SRC/zhprfs.f(3)

💖 SRC/zhprfs.f 💖

okay bestie, this is the Library Functions Manual entry for SRC/zhprfs.f(3), and it's giving very-coded Hermitian linear algebra, no cap. 💅

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✨ NAME ✨

• SRC/zhprfs.f — that's the file, periodt. 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

ZHPRFS — our main character routine. 👑

🌸 Function/Subroutine Documentation 🌸

subroutine zhprfs (character uplo, integer n, integer nrhs, complex*16,
     dimension( * ) ap, complex*16, dimension( * ) afp, integer, dimension( *
     ) ipiv, 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)

ZHPRFS 💖

🎯 Purpose

okay so ZHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution. it's literally that girl. ✨

🧮 Parameters

• UPLO — UPLO is CHARACTER*1. it tells us which triangle we're in, bestie:
  • = '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*16 array, dimension (N*(N+1)/2). it's 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 like this:
  • 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*16 array, dimension (N*(N+1)/2). this is the factored form of 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 ZHPTRF, 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 ZHPTRF. 👑
• 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). on entry, the solution matrix X, as computed by ZHPTRS. 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 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

🔧 Internal Parameters:

• ITMAX — is the maximum number of steps of iterative refinement. ✨

👑 Author

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

Definition at line 178 of file zhprfs.f. 🫶

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — LAPACK Version 3.12.0, source SRC/zhprfs.f(3) 🫶✨