SRC/zhegv.f(3)

hey bestie 💖 welcome to SRC/zhegv.f(3) from the Library Functions Manual — we’re doing complex Hermitian math today and it’s giving main character energy ✨

🌸 NAME 🌸

SRC/zhegv.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

📚 Function/Subroutine Documentation 📚

🦋 subroutine zhegv 🦋

subroutine zhegv (integer itype, character jobz, character uplo, integer n,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldb, * ) b, integer ldb, double precision, dimension( * ) w, complex*16,
    dimension( * ) work, integer lwork, double precision, dimension( * )
    rwork, integer info)
    ZHEGV

🎯 Purpose:

okay so ZHEGV 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. lowkey iconic problem setup, ngl 💅

💅 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*16 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. 💀 dramatic but true.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is COMPLEX*16 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 DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. cute and ordered 🎀
• 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 length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD 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 DOUBLE PRECISION 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: ZPOTRF or ZHEEV returned an error code:
    • <= N: if INFO = i, ZHEEV 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 zhegv.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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