TESTING/LIN/ctpt05.f(3)

💖 NAME 💖

okay so bestie, this is the TESTING/LIN/ctpt05.f manual page — TESTING/LIN/ctpt05.f(3) if you're being formal 💅 — and it's literally all about CTPT05, the subroutine that tests error bounds for iterative refinement when your matrix A is triangular and packed. slay. ✨

🌈 SYNOPSIS 🌈

   Functions/Subroutines
       subroutine ctpt05 (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, xact,
           ldxact, ferr, berr, reslts)
           CTPT05

🧚 Function/Subroutine Documentation 🧚

   subroutine ctpt05 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, *
       ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex,
       dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr,
       real, dimension( * ) berr, real, dimension( * ) reslts)
       CTPT05

✨ Purpose ✨

okay so CTPT05 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. 💖

and it drops two things into RESLTS, like:

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 )

🚨 real talk: a large value is returned if that first ratio is not less than one. that's the whole vibe check. 😭

🎀 Parameters 🎀

• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular, = 'L': Lower triangular. 💅
• TRANS — TRANS is CHARACTER*1. Specifies 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. Specifies 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (LDXACT,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 173 of file ctpt05.f. 📍

that's where the magic lives, bestie. ✨

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. 🫶

---

that's the whole tea, bestie: from LAPACK Version 3.12.0, page TESTING/LIN/ctpt05.f(3). periodt. 💅✨