SRC/chprfs.f(3)

🌸 NAME

Okay bestie, this is SRC/chprfs.f(3) from the Library Functions Manual — and it's all about the CHPRFS subroutine. Buckle up 💖

✨ SYNOPSIS

Functions/Subroutines

• subroutine chprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info) — CHPRFS is here to improve your computed solution and hand you those error bounds, periodt 💅

subroutine chprfs (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr,
     berr, work, rwork, info)

🫶 Function/Subroutine Documentation

subroutine chprfs (character uplo, integer n, integer nrhs, complex,
     dimension( * ) ap, complex, dimension( * ) afp, integer, dimension( * )
     ipiv, 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)

CHPRFS — yes queen, this is the one 💖

Purpose

CHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and it provides error bounds and backward error estimates for the solution. It's giving solver-glow-up energy ✨

Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• 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 triangle of the Hermitian 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
• AFP — AFP is COMPLEX array, dimension (N*(N+1)/2)
  • The factored form of the matrix A. AFP contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as a packed triangular matrix.
• IPIV — IPIV is INTEGER array, dimension (N)
  • Details of the interchanges and the block structure of D as determined by CHPTRF.
• 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 CHPTRS.
  • 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 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 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

Internal Parameters

ITMAX is the maximum number of steps of iterative refinement. That's the internal tea ☕✨

Author

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

Definition at line 178 of file chprfs.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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Footer sign-off, with all the source/version energy: LAPACK, Version 3.12.0, SRC/chprfs.f(3) — and the footer didn't bring a date, so we're not inventing one, periodt 💅✨