SRC/dpprfs.f(3)

💖 NAME 💖

This is SRC/dpprfs.f(3) from the Library Functions Manual — yes bestie, the SRC/dpprfs.f page. Periodt. 💅

---

✨ SYNOPSIS ✨

🦋 Functions/Subroutines

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

---

🌸 Function/Subroutine Documentation 🌸

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 it provides error bounds and backward error estimates for the solution. Iconic behavior, 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.
• 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.
• 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. 🫶
• 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. Slay, iterative refinement. ✨

---

👑 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.

---

And that’s the whole page, bestie: LAPACK, Version 3.12.0, chilling at SRC/dpprfs.f(3). Byeee 💖🎀🦋