SPBT05(3)

💅 SPBT05(3) 💅

okay bestie, this is the Library Functions Manual entry for SPBT05 — header title and manual name folded in near the top like a little intro. The vibe is error-bound testing, but make it cute. ✨

NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/spbt05.f

SYNOPSIS

🧸 Functions/Subroutines 🧸

subroutine SPBT05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact,
    ldxact, ferr, berr, reslts)
    SPBT05

Function/Subroutine Documentation

Here’s the full typed signature, bestie — copy it exactly:

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. periodt. 💅

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(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 🌸 Specifies 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 169 of file spbt05.f.

👑 Author (auto-generated bestie)

Generated automatically by Doxygen for LAPACK from the source code.

🫶 that’s the whole page, bestie. footer tea: source/version = LAPACK · Version 3.12.0 · page path = /home/abui...IN/spbt05.f(3) · date = not listed in this copy. 💖