ZPORFS(3)

💅 NAME 💅

okay so bestie, this is the zporfs.f(3) page from the Library Functions Manual, and the main character file is:

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zporfs.f — that’s the file, no cap. 💖

---

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

the synopsis is literally this, character-for-character:

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

---

🫶 FUNCTION/SUBROUTINE DOCUMENTATION 🫶

here’s the full signature, also exactly as it appears:

   subroutine ZPORFS (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af,
       integer ldaf, 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)
       ZPORFS

🌸 Purpose 🌸

ZPORFS 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. slay, 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.
• A — A is COMPLEX*16 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 — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N).
• AF — AF is COMPLEX*16 array, dimension (LDAF,N)
  • The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
• LDAF — LDAF is INTEGER
  • The leading dimension of the array AF. LDAF >= max(1,N).
• B — B is COMPLEX*16 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*16 array, dimension (LDX,NRHS)
  • On entry, the solution matrix X, as computed by ZPOTRS. 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 COMPLEX*16 array, dimension (2*N)
• RWORK — RWORK is DOUBLE PRECISION 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. that’s the whole tea. 🫖

👑 Author 👑

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

📍 Definition at line 181 of file zporfs.f.

🧚 Author (Doxygen-generated) 🧚

Generated automatically by Doxygen for LAPACK from the source code. 💫

---

and that’s the page, bestie! 🌈 this cutie is from LAPACK Version 3.12.0, with the footer path /home/abui...RC/zporfs.f(3) — the original footer doesn’t show a separate date, so I’m not inventing one. periodt. 💅