SRC/chegv.f(3)

💖 CHEGV 💖

okay bestie, this is the page for SRC/chegv.f(3) from the Library Functions Manual, and the main character is CHEGV 🫶. It's giving complex generalized Hermitian-definite eigenproblem energy, and yes, we're keeping every single detail.

✨ NAME ✨

SRC/chegv.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine chegv — CHEGV

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

CHEGV

🦋 Function/Subroutine Documentation 🦋

🫶 subroutine chegv

subroutine chegv (integer itype, character jobz, character uplo, integer n,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
    ) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work,
    integer lwork, real, dimension( * ) rwork, integer info)

CHEGV

💡 Purpose

CHEGV computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-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 Hermitian and B is also positive definite. ✨

🎀 Parameters

• ITYPE — ITYPE is 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 — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — N is INTEGER. The order of the matrices A and B. N >= 0.
• A — A is COMPLEX array, dimension (LDA, N). On entry, the Hermitian 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**H*B*Z = I;
• if ITYPE = 3, Z**H*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. 💀

• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is COMPLEX array, dimension (LDB, N). On entry, the Hermitian 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**H*U or B = L*L**H.

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

• RWORK — RWORK is REAL array, dimension (max(1, 3*N-2)).
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: CPOTRF or CHEEV returned an error code:
    • <= N: if INFO = i, CHEEV 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 179 of file chegv.f.

🌀 Author

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