SSBGVX(3)

📦 version 3.12.0, in opensuse-leap 16.0

🎀 NAME 🎀

okay so bestie, this is ssbgvx.f(3) from LAPACK, and the source path is literally this whole iconic little string:

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine SSBGVX (jobz, range, uplo, n, ka, kb, ab, ldab, bb, ldbb, q,
     ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)
     SSBGVX

👑 Function/Subroutine Documentation 👑

subroutine SSBGVX (character jobz, character range, character uplo, integer
     n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab,
     real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( ldq, * )
     q, integer ldq, real vl, real vu, integer il, integer iu, real abstol,
     integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer
     ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer,
     dimension( * ) ifail, integer info)
     SSBGVX

🦋 Purpose 🦋

okay so what does this queen actually do? SSBGVX computes selected eigenvalues, and optionally, 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. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, a range of values or a range of indices for the desired eigenvalues. 💅

🍓 Parameters 🍓

  • JOBZ — JOBZ is CHARACTER*1; = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. ✨
  • RANGE — RANGE is CHARACTER*1; = 'A': all eigenvalues will be found. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found. = 'I': the IL-th through IU-th eigenvalues will be found. 🎀
  • 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. 🔥

  • 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).

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. 🌈
  • Q — Q is REAL array, dimension (LDQ, N). If JOBZ = 'V', the n-by-n matrix used in the reduction of A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, and consequently C to tridiagonal form. If JOBZ = 'N', the array Q is not referenced. 💫
  • LDQ — LDQ is INTEGER. The leading dimension of the array Q. If JOBZ = 'N', LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N). 🌟
  • VL — VL is REAL. If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. 🍓
  • VU — VU is REAL. If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. 🍓
  • IL — IL is INTEGER. If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. 🎀
  • IU — IU is INTEGER. If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. 🎀
  • ABSTOL — ABSTOL is REAL. The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to
ABSTOL + EPS *   max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). 💀

  • M — M is INTEGER. The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. 👑
  • W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🌸
  • 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. 🦋
  • 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 (7*N). 💖
  • IWORK — IWORK is INTEGER array, dimension (5*N). 💖
  • IFAIL — IFAIL is INTEGER array, dimension (M). If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvalues that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. 🙈
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • <= N: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in IFAIL.
    • > N: SPBSTF returned an error code; i.e., if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. 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 291 ⭐

Definition at line 291 of file ssbgvx.f. 💅

💌 Author 💌

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mwah 💋 that’s the whole page, bestie — footer vibe is LAPACK, Version 3.12.0, and /home/abui...RC/ssbgvx.f(3). No date is shown in the footer, so I’m not inventing one — periodt. 👑💖

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