DTPRFS(3)

💅 DTPRFS(3) 💅

okay bestie, welcome to DTPRFS(3) from the Library Functions Manual. The header path is /home/abui...RC/dtprfs.f(3) — yes, that truncated-looking path is literally what the header shows. The NAME section points at the source file, and it's giving LAPACK 3.12.0 energy. 🦋

📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtprfs.f

✨ SYNOPSIS ✨

Functions/Subroutines

   subroutine DTPRFS (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr,
       berr, work, iwork, info)
       DTPRFS

📚 Function/Subroutine Documentation 📚

   subroutine DTPRFS (character uplo, character trans, character diag, integer
       n, integer nrhs, double precision, dimension( * ) ap, 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)
       DTPRFS

🎯 Purpose 🎯

okay so DTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. That's the whole assignment. 💅

The solution matrix X must be computed by DTPTRS or some other means before entering this routine. DTPRFS does not do iterative refinement because doing so cannot improve the backward error. Not it trying to reinvent the solve, bestie. 😭

🧸 Parameters 🧸

• UPLO — CHARACTER*1. This is the triangle selector: = 'U': A is upper triangular; = 'L': A is lower triangular.
• 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)
• DIAG — CHARACTER*1. = 'N': A is non-unit triangular; = 'U': A is unit triangular.
• 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.
• AP — DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
• 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). The 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.

🫶 Author 🫶

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

Definition at line 173 of file dtprfs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off: LAPACK Version 3.12.0 · footer path /home/abui...RC/dtprfs.f(3). The footer doesn't list a date, so no fake date, bestie — just the version and the path, periodt. 💖✨