SPBRFS(3)

🌸 NAME 🌸

Okay bestie, this is SPBRFS(3) from the Library Functions Manual — the page path is /home/abui...RC/spbrfs.f(3), and the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spbrfs.f. ✨

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🦋 SYNOPSIS 🦋

Functions/Subroutines — here’s the whole group-chat invite, no cap:

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

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🎀 Function/Subroutine Documentation 🎀

✨ subroutine SPBRFS ✨

subroutine SPBRFS (character uplo, integer n, integer kd, integer nrhs,
       real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * )
       afb, integer ldafb, real, dimension( ldb, * ) b, integer ldb, real,
       dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real,
       dimension( * ) berr, real, dimension( * ) work, integer, dimension( * )
       iwork, integer info)
       SPBRFS

💖 Purpose 💖

SPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, and it provides error bounds and backward error estimates for the solution. It’s giving “clean up the solution and tell me how confident we are.” 💅

🫶 Parameters 🫶

• UPLO — CHARACTER*1. Tells us which triangle of A is stored: = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Pick your side, bestie.
• 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 — REAL array, dimension (LDAB,N). The upper or lower triangle of the symmetric 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 — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• AFB — REAL array, dimension (LDAFB,N). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A as computed by SPBTRF, in the same storage format as A (see AB).
• LDAFB — INTEGER. The leading dimension of the array AFB. LDAFB >= KD+1.
• B — REAL array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — REAL array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by SPBTRS. On exit, the improved solution matrix X. Glow-up arc, literally.
• 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 — REAL array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. so if it’s negative, someone did not read the assignment. 💀

🧚 Internal Parameters 🧚

• ITMAX — is the maximum number of steps of iterative refinement. Obsessed with her little refinement loop.

👑 Author 👑

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

Definition at line 187 of file spbrfs.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶✨ — LAPACK Version 3.12.0, footer path /home/abui...RC/spbrfs.f(3). byeee 💅🎀