SRC/cpbrfs.f(3)

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

okay bestie, this is the manual page for SRC/cpbrfs.f, and it's literally the CPBRFS routine doing its banded Hermitian positive definite thing. no cap, it's giving linear-algebra main character energy. 🦋

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🌸 NAME 🌸

SRC/cpbrfs.f — that's the name, periodt. 💖

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✨ SYNOPSIS ✨

💖 Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

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

💖 Purpose:

okay so CPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution. slay. 💅

🔥 Parameters

• UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 🎀
• N — N is INTEGER. The order of the matrix A. N >= 0. ✨
• KD — KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. 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 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; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 🌸
• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🫶
• AFB — AFB is COMPLEX 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 CPBTRF, in the same storage format as A (see AB). 💜
• LDAFB — LDAFB is INTEGER. The leading dimension of the array AFB. LDAFB >= KD+1. 💫
• B — B is COMPLEX 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 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by CPBTRS. On exit, the improved 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 COMPLEX array, dimension (2*N). 🔥
• RWORK — RWORK is REAL array, dimension (N). 🌸
• INFO — INFO is INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 👑

🧚 Internal Parameters:

• ITMAX — ITMAX is 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 cpbrfs.f. 📌

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🌈 Author

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🫶 and that's the whole page, bestie — brought to you by LAPACK, Version 3.12.0, page SRC/cpbrfs.f(3). bye 💖