SRC/dgerfs.f(3)

🌸 SRC/dgerfs.f(3) 🌸

okay so bestie, welcome to the SRC/dgerfs.f(3) page from the Library Functions Manual 💖 it’s giving extremely specific linear-algebra energy, and honestly? we respect it.

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💖 NAME 💖

SRC/dgerfs.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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🎀 Function/Subroutine Documentation 🎀

💫 subroutine dgerfs 💫

   subroutine dgerfs (character trans, integer n, integer nrhs, double
       precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( ldx, * ) x, integer ldx, double precision, dimension( * )
       ferr, double precision, dimension( * ) berr, double precision,
       dimension( * ) work, integer, dimension( * ) iwork, integer info)
       DGERFS

🌸 Purpose 🌸

DGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. that’s the whole purpose, and it ate. 💅

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💅 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 = 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by DGETRF.
• LDAF — INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — INTEGER array, dimension (N). The pivot indices from DGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DGETRS. 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.
• 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 — DOUBLE PRECISION array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — INTEGER:
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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🌈 Internal Parameters 🌈

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 183 of file dgerfs.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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💖 that’s the whole page, bestie — LAPACK Version 3.12.0, sourced from SRC/dgerfs.f(3). periodt. 🎀