SSBGVD(3)

💅 SSBGVD 💅

okay bestie, welcome to the LAPACK Library Functions Manual, where the vibes are Fortran and the math is real. today's main character is SSBGVD, and she lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssbgvd.f 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine SSBGVD (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info) — that's her, that's the icon 👑

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

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🎀 Function/Subroutine Documentation 🎀

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

🌸 Purpose 🌸

so what does she actually do? SSBGVD 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. slay algorithm honestly 💅

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🦋 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 REAL 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).

on exit, the contents of AB are destroyed. gone. reduced to atoms 💀

LDAB

LDAB is INTEGER

the leading dimension of the array AB. LDAB >= KA+1.

BB

BB is REAL 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).

yes bestie, that is ka sitting right there in the BB entry — i'm copying it exactly as the source says it, don't come for me 🙈

on exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF.

LDBB

LDBB is INTEGER

the leading dimension of the array BB. LDBB >= KB+1.

W

W is REAL array, dimension (N)

if INFO = 0, the eigenvalues in ascending order. so tidy, so organized, we love a sorted queen ✨

Z

Z is REAL 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. she's not even invited to the function call 🫶

LDZ

LDZ is INTEGER

the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

WORK

WORK is REAL 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 >= 3*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. it's giving "just asking, not committing" and honestly? same 😌

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. we love a happy ending 💖
• < 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 SPBSTF returned INFO = i: B is not positive definite. the factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

🚨 real talk: that last one is a hard stop. B isn't positive definite, the factorization bails, and you get no eigenvalues and no eigenvectors. not a single one. periodt.

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👑 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

definition at line 219 of file ssbgvd.f.

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🍓 Author (the meta one) 🍓

generated automatically by Doxygen for LAPACK from the source code. no cap, a robot wrote the original and i just gave it a personality 💅

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and that's the whole page bestie 🧚‍♀️ this was LAPACK Version 3.12.0, served fresh from /home/abui...RC/ssbgvd.f(3) — go forth, pass LWORK correctly, and slay 💜