SRC/dsprfs.f(3)

🎀 NAME 🎀

SRC/dsprfs.f — okay bestie, this is the LAPACK page for the DSPRFS subroutine, folded in from the Library Functions Manual. No cap, it’s giving “symmetric indefinite packed matrix” main character energy.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

🌸 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

🎯 Purpose 🎯

Okay so the whole vibe of DSPRFS is: it improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and it also provides error bounds and backward error estimates for the solution. Slay.

🧸 Parameters 🧸

• UPLO — CHARACTER*1; = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
• N — INTEGER; the order of the matrix A. N >= 0.
• 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.
• 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).
• IWORK — INTEGER array, dimension (N).
• INFO — INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

🔧 Internal Parameters 🔧

• ITMAX — the maximum number of steps of iterative refinement.

👑 Author 👑

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

📍 Definition 📍

Definition at line 177 of file dsprfs.f.

🫶 Author (the Doxygen one) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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made with 💖 by LAPACK, Version 3.12.0 — page SRC/dsprfs.f(3) — and the footer’s date slot was giving empty, so I’m not making one up, bestie 😭🫶