TESTING/LIN/cgbt05.f(3)

🌸 NAME 🌸

okay so bestie, this page is TESTING/LIN/cgbt05.f — and in the Library Functions Manual it shows up as TESTING/LIN/cgbt05.f(3). That’s the whole name vibe. 💖

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine cgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx,
           xact, ldxact, ferr, berr, reslts)

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🦋 Function/Subroutine Documentation 🦋

   subroutine cgbt05 (character trans, integer n, integer kl, integer ku,
       integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex,
       dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x,
       integer ldx, complex, dimension( ldxact, * ) xact, integer ldxact, real,
       dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * )
       reslts)

CGBT05 👑

🎯 Purpose 🎯

CGBT05 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, A**T, or A**H, depending on TRANS. slay. 💅

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

💅 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. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0. 💖

KL

KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.

NRHS

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

AB

AB is COMPLEX array, dimension (LDAB,N). 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. The leading dimension of the array AB. LDAB >= KL+KU+1. 🫶

B

B is COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.

LDB

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

X

X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X. ✨

LDX

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

XACT

XACT is COMPLEX array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.

LDXACT

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

FERR

FERR is REAL array, dimension (NRHS). 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 REAL array, dimension (NRHS). 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 REAL array, dimension (2). 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 cgbt05.f.

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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source/version + date check: LAPACK Version 3.12.0, page TESTING/LIN/cgbt05.f(3) — and the footer doesn’t print a date, so no invented date here, periodt 💅✨