ZTBRFS(3)

💖 NAME 💖

okay so this is ZTBRFS(3) from the Library Functions Manual, and she is a whole LAPACK icon 💅✨

< purple>Bestie, the NAME section is literally just this path, no extra lore:

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

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✨ SYNOPSIS ✨

Functions/Subroutines — here's the signature exactly as written, no edits:

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

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🦋 Function/Subroutine Documentation 🦋

🌸 Full signature 🌸

   subroutine ZTBRFS (character uplo, character trans, character diag, integer
       n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,
       integer ldab, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( ldx, * ) x, integer ldx, double precision,
       dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,
       dimension( * ) work, double precision, dimension( * ) rwork, integer
       info)
       ZTBRFS

yep, that's ZTBRFS again, main character energy 👑

💅 Purpose 💅

ZTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. That's the whole assignment, and she understood it 💖

Important lore, bestie: the solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error. No cap, that's literally why.

🎀 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)

🎀 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 COMPLEX*16 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 COMPLEX*16 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*16 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 COMPLEX*16 array, dimension (2*N)

🍓 RWORK 🍓

RWORK is DOUBLE PRECISION 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 📌

Definition at line 186 of file ztbrfs.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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Later, bestie 🫶 — source/version check: LAPACK Version 3.12.0, footer path /home/abui...RC/ztbrfs.f(3), and the date? It's not listed, so I'm not inventing one 💀💖