SRC/dsbgv.f(3)

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version 3.12.1 · 4 versions
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💅 SRC/dsbgv.f — like, the dsbgv manpage bestie

okay so this is a page from the LAPACK manual, section 3 (library functions, bestie, we're fancy). Buckle up, we're talking about dsbgv and honestly? she's iconic. 🌸

✨ SYNOPSIS ✨

🫶 Functions/Subroutines

  • subroutine dsbgv (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info) — literally the whole vibe of this page, it's DSBGV

💖 Function/Subroutine Documentation 💖

subroutine dsbgv (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 info)

DSBGV 👑 (yes she's all caps, she's that girl)

🦋 Purpose

okay so picture this: DSBGV 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. that's the whole assignment, no cap. ✨

🎀 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).
⚠️ On exit, the contents of AB are destroyed. she ate and left no crumbs, bestie. 💀

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(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 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 that Z**T*B*Z = I.

If JOBZ = 'N', then Z is not referenced. like, she's not even invited to the function, don't worry about her. 🙈

LDZ

  • LDZ is INTEGER — the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.

WORK

  • WORK is DOUBLE PRECISION array, dimension (3*N) 🔥

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.

Definition at line 175 of file dsbgv.f. 📍

💜 Author (the meta one) 💜

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page bestie, you're literally a LAPACK girlie now, periodt 💅✨

LAPACK — Version 3.12.0 · SRC/dsbgv.f(3) · mwah, kisses, go converge something 🎀🦋

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