DSBGVD(3)

💅 DSBGVD(3) 💅

Manual name, folded in: Library Functions Manual. Page header vibe: /home/abui...RC/dsbgvd.f(3). Bestie, this is the whole glow-up of the DSBGVD page from LAPACK, and yes we are reading all of it. 💖

🌸 NAME 🌸

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

That’s the file, no cap. This is the Library Functions Manual page for /home/abui...RC/dsbgvd.f(3). ✨

🌈 SYNOPSIS 🌈

🎀 Functions/Subroutines 🎀

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

• DSBGVD — the icon, the moment, the subroutine. 💅

✨ Function/Subroutine Documentation ✨

🫶 subroutine DSBGVD 🫶

subroutine DSBGVD (character jobz, character uplo, integer n, integer ka,
    integer kb, double precision, dimension( ldab, * ) ab, integer ldab,
    double precision, dimension( ldbb, * ) bb, integer ldbb, double
    precision, dimension( * ) w, double precision, dimension( ldz, * ) z,
    integer ldz, double precision, dimension( * ) work, integer lwork,
    integer, dimension( * ) iwork, integer liwork, integer info)

DSBGVD again, because main character energy. 👑

💖 Purpose 💖

DSBGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. 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 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 DOUBLE PRECISION array, dimension (LDAB, N). On entry, the upper or lower triangle of the symmetric 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).

💀 heads up: 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 DOUBLE PRECISION array, dimension (LDBB, N). On entry, the upper or lower triangle of the symmetric 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(ka+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**T*S, as returned by DPBSTF.

• 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 DOUBLE PRECISION 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 Z**T*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 >= max(1,N).
• WORK — WORK is DOUBLE PRECISION 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 >= 2*N.
If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.

• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
• LIWORK — LIWORK is INTEGER. The dimension of the 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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 DPBSTF
          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 219 of file dsbgvd.f. ⭐

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole page, bestie. Footer/source/version vibe check: LAPACK, Version 3.12.0, page /home/abui...RC/dsbgvd.f(3) — and the footer line doesn’t print a date, just so you know. Bye bestie 💖✨🎀