TESTING/LIN/zpbt02.f(3)

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version 3.12.1 · 2 versions
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okay bestie, welcome to TESTING/LIN/zpbt02.f(3) — from the Library Functions Manual, and it’s giving “residual check for a Hermitian banded solve” energy. 🎀

NAME 💅

TESTING/LIN/zpbt02.f — yes, that’s the whole name, iconic and to the point. 💖

SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine zpbt02 (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork,
     resid)
    ZPBT02

Function/Subroutine Documentation 💜

subroutine zpbt02 (character uplo, integer n, integer kd, integer nrhs,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb,
     double precision, dimension( * ) rwork, double precision resid)
    ZPBT02

Purpose 🌸

okay so ZPBT02 computes the residual for a solution of a Hermitian banded system of equations A*x = b:

RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)

where EPS is the machine precision. literally that’s the whole vibe. 🫶

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. 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.

NRHS 🌈

NRHS is INTEGER — the number of right hand sides. NRHS >= 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. periodt. 💅

LDA 🍓

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

X 🔥

X is COMPLEX*16 array, dimension (LDX,NRHS) — the computed solution vectors for the system of linear equations.

LDX 🧚

LDX is INTEGER — the leading dimension of the array X. LDX >= max(1,N).

B 💀

B is COMPLEX*16 array, dimension (LDB,NRHS) — on entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.

LDB 🙈

LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).

RWORK 🎀

RWORK is DOUBLE PRECISION array, dimension (N).

RESID 💖

RESID is DOUBLE PRECISION — the maximum over the number of right hand sides of

norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author 🫶

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

Definition at line 134 of file zpbt02.f. 📍

Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. no cap, that’s literally what it says. 😭

and that’s the sign-off bestie: LAPACK Version 3.12.0 for TESTING/LIN/zpbt02.f(3) — mwah 💋✨

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