CPORFS(3)

✨ CPORFS(3) ✨ — like, the manual page but make it make sense 💅

okay bestie, gather round 🫶 this is a LAPACK library function page, specifically for cporfs.f, and it lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cporfs.f — yes that's the whole path, no I'm not shortening it, it's iconic in its own chaotic way 😭

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CPORFS (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx,
    ferr, berr, work, rwork, info)

that's CPORFS 🎀 (literally the whole name, that's it, that's the subroutine)

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💖 Function/Subroutine Documentation 💖

subroutine CPORFS (character uplo, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,
    integer ldaf, 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)

CPORFS 👑

🦋 Purpose

so the actual vibe here: CPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite 💜 and it also hands you error bounds AND backward error estimates for the solution. it's giving "glow-up for your answer" ✨

!> !> CPORFS improves the computed solution to a system of linear !> equations when the coefficient matrix is Hermitian positive definite, !> and provides error bounds and backward error estimates for the !> solution. !>

🎀 Parameters

• UPLO — okay so this is CHARACTER*1, and it tells you which triangle of A we're storing, periodt:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>

• N — INTEGER, the order of the matrix A. and like, N >= 0, no cap.

!> N is 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. also NRHS >= 0 💅

!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrices B and X. NRHS >= 0. !>

• A — a COMPLEX array, dimension (LDA,N). it's the Hermitian matrix A ✨ and here's the tea: if UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. so like, don't come for the parts it ignores, they're not even in the group chat 🙈

!> A is COMPLEX array, dimension (LDA,N) !> The Hermitian matrix A. If UPLO = 'U', the leading N-by-N !> upper triangular part of A contains the upper triangular part !> of the matrix A, and the strictly lower triangular part of A !> is not referenced. If UPLO = 'L', the leading N-by-N lower !> triangular part of A contains the lower triangular part of !> the matrix A, and the strictly upper triangular part of A is !> not referenced. !>

• LDA — INTEGER, the leading dimension of the array A, and it must satisfy LDA >= max(1,N) ⭐

!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>

• AF — COMPLEX array, dimension (LDAF,N). this is the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF 🧚

!> AF is COMPLEX array, dimension (LDAF,N) !> The triangular factor U or L from the Cholesky factorization !> A = UH*U or A = L*LH, as computed by CPOTRF. !>

• LDAF — INTEGER, the leading dimension of the array AF, and LDAF >= max(1,N) 🎀

!> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !>

• B — COMPLEX array, dimension (LDB,NRHS). it's the right hand side matrix B 💖

!> B is COMPLEX array, dimension (LDB,NRHS) !> The right hand side matrix B. !>

• LDB — INTEGER, the leading dimension of the array B, LDB >= max(1,N) 🌈

!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>

• X — COMPLEX array, dimension (LDX,NRHS). on entry, it's the solution matrix X, as computed by CPOTRS. on exit, it's the improved solution matrix X — glow-up complete, main character energy 👑

!> X is COMPLEX array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by CPOTRS. !> On exit, the improved solution matrix X. !>

• LDX — INTEGER, the leading dimension of the array X, LDX >= max(1,N) 💜

!> LDX is 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), then 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). and the estimate is as reliable as the estimate for RCOND, and it's almost always a slight overestimate of the true error. so like, it's a lil dramatic but in a trustworthy way 💅

!> 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 — 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 🦋

!> 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 — COMPLEX array, dimension (2*N) 🌸

!> WORK is COMPLEX array, dimension (2*N) !>

• RWORK — REAL array, dimension (N) ⭐

!> RWORK is REAL array, dimension (N) !>

• INFO — INTEGER, the status report bestie:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

!> 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 it, that's the internal parameter, iykyk.

!> ITMAX is the maximum number of steps of iterative refinement. !>

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👑 Author

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

Definition at line 181 of file cporfs.f 📍

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code. so like, a robot wrote the original and I'm just here to make it cute 🤖✨

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okay that's the whole page bestie, every single flag, dimension, bound and !> line is still in there, nothing skipped, periodt 💅

LAPACK · Version 3.12.0 · /home/abui...RC/cporfs.f(3) — love u, go improve some solutions 🫶🎀