TESTING/LIN/dgbt05.f(3)

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💖 TESTING/LIN/dgbt05.f 💖

okay bestie, we're in the Library Functions Manual and this page is all about TESTING/LIN/dgbt05.f — LAPACK's little testing subroutine moment. Let's get into it, no cap. ✨

💅 NAME 💅

TESTING/LIN/dgbt05.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine dgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx,
           xact, ldxact, ferr, berr, reslts)
           DGBT05

🌈 Function/Subroutine Documentation 🌈

subroutine dgbt05 (character trans, integer n, integer kl, integer ku,
       integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( ldx, * ) x, integer ldx, double precision, dimension( ldxact,
       * ) xact, integer ldxact, double precision, dimension( * ) ferr, double
       precision, dimension( * ) berr, double precision, dimension( * ) reslts)

DGBT05

🎯 Purpose 🎯

Okay so DGBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general band matrix of order n with kl subdiagonals and ku superdiagonals and op(A) = A or A**T, depending on TRANS. 💖

Then the receipts:

RESLTS(1) = test of the error bound
          = norm(X - XACT) / ( norm(X) * FERR )

A large value is returned if this ratio is not less than one. 🚨

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

No skipping, bestie — that's the whole formula vibe. 🧮✨

🧾 Parameters 🧾

🔤 TRANS

TRANS is CHARACTER*1. It specifies the form of the system of equations:

  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)

🔢 N

N is INTEGER. It's the number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0. 🫶

🔢 KL

KL is INTEGER. It's the number of subdiagonals within the band of A. KL >= 0.

🔢 KU

KU is INTEGER. It's the number of superdiagonals within the band of A. KU >= 0.

🔢 NRHS

NRHS is INTEGER. It's the number of columns of the matrices X, B, and XACT. NRHS >= 0.

🧱 AB

AB is a DOUBLE PRECISION array, dimension (LDAB,N). It's the original band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

🧱 LDAB

LDAB is INTEGER. It's the leading dimension of the array AB. LDAB >= KL+KU+1. don't mess this one up! 😭

🧱 B

B is a DOUBLE PRECISION array, dimension (LDB,NRHS). These are the right hand side vectors for the system of linear equations.

🧱 LDB

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

🧱 X

X is a DOUBLE PRECISION array, dimension (LDX,NRHS). These are the computed solution vectors. Each vector is stored as a column of the matrix X.

🧱 LDX

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

🧱 XACT

XACT is a DOUBLE PRECISION array, dimension (LDX,NRHS). These are the exact solution vectors. Each vector is stored as a column of the matrix XACT.

🧱 LDXACT

LDXACT is INTEGER. It's the leading dimension of the array XACT. LDXACT >= max(1,N).

📏 FERR

FERR is a DOUBLE PRECISION array, dimension (NRHS). It's the estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.

📏 BERR

BERR is a DOUBLE PRECISION array, dimension (NRHS). It's the componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).

📊 RESLTS

RESLTS is a DOUBLE PRECISION array, dimension (2). It's the maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )

👑 Author 👑

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

Definition at line 174 of file dgbt05.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

💖 And that's the page, bestie! This iconic little number is from LAPACK Version 3.12.0, for TESTING/LIN/dgbt05.f(3) — slay and goodbye! 💅✨

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