CSPRFS(3)

💖 CSPRFS(3) — Library Functions Manual 💖

okay so bestie, this is the CSPRFS(3) page, and the header is giving Library Functions Manual with /home/abui...RC/csprfs.f(3) on both sides. We’re folding that whole vibe in right here, and then we’re getting into the actual sections. 💅

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csprfs.f

🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

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

💜 Function/Subroutine Documentation 💜

subroutine CSPRFS (character uplo, integer n, integer nrhs, complex,
       dimension( * ) ap, complex, dimension( * ) afp, integer, dimension( * )
       ipiv, 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)
       CSPRFS

✨ Purpose ✨

CSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution. That’s the main character energy right there. 🫶

💅 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). It’s 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 — AFP is COMPLEX 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 CSPTRF, stored as a packed triangular matrix. iykyk 🧚
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSPTRF.
• 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 CSPTRS. 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. Not me knowing that by heart. 😭

👑 Author 👑

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

Definition at line 178 of file csprfs.f.

🧚 Author — auto-generated by Doxygen 🧚

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that’s the whole CSPRFS(3) manual. The footer vibe is: LAPACK Version 3.12.0, file /home/abui...RC/csprfs.f(3) — no extra date stamp shown on this page, so we’re not inventing one. Slay, and may your packed symmetric indefinite solves be iconic. 💅✨