CTBT05(3)

NAME 🌸

Okay so this is CTBT05(3), bestie — manual page ctbt05.f(3) from the Library Functions Manual. The actual source file is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctbt05.f

The header also shows the shortened path /home/abui...IN/ctbt05.f(3), iykyk. Periodt.

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SYNOPSIS ✨

🎀 Functions/Subroutines

subroutine CTBT05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
    ldx, xact, ldxact, ferr, berr, reslts)

CTBT05

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Function/Subroutine Documentation 💖

subroutine CTBT05 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
    ldab, 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)

CTBT05

🫶 Purpose:

So this icon tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular band matrix. Here’s the formula tea, fr fr:

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

🚨 Lowkey important: a large value comes back if that ratio is not less than one. That’s the whole vibe check.

🧚 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.
• 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 — COMPLEX array, dimension (LDAB,N). The upper or lower triangular 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). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• 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.
• 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 / ( NZ*EPS + (*) ).

👑 Author

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

📜 Definition at line 187 of file ctbt05.f.

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Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie. Footer vibe: LAPACK Version 3.12.0, source path /home/abui...IN/ctbt05.f(3). Slay, bye 💅💖