ZPBRFS(3)

🌸 NAME 🌸

Bestie, this is the manual page for ZPBRFS(3) — yes, the LAPACK Library Functions Manual one — and the source file it points at is:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZPBRFS (uplo, n, kd, nrhs, ab, ldab, afb, ldafb, b, ldb, x,
           ldx, ferr, berr, work, rwork, info)
           ZPBRFS

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🦋 Function/Subroutine Documentation 🦋

subroutine ZPBRFS (character uplo, integer n, integer kd, integer nrhs,
     complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,
     dimension( ldafb, * ) afb, integer ldafb, 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)
     ZPBRFS

🎯 Purpose: 🎯

Okay so ZPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded. It also provides error bounds and backward error estimates for the solution. It is giving “accuracy glow-up” energy, fr fr. ✨

🌈 Parameters 🌈

• UPLO — CHARACTER*1. It tells you which triangle of A is stored: 'U' means the upper triangle of A is stored; 'L' means the lower triangle of A is stored.
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. 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*16 array, dimension (LDAB,N). The upper or lower triangle of the Hermitian 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; and if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• AFB — COMPLEX*16 array, dimension (LDAFB,N). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A as computed by ZPBTRF, in the same storage format as A (see AB).
• LDAFB — INTEGER. The leading dimension of the array AFB. LDAFB >= KD+1.
• B — COMPLEX*16 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*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZPBTRS. On exit, the improved solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — 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. So like, it’s a tiny bit dramatic but in a safe way. 💅
• BERR — 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 — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• INFO — INTEGER. Exit status: = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. So if INFO is negative, something in the arguments did not pass the vibe check. 😭

🧠 Internal Parameters: 🧠

• ITMAX — the maximum number of steps of iterative refinement.

👑 Author 👑

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

📌 Definition at line 187 of file zpbrfs.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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Footer sign-off, bestie: LAPACK Version 3.12.0, source path /home/abui...RC/zpbrfs.f(3) — and there’s no extra date line in this footer. That’s the whole page, slay, stay accurate. 💅✨