SRC/dtbrfs.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

SRC/dtbrfs.f(3) 🌈

okay so bestie, this page is from the Library Functions Manual, and it's all about SRC/dtbrfs.f — specifically the DTBRFS subroutine. It's giving linear algebra error-bound realness, and honestly? iconic.

NAME ✨

SRC/dtbrfs.f — that's the name, bestie. Nothing extra in this section, no cap.

SYNOPSIS 🎀

Functions/Subroutines

subroutine dtbrfs (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
    ldx, ferr, berr, work, iwork, info)
    DTBRFS

That's the little cast list. Now for the full glam signature.

Function/Subroutine Documentation 💅

subroutine dtbrfs (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,
    integer ldab, 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)
    DTBRFS

This is the whole subroutine signature, exactly as written.

Purpose 🎯

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

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

⚠️ so yeah, bestie: it's not doing iterative refinement for you. Doing so cannot improve the backward error. That's the whole point.

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.

KD

KD is INTEGER

The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 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.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)

The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

LDAB

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KD+1.

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

Author 👑

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

Definition at line 186 of file dtbrfs.f.

Author 🛠️

Generated automatically by Doxygen for LAPACK from the source code.

bye bestie 💖 — this page came from LAPACK Version 3.12.0, source page SRC/dtbrfs.f(3). periodt.

📦 where this page comes from