SPBT01(3)

🎀 spbt01.f(3) — Library Functions Manual 🎀

okay so bestie, the page header vibe is /home/abui...IN/spbt01.f(3) and the manual name is Library Functions Manual. This is the LAPACK page for spbt01.f, and we are going to cover every single parameter with zero skips. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/spbt01.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine SPBT01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
    SPBT01

🦋 Function/Subroutine Documentation 🦋

subroutine SPBT01 (character uplo, integer n, integer kd, real, dimension(
       lda, * ) a, integer lda, real, dimension( ldafac, * ) afac, integer
       ldafac, real, dimension( * ) rwork, real resid)

SPBT01 ✨

🎯 Purpose 🎯

So SPBT01 reconstructs a symmetric positive definite band matrix A from its L*L' or U'*U factorization and computes the residual

norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),

where EPS is the machine epsilon, L' is the conjugate transpose of L, and U' is the conjugate transpose of U. no cap, that’s the whole purpose. 🫶

💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. It’s the number of rows and columns of the matrix A. N >= 0.
• KD — KD is INTEGER. It’s the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• A — A is REAL array, dimension (LDA,N). It’s the original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See SPBTRF for further details.
• LDA — LDA is INTEGER. It’s the leading dimension of the array A. LDA >= max(1,KD+1).
• AFAC — AFAC is REAL array, dimension (LDAFAC,N). It’s the factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by SPBTRF.
• LDAFAC — LDAFAC is INTEGER. It’s the leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
• RWORK — RWORK is REAL array, dimension (N).
• RESID — RESID is REAL. 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 ).

👑 Author 👑

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

📌 Definition at line 117 of file spbt01.f. 📌

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off bestie: the footer says LAPACK Version 3.12.0 and /home/abui...IN/spbt01.f(3) — no date listed, so that’s the source/version vibe periodt. 💖✨