SRC/ctbrfs.f(3)

💅 SRC/ctbrfs.f(3) — Library Functions Manual 💅

🎀 NAME 🎀

SRC/ctbrfs.f — yep, that's the name, bestie. Just the file path. Short, sweet, main character energy.

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🌈 SYNOPSIS 🌈

🦋 Functions/Subroutines 🦋

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

🦋 Function/Subroutine Documentation 🦋

       subroutine ctbrfs (character uplo, character trans, character diag, integer
           n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
           ldab, 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)
           CTBRFS

CTBRFS is literally the subroutine, bestie. She's giving linear algebra error-bound realness.

💫 Purpose 💫

Okay so CTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. No cap.

The solution matrix X must be computed by CTBTRS or some other means before entering this routine. CTBRFS does not do iterative refinement because doing so cannot improve the backward error. That's just the tea, fr fr.

🌸 Parameters 🌸

Bestie, here's every single parameter — don't skip a single one.

• UPLO — CHARACTER*1. Tells you which triangle is living its truth:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — 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 — CHARACTER*1. Unit triangular or non-unit triangular, that is the question:
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AB — COMPLEX 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 — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• B — COMPLEX array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX array, dimension (LDX,NRHS). The solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — 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 — 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 — COMPLEX array, dimension (2*N).
• RWORK — REAL array, dimension (N).
• INFO — INTEGER. Exit status tea:
  • = 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 ctbrfs.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. iykyk.

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💖 That's the whole vibe check, bestie — the footer signs off with LAPACK, Version 3.12.0, and SRC/ctbrfs.f(3) (no date shown, fr fr). 💖