SRC/ctprfs.f(3)

💅 SRC/ctprfs.f(3) 💅

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🌸 NAME 🌸

SRC/ctprfs.f — literally the name, no cap. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine ctprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr,
           berr, work, rwork, info)
           CTPRFS

💖 Function/Subroutine Documentation 💖

   subroutine ctprfs (character uplo, character trans, character diag, integer
       n, integer nrhs, complex, dimension( * ) ap, 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)
       CTPRFS

🎯 Purpose: 🎯

CTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. 💅

The solution matrix X must be computed by CTPTRS or some other means before entering this routine. No cap: CTPRFS does not do iterative refinement because doing so cannot improve the backward error.

🌈 Parameters 🌈

• 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). 🦋
• 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 — COMPLEX 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)*(2n-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 — COMPLEX 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 array, dimension (LDX,NRHS). The solution matrix X. 🫶
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N). ✨
• FERR — REAL 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 — 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 — COMPLEX array, dimension (2*N). 💜
• RWORK — REAL 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 172 of file ctprfs.f.

🫶 Author 🫶

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