SRC/zgtrfs.f(3)

💅 NAME

SRC/zgtrfs.f — page header says SRC/zgtrfs.f(3), and the manual is Library Functions Manual. Okay so that’s the intro, bestie — now let’s get into the actual routine. ✨

🎀 SYNOPSIS

🦋 Functions/Subroutines

       subroutine zgtrfs (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv,
           b, ldb, x, ldx, ferr, berr, work, rwork, info)
           ZGTRFS

📚 Function/Subroutine Documentation

   subroutine zgtrfs (character trans, integer n, integer nrhs, complex*16,
       dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(
       * ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df,
       complex*16, dimension( * ) duf, complex*16, dimension( * ) du2, 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)
       ZGTRFS

🎯 Purpose

Okay so ZGTRFS is here to improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and it also provides error bounds and backward error estimates for the solution. It’s giving “your answer but make it more trustworthy.” 💖

🧾 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 matrix B. NRHS >= 0.
• DL — COMPLEX*16 array, dimension (N-1). The (n-1) subdiagonal elements of A.
• D — COMPLEX*16 array, dimension (N). The diagonal elements of A.
• DU — COMPLEX*16 array, dimension (N-1). The (n-1) superdiagonal elements of A.
• DLF — COMPLEX*16 array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.
• DF — COMPLEX*16 array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
• DUF — COMPLEX*16 array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
• DU2 — COMPLEX*16 array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
• IPIV — INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
• 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 ZGTTRS. 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 — 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.

👑 Author

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

Definition at line 207 of file zgtrfs.f.

📜 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, file SRC/zgtrfs.f(3). Slay and bye! 🎀