TESTING/LIN/spst01.f(3)

✨ NAME ✨

okay so bestie, this is TESTING/LIN/spst01.f, from the Library Functions Manual, and it's the page for the spst01 subroutine. It's giving “numerical linear algebra but make it cute” energy, and we're gonna get through every single detail together 💅✨

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

subroutine spst01 (uplo, n, a, lda, afac, ldafac, perm, ldperm, piv,
           rwork, resid, rank)

• spst01 — 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 then 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. ✨

💜 Parameters 💜

• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. The number of rows and columns of the matrix A. N >= 0.
• A — REAL array, dimension (LDA,N). The original symmetric matrix A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N)
• AFAC — REAL array, dimension (LDAFAC,N). The factor L or U from the L*L' or U'*U factorization of A.
• LDAFAC — INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,N).
• PERM — REAL array, dimension (LDPERM,N). Overwritten with the reconstructed matrix, and then with the difference P*L*L'*P' - A (or P*U'*U*P' - A).
• LDPERM — INTEGER. The leading dimension of the array PERM. LDAPERM >= max(1,N).

bestie, yes, the page literally says LDAPERM right there — I'm quoting it exactly, no autocorrect, no cap 😭

• PIV — INTEGER array, dimension (N). PIV is such that the nonzero entries are P( PIV( K ), K ) = 1.
• RWORK — REAL array, dimension (N).
• RESID — REAL. If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ). If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ).
• RANK — INTEGER. number of nonzero singular values of A.

💖 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 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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cute little sign-off, bestie: this page comes from LAPACK Version 3.12.0, page TESTING/LIN/spst01.f(3), and the footer doesn't show a date — so I'm not inventing one, periodt 💋🫶