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

💖 DSYGV — /home/abui...RC/dsygv.f(3) 💖

okay so this is a Library Functions Manual page, bestie, and the manual name is literally /home/abui...RC/dsygv.f(3). We’re about to make a generalized symmetric-definite eigenproblem feel less like a boss fight and more like a group project where everyone actually does their part. 🦋

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🌸 NAME 🌸

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

Yes, the whole path is the name. No cap. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine DSYGV (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    info)
    DSYGV

🫶 Function/Subroutine Documentation 🫶

subroutine DSYGV (integer itype, character jobz, character uplo, integer n,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,
    double precision, dimension( * ) work, integer lwork, integer info)
    DSYGV

DSYGV is the main character here, fr fr. 👑

🎯 Purpose 🎯

DSYGV computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric and B is also positive definite. That last bit is important, bestie — B has to be positive definite, iykyk. 💖

🧾 Parameters 🧾

• ITYPE — INTEGER. Specifies the problem type to be solved:
  • = 1: A*x = (lambda)*B*x
  • = 2: A*B*x = (lambda)*x
  • = 3: B*A*x = (lambda)*x
• JOBZ — CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — CHARACTER*1.
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — INTEGER. The order of the matrices A and B. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA, N).

On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:

• if ITYPE = 1 or 2, Z**T*B*Z = I;
• if ITYPE = 3, Z**T*inv(B)*Z = I.

If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. That means yeeted, bestie — the original triangle is gone. 💀

• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — DOUBLE PRECISION array, dimension (LDB, N).

On entry, the symmetric positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.

• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🌈
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The length of the array WORK. LWORK >= max(1,3*N-1). For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for DSYTRD returned by ILAENV.

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: DPOTRF or DSYEV returned an error code:
    • <= N: if INFO = i, DSYEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
    • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

👑 Author 👑

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

📍 Definition at line 173 of file dsygv.f. 📍

Definition at line 173 of file dsygv.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 That’s the page, bestie — source/version: LAPACK Version 3.12.0; page: /home/abui...RC/dsygv.f(3). The footer doesn’t give a separate date, so I’m not making one up. 🫶