SRC/chegvd.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💖 NAME 💖

SRC/chegvd.f — this page is from the SRC/chegvd.f(3) page in the Library Functions Manual, bestie, and it's the home of the chegvd subroutine: your go-to for complex generalized Hermitian-definite eigenproblems. Iconic.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine chegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    rwork, lrwork, iwork, liwork, info)
    CHEGVD

🦋 Function/Subroutine Documentation 🦋

chegvd

subroutine chegvd (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 lrwork, integer,
    dimension( * ) iwork, integer liwork, integer info)
CHEGVD

Purpose:

Okay so CHEGVD computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite eigenproblem, in one of these forms:

  • A*x=(lambda)*B*x
  • A*Bx=(lambda)*x
  • B*A*x=(lambda)*x

Here A and B are assumed to be Hermitian, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. Obsessed with the efficiency, honestly.

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.

💀 Bestie, that last bit is not a drill: with JOBZ = 'N', the triangle of A you're using — diagonal included — gets absolutely cooked on exit.
  • 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 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.
    • If N <= 1, LWORK >= 1.
    • If JOBZ = 'N' and N > 1, LWORK >= N + 1.
    • If JOBZ = 'V' and N > 1, LWORK >= 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 >= 1.
    • If JOBZ = 'N' and N > 1, LRWORK >= N.
    • If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
    • If JOBZ = 'N' and N > 1, LIWORK >= 1.
    • If JOBZ = 'V' and N > 1, LIWORK >= 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: CPOTRF or CHEEVD returned an error code:
      • <= N: 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);
      • > 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.

🔥 Further Details: 🔥

Heads up, bestie: this version is modified so that no backsubstitution is performed if CHEEVD fails to converge (NEIG in old code could be greater than N, causing out of bounds reference to A — reported by Ralf Meyer). Also corrected the description of INFO and the test on ITYPE. Sven, 16 Feb 05. Periodt.

🎀 Contributors: 🎀

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA.

Definition at line 241 of file chegvd.f.

🌈 Author 🌈

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