten. same story, bestie. 🍑
LDB — INTEGER; the leading dimension of B. LDB >= max(1,N). ✨
ALPHAR — DOUBLE PRECISION array, dimension (N). 💖
ALPHAI — DOUBLE PRECISION array, dimension (N). 💖
BETA — part 2 is about to spill the rest of this parameter's deets, bestie — the page cuts off right here in part 1 💅

part 1 out, part 2 incoming — don't touch that dial, we're not done slaying ✨

BETA — DOUBLE PRECISION array, dimension (N). On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero then the j-th eigenvalue is real; if it's positive then the j-th and (j+1)-st eigenvalues form a complex conjugate pair, and ALPHAI(j+1) is negative. 🌀

⚠️ bestie, listen: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) may easily over- or underflow, and BETA(j) may even be zero. So please, do not naively compute the ratio alpha/beta 😭. That said, ALPHAR and ALPHAI will always be less than and usually comparable with norm(A) in magnitude, and BETA always less than and usually comparable with norm(B). 💅

VL — 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 the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th 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). 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 — 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 the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th 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). 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 — DOUBLE PRECISION 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(1,8*N). For good performance, LWORK should generally be larger — like, treat yourself, give it room to breathe 🫶.

🧚 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. It's giving "just asking, not committing" energy.

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 ALPHAR(j), ALPHAI(j), and BETA(j) should be correct for j=INFO+1,...,N. 😭
- > N: =N+1: other than QZ iteration failed in DLAQZ0. =N+2: error return from DTGEVC. 💀

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 225 of file dggev3.f. 🌟

🌈 subroutine `sggev3`

subroutine sggev3 (character jobvl, character jobvr, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer
    ldb, real, dimension( * ) alphar, real, dimension( * ) alphai, real,
    dimension( * ) beta, real, dimension( ldvl, * ) vl, integer ldvl, real,
    dimension( ldvr, * ) vr, integer ldvr, real, dimension( * ) work,
    integer lwork, integer info)

SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm) 🔥

🎀 Purpose:

Okay so picture this: SGGEV3 computes for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. 💫

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's usually represented as the pair (alpha,beta), because there's a reasonable interpretation for beta=0, and even for both being zero. 🧠✨

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

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

The left eigenvector u(j) corresponding to the eigenvalue 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). 🦋 (yes the **H goes on the outside, it's that girl)

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 — REAL array, dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten. 😬 yeah she's gone, hope you didn't need her.
LDA — INTEGER. The leading dimension of A. LDA >= max(1,N). 📏
B — REAL array, dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten. 💀 same deal, she's not coming back.
LDB — INTEGER. The leading dimension of B. LDB >= max(1,N). 📐
ALPHAR — REAL array, dimension (N). 🌸
ALPHAI — REAL array, dimension (N). 🌸
BETA — REAL array, dimension (N). On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will be the generalized eigenvalues. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative. 🌀

⚠️ the quotients ALPHAR(j)/BETA(j) and ALPHAI(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, ALPHAR and ALPHAI 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 — 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 the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-th 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). 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 — 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 the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-th 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). 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 — 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(1,8*N). For good performance, LWORK should 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. Same vibe check as before, no cap.

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 ALPHAR(j), ALPHAI(j), and BETA(j) should be correct for j=INFO+1,...,N. 😭
- > N: =N+1: other than QZ iteration failed in SLAQZ0. =N+2: error return from STGEVC. 💀

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

okay bestie that's the subroutine rundown, and next up we've got the rest of the parameter tea to spill 💜

Univ. of Colorado Denver

NAG Ltd.

Definition at line 225 of file sggev3.f.

🌸 `zggev3` — complex generalized eigenvalues, bestie 🌸

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)

Short version, because we love a summary: ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices — blocked algorithm edition. 💅

💖 Purpose 💖

Okay so ZGGEV3 computes, for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally the left and/or right generalized eigenvectors. Main character math energy, honestly.

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), as there is a reasonable interpretation for beta=0, and even for both being zero. Yes bestie, both zero is allowed to be a whole mood.

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). Conjugate-transpose is iconic, she contains multitudes.

📋 Parameters 📋

JOBVL — JOBVL is CHARACTER*1; = 'N': do not compute the left generalized eigenvectors; = 'V': compute the left generalized eigenvectors.
JOBVR — JOBVR is CHARACTER*1; = 'N': do not compute the right generalized eigenvectors; = 'V': compute the right generalized eigenvectors.
N — N is INTEGER; the order of the matrices A, B, VL, and VR. N >= 0.
A — A is COMPLEX*16 array, dimension (LDA, N). On entry, the matrix A in the pair (A,B). On exit, A has been overwritten.
LDA — LDA is INTEGER; the leading dimension of A. LDA >= max(1,N).
B — B is COMPLEX*16 array, dimension (LDB, N). On entry, the matrix B in the pair (A,B). On exit, B has been overwritten.
LDB — LDB is INTEGER; the leading dimension of B. LDB >= max(1,N).
ALPHA — ALPHA is COMPLEX*16 array, dimension (N).
BETA — BETA is 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). So the vibes are bounded-ish, but do not be feral with the raw ratio.
VL — VL is 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 — LDVL is INTEGER; the leading dimension of the matrix VL. LDVL >= 1, and if JOBVL = 'V', LDVL >= N.
VR — VR is 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 — LDVR is INTEGER; the leading dimension of the matrix VR. LDVR >= 1, and if JOBVR = 'V', LDVR >= N.
WORK — WORK is COMPLEX*16 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(1,2*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. Workspace query is the shortcut queen, no cap.
RWORK — RWORK is DOUBLE PRECISION array, dimension (8*N).
INFO — INFO is 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. Read those statuses carefully, bestie — they are literally telling you where the drama happened.

🌟 Author 🌟

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 215 of file zggev3.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

Footer cuteness: LAPACK Version 3.12.0, page ggev3(3), generated automatically by Doxygen for LAPACK from the source code. Date? The footer line we were handed doesn’t print a separate date, so I’m not inventing one — bestie honesty only. 💖

📦 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

ggev3(3)

✨ ggev3(3) — Library Functions Manual, but make it cute ✨

🌸 NAME 🌸

🦋 SYNOPSIS 🦋

✨ Functions ✨

💖 DETAILED DESCRIPTION 💖

🎀 FUNCTION DOCUMENTATION 🎀

🦋 subroutine cggev3 🦋

🌟 Purpose 🌟

🌟 Parameters 🌟

👑 Author 👑

📌 Definition at line 215 of file cggev3.f. 📌

🦋 subroutine dggev3 🦋

🌟 Purpose 🌟

🌟 Parameters 🌟

👑 Author

🌈 subroutine sggev3

🎀 Purpose:

Parameters

🌸 Author

🌸 zggev3 — complex generalized eigenvalues, bestie 🌸

💖 Purpose 💖

📋 Parameters 📋

🌟 Author 🌟

🪄 Author 🪄

✨ `ggev3(3)` — Library Functions Manual, but make it cute ✨

🌈 subroutine `sggev3`

🌸 `zggev3` — complex generalized eigenvalues, bestie 🌸