TESTING/LIN/zgbt05.f(3)

🦋 TESTING/LIN/zgbt05.f 🦋

okay so this is the Library Functions Manual entry for TESTING/LIN/zgbt05.f, and it's giving very specific LAPACK test-routine energy 💅✨

💖 NAME 💖

TESTING/LIN/zgbt05.f — that's the file name, periodt 🎀

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine zgbt05 (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx,
    xact, ldxact, ferr, berr, reslts)
    ZGBT05

🎀 Function/Subroutine Documentation 🎀

subroutine zgbt05 (character trans, integer n, integer kl, integer ku,
    integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
    ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact,
    integer ldxact, double precision, dimension( * ) ferr, double precision,
    dimension( * ) berr, double precision, dimension( * ) reslts)
    ZGBT05

🌟 Purpose 🌟

okay bestie, ZGBT05 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. 🫶

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 — CHARACTER*1. 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 — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — COMPLEX*16 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 — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
• B — COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — COMPLEX*16 array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 zgbt05.f.

🧚 Author 🧚

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later, bestie 💖 — this page came from LAPACK Version 3.12.0 and TESTING/LIN/zgbt05.f(3). The footer didn't hand us a date, so we're not inventing one 🙈✨