SRC/zsptri.f(3)

💖 SRC/zsptri.f(3) 💖

okay so this is the SRC/zsptri.f(3) page from the Library Functions Manual — yes bestie, the whole vibe is LAPACK docs, and we're getting into it 🫶

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🌸 NAME 🌸

SRC/zsptri.f — that's the name, literally, no extra crumbs 💅

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine zsptri (uplo, n, ap, ipiv, work, info)
    ZSPTRI

The main character is ZSPTRI, and it's showing up with signature subroutine zsptri (uplo, n, ap, ipiv, work, info) — iconic behavior, no cap ✨

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💅 Function/Subroutine Documentation 💅

Here's the full signature, preserved exactly because we do not mess with code in this group chat:

subroutine zsptri (character uplo, integer n, complex*16, dimension( * ) ap,
    integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer
    info)

ZSPTRI 🎀

🎯 Purpose: 🎯

ZSPTRI computes the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF 💖

🌈 Parameters 🌈

💖 UPLO 💖

UPLO is CHARACTER*1 — it tells you whether the factorization details are stored as an upper or lower triangular matrix, bestie:

• = 'U': Upper triangular, form is A = U*D*U**T;
• = 'L': Lower triangular, form is A = L*D*L**T.

💖 N 💖

N is INTEGER — it's the order of the matrix A. The rule is N >= 0 🦋

💖 AP 💖

AP is COMPLEX*16 array, dimension (N*(N+1)/2) ✨

On entry, it holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSPTRF, stored as a packed triangular matrix 💅

On exit, if INFO = 0, it holds the (symmetric) inverse of the original matrix, stored as a packed triangular matrix. The j-th column of inv(A) is stored in the array AP as follows:

• if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
• if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

💖 IPIV 💖

IPIV is INTEGER array, dimension (N) — it holds the details of the interchanges and the block structure of D as determined by ZSPTRF 👑

💖 WORK 💖

WORK is COMPLEX*16 array, dimension (N) ⭐

💖 INFO 💖

INFO is INTEGER — the exit-status tea is:

• = 0: successful exit;
• < 0: if INFO = -i, the i-th argument had an illegal value;
• > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed 💀

👑 Author 👑

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

Definition at line 108 of file zsptri.f. 🌸

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code 🫶

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and that's the whole page, bestie — footer flex is LAPACK, Version 3.12.0, SRC/zsptri.f(3), and it ate, periodt 💖✨