ZHBEVX(3)

💅 NAME 💅

zhbevx.f(3) from the Library Functions Manual — okay bestie, this is the page for the LAPACK source file:

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

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🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

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

ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💖

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✨ Function/Subroutine Documentation ✨

subroutine ZHBEVX (character jobz, character range, character uplo, integer
    n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldq, * ) q, integer ldq, double precision vl,
    double precision vu, integer il, integer iu, double precision abstol,
    integer m, double precision, dimension( * ) w, complex*16, dimension(
    ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double
    precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer,
    dimension( * ) ifail, integer info)

ZHBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 🌸

🎀 Purpose: 🎀

Okay so the actual purpose, no cap: ZHBEVX 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. Periodt. 💅

💖 Parameters 💖

• JOBZ — is CHARACTER*1.
  • = 'N': compute eigenvalues only;
  • = 'V': compute eigenvalues and eigenvectors.
• 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 — is CHARACTER*1.
  • = 'U': upper triangle of A is stored;
  • = 'L': lower triangle of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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 — is COMPLEX*16 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 — is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.
• Q — is COMPLEX*16 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 — is INTEGER. The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N).
• 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 — 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 — 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 — 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 — 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 AB 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').

See by Demmel and Kahan, LAPACK Working Note #3. (yes, exactly like that in the source tea 🫖)

• 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 — is DOUBLE PRECISION array, dimension (N). The first M elements contain the selected eigenvalues in ascending order.
• Z — is COMPLEX*16 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 — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — is COMPLEX*16 array, dimension (N).
• RWORK — is DOUBLE PRECISION array, dimension (7*N).
• IWORK — is INTEGER array, dimension (5*N).
• 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 — 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 zhbevx.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. iykyk, bestie 🫶

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Okay that’s the whole page — footer tea, no invented date: LAPACK · Version 3.12.0 · /home/abui...RC/zhbevx.f(3) 🌈✨💜