DPBT05(3)

💖 DPBT05(3) 💖

okay so this page is DPBT05(3), and it comes from the Library Functions Manual. bestie, we are about to vibe-check iterative refinement error bounds for a symmetric band matrix, and every single parameter is coming with us. no cap. ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dpbt05.f

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📜 SYNOPSIS 📜

Functions/Subroutines

   subroutine DPBT05 (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact,
       ldxact, ferr, berr, reslts)
       DPBT05

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🧚 Function/Subroutine Documentation 🧚

       subroutine DPBT05 (character uplo, integer n, integer kd, 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)

this is the one and only DPBT05. iconic. 💅

🎯 Purpose

DPBT05 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. yes, we love a structured queen. 🫶

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

bestie, if that ratio is not less than one, RESLTS(1) comes back large — that is literally the test. 😭

🌈 Parameters

• UPLO — CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular and = 'L': Lower triangular. 💖
• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0. ✨
• KD — 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 — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0. 🌸
• AB — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 👑
• B — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 169 of file dpbt05.f.

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🦋 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that is the whole page, bestie 🫶 — LAPACK Version 3.12.0, footer date/path: /home/abui...IN/dpbt05.f(3). go forth and test those error bounds. mwah 💋