TESTING/LIN/cpbt01.f(3)

🎀 NAME 🎀

TESTING/LIN/cpbt01.f — okay bestie, this is the manual page for cpbt01, and it lives in the LAPACK Library Functions Manual. It’s giving “reconstructs a Hermitian positive definite band matrix A” energy, and honestly? Iconic. ✨

---

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine cpbt01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
    CPBT01

---

🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, no cap:

   subroutine cpbt01 (character uplo, integer n, integer kd, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( ldafac, * )
       afac, integer ldafac, real, dimension( * ) rwork, real resid)
       CPBT01

🧚 Purpose 🧚

Okay so CPBT01 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. Math but make it fashion. 💅

🦋 Parameters 🦋

UPLO

UPLO is CHARACTER*1 — 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. Constraint: 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'. Constraint: KD >= 0.

A

A is COMPLEX 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 CPBTRF for further details.

LDA

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

AFAC

AFAC is COMPLEX 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 CPBTRF.

LDAFAC

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

RWORK

RWORK is REAL array, dimension (N) — that’s the whole vibe. 🫶

RESID

RESID is REAL — if UPLO = 'L', then norm(L*L' - A) / ( N * norm(A) * EPS ); if UPLO = 'U', then 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 cpbt01.f.

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

---

💖 Sign-off time, bestie 💖 Source/version check: LAPACK Version 3.12.0, page TESTING/LIN/cpbt01.f(3). The page doesn’t print a date, so I’m not inventing one — periodt. 🫶💅