DSPRFS(3)

💖 DSPRFS(3) — like, the dsprfs.f page but make it make sense 💖

okay so real talk, this is a page from the LAPACK manual — specifically the one for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsprfs.f, bestie. Yes that's the whole path, no I'm not shortening it, it's literally the name. Buckle up 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsprfs.f — that's the file, that's the vibe, that's the whole identity 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

DSPRFS — say it with me, D-S-P-R-F-S 🗣️

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🦋 Function/Subroutine Documentation 🦋

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

DSPRFS (again, iconic, no notes) ✨

🎀 Purpose 🎀

!> !> DSPRFS improves the computed solution to a system of linear !> equations when the coefficient matrix is symmetric indefinite !> and packed, and provides error bounds and backward error estimates !> for the solution. !>

so basically: you already got a solution, and DSPRFS is your bestie who shows up with a little touch-up kit 💖 It improves the computed solution to a system of linear equations — specifically when the coefficient matrix is symmetric indefinite and packed — and it hands you back error bounds plus backward error estimates for that solution. Obsessed, honestly.

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🌈 Parameters 🌈

• UPLO — CHARACTER*1. Which triangle of A we're storing, periodt:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER. The order of the matrix A. N >= 0. (No negative orders, that's not a thing, don't do it 🙈)
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AP — 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
• AFP — DOUBLE PRECISION array, dimension (N*(N+1)/2). The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as a packed triangular matrix.
• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSPTRF.
• B — DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DSPTRS. On exit, the improved solution matrix X. (Glow-up arc ✨)
• 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.

• 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 — DOUBLE PRECISION array, dimension (3*N). That's it, that's the workspace, three N's worth 🫶
• IWORK — INTEGER array, dimension (N). Integer workspace, one N, slay.
• INFO — INTEGER. The receipts 📋
  • = 0: successful exit (we love to see it 👑)
  • < 0: if INFO = -i, the i-th argument had an illegal value

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💜 Internal Parameters 💜

!> ITMAX is the maximum number of steps of iterative refinement. !>

ITMAX — the maximum number of steps of iterative refinement. That's the internal one, not your problem, but now you know 😌

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🧚 Author 🧚

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

(the whole academic squad, fr fr 🎓)

⭐ Definition at line 177 of file dsprfs.f. ⭐

Like, literally line 177. In dsprfs.f. Go look 👀

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🌸 Author (the doumentation one) 🌸

Generated automatically by Doxygen for LAPACK from the source code. (Doxygen said "I'll write your docs for you" and honestly? it ate 🤖✨)

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k byeeee, ily, go refine those solutions responsibly 🦋💖

— this lil page came from LAPACK, Version 3.12.0, dated /home/abui...RC/dsprfs.f(3) — mwah, take care bestie 🫶🎀