/home/abui...RC/ssbgv.f(3)

💅 SSBGV — ssbgv.f

okay bestie, so this page is from the LAPACK Library Functions Manual, and the file it's documenting is literally:

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

no cap, that's the whole path. it's giving deep in the build tree energy 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssbgv.f — that's it, that's the name, the manpage literally just names the source file 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SSBGV (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
    work, info)

SSBGV 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine SSBGV (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
    info)

SSBGV 💫 (yes, again — the page says it twice, so we say it twice, periodt)

💖 Purpose 💖

!> !> SSBGV 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. !>

so like, tl;dr: it hunts down all the eigenvalues (and the eigenvectors too if you ask nicely 🥺) of a real generalized symmetric-definite banded eigenproblem. the form is A*x=(lambda)*B*x. A and B are assumed symmetric and banded, and B has to be positive definite — that part is non-negotiable, bestie. 🚨

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🎀 Parameters 🎀

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

so like, eigenvalues only? 'N'. the whole package deal, vectors included? 'V'. choose your fighter 💅

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.

which triangle are we storing, bestie? upper or lower, pick one 🌈

• N — N is INTEGER
  • The order of the matrices A and B. N >= 0.

(and yes, zero is allowed, >= is not a suggestion 💀)

• 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.

KA is for A, KB is for B. iconic symmetry, we love to see it ✨

• 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. 😭 literally gone. don't come crying to me, she's been through enough.
• 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(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**T*S, as returned by SPBSTF.

so BB gets redecorated on the way out 🎨 it comes back holding S from that split Cholesky moment.

• 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.

ascending. sorted. 10/10 organized 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 that Z**T*B*Z = I.
  • If JOBZ = 'N, then Z is not referenced.

not even looked at. Z is off living her best life, unbothered 🙈

• LDZ — LDZ is INTEGER
  • The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.
• WORK — WORK is REAL array, dimension (3*N)

that's 3*N bestie, not N, not 2*N, three whole N's of workspace 🍓

• 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 SPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

fr fr read that last one carefully: if B isn't positive definite, the factorization of B could not be completed and no eigenvalues or eigenvectors were computed. nothing. nada. the whole thing just stops. 💀 that's the vibe check failing, hard.

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👑 Author 👑

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

the whole squad contributed, we stan a collaborative effort 🫶

Definition at line 175 of file ssbgv.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (not a human, a machine wrote this, and honestly? slay 🤖✨)

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and that's the page, bestie! 💜 sign-off time: this whole thing is LAPACK, Version 3.12.0, documented at /home/abui...RC/ssbgv.f(3) 🎀🦋🌸