ZTRRFS(3)

🌸 NAME

Bestie, this page is from the Library Functions Manual and it’s all about ZTRRFS(3) from LAPACK. The official NAME is that whole build-path situation, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztrrfs.f

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✨ SYNOPSIS

🧚 Functions/Subroutines

Here’s the call, verbatim, because we do not play fast and loose with signatures 💅:

subroutine ZTRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
    ferr, berr, work, rwork, info)
    ZTRRFS

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💖 Function/Subroutine Documentation

🎀 subroutine ZTRRFS

Full signature, copied exactly because she is iconic and we respect her:

subroutine ZTRRFS (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
    ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double
    precision, dimension( * ) berr, complex*16, dimension( * ) work, double
    precision, dimension( * ) rwork, integer info)
    ZTRRFS

🦋 Purpose

Okay so ZTRRFS gives you error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. That’s the whole assignment, fr fr.

The solution matrix X must be computed by ZTRTRS or some other means before entering this routine. Important: ZTRRFS does not do iterative refinement, because doing so cannot improve the backward error. Not me pointing at the “no extra glow-up” rule 😭

🌈 Parameters

• UPLO — CHARACTER*1. = 'U': A is upper triangular; = 'L': A is lower triangular.
• TRANS — CHARACTER*1. Specifies the form of the system of equations: = 'N': A * X = B (No transpose); = 'T': A**T * X = B (Transpose); = 'C': A**H * X = B (Conjugate transpose).
• DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — COMPLEX*16 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*16 array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX*16 array, dimension (LDX,NRHS). The solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — DOUBLE PRECISION array, dimension (NRHS). The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
• BERR — DOUBLE PRECISION array, dimension (NRHS). The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
• WORK — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

👑 Author

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

Definition at line 180 of file ztrrfs.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Mwah 💋 — that’s the whole vibe: LAPACK, Version 3.12.0, footer path /home/abui...RC/ztrrfs.f(3), and no date line on this one, bestie, so no fake-date energy 🙈✨