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

💅 NAME 💅

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

From the LAPACK Library Functions Manual, this is the dggev.f(3) page, bestie. We're talking about DGGEV, and it's lowkey iconic.

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices. periodt.

🧚 Function/Subroutine Documentation 🧚

subroutine DGGEV (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)

DGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices. iykyk.

🎯 Purpose 🎯

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

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 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).

🎀 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.
• 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.
• LDB — INTEGER
  • The leading dimension of B. LDB >= max(1,N).
• ALPHAR — DOUBLE PRECISION array, dimension (N)
  • That's the whole description, bestie. No extra lore here.
• ALPHAI — DOUBLE PRECISION array, dimension (N)
  • Same energy as ALPHAR: just the array and its dimension.
• 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 positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with ALPHAI(j+1) negative.
  • Careful, bestie: 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 — 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 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.
  • = 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 DHGEQZ.
    • =N+2: error return from DTGEVC.

🌸 Author 🌸

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

Definition at line 224 of file dggev.f.

🧾 Author 🧾

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page — no cap, no skipped details. Cute sign-off from LAPACK Version 3.12.0, source file /home/abui...RC/dggev.f(3). 💖✨🎀🦋💅