DSPTRI(3)

💖 DSPTRI(3) — Library Functions Manual 💖

okay bestie, this is the LAPACK page for DSPTRI, and the header vibe is DSPTRI(3) from the Library Functions Manual. We're about to compute the inverse of a real symmetric indefinite matrix in packed storage, using the factorization from DSPTRF. Slay. 💅

🌸 NAME 🌸

The NAME is literally this source-file path, no cap:

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

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DSPTRI (uplo, n, ap, ipiv, work, info)
           DSPTRI

💫 Function/Subroutine Documentation 💫

subroutine DSPTRI

subroutine DSPTRI (character uplo, integer n, double precision, dimension( *
) ap, integer, dimension( * ) ipiv, double precision, dimension( * )
work, integer info)
       DSPTRI

🎯 Purpose 🎯

DSPTRI computes the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. That's the whole purpose, and it ate. ✨

🍓 Parameters 🍓

UPLO

UPLO is CHARACTER*1. It says whether the details of the factorization are stored as an upper or lower triangular matrix.

• = '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, and N >= 0.

AP

AP is a DOUBLE PRECISION array with 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 DSPTRF, 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 like this:

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 an INTEGER array with dimension (N). It holds the details of the interchanges and the block structure of D as determined by DSPTRF. 🔥

WORK

WORK is a DOUBLE PRECISION array with dimension (N). That's it, that's the workspace.

INFO

INFO is INTEGER, and here's the vibe check:

• = 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 dsptri.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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That's the page, bestie! 🫶 Cute sign-off from the footer: LAPACK — Version 3.12.0, page path /home/abui...RC/dsptri.f(3). (The footer didn't show a date, so I'm not inventing one — periodt.) 💖