SRC/cptrfs.f(3)

💖 NAME 💖

SRC/cptrfs.f — okay so bestie, this is the Library Functions Manual page for CPTRFS, and it lives at SRC/cptrfs.f(3). It's here to improve your computed solution to a Hermitian positive definite tridiagonal linear system, and honestly? iconic. ✨

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

🦋 Function/Subroutine Documentation 🦋

   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 improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, and it provides error bounds and backward error estimates for the solution. it's giving accuracy aftercare, periodt. 💅

🌈 Parameters 🌈

every single one, no skipping, bestie:

• UPLO — UPLO is CHARACTER*1. It 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 — ITMAX is the maximum number of steps of iterative refinement. that's the whole section, but it matters. 💜

👑 Author 👑

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

Definition at line 181 of file cptrfs.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — this cutie is SRC/cptrfs.f(3) from LAPACK Version 3.12.0. go improve those solutions and slay. 💖✨