SRC/ztprfs.f(3)

💖 NAME 💖

SRC/ztprfs.f — okay so bestie, this is the SRC/ztprfs.f(3) page from the Library Functions Manual, and it’s all about the ZTPRFS subroutine. ✨

🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

• ZTPRFS — the subroutine in question, fr fr:

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

🦋 Function/Subroutine Documentation 🦋

💜 subroutine ztprfs 💜

subroutine ztprfs (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(
    ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,
    double precision, dimension( * ) ferr, double precision, dimension( * )
    berr, complex*16, dimension( * ) work, double precision, dimension( * )
    rwork, integer info)
    ZTPRFS

✨ Purpose ✨

Okay so ZTPRFS 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 ZTPTRS or some other means before entering this routine. ZTPRFS does not do iterative refinement because doing so cannot improve the backward error. No cap. 🫶

🍓 Parameters 🍓

• UPLO — UPLO is CHARACTER*1; = 'U': A is upper triangular; = 'L': A is lower triangular.
• TRANS — TRANS is 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 — DIAG is CHARACTER*1; = 'N': A is non-unit triangular; = 'U': A is unit triangular.
• 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 matrices B and X. NRHS >= 0.
• AP — AP is COMPLEX*16 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 — B is COMPLEX*16 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*16 array, dimension (LDX,NRHS); the solution matrix X.
• LDX — LDX is INTEGER; the leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is 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 — BERR is 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 — WORK is COMPLEX*16 array, dimension (2*N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• INFO — INFO is 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 ztprfs.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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