DPBRFS(3)

💖 DPBRFS(3) — Library Functions Manual 💖

🌸 NAME 🌸

The file this page is documenting is literally:

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

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

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

🎀 Purpose 🎀

Okay so bestie, DPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded. It also provides error bounds and backward error estimates for the solution. Iconic, honestly. 💅

👑 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 DOUBLE PRECISION 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 — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• AFB — AFB is DOUBLE PRECISION 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 DPBTRF, 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DPBTRS. 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 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 DOUBLE PRECISION array, dimension (3*N).
• IWORK — IWORK is INTEGER 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 is the maximum number of steps of iterative refinement. Periodt.

🌸 Author 🌸

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

Definition at line 187 of file dpbrfs.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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With all the love and zero cap: LAPACK, Version 3.12.0 — /home/abui...RC/dpbrfs.f(3) 💖