ZSPRFS(3)

💅 ZSPRFS(3) — Library Functions Manual 💅

okay bestie, welcome to ZSPRFS(3) from the Library Functions Manual. This is giving linear algebra main character energy: it improves your computed solution and hands you error bounds. No cap. 🦋

💖 NAME 💖

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

✨ SYNOPSIS ✨

Functions/Subroutines

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

🌸 Function/Subroutine Documentation 🌸

subroutine ZSPRFS (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)
    ZSPRFS

🎯 Purpose

ZSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and provides error bounds and backward error estimates for the solution. Slay. ✨

🎀 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 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 triangle of the symmetric 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*16 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**T or A = L*D*L**T as computed by ZSPTRF, stored as a packed triangular matrix. Iconic factorization behavior. 🎀

IPIV

IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSPTRF.

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 ZSPTRS. On exit, the improved solution matrix X. glow-up complete 💅

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 zsprfs.f.

📝 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that’s the whole page bestie 🫶 Footer sign-off: LAPACK Version 3.12.0, source /home/abui...RC/zsprfs.f(3). No date in this footer, just version + path and immaculate LAPACK vibes. 💅✨