DPPRFS(3)

okay bestie, welcome to DPPRFS(3) from the LAPACK pages in the Library Functions Manual — this is the whole page, and it's giving "precision linear algebra but make it cute" energy. ✨

🎀 NAME 🎀

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

okay so the function lineup is short and iconic:

subroutine DPPRFS (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr,
    work, iwork, info)
    DPPRFS

🌸 Function/Subroutine Documentation 🌸

here's the full signature, copied exactly because we do not freestyle code in this group chat:

subroutine DPPRFS (character uplo, integer n, integer nrhs, double
    precision, dimension( * ) ap, double precision, dimension( * ) afp,
    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)
    DPPRFS

💖 Purpose 💖

okay so DPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution. that's the assignment, and it ate. 💅

🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. pick your triangle, bestie. 💜
• N — N is INTEGER; the order of the matrix A. N >= 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.
• AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2); the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. packing, no cap. 🍓
• AFP — AFP is DOUBLE PRECISION array, dimension (N*(N+1)/2); the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPPTRF/ZPPTRF, packed columnwise in a linear array in the same format as A (see AP).
• 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 DPPTRS. 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. she's honest about being a tiny overestimate. 😭
• 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. illegal-value vibe check, bestie. 👀

🌟 Internal Parameters 🌟

• ITMAX is the maximum number of steps of iterative refinement. that's the internal tea, and it's lowkey important. ☕

👑 Author 👑

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

Definition at line 169 of file dpprfs.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. not me writing this by hand, Doxygen did that. 💅

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bye bestie! this page is from LAPACK, Version 3.12.0, with footer path /home/abui...RC/dpprfs.f(3) — that's the source/version info, and there's no separate date line in the footer, periodt. 🫶✨