CTRRFS(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 ctrrfs.f(3) — Library Functions Manual 💖

Okay bestie, this is the ctrrfs.f(3) page from the Library Functions Manual, and it's here to hand you error bounds and backward error estimates for a triangular-system solution. No cap, it's a whole vibe. 🫶

🎀 NAME 🎀

The source file is literally:

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

✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

The synopsis is giving:

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

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, exactly as the source has it:

   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 gives you 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.

🌸 Parameters 🌸

🌺 UPLO

UPLO is CHARACTER*1.

  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.

🌺 TRANS

TRANS is CHARACTER*1.

It 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 at line 180 of file ctrrfs.f.

🌈 Author 🌈

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