TESTING/LIN/ctrt05.f(3)

✨ TESTING/LIN/ctrt05.f(3) ✨

okay so bestie, this is the TESTING/LIN/ctrt05.f page from the Library Functions Manual, and it’s literally all about a subroutine called ctrt05. stay with me, it’s giving numerical linear algebra but make it cute. 💖

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🎀 NAME 🎀

TESTING/LIN/ctrt05.f — the manual page for this routine, 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 is the main character here. 💅

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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)

also known as CTRT05, because apparently one name wasn’t enough. iconic. 👑

💫 Purpose 💫

okay so the whole vibe: CTRT05 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. 🧚

the receipts are:

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. so yeah, if it’s big, that’s the universe telling you something. 😭

and:

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 )

that +abs(b) spacing is exactly what the page says, bestie — we don’t “fix” the icon’s formatting. 🫶

🌸 Parameters 🌸

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular; = 'L': Lower triangular. 💅
• TRANS — 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 — CHARACTER*1. Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular; = 'U': Unit triangular. 🎀
• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0. 🦋
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0. 🌸
• A — 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 🔥
• B — COMPLEX 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 — COMPLEX 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 — COMPLEX array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT. (yes, it says LDX here — we’re keeping it exactly as the page says. 👀)
• LDXACT — INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N). 🧚
• FERR — 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 — 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 — 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. 📌

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. the bot did its thing. 🤖✨

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okay bye bestie 💖 this cutie came from TESTING/LIN/ctrt05.f(3) and the footer is giving LAPACK Version 3.12.0 — slay, periodt. 🎀