SRC/dsygv.f(3)

🩷 SRC/dsygv.f

From the Library Functions Manual, with love: this is the DSYGV page, and it's lowkey iconic. 💅✨

✨ NAME ✨

SRC/dsygv.f

🦋 SYNOPSIS 🦋

🎀 Functions/Subroutines 🎀

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

🌈 Function/Subroutine Documentation 🌈

🧚 subroutine dsygv

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

🔥 Purpose

Bestie, DSYGV computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem. It handles one of these three forms, exactly: 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. 🫶

🌸 Parameters

• ITYPE — is INTEGER. It 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 — is CHARACTER*1.
  • = 'N': compute eigenvalues only;
  • = 'V': compute eigenvalues and eigenvectors.
• UPLO — is CHARACTER*1.
  • = 'U': upper triangles of A and B are stored;
  • = 'L': lower triangles of A and B are stored.
• N — is INTEGER. The order of the matrices A and B. N >= 0.
• A — is DOUBLE PRECISION array, dimension (LDA, N). On entry, it's 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.

💀 Danger tea: that destruction is real, bestie — including the diagonal.

• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — is DOUBLE PRECISION array, dimension (LDB, N). On entry, it's 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 — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• W — is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• WORK — is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — is 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 — is 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.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the tea, bestie: this page is from LAPACK, Version 3.12.0, and it's page SRC/dsygv.f(3). No separate date is listed on the footer. 💖✨