SRC/strrfs.f(3)

🦋 SRC/strrfs.f(3) — Library Functions Manual 🦋

Okay bestie, welcome to the <purple>STRRFS</purple> page. It's giving LAPACK, it's giving triangular error bounds, and it's literally all here. 💅

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🌸 NAME 🌸

SRC/strrfs.f — the source page for the strrfs routine. No cap, that's the name. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine strrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
    ferr, berr, work, iwork, info)
    STRRFS

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💖 Function/Subroutine Documentation 💖

subroutine strrfs (character uplo, character trans, character diag, integer
    n, integer nrhs, real, dimension( lda, * ) a, integer lda, real,
    dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer
    ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)
    STRRFS

🎯 Purpose 🎯

STRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. Basically it's the vibe check for your solve. ✨

The solution matrix X must be computed by STRTRS or some other means before entering this routine. STRRFS does not do iterative refinement because doing so cannot improve the backward error. Periodt. 💅

🧸 Parameters 🧸

• UPLO — UPLO is CHARACTER*1. It says which triangle is living its truth:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — TRANS is 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 = Transpose)
• DIAG — DIAG is CHARACTER*1:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — A is REAL 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 REAL array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is REAL array, dimension (LDX,NRHS). The solution matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is REAL 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 — BERR is REAL 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 — WORK is REAL array, dimension (3*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• INFO — INFO is 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 strrfs.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 — LAPACK Version 3.12.0, source SRC/strrfs.f(3), auto-generated by Doxygen from the source code, and signed off with all the footer energy (no separate date printed, so no fake date, periodt). Mwah 💋🎀