SRC/zppsv.f(3)

okay bestie, welcome to the manual page for SRC/zppsv.f — it's part of the Library Functions Manual, and it's honestly giving “I do linear algebra and I do it fabulously” energy. ✨ This is the page for the zppsv subroutine, and yes, we're keeping every single technical detail. No skips, no cap. 💅

💖 NAME 💖

SRC/zppsv.f — that's the name of this page, periodt. 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine zppsv (uplo, n, nrhs, ap, b, ldb, info) — ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices. 🫶

🌈 Function/Subroutine Documentation 🌈

okay so here's the exact signature, bestie:

subroutine zppsv (character uplo, integer n, integer nrhs, complex*16,
       dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb,
       integer info)

And the one-liner is: ZPPSV computes the solution to system of linear equations A * X = B for OTHER matrices. (Yes, “OTHER matrices” is literally what it says. We don't make the rules.) 😭

💜 Purpose 💜

okay so ZPPSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as

A = U**H * U,  if UPLO = 'U', or
A = L * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. 🦋

🌸 Parameters 🌸

• UPLO — is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 💜
• N — is INTEGER. The number of linear equations, i.e., 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 matrix B. NRHS >= 0. 🦋
• AP — is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, 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.

See below for further details. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. 🔥

• B — is COMPLEX*16 array, dimension (LDB,NRHS). On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. 🌈
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 👑
• INFO — is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed. 💀

👑 Author 👑

These are the author credits, bestie:

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

🦋 Further Details 🦋

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the Hermitian matrix A:

   a11 a12 a13 a14
       a22 a23 a24
           a33 a34     (aij = conjg(aji))
               a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 143 of file zppsv.f. ✨

🧚 Author 🧚

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

---

okay that's the whole page, bestie — source/version vibes: SRC/zppsv.f(3) from LAPACK Version 3.12.0. Go forth and solve cute systems. 💖✨🎀