SRC/chbevx.f(3)

💖 NAME 💖

SRC/chbevx.f is the star of this page, bestie — and it comes from the Library Functions Manual. We're talking about the chbevx subroutine, and it's a whole vibe. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine chbevx (jobz, range, uplo, n, kd, ab, ldab, q, ldq, vl, vu,
    il, iu, abstol, m, w, z, ldz, work, rwork, iwork, ifail, info)

CHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. ✨

🔥 Function/Subroutine Documentation 🔥

subroutine chbevx (character jobz, character range, character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldq, * ) q, integer ldq, 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)

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

🦋 Purpose 🦋

Okay so the purpose is literally this: CHBEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. That's the assignment, no cap. 💜

🎀 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.

💜 KD

KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

💜 AB

AB is a COMPLEX array, dimension (LDAB, N).

On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the reduction to tridiagonal form.

💜 LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.

💜 Q

Q is a COMPLEX array, dimension (LDQ, N).

• If JOBZ = 'V', the N-by-N unitary matrix used in the reduction to tridiagonal form.
• If JOBZ = 'N', the array Q is not referenced.

💜 LDQ

LDQ is INTEGER. The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= 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 AB 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').

Also, the page drops this reference:

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 a REAL array, dimension (N). The first M elements contain the selected eigenvalues in ascending order.

💜 Z

Z is a 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.

💜 LDZ

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

💜 WORK

WORK is a COMPLEX array, dimension (N).

💜 RWORK

RWORK is a REAL array, dimension (7*N).

💜 IWORK

IWORK is an INTEGER array, dimension (5*N).

💜 IFAIL

IFAIL is an 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 264 of file chbevx.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

💖 That's the whole tea, bestie — this page is from LAPACK Version 3.12.0 and lives at SRC/chbevx.f(3). Slay! 💅✨