TESTING/LIN/zpbt01.f(3)

🦋 TESTING/LIN/zpbt01.f(3)

okay so this is the Library Functions Manual page for TESTING/LIN/zpbt01.f, and it's giving iconic subroutine-documentation energy. No cap.

🌸 NAME

TESTING/LIN/zpbt01.f

✨ SYNOPSIS

🛠️ Functions/Subroutines

• subroutine zpbt01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid) — ZPBT01

💖 Function/Subroutine Documentation

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)

ZPBT01

🎯 Purpose

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. literally the whole vibe of this routine.

🧸 Parameters

UPLO

UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

• = 'U': Upper triangular
• = 'L': Lower triangular

N

N is INTEGER. The number of rows and columns of the matrix A. N >= 0.

KD

KD is 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

A is 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

LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).

AFAC

AFAC is 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

LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).

RWORK

RWORK is DOUBLE PRECISION array, dimension (N).

RESID

RESID is 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.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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