SRC/zhbgvd.f(3)

💖 SRC/zhbgvd.f(3) — ZHBGVD, but make it cute 💖

okay so bestie, this is the SRC/zhbgvd.f(3) page from the Library Functions Manual, and we're talking about the <rainbow>ZHBGVD</rainbow> subroutine. She computes eigenvalues and optionally eigenvectors for a complex generalized Hermitian-definite banded eigenproblem, and honestly? main character energy. 💅

🌸 NAME 🌸

SRC/zhbgvd.f — that's the file, periodt. The whole page is serving this one subroutine.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zhbgvd (...) — ZHBGVD

subroutine zhbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
    work, lwork, rwork, lrwork, iwork, liwork, info)
    ZHBGVD

🔥 Function/Subroutine Documentation 🔥

💅 subroutine zhbgvd 💅

subroutine zhbgvd (character jobz, character uplo, integer n, integer ka,
    integer kb, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldbb, * ) bb, integer ldbb, 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)
    ZHBGVD

🦋 Purpose 🦋

okay so <hotpink>ZHBGVD</hotpink> 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. If eigenvectors are desired, it uses a divide and conquer algorithm. No cap, that's the whole vibe. ✨

🍓 Parameters 🍓

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• 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*16 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*16 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 ZPBSTF.

• LDBB — LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+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 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*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 >= 1.
  • If JOBZ = 'N' and N > 1, LWORK >= N.
  • If JOBZ = 'V' and N > 1, LWORK >= 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 (MAX(1,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 >= 1.
  • If JOBZ = 'N' and N > 1, LRWORK >= N.
  • If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1.
  • If JOBZ = 'V' and N > 1, LIWORK >= 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, and i is:
    • <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
    • > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF 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 243 of file zhbgvd.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page! mwah 💋 this gem is from LAPACK Version 3.12.0, page SRC/zhbgvd.f(3). no date in the footer, but the slay is eternal. 🫶