SRC/dsygvd.f(3)

✨ NAME ✨

SRC/dsygvd.f(3) — okay so this is the Library Functions Manual page for the DSYGVD routine in SRC/dsygvd.f, and it's lowkey iconic. 💅

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine dsygvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork,
    iwork, liwork, info)
           DSYGVD

🧚‍♀️ Function/Subroutine Documentation 🧚‍♀️

subroutine dsygvd (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,
    dimension( * ) iwork, integer liwork, integer info)
       DSYGVD

DSYGVD — the main character. 👑

Purpose

Okay bestie, here's the vibe: DSYGVD computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem. The forms are 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. If eigenvectors are desired, it uses a divide and conquer algorithm. Slay. ✨

Parameters

• ITYPE — 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 — CHARACTER*1:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• UPLO — CHARACTER*1:
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — INTEGER. The order of the matrices A and B. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA, N). On entry, 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.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — DOUBLE PRECISION array, dimension (LDB, N). On entry, the symmetric 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 — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — INTEGER. The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
• IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
• INFO — INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: DPOTRF or DSYEVD 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

Okay so this routine was modified so that no backsubstitution is performed if DSYEVD 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. 🫶

Contributors

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

Definition at line 219 of file dsygvd.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole vibe, bestie. This page is from LAPACK Version 3.12.0 and it lives at SRC/dsygvd.f(3). Bye! 💖✨