STBRFS(3)

🎀 NAME

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

okay so this page is stbrfs.f(3) from the Library Functions Manual, and yes the whole path above is literally the NAME section. no cap. 💅

✨ SYNOPSIS

Functions/Subroutines

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

📚 Function/Subroutine Documentation

The full signature is giving main-character Fortran energy:

subroutine STBRFS (character uplo, character trans, character diag, integer
     n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
     ldab, 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)
     STBRFS

🎯 Purpose

STBRFS 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 STBTRS or some other means before entering this routine. STBRFS does not do iterative refinement because doing so 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 = 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 REAL 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 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 186 of file stbrfs.f.

👑 Author

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