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

Okay bestie, welcome to the zppsv.f(3) page from the Library Functions Manual — this is the LAPACK subroutine that’s lowkey carrying your complex Hermitian positive-definite solver era, and it’s literally iconic. Let’s get into it 💅✨

💖 NAME 💖

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

That’s the source file, fr fr 🫶

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✨ 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.

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🌸 Function/Subroutine Documentation 🌸

Here’s the full signature, character for character, no cap:

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

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

🦋 Purpose 🦋

Okay so picture this: 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

UPLO is CHARACTER*1. It tells you which triangle of A is stored, periodt:

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

N

N is INTEGER. It’s the number of linear equations, i.e., the order of the matrix A. N >= 0.

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*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

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

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER. The exit-status tea:

• = 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 💌

• 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.

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And that’s the whole page, bestie! Source: LAPACK, Version 3.12.0, /home/abui...RC/zppsv.f(3) — slay and stay packed 💅✨🫶