SRC/ctrrfs.f(3)

🌸 NAME 🌸

okay so this page is SRC/ctrrfs.f(3) from the Library Functions Manual, and it's literally all about CTRRFS, bestie. It's the subroutine that gives you error bounds and backward error estimates. slay.

💅 SYNOPSIS 💅

✨ Functions/Subroutines ✨

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

🎀 Function/Subroutine 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. no cap, it's just not that kind of routine 💅

🦋 Parameters 🦋

• UPLO is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• 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 is CHARACTER*1
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N is INTEGER
  • The order of the matrix A. N >= 0.
• NRHS is INTEGER
  • The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• 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 is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• B is COMPLEX array, dimension (LDB,NRHS)
  • The right hand side matrix B.
• LDB is INTEGER
  • The leading dimension of the array B. LDB >= max(1,N).
• X is COMPLEX array, dimension (LDX,NRHS)
  • The solution matrix X.
• LDX is INTEGER
  • The leading dimension of the array X. LDX >= max(1,N).
• 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 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 is COMPLEX array, dimension (2*N)
• RWORK is REAL array, dimension (N)
• 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 ctrrfs.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 💖 — it's from LAPACK Version 3.12.0, and the file is SRC/ctrrfs.f(3). mwah 💋