SRC/sstevd.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 SRC/sstevd.f — from the LAPACK Library Functions Manual, bestie 🎀

okay so picture this: it's a Fortran file, it's called SRC/sstevd.f, and it's about to make your tridiagonal matrix very famous. let's get into it ✨

🌸 NAME 🌸

SRC/sstevd.f — the file, the moment, the legend. no cap.

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine sstevd (jobz, n, d, e, z, ldz, work, lwork, iwork, liwork,
    info)

SSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💖

🎀 Function/Subroutine Documentation 🎀

subroutine sstevd (character jobz, integer n, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( ldz, * ) z, integer ldz, real,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

SSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. that's the whole assignment and she ate 🔥

✨ Purpose ✨

!> !> SSTEVD computes all eigenvalues and, optionally, eigenvectors of a !> real symmetric tridiagonal matrix. If eigenvectors are desired, it !> uses a divide and conquer algorithm. !> !>

so like — real symmetric tridiagonal matrix, all the eigenvalues, and if you want eigenvectors too she'll hook you up, and she does it with a divide and conquer algorithm, which is genuinely iconic behavior 👑

🌈 Parameters 🌈

  • JOBZ
!> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !>
  • N
!> N is INTEGER !> The order of the matrix. N >= 0. !>
  • D
!> D is REAL array, dimension (N) !> On entry, the n diagonal elements of the tridiagonal matrix !> A. !> On exit, if INFO = 0, the eigenvalues in ascending order. !>
  • E
!> E is REAL array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix A, stored in elements 1 to N-1 of E. !> On exit, the contents of E are destroyed. !>
⚠️ heads up bestie — E does not survive this. on exit the contents of E are destroyed. she's not sorry either 💀
  • Z
!> Z is REAL array, dimension (LDZ, N) !> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal !> eigenvectors of the matrix A, with the i-th column of Z !> holding the eigenvector associated with D(i). !> If JOBZ = 'N', then Z is not referenced. !>
🫶 note: if JOBZ = 'N', Z is literally not referenced. she doesn't even look at it. not one glance.
  • 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 (LWORK) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
(yes the original really does have that dramatic line break in the middle of the dimension clause. we respect the formatting choices 😭)
  • LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. !> If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. !> If JOBZ = 'V' and N > 1 then LWORK must be at least !> ( 1 + 4*N + 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. !>
💡 the workspace-query glow-up: pass LWORK = -1 and she just tells you the optimal sizes of WORK and IWORK, drops them into the first entries of the WORK and IWORK arrays, and XERBLA keeps its mouth shut about LWORK or LIWORK. no error, just vibes ✨
  • IWORK
!> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. !>
  • LIWORK
!> LIWORK is INTEGER !> The dimension of the array IWORK. !> If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. !> If JOBZ = 'V' and N > 1 then LIWORK must be at least 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. !>
same deal as LWORK but for the integer side: LIWORK = -1 means a workspace query, she computes the optimal sizes, hands them back as the first entries of WORK and IWORK, and XERBLA stays quiet about LWORK or LIWORK 🧚
  • INFO
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the algorithm failed to converge; i !> off-diagonal elements of E did not converge to zero. !>
🚨 okay so INFO > 0 means the algorithm failed to converge and i off-diagonal elements of E did not converge to zero. that's the bad timeline. INFO = 0 is the slay timeline 💖

👑 Author 👑

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

Definition at line 155 of file sstevd.f. 📍

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (she was built different, by robots, and we love that for her 🤖💅)

🍓 bye bestie!! this page is from LAPACK, Version 3.12.0, file SRC/sstevd.f(3) — go get those eigenvalues, iykyk 🌟🎀
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