SPPRFS(3)

💅 SPPRFS(3) — Library Functions Manual 💅

okay so this is the spprfs.f(3) page from the Library Functions Manual, and it's giving “LAPACK subroutine that fixes up your solution and hands you error receipts.” 💖

---

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spprfs.f — that's the file, bestie. No cap.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine SPPRFS (...) — SPPRFS

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

💖 Function/Subroutine Documentation 💖

   subroutine SPPRFS (character uplo, integer n, integer nrhs, real, dimension(
       * ) ap, real, dimension( * ) afp, 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)
       SPPRFS

🎀 Purpose 🎀

okay so SPPRFS does the most: it improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed. It also provides error bounds and backward error estimates for the solution. Obsessed. 💅

🦋 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 — REAL 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.
• AFP — REAL 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 SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see AP).
• 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 SPPTRS. On exit, the improved solution matrix X.
• 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.

🚨 lowkey important: those >= constraints and the INFO = -i illegal-argument case are not decorative — they're the actual contract.

🌸 Internal Parameters 🌸

ITMAX is the maximum number of steps of iterative refinement. That's it, that's the internal parameter. ✨

👑 Author 👑

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

Definition at line 169 of file spprfs.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

---

Source/version check: LAPACK Version 3.12.0, straight from the spprfs.f(3) page (/home/abui...RC/spprfs.f(3) in the footer). Date? The footer didn't hand us one, bestie — just the version and the path. That's the cute sign-off, periodt. 💅💖