ZPPRFS(3)

💅 ZPPRFS(3) · zpprfs.f(3) · Library Functions Manual 💅

okay so this is the zpprfs.f(3) page from the Library Functions Manual, and it’s all about a very specific little LAPACK subroutine. bestie, we’re getting into iterative refinement territory. 💖

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zpprfs.f — that’s the file this page is serving, no cap. 🫶

🎀 SYNOPSIS 🎀

   Functions/Subroutines
       subroutine ZPPRFS (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr,
           work, rwork, info)
           ZPPRFS

🌸 Function/Subroutine Documentation 🌸

💫 subroutine ZPPRFS 💫

   subroutine ZPPRFS (character uplo, integer n, integer nrhs, complex*16,
       dimension( * ) ap, complex*16, dimension( * ) afp, complex*16,
       dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x,
       integer ldx, double precision, dimension( * ) ferr, double precision,
       dimension( * ) berr, complex*16, dimension( * ) work, double precision,
       dimension( * ) rwork, integer info)
       ZPPRFS

🎯 Purpose 🎯

okay so picture this: you’ve got a system of linear equations, and the coefficient matrix is Hermitian positive definite and packed. ZPPRFS improves the computed solution to that system, and it also hands you error bounds and backward error estimates for the solution. it’s giving “let me clean that up for you.” ✨

🌈 Parameters 🌈

• UPLO — is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AP — is COMPLEX*16 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 — is COMPLEX*16 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 DPPTRF/ZPPTRF, packed columnwise in a linear array in the same format as A (see AP). 🦋
• B — is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — is COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZPPTRS. On exit, the improved solution matrix X. 🔥
• LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• 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 — 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 — is COMPLEX*16 array, dimension (2*N).
• RWORK — is DOUBLE PRECISION array, dimension (N).
• 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. that’s the whole internal-parameters moment, bestie. 💅

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 169 of file zpprfs.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 💖 — this page is LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/zpprfs.f(3). slay. 🫶