ZPBT01(3)

💅 ZPBT01(3) 💅

okay so bestie, we are officially in the Library Functions Manual and this page is ZPBT01(3). It's giving "Hermitian band matrix reconstruction with main character energy", and we're gonna walk through every single detail without skipping a thing. 🫶

📛 NAME

This page is for this exact file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zpbt01.f

✨ SYNOPSIS

Functions/Subroutines

subroutine ZPBT01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
           ZPBT01

📚 Function/Subroutine Documentation

Here's the full subroutine signature, exactly as printed:

subroutine ZPBT01 (character uplo, integer n, integer kd, complex*16,
     dimension( lda, * ) a, integer lda, complex*16, dimension( ldafac, * )
     afac, integer ldafac, double precision, dimension( * ) rwork, double
     precision resid)

The label right under that signature is just ZPBT01.

🎯 Purpose

Okay so here's the vibe: ZPBT01 reconstructs a Hermitian 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. slay. 🌈

🌸 Parameters

• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — INTEGER. The number of rows and columns of the matrix A. N >= 0.
• KD — INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). The original Hermitian 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 ZPBTRF for further details.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
• AFAC — COMPLEX*16 array, dimension (LDAFAC,N). 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 ZPBTRF.
• LDAFAC — INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
• RWORK — DOUBLE PRECISION array, dimension (N).
• RESID — DOUBLE PRECISION. If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ); if UPLO = 'U', 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 118 of file zpbt01.f. iconic.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole page, bestie. Source/version is LAPACK, Version 3.12.0, and the footer path is /home/abui...IN/zpbt01.f(3). periodt. 💖✨