DSBGVX(3)

💅 DSBGVX(3) ✨ — Library Functions Manual

okay bestie, welcome to the DSBGVX page 🫶 the header source path vibe is /home/abui...RC/dsbgvx.f(3), and yes this is the LAPACK banded generalized symmetric-definite eigenproblem subroutine. Main character energy fr fr 👑

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🎀 NAME

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

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🌸 SYNOPSIS

🧚 Functions/Subroutines

subroutine DSBGVX (jobz, range, uplo, n, ka, kb, ab, ldab, bb, ldbb, q,
    ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)
    DSBGVX

• DSBGVX

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🔥 Function/Subroutine Documentation 🔥

Here’s the full signature so you can copy-paste it exactly, bestie 💖

💜 subroutine DSBGVX

subroutine DSBGVX (character jobz, character range, character uplo, integer
    n, integer ka, integer kb, double precision, dimension( ldab, * ) ab,
    integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb,
    double precision, dimension( ldq, * ) q, integer ldq, 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, dimension( * ) iwork, integer, dimension( * ) ifail,
    integer info)
    DSBGVX

✨ Purpose:

DSBGVX computes selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, a range of values or a range of indices for the desired eigenvalues.

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🌈 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 triangles of A and B are stored;
• = 'L': Lower triangles of A and B are stored.

⭐ N

N is INTEGER

The order of the matrices A and B. N >= 0.

⭐ KA

KA is INTEGER

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

⭐ KB

KB is INTEGER

The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.

⭐ AB

AB is DOUBLE PRECISION array, dimension (LDAB, N)

On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed. 💀

⭐ LDAB

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KA+1.

⭐ BB

BB is DOUBLE PRECISION array, dimension (LDBB, N)

On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows:

if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).

On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by DPBSTF.

⭐ LDBB

LDBB is INTEGER

The leading dimension of the array BB. LDBB >= KB+1.

⭐ Q

Q is DOUBLE PRECISION array, dimension (LDQ, N)

If JOBZ = 'V', the n-by-n matrix used in the reduction of A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, and consequently C 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 = 'N', LDQ >= 1. If JOBZ = 'V', LDQ >= 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 A to tridiagonal form.

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'). 🫠

⭐ 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)

If INFO = 0, the eigenvalues in ascending order.

⭐ Z

Z is DOUBLE PRECISION array, dimension (LDZ, N)

If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.

⭐ 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 (7*N)

⭐ IWORK

IWORK is INTEGER array, dimension (5*N)

⭐ IFAIL

IFAIL is INTEGER array, dimension (M)

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 eigenvalues 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
• <= N: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in IFAIL.
• > N: DPBSTF returned an error code; i.e., 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.

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👑 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 at line 291 of file dsbgvx.f.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, your LAPACK bestie 💖 — LAPACK Version 3.12.0, and the footer stamp is from /home/abui...RC/dsbgvx.f(3) 🎀✨