SPST01(3)

💅 SPST01(3) — like, the LAPACK testing routine for reconstructing a symmetric positive semidefinite matrix, bestie ✨

okay so first things first: this page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/spst01.f and it's part of the LAPACK library functions manual (3). That's the whole vibe. It's a testing routine, which means it exists to check that other routines did their job right — the hype squad of linear algebra, lowkey. 🎀

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

subroutine SPST01 (uplo, n, a, lda, afac, ldafac, perm, ldperm, piv,
    rwork, resid, rank)

SPST01 🫶

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🦋 Function/Subroutine Documentation 🦋

subroutine SPST01 (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( ldafac, * ) afac, integer ldafac, real,
    dimension( ldperm, * ) perm, integer ldperm, integer, dimension( * )
    piv, real, dimension( * ) rwork, real resid, integer rank)

SPST01 ⭐

👑 Purpose:

!> !> SPST01 reconstructs a symmetric positive semidefinite matrix A !> from its L or U factors and the permutation matrix P and computes !> the residual !> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or !> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ), !> where EPS is the machine epsilon. !>

So like, it takes your factors, rebuilds A from them, throws the permutation matrix P into the mix, and then measures how far off the reconstruction is from the original. It's giving "trust but verify" energy. 💖

💜 Parameters

• UPLO — okay so UPLO is CHARACTER*1 and it tells us which triangular half of the symmetric matrix A is actually stored:
  • = 'U': Upper triangular 🌈
  • = 'L': Lower triangular 🌸
• N — N is INTEGER, the number of rows and columns of the matrix A (it's square, obvi). Constraint: N >= 0. ✨
• A — A is REAL array, dimension (LDA,N). It's the original symmetric matrix A, the main character. 👑
• LDA — LDA is INTEGER, the leading dimension of the array A. Constraint: LDA >= max(1,N). Don't skimp on this one bestie. 🫶
• AFAC — AFAC is REAL array, dimension (LDAFAC,N), holding the factor L or U from the L*L' or U'*U factorization of A. 🎀
• LDAFAC — LDAFAC is INTEGER, the leading dimension of the array AFAC. Constraint: LDAFAC >= max(1,N). 💅
• PERM — PERM is REAL array, dimension (LDPERM,N), and it gets overwritten with the reconstructed matrix, and then with the difference P*L*L'*P' - A (or P*U'*U*P' - A). So yeah, it's not coming back the same, fair warning 🙈
• LDPERM — LDPERM is INTEGER, the leading dimension of the array PERM. Constraint: LDAPERM >= max(1,N). (yes, the original really does spell it LDAPERM here — we don't fix, we report 🫡)
• PIV — PIV is INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV( K ), K ) = 1. That's the permutation, periodt. 🔥
• RWORK — RWORK is REAL array, dimension (N). That's it, that's the whole description. Scratch space doing its little job. 🧚
• RESID — RESID is REAL, the actual residual:
  • If UPLO = 'L', it's norm(L*L' - A) / ( N * norm(A) * EPS )
  • If UPLO = 'U', it's norm(U'*U - A) / ( N * norm(A) * EPS )

iykyk 💀

• RANK — RANK is INTEGER, the number of nonzero singular values of A. 💖

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🌟 Author 🌟

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

Definition at line 132 of file spst01.f. 📍

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🎀 Author (the meta one) 🎀

Generated automatically by Doxygen for LAPACK from the source code. Not me writing fanfic, the robots did it. 🤖✨

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k bye bestie, go check those residuals 💅 — this iconic page is from LAPACK, Version 3.12.0, and it was served fresh from /home/abui...IN/spst01.f(3). Slay 🦋🌸