/home/abui...RC/chpsv.f(3)

okay bestie, welcome to the LAPACK Library Functions Manual — today's absolute main character is chpsv.f 💅✨

🌸 NAME 🌸

The NAME here is literally this whole source path, no cutesy shortening, periodt:

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

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine CHPSV (uplo, n, nrhs, ap, ipiv, b, ldb, info)
     CHPSV computes the solution to system of linear equations A * X = B
    for OTHER matrices

🎀 Function/Subroutine Documentation 🎀

Here's the full signature, bestie — copy it exactly, no vibes-based renaming:

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

CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices. Iconic. 💖

🎯 Purpose 🎯

CHPSV computes the solution to a complex system of linear equations

A * X = B,

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

The diagonal pivoting method is used to factor A as

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

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. That's the whole arc, no cap. 🦋

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. Choose your fighter 💅
• N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. Respect the bound, bestie.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
• AP — AP is COMPLEX 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, 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 CHPTRF, stored as a packed triangular matrix in the same storage format as A. Same energy, different contents.
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D, as determined by CHPTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. It's giving very detailed swap lore 🔁
• B — B is COMPLEX 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. Glow-up complete ✨
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). Do not play with this one.
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. That's the dramatic plot twist 😭

👑 Author 👑

• 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 ]

Packed and cute. No wasted space, we love a storage queen 🍓

Definition at line 161 of file chpsv.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. The robots wrote this one, bestie 🤖💜

---

Cute sign-off time: this page's footer says LAPACK Version 3.12.0 and points back to /home/abui...RC/chpsv.f(3); there was no date line in the footer I got, so I'm not inventing one 🫶💅