SRC/zhbevd.f(3)

okay bestie, this is SRC/zhbevd.f(3) from the Library Functions Manual — a Fortran LAPACK page about zhbevd, and we are about to give band-matrix eigenvalues the group-chat treatment 💅✨

💖 NAME 💖

SRC/zhbevd.f

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🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

subroutine zhbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork,
           rwork, lrwork, iwork, liwork, info)

The vibe in one line: ZHBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices.

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🔥 Function/Subroutine Documentation 🔥

here is the whole signature, no cap:

subroutine zhbevd (character jobz, character uplo, integer n, integer kd,
    complex*16, dimension( ldab, * ) ab, integer ldab, double precision,
    dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

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

💫 Purpose 💫

okay so the purpose is literally this: ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

💖 Parameters 💖

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• 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 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. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.
• LDAB — LDAB is INTEGER
  • The leading dimension of the array AB. LDAB >= KD + 1.
• W — W is DOUBLE PRECISION array, dimension (N)
  • If INFO = 0, the eigenvalues in ascending order.
• Z — Z is COMPLEX*16 array, dimension (LDZ, N)
  • If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(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 COMPLEX*16 array, dimension (MAX(1,LWORK))
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER
  • The dimension of the array WORK.
  • If N <= 1, LWORK must be at least 1.
  • If JOBZ = 'N' and N > 1, LWORK must be at least N.
  • If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2.
  • If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (LRWORK)
  • On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
• LRWORK — LRWORK is INTEGER
  • The dimension of array RWORK.
  • If N <= 1, LRWORK must be at least 1.
  • If JOBZ = 'N' and N > 1, LRWORK must be at least N.
  • If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2.
  • If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK))
  • On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — LIWORK is INTEGER
  • The dimension of array IWORK.
  • If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
  • If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N .
  • If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
• INFO — INFO is INTEGER
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 207 of file zhbevd.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 this page is from LAPACK Version 3.12.0, source SRC/zhbevd.f(3), and that’s the whole vibe. periodt 🫶