SRC/dstev.f(3)

💖 SRC/dstev.f 💖

okay bestie, welcome to dstev.f, part of the Library Functions Manual — this is a Fortran LAPACK gem and honestly it's kind of iconic. it's giving "quiet math baddie who does all the work." let's get into it ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine dstev (jobz, n, d, e, z, ldz, work, info) — DSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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🦋 Function/Subroutine Documentation 🦋

✨ subroutine dstev (character jobz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info) ✨

DSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices — no cap, that's literally what it does 🫶

🎀 Purpose:

!>
!> DSTEV computes all eigenvalues and, optionally, eigenvectors of a
!> real symmetric tridiagonal matrix A.
!>

so yeah, it's out here solving the whole eigenvalue problem for a real symmetric tridiagonal matrix A. all of them. every single one. main character energy 💅

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💜 Parameters

• JOBZ — JOBZ is CHARACTER*1, and it's the vibe check for what you actually want:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
• N — N is INTEGER, the order of the matrix. N >= 0. that's it, that's the size 🌈
• D — D is DOUBLE PRECISION array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, if INFO = 0, the eigenvalues in ascending order. so it enters as input and leaves as a whole glow-up 😭✨
• E — E is DOUBLE PRECISION 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. yeah. destroyed. gone. not me being dramatic, that's literally the manpage 🫣
• Z — Z is DOUBLE PRECISION 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. she said "don't perceive me" 🙈
• LDZ — LDZ is INTEGER, the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). read that constraint twice bestie, it's not optional 💅
• WORK — WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)). If JOBZ = 'N', WORK is not referenced. it's just chilling in the background, unbothered 🦋
• INFO — INFO is INTEGER, the final report card:
  • = 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 a positive INFO is the "it tried its best but no" situation — the algorithm failed to converge and i off-diagonal elements of E didn't hit zero. not a vibe, but now you know 💀

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👑 Author

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

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🌟 Definition at line 115 of file dstev.f.

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🧚 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. so this page wasn't even hand-written, it was born this way 💖

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and that's the whole page, bestie — <rainbow>LAPACK, Version 3.12.0, page SRC/dstev.f(3)</rainbow> 🎀 thanks for coming to my TED talk, go compute some eigenvalues, ily 🫶✨💜