TESTING/LIN/stpt05.f(3)

🎀 NAME 🎀

okay so bestie, welcome to the TESTING/LIN/stpt05.f(3) page from the Library Functions Manual 💅 This is the TESTING/LIN/stpt05.f page, and it is literally all about STPT05. ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine stpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — STPT05

💅 Function/Subroutine Documentation 💅

Here is the full signature, copied exactly because we do not mess with code, periodt:

subroutine stpt05 (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( * ) ap, 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)

STPT05

🌟 Purpose 🌟

STPT05 tests the error bounds from iterative refinement for the
computed solution to a system of equations A*X = B, where A is a
triangular matrix in packed storage format.

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 / ( (n+1)*EPS + (*) ), where
            (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. It says whether the matrix A is upper or lower triangular: 'U' = upper triangular, 'L' = lower triangular. slay ✨
• TRANS — TRANS is CHARACTER*1. It says the form of the system of equations: 'N': A * X = B (No transpose); 'T': A'* X = B (Transpose); 'C': A'* X = B (Conjugate transpose = Transpose).
• DIAG — DIAG is CHARACTER*1. It says whether or not the matrix A is unit triangular: 'N': Non-unit triangular; 'U': Unit 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.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AP — AP is REAL array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 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 / ( (n+1)*EPS + (*) )

🌸 Author 🌸

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 172 of file stpt05.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

💖 That's the whole page, bestie! Source/version: LAPACK Version 3.12.0; date: not shown in the footer on this one, no cap. The footer also shows TESTING/LIN/stpt05.f(3), so there you go — iconic, honestly. 🎀