SRC/chbgvx.f(3)

okay bestie, welcome to the SRC/chbgvx.f(3) page from the Library Functions Manual — yes, that exact manual name, and yes we are getting into it 💅

💅 NAME 💅

SRC/chbgvx.f — that’s the name entry, straight up, no extra lore.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

🌸 Function/Subroutine Documentation 🌸

subroutine chbgvx (character jobz, character range, character uplo, integer
    n, integer ka, integer kb, complex, dimension( ldab, * ) ab, integer
    ldab, complex, dimension( ldbb, * ) bb, integer ldbb, 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)
    CHBGVX

🦋 Purpose 🦋

okay so CHBGVX computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 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. iconic behavior fr fr 👑

🌈 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 COMPLEX array, dimension (LDAB, N). On entry, the upper or lower triangle of the Hermitian 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 COMPLEX array, dimension (LDBB, N). On entry, the upper or lower triangle of the Hermitian 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(kb+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**H*S, as returned by CPBSTF.
• LDBB — LDBB is INTEGER. The leading dimension of the array BB. LDBB >= KB+1.
• Q — Q is COMPLEX 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 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').
• 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 eigenvalues in ascending order.
• Z — Z is COMPLEX 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 that Z**H*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 >= N.
• WORK — WORK is COMPLEX array, dimension (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, and i is: <= N: then i eigenvectors failed to converge. Their indices are stored in array IFAIL. > N: if INFO = N + i, for 1 <= i <= N, then CPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 💀

👑 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

Definition at line 297 of file chbgvx.f.

👑 Author 👑

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and that’s the whole page, bestie — the footer vibes are LAPACK Version 3.12.0 and the page is SRC/chbgvx.f(3). periodt. 💖✨🦋