SRC/zgerfs.f(3)

💖 NAME 💖

SRC/zgerfs.f — yes bestie, that's the page title, and this is from the Library Functions Manual. It's giving LAPACK Fortran subroutine realness, and we're gonna get through every single detail together. 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

   subroutine zgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
       ldx, ferr, berr, work, rwork, info)

ZGERFS — that's the subroutine's name, and yes it's iconic. 💅

🦋 Function/Subroutine Documentation 🦋

   subroutine zgerfs (character trans, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af,
       integer ldaf, integer, dimension( * ) ipiv, 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)

ZGERFS — okay so this is the full signature, and it ate. 💅

🌟 Purpose 🌟

Okay so ZGERFS improves the computed solution to a system of linear equations and gives you error bounds and backward error estimates for that solution. It's literally the glow-up pass for your solution, bestie. ✨

🌸 Parameters 🌸

• TRANS — CHARACTER*1. Specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• N — 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. NRHS >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). The original N-by-N matrix A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — COMPLEX*16 array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by ZGETRF.
• LDAF — INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — INTEGER array, dimension (N). The pivot indices from ZGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — COMPLEX*16 array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZGETRS. On exit, the improved solution matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — 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. Not me loving a reliable little error bound. 😭
• BERR — 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 — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• INFO — INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🔥 Internal Parameters 🔥

• ITMAX — the maximum number of steps of iterative refinement. That's it, no cap. 🎀

👑 Author 👑

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

📍 Definition at line 184 of file zgerfs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bye bestie! 💖 The footer energy is LAPACK Version 3.12.0, source SRC/zgerfs.f(3), and the date slot isn't printed on this page — that's the whole sign-off, periodt. 🎀