TESTING/LIN/spbt05.f(3)

💅 TESTING/LIN/spbt05.f(3) — Library Functions Manual 💅

🌸 NAME 🌸

TESTING/LIN/spbt05.f — that’s the page/file, bestie. The routine living here is SPBT05. 💖

✨ SYNOPSIS ✨

🛠️ Functions/Subroutines

subroutine spbt05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)

• SPBT05 — the routine name, periodt. 🫶

💖 Function/Subroutine Documentation 💖

🫶 subroutine spbt05 — the signature

subroutine spbt05 (character uplo, integer n, integer kd, integer nrhs,
    real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * )
    b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real,
    dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr,
    real, dimension( * ) berr, real, dimension( * ) reslts)

SPBT05

🎀 Purpose 🎀

Okay so SPBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric band matrix. Slay. ✨

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

If that ratio is not less than one, you get a large value back — that’s the vibe check. 🚨

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

🍓 Parameters 🍓

• UPLO — UPLO is CHARACTER*1; it says whether the upper or lower triangular part of the symmetric matrix A is stored.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER; the number of rows of the matrices X, B, and XACT, and the order 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 columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — AB is REAL array, dimension (LDAB,N); the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KD+1.
• B — B is REAL 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 REAL 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 REAL 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 … 📌

Definition at line 169 of file spbt05.f.

💌 Author 💌

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie! Shoutout to LAPACK Version 3.12.0 for the source/version energy — and no date line was printed on the original page, so we’re not inventing one. Stay slay, and may your error bounds always be less than one. 💅✨🎀