SSPEVX(3)

hey bestie! 💖 welcome to the sspevx.f(3) page from the Library Functions Manual — this is the LAPACK page where SSPEVX lives, and it’s about to be your new fave for selected eigenvalues/eigenvectors of a real symmetric matrix in packed storage. No cap. ✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sspevx.f — literally the source file path this page is for. That’s the name section, and yes it’s giving “source file realness”. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine SSPEVX (jobz, range, uplo, n, ap, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info) — SSPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices.

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

🫶 Function/Subroutine Documentation 🫶

okay so here’s the full function/subroutine doc, bestie 🌈

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

SSPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 💫

🌟 Purpose 🌟

The doc comment says: SSPEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Periodt. 👑

💅 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 REAL array, dimension (N*(N+1)/2).

On entry, the upper or lower triangle of the symmetric 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. 🌀

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').

There’s also a reference line that literally says: 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.

Z

Z is REAL 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. 🫡

LDZ

LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

WORK

WORK is REAL array, dimension (8*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 231 of file sspevx.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that’s the whole page, bestie — mwah! 💋 The footer energy is LAPACK Version 3.12.0 and the page path /home/abui...RC/sspevx.f(3); the original footer doesn’t show a date, so no fake date here. 🫶✨