SRC/csprfs.f(3)

SRC/csprfs.f(3) · Library Functions Manual ✨ okay bestie, buckle up, we're doing the CSPRFS glow-up 🫶

💖 NAME 💖

SRC/csprfs.f — that's the name, and we're keeping it exactly like that 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

Here's the function/subroutine energy:

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

💅 Function/Subroutine Documentation 💅

Okay so the main character is this subroutine, and its whole signature is right here:

subroutine csprfs (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)
    CSPRFS

🎯 Purpose: 🎯

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

🧾 Parameters 🧾

• UPLO — it's a CHARACTER*1, and it picks which triangle of A we're storing: = 'U' means the upper triangle of A is stored; = 'L' means the lower triangle of A is stored. 🦋
• N — N is INTEGER, and it's the order of the matrix A. N >= 0 👑
• NRHS — NRHS is INTEGER, and it's 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). It holds 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 array, dimension (N*(N+1)/2). It's 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 CSPTRF, stored as a packed triangular matrix. iconic 🔥
• IPIV — IPIV is INTEGER array, dimension (N). It has the details of the interchanges and the block structure of D as determined by CSPTRF. 🫶
• B — B is COMPLEX array, dimension (LDB,NRHS). It's the right hand side matrix B. 💖
• LDB — LDB is INTEGER, and it's the leading dimension of the array B. LDB >= max(1,N) 🌸
• X — X is COMPLEX array, dimension (LDX,NRHS). On entry, it's the solution matrix X, as computed by CSPTRS. On exit, it's the improved solution matrix X. ✨
• LDX — LDX is INTEGER, and it's the leading dimension of the array X. LDX >= max(1,N) 🦋
• FERR — FERR is REAL array, dimension (NRHS). It's 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). It's 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 — this 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 csprfs.f. 📌

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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And that's the whole vibe, bestie 💜 this one comes from <rainbow>LAPACK Version 3.12.0</rainbow>, page SRC/csprfs.f(3) — footer energy, but make it cute ✨