CTRT05(3)

✨ NAME ✨

okay bestie, this is CTRT05(3) from the Library Functions Manual — header path is /home/abui...IN/ctrt05.f(3), and the full file path is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctrt05.f

that path is literally the NAME, no cap 💅

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

       subroutine CTRT05 (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
           xact, ldxact, ferr, berr, reslts)
           CTRT05

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💖 Function/Subroutine Documentation 💖

   subroutine CTRT05 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( lda, * ) a, integer lda, 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)
       CTRT05

🦋 Purpose 🦋

okay so the whole vibe of CTRT05 is: it tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular n by n matrix. iconic honestly.

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

if that ratio is not less than one, a large value is returned — that’s the vibe check failing, bestie 😭

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. tells you whether the matrix A is upper or lower triangular. = 'U': Upper triangular. = 'L': Lower triangular. 💅
• TRANS — TRANS is CHARACTER*1. tells you 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. 🫶
• A — A is COMPLEX array, dimension (LDA,N). the triangular matrix A. if UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. 👑
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). 🌈
• 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 (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 180 of file ctrt05.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off time, bestie: this footer says LAPACK Version 3.12.0 and /home/abui...IN/ctrt05.f(3) — no separate date is shown, just those header/footer goodies. mwah 💋✨