DSTEQR2(l)

DSTEQR2 💅✨

ok so bestie, welcome to a LAPACK routine, and not just any routine — this is a modified one, from LAPACK routine version 2.0. She's a little special, a little niche, and honestly kind of iconic for it. 🎀

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🌸 NAME 🌸

DSTEQR2 — it's a modified version of LAPACK routine DSTEQR. that's the whole vibe. no cap.

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✨ SYNOPSIS ✨

SUBROUTINE DSTEQR2( COMPZ, N, D, E, Z, LDZ, NR, WORK, INFO )

    CHARACTER       COMPZ

    INTEGER         INFO, LDZ, N, NR

    DOUBLE          PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

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🦋 PURPOSE 🦋

okay so real talk: DSTEQR2 is a modified version of LAPACK routine DSTEQR. she computes all eigenvalues and, if you want them, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. slay.

and here's the tea — the way she's different from DSTEQR is that DSTEQR2 is modified to let each ScaLAPACK process running DSTEQR2 perform updates on a distributed matrix Q. distributed queen behavior honestly 💅

if you wanna know the proper usage of DSTEQR2, you can glean it from examining ScaLAPACK's PDSYEV. that's where the lore lives. iykyk 🫶

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👑 ARGUMENTS 👑

• COMPZ (input) CHARACTER*1 — the main character deciding what we're even doing here:
  • = 'N': compute eigenvalues only. just the numbers, no vectors, we're keeping it simple bestie.
  • = 'I': compute eigenvalues and eigenvectors of the tridiagonal matrix. ⚠️ heads up tho — Z must be initialized to the identity matrix by PDLASET or DLASET prior to entering this subroutine. don't skip that step, fr fr.
• N (input) INTEGER — the order of the matrix. N >= 0. that's it that's the rule. 💜
• D (input/output) DOUBLE PRECISION array, dimension (N) — on entry, the diagonal elements of the tridiagonal matrix. on exit, if INFO = 0, the eigenvalues in ascending order. glow up arc honestly ✨
• E (input/output) DOUBLE PRECISION array, dimension (N-1) — on entry, the (n-1) subdiagonal elements of the tridiagonal matrix. on exit, E has been destroyed. 💀 she's gone. not coming back. the sacrifice was necessary.
• Z (local input/local output) DOUBLE PRECISION array, global dimension (N, N), local dimension (LDZ, NR) — on entry, if COMPZ = 'V', then Z contains the orthogonal matrix used in the reduction to tridiagonal form. on exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. and if COMPZ = 'N', then Z is not referenced — she's simply not invited to the function. 🙈
• LDZ (input) INTEGER — the leading dimension of the array Z. LDZ >= 1, and if eigenvectors are desired, then LDZ >= max(1,N). respect the constraints bestie. 🎀
• NR (input) INTEGER — NR = MAX(1, NUMROC( N, NB, MYPROW, 0, NPROCS ) ). if COMPZ = 'N', then NR is not referenced. she said "i'm not needed today" 💅
• WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2*N-2)) — if COMPZ = 'N', then WORK is not referenced. also sitting this one out.
• INFO (output) INTEGER — the receipts, the vibe check, the final report:
  • = 0: successful exit. 🎉 we ate.
  • < 0: if INFO = -i, the i-th argument had an illegal value. someone did not read the rules 😭
  • > 0: the algorithm has failed to find all the eigenvalues in a total of 30*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is orthogonally similar to the original matrix. not the ending we wanted but it's still mathematically something, periodt. 💀

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gentle reminder bestie: E gets destroyed, Z and NR and WORK might not even be referenced depending on COMPZ, and if INFO > 0 you got convergence drama. read your outputs before you trust them. 🫶

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and that's the whole page, my love 🌈 mwah. this cutie is a modified LAPACK routine, dated 12 May 1997 — vintage but still serving. go forth and diagonalize, bestie. 🎀💖✨🦋🌸