CHPEVX(3)

💅 CHPEVX(3) — Library Functions Manual 💅

okay so you're reading the CHPEVX(3) page from the Library Functions Manual, and it lives in the LAPACK source at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chpevx.f. slay, let's get into it 💖

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✨ NAME ✨

Officially, the NAME section is literally this path, bestie:

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

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CHPEVX (jobz, range, uplo, n, ap, vl, vu, il, iu, abstol, m,
    w, z, ldz, work, rwork, iwork, ifail, info)

CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices — that's the official little tagline, no cap 🫶

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature with all the types, exactly as written:

subroutine CHPEVX (character jobz, character range, character uplo, integer
    n, complex, dimension( * ) ap, real vl, real vu, integer il, integer iu,
    real abstol, integer m, real, dimension( * ) w, complex, dimension( ldz,
    * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * )
    rwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail,
    integer info)

And the vibe is still: CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💜

🎀 Purpose 🎀

So, CHPEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. You can pick which eigenvalues/vectors you want by specifying either a range of values or a range of indices for the desired eigenvalues. iconic behavior, honestly 💅

✨ Parameters ✨

• JOBZ — JOBZ is CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• 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 is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• AP — AP is COMPLEX array, dimension (N*(N+1)/2).
  • On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
  • On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A. so yes, it gets rewritten — do not expect your original AP back, bestie 😭
• VL — VL is REAL. 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 REAL. 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 REAL. 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 AP to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S').

See by Demmel and Kahan, LAPACK Working Note #3.

• 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 REAL array, dimension (N). If INFO = 0, the selected eigenvalues in ascending order. cute and ordered 💖
• Z — Z is COMPLEX array, dimension (LDZ, max(1,M)).
  • 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).
  • 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.
  • If JOBZ = 'N', then Z is not referenced.
  • 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. so plan ahead, bestie 🫶
• LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — WORK is COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL array, dimension (7*N).
• 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: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.

👑 Author 👑

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

Definition at line 237 of file chpevx.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay final sign-off, bestie 🎀 this page is LAPACK Version 3.12.0, footer path /home/abui...RC/chpevx.f(3), and there's no date printed on this footer — just the version and that path. periodt 💅✨