SRC/spptri.f(3)

✨ SRC/spptri.f(3) ✨

okay so this is a page from the Library Functions Manual and it's literally the glow-up era of your linear algebra life 💅 buckle up bestie, we're inverting matrices

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💖 NAME 💖

SRC/spptri.f — yes that's the whole name, she's lowkey mysterious like that 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine spptri (uplo, n, ap, info)

SPPTRI 👑 (that's her name, say it with your chest)

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🌸 Function/Subroutine Documentation 🌸

subroutine spptri (character uplo, integer n, real, dimension( * ) ap,
    integer info)

SPPTRI ✨ (again, iconic, we love a consistent queen)

🎀 Purpose:

SPPTRI computes the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF.

so basically: you already did the hard part and got your Cholesky factorization from SPPTRF, and now SPPTRI takes that and hands you the inverse 💖 fr fr, no cap, that's the whole vibe check.

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🫶 Parameters 🫶

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangular factor is stored in AP;
= 'L':  Lower triangular factor is stored in AP.

she's a CHARACTER*1 and she's picking a side 😭

• 'U' — the upper triangular factor is the one chillin' in AP
• 'L' — nope, it's the lower triangular factor stored in AP

N

N is INTEGER
The order of the matrix A.  N >= 0.

N is an INTEGER and it's the order of the matrix A. The rule is N >= 0 — don't try her with negatives, she will not be normal about it 🙈

AP

AP is REAL array, dimension (N*(N+1)/2)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, packed columnwise as
a linear array.  The j-th column of U or L is stored in the
array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

On exit, the upper or lower triangle of the (symmetric)
inverse of A, overwriting the input factor U or L.

okay this one's the main character 💅 AP is a REAL array with dimension (N*(N+1)/2).

On entry it's holding the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise as a linear array. Here's exactly how the j-th column of U or L sits in AP:

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

On exit, AP becomes the upper or lower triangle of the (symmetric) inverse of A — and yes, it straight up overwrites the input factor U or L. say goodbye to the old her, she's gone 😭

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the (i,i) element of the factor U or L is
      zero, and the inverse could not be computed.

INFO is an INTEGER and she's the group chat read receipt:

• = 0 — successful exit, we ate 🔥
• < 0 — if INFO = -i, the i-th argument had an illegal value 🙈
• > 0 — if INFO = i, the (i,i) element of the factor U or L is zero, and the inverse could not be computed 💀

⚠️ bestie pls notice: INFO > 0 literally means a diagonal element of the factor came back zero and the inverse was not computed. that's not a vibe. check your matrix 🥲

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👑 Author 👑

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

(four whole institutions collaborated on this and honestly? teamwork makes the dream work 🌈)

Definition at line 92 of file spptri.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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so yeah 🎀 that's the whole page. no notes, she's perfect.

and that's a wrap on LAPACK 🫶 Version 3.12.0 🦋 from SRC/spptri.f(3) — go invert something symmetric positive definite, ily, bye bestie 💜✨🍓