DTBRFS(3)

hiii bestie 💖 okay so this is dtbrfs.f(3) from the Library Functions Manual — yes, the dtbrfs.f page — and we're gonna get you comfy with it. No cap.

🌸 NAME 🌸

This page is about this exact file path, character for character:

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

✨ SYNOPSIS ✨

Functions/Subroutines:

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

🦋 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

🎀 Purpose 🎀

okay so DTBRFS gives you error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. iconic.

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

💅 Parameters 💅

• UPLO — <cyan>CHARACTER*1</cyan>. Tells you which triangle of A is the main character:
  • 'U': A is upper triangular;
  • 'L': A is lower triangular.
• TRANS — <cyan>CHARACTER*1</cyan>. 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 — <cyan>CHARACTER*1</cyan>:
  • 'N': A is non-unit triangular;
  • 'U': A is unit triangular.
• N — <cyan>INTEGER</cyan>. The order of the matrix A. N >= 0.
• KD — <cyan>INTEGER</cyan>. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — <cyan>INTEGER</cyan>. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AB — <cyan>DOUBLE PRECISION array, dimension (LDAB,N)</cyan>. 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 — <cyan>INTEGER</cyan>. The leading dimension of the array AB. LDAB >= KD+1.
• B — <cyan>DOUBLE PRECISION array, dimension (LDB,NRHS)</cyan>. The right hand side matrix B.
• LDB — <cyan>INTEGER</cyan>. The leading dimension of the array B. LDB >= max(1,N).
• X — <cyan>DOUBLE PRECISION array, dimension (LDX,NRHS)</cyan>. The solution matrix X.
• LDX — <cyan>INTEGER</cyan>. The leading dimension of the array X. LDX >= max(1,N).
• FERR — <cyan>DOUBLE PRECISION array, dimension (NRHS)</cyan>. 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 — <cyan>DOUBLE PRECISION array, dimension (NRHS)</cyan>. 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 — <cyan>DOUBLE PRECISION array, dimension (3*N)</cyan>.
• IWORK — <cyan>INTEGER array, dimension (N)</cyan>.
• INFO — <cyan>INTEGER</cyan>:
  • = 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.

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