trrfs(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💖 NAME

okay so bestie, this is trrfs(3) — straight out of the Library Functions Manual — and it's literally called trrfs, which stands for trrfs: triangular iterative refinement. iconic name, iykyk 💅

✨ SYNOPSIS

🎀 Functions

  • subroutine ctrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info) — CTRRFS
  • subroutine dtrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info) — DTRRFS
  • subroutine strrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info) — STRRFS
  • subroutine ztrrfs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info) — ZTRRFS

🦋 DETAILED DESCRIPTION

💜 Function Documentation

🧚 subroutine ctrrfs (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, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CTRRFS 👑

🌟 Purpose

!>
!> CTRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by CTRTRS or some other
!> means before entering this routine.  CTRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

so real talk: it hands you error bounds and backward error estimates for a triangular system. and heads up — your X has to already exist before you walk in here (computed by CTTRTRS... no wait, by CTRTRS or "some other means"). and it does not do iterative refinement, because apparently that cannot improve the backward error. periodt. 💀

🍓 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = '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)
  • 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 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 matrix B.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • X — X is COMPLEX 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 COMPLEX array, dimension (2*N)
  • RWORK — RWORK is REAL 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

Definition at line 180 of file ctrrfs.f.

🧚 subroutine dtrrfs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DTRRFS 👑

🌟 Purpose

!>
!> DTRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by DTRTRS or some other
!> means before entering this routine.  DTRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

same energy, double precision edition 🫶 — error bounds + backward error estimates for a triangular-coefficient system, X must already be computed by DTRTRS or some other means before you enter, and nope, no iterative refinement here either, because it cannot improve the backward error. no cap.

🍓 Parameters

  • UPLO — UPLO is CHARACTER*1
    • = '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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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 — BERR is 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 — WORK is DOUBLE PRECISION 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
🔥 bestie note the glow-up: WORK is 3*N here (not 2*N like the complex one) and there's an IWORK integer array of dimension (N) instead of an RWORK.

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

⭐ Definition

Definition at line 180 of file dtrrfs.f.

🧚 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.
!>
!> 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.
!>

single precision version, same whole vibe 💜 — error bounds and backward error estimates for a triangular coefficient matrix, X precomputed by STRTRS or some other means, and no iterative refinement because it cannot improve the backward error. that's the whole thesis, fr fr.

🍓 Parameters

🌸 UPLO

(okay so this one picks up right here — part 2 has the rest, don't leave me hanging 🫶)

okay bestie, we're mid-parameter-list and I would never leave you hanging 💅 here's every single one for strrfs, no cap:

  • UPLO — UPLO is CHARACTER*1. = '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.

💖 subroutine ztrrfs — the complex one, she's here

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

ZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix.

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

💅 Parameters

  • UPLO — UPLO is CHARACTER*1. = '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). ✨
  • 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 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 — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 🔥
  • B — B is COMPLEX*16 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 COMPLEX*16 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 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 — BERR is 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 — WORK is COMPLEX*16 array, dimension (2*N). 🍓
  • RWORK — RWORK is DOUBLE PRECISION 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 ztrrfs.f.

🌸 Author (auto-generated, bestie) 🌸

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💖 that's the whole trrfs(3) page — source/version is LAPACK, Version 3.12.0, and the page is trrfs(3). bye bestie, you ate that! 🎀👑

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