CPTRFS(3)

CPTRFS(3) — Library Functions Manual 🦋

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💖 NAME

/home/abui...RC/cptrfs.f(3) — that’s the name line, bestie, and it’s giving “CPTRFS source path realness.” 🫶

🌸 SYNOPSIS

Functions/Subroutines

subroutine CPTRFS (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info)

CPTRFS — that’s the subroutine, periodt. 💅

🛠️ Function/Subroutine Documentation

✨ subroutine CPTRFS — full signature, no cap ✨

subroutine CPTRFS (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, real, dimension( * ) df, complex, dimension( * ) ef, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPTRFS

🎀 Purpose:

okay so CPTRFS is here to improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and it also provides error bounds and backward error estimates for the solution. that’s the whole serve. 💅

🧚 Parameters

every parameter, no skips, bestie:

• UPLO — UPLO is CHARACTER*1; specifies whether the superdiagonal or the subdiagonal of the tridiagonal matrix A is stored and the form of the factorization:
  • = 'U': E is the superdiagonal of A, and A = U**H*D*U;
  • = 'L': E is the subdiagonal of A, and A = L*D*L**H. The two forms are equivalent if A is real. 🦋
• N — N is INTEGER; the order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER; the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• D — D is REAL array, dimension (N); the n real diagonal elements of the tridiagonal matrix A.
• E — E is COMPLEX array, dimension (N-1); the (n-1) off-diagonal elements of the tridiagonal matrix A (see UPLO).
• DF — DF is REAL array, dimension (N); the n diagonal elements of the diagonal matrix D from the factorization computed by CPTTRF.
• EF — EF is COMPLEX array, dimension (N-1); the (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by CPTTRF (see UPLO).
• B — B is COMPLEX array, dimension (LDB,NRHS); the right hand side matrix B.
• LDB — LDB is INTEGER; the leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX array, dimension (LDX,NRHS); on entry, the solution matrix X, as computed by CPTTRS. On exit, the improved solution matrix X.
• LDX — LDX is INTEGER; the leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS); the 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).
• BERR — BERR is REAL 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 — WORK is COMPLEX array, dimension (N).
• RWORK — RWORK is REAL array, dimension (N).
• INFO — INFO is 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 181 of file cptrfs.f.

📝 Author

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LAPACK Version 3.12.0, source /home/abui...RC/cptrfs.f(3) — that’s the footer sign-off, bestie 🎀✨