CTPRFS(3)

okay so bestie, welcome to the ctprfs.f(3) page — manual name is Library Functions Manual, and this is your LAPACK girl for error bounds and backward error estimates on a triangular packed system. slay 💅 not me being obsessed with a packed triangular coefficient matrix, no cap.

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ctprfs.f

🦋 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 🎀

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

The solution matrix X must be computed by CTPTRS or some other means before entering this routine. periodt. CTPRFS does not do iterative refinement because doing so cannot improve the backward error — that’s the whole vibe.

💅 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 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 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); the 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 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. the way that’s lowkey reassuring ✨
• 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 (2*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

👑 Author 👑

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

Definition at line 172 of file ctprfs.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page. Signing off from LAPACK Version 3.12.0 with footer path /home/abui...RC/ctprfs.f(3) — periodt 💖🫶