SRC/cheevd.f(3)

💖 NAME 💖

SRC/cheevd.f — okay bestie, welcome to the manual page for SRC/cheevd.f(3), living under the Library Functions Manual umbrella. This is the cheevd era, and it's giving major eigenvalue/eigenvector main-character energy. 💅

---

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine cheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork,
    iwork, liwork, info)

CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices. periodt. 💖

---

🦋 Function/Subroutine Documentation 🦋

💅 subroutine cheevd 💅

subroutine cheevd (character jobz, character uplo, integer n, complex,
    dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,
    dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer
    lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices.

🌸 Purpose 🌸

okay so the actual purpose is this: CHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. no cap, that's the whole vibe. ✨

💅 Parameters 💅

• JOBZ — JOBZ is CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — UPLO is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. The order of the matrix A. 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 orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= 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. If N <= 1, LWORK must be at least 1. If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• RWORK — RWORK is REAL array, dimension (MAX(1,LRWORK)). On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
• LRWORK — LRWORK is INTEGER. The dimension of the array RWORK. If N <= 1, LRWORK must be at least 1. If JOBZ = 'N' and N > 1, LRWORK must be at least N. If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — LIWORK is INTEGER. The dimension of the array IWORK. If N <= 1, LIWORK must be at least 1. If JOBZ = 'N' and N > 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

🫶 Author 🫶

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

🔥 Further Details 🔥

Modified description of INFO. Sven, 16 Feb 05.

🧚 Contributors 🧚

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 196 of file cheevd.f.

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bye bestie — this whole diva is LAPACK Version 3.12.0 on source page SRC/cheevd.f(3), with Sven's 16 Feb 05 note in the mix. 💜✨