SRC/cpprfs.f(3)

🌸 NAME 🌸

SRC/cpprfs.f — okay bestie, this is a page from the Library Functions Manual, and it's literally all about the cpprfs subroutine. 💅✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

CPPRFS

🦋 Function/Subroutine Documentation 🦋

subroutine cpprfs (character uplo, integer n, integer nrhs, complex,
    dimension( * ) ap, complex, dimension( * ) afp, complex, dimension( ldb,
    * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,
    dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )
    work, real, dimension( * ) rwork, integer info)

CPPRFS

💖 Purpose 💖

CPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and it provides error bounds and backward error estimates for the solution. No cap, that's the whole glow-up. 🌟

🌟 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 COMPLEX array, dimension (N*(N+1)/2); the upper or lower triangle of the Hermitian 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 COMPLEX array, dimension (N*(N+1)/2); the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see AP).
• B — B is COMPLEX 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 COMPLEX array, dimension (LDX,NRHS); on entry, the solution matrix X, as computed by CPPTRS; 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 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 — BERR is 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 — WORK is COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL 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.

💜 Author 💜

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

Definition at line 169 of file cpprfs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💌 cute sign-off: from the Library Functions Manual, LAPACK Version 3.12.0, source SRC/cpprfs.f(3), generated by Doxygen. That's the footer vibe, bestie — mwah! 💖✨🫶