SRC/dtprfs.f(3)

🌸 NAME 🌸

Okay so this is SRC/dtprfs.f(3) — the Library Functions Manual page for DTPRFS, and it’s giving “triangular packed matrix error-bound main character energy.” 💅

SRC/dtprfs.f — that’s the name, bestie. Periodt.

✨ 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 🦋

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 — iconic, no cap. 🌟

🎯 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. It’s giving error-bound royalty, fr fr. 💖

The solution matrix X must be computed by DTPTRS or some other means before entering this routine. And bestie, DTPRFS does not do iterative refinement because doing so cannot improve the backward error. That’s the tea. Periodt.

🚨 Important vibe check: X needs to be ready before you call this routine, and there’s no iterative-refinement era here because it cannot improve the backward error.

🧾 Parameters 🧾

Not me being obsessed with a CHARACTER*1 option list, but here we are. 😭

• UPLO — CHARACTER*1
  • = '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. Highkey important, ngl. 🫶
• 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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🎀 That’s the whole page, bestie: LAPACK Version 3.12.0, source SRC/dtprfs.f(3). No date in the footer, so no invented date — just the source/version sign-off. Slay and stay triangular. 💅