SRC/chbevd.f(3)

🌸 NAME 🌸

SRC/chbevd.f — this is the Library Functions Manual page for the file itself, bestie. We're talking about the chbevd subroutine, and yes, it's giving linear algebra main character energy 💅.

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💅 SYNOPSIS 💅

🌈 Functions/Subroutines 🌈

subroutine chbevd (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork,
    rwork, lrwork, iwork, liwork, info)
     CHBEVD computes the eigenvalues and, optionally, the left and/or
    right eigenvectors for OTHER matrices

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🎀 Function/Subroutine Documentation 🎀

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

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

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✨ Purpose ✨

CHBEVD 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. Obsessed with her divide and conquer era. 🌸

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🧚 Parameters 🧚

• JOBZ — is CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• 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 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 — is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.
• W — is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• Z — is COMPLEX 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. Not even looked at. Respect. 🫶

• LDZ — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — is COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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. Workspace query era, iykyk. 🔥

• RWORK — is REAL array, dimension (LRWORK). On exit, if INFO = 0, RWORK(1) returns the optimal 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 — is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal 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 — 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.

If it's negative, somebody fed an argument illegal values. If it's positive, the algorithm said "bestie I tried but it did not converge." 😭

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👑 Author 👑

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

Definition at line 207 of file chbevd.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page — LAPACK Version 3.12.0, from SRC/chbevd.f(3), mwah 💖✨🎀