SSYEVX(3)

💖 ssyevx.f(3) — Library Functions Manual, bestie 💖

okay so the header title/path vibe is /home/abui...RC/ssyevx.f(3) and the manual name is Library Functions Manual — we're in LAPACK land and it's giving linear algebra main character energy. 🫶

🌸 NAME 🌸

This page's NAME is literally this path, no cap:

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

SSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 💅

📚 Function/Subroutine Documentation 📚

subroutine SSYEVX (character jobz, character range, character uplo, integer
    n, real, dimension( lda, * ) a, integer lda, 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
    lwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail,
    integer info)

SSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

🎀 Purpose 🎀

Okay bestie, the whole point: SSYEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. You get to choose which ones by specifying either a range of values or a range of indices for the desired eigenvalues. It's literally a selection menu for eigenvalues. ✨

💅 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.

A

A is REAL 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.

LDA

LDA is INTEGER

The leading dimension of the array A. LDA >= max(1,N).

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 A 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 this reference line: 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)

On normal exit, the first M elements contain 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 (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 >= 1, when N <= 1; otherwise 8*N. For optimal efficiency, LWORK >= (NB+3)*N, where NB is the max of the blocksize for SSYTRD and SORMTR 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: 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 250 of file ssyevx.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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