DSYGVX(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 DSYGVX(3) — Library Functions Manual 💖

okay so bestie, welcome to DSYGVX(3) from the Library Functions Manual — it's a LAPACK routine, and it's lowkey carrying the whole generalized symmetric-definite eigenproblem situation on its back. ✨

🌸 NAME 🌸

this page is literally for this file:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsygvx.f

yes bestie, that's the whole NAME section — it's a path, not a drill. 💅

🧚 SYNOPSIS 🧚

🫶 Functions/Subroutines 🫶

here's the short version, typed exactly as it should be:

subroutine DSYGVX (itype, jobz, range, uplo, n, a, lda, b, ldb, vl, vu,
    il, iu, abstol, m, w, z, ldz, work, lwork, iwork, ifail, info)
    DSYGVX

🦋 Function/Subroutine Documentation 🦋

full signature incoming — all the types, all the dimensions, no cap:

subroutine DSYGVX (integer itype, character jobz, character range, character
     uplo, integer n, double precision, dimension( lda, * ) a, integer lda,
     double precision, dimension( ldb, * ) b, integer ldb, double precision
     vl, double precision vu, integer il, integer iu, double precision
     abstol, integer m, double precision, dimension( * ) w, double precision,
     dimension( ldz, * ) z, integer ldz, double precision, dimension( * )
     work, integer lwork, integer, dimension( * ) iwork, integer, dimension(
     * ) ifail, integer info)
     DSYGVX

✨ Purpose ✨

DSYGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-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 symmetric and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. iconic behavior, 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. pick your fighter, bestie.
  • JOBZ — JOBZ is CHARACTER*1. = 'N': compute eigenvalues only; = 'V': compute eigenvalues and eigenvectors. so like, eigenvectors are optional but very main character.
  • RANGE — RANGE is CHARACTER*1. = 'A': all eigenvalues will be found. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found. = 'I': the IL-th through IU-th eigenvalues will be found.
  • UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A and B are stored; = 'L': lower triangle of A and B are stored.
  • N — N is INTEGER. The order of the matrix pencil (A,B). N >= 0.
  • A — A is 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, the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. yes, destroyed destroyed. 😭
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • B — B is 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. slay, but also know that your B is getting rewritten. 💅
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • VL — VL is DOUBLE PRECISION. If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
  • VU — VU is DOUBLE PRECISION. If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
  • IL — IL is INTEGER. If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
  • IU — IU is INTEGER. If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
  • ABSTOL — ABSTOL is DOUBLE PRECISION. The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ), where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing C to tridiagonal form, where C is the symmetric matrix of the standard symmetric problem to which the generalized problem is transformed. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S'). bestie, this is the "be precise or be sorry" parameter. 🎯
  • M — M is INTEGER. The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
  • W — W is DOUBLE PRECISION array, dimension (N). On normal exit, the first M elements contain the selected eigenvalues in ascending order.
  • Z — Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)). If JOBZ = 'N', then Z is not referenced. If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). 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 an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. read that note again, bestie — it's giving "do not skimp on your array." 👑💀
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
  • WORK — WORK is DOUBLE PRECISION 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(1,8*N). For optimal efficiency, LWORK >= (NB+3)*N, where NB is the blocksize for DSYTRD 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.
  • IWORK — IWORK is INTEGER array, dimension (5*N).
  • IFAIL — IFAIL is INTEGER array, dimension (N). If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.
  • INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: DPOTRF or DSYEVX returned an error code: <= N: if INFO = i, DSYEVX failed to converge; i eigenvectors failed to converge. Their indices are stored in array IFAIL. > 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. okay so if this hits > N, it's not a vibe — no eigenvalues, no eigenvectors, no nothing. 🙈

👑 Author 👑

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

🌈 Contributors 🌈

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

📌 Definition 📌

Definition at line 294 of file dsygvx.f.

🫶 Author 🫶

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💖 and that's the whole page, bestie! it came from LAPACK, version 3.12.0, with the footer path /home/abui...RC/dsygvx.f(3). no extra date line was in the footer, so I'm not inventing one — periodt. 🎀🦋

📦 where this page comes from