SRC/zpprfs.f(3)

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version 3.12.1 · 4 versions
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💖 SRC/zpprfs.f(3) 💖

okay so welcome to the Library Functions Manual page for SRC/zpprfs.f — it's giving LAPACK subroutine realness, and we're gonna get you through it together, bestie. 🫶

🌸 NAME 🌸

SRC/zpprfs.f — that's the name, no cap. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

🦋 Function/Subroutine Documentation 🦋

💫 subroutine zpprfs 💫

   subroutine zpprfs (character uplo, integer n, integer nrhs, complex*16,
       dimension( * ) ap, complex*16, dimension( * ) afp, 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)
       ZPPRFS

🎯 Purpose 🎯

ZPPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, and provides error bounds and backward error estimates for the solution. ✨

🌈 Parameters 🌈

  • UPLO — is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. 👑
  • N — is INTEGER. The order of the matrix A. N >= 0.
  • NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
  • AP — is COMPLEX*16 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)*(2n-j)/2) = A(i,j) for j<=i<=n. 🫶
  • AFP — is COMPLEX*16 array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by DPPTRF/ZPPTRF, packed columnwise in a linear array in the same format as A (see AP). 💖
  • B — is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side matrix B. 🎀
  • LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N). ✨
  • X — is COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZPPTRS. On exit, the improved solution matrix X. 🌟
  • LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,N). 🌸
  • 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 — 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 — is COMPLEX*16 array, dimension (2*N). 🧚
  • RWORK — is DOUBLE PRECISION array, dimension (N). 🍓
  • 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 169 of file zpprfs.f. 📌

👑 Author 👑

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