SSPGST(3)

💅 SSPGST(3) — like, the LAPACK Library Functions Manual page, bestie ✨

okay so first things first: this is a page straight outta the LAPACK Library Functions Manual (that's the manual name, mwah 💖) and it's all about one very specific little Fortran file, namely:

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

that's the whole NAME section, no notes, that's literally it. iconic behavior honestly 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine SSPGST (itype, uplo, n, ap, bp, info)
    SSPGST

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🌸 Function/Subroutine Documentation 🌸

subroutine SSPGST (integer itype, character uplo, integer n, real,
    dimension( * ) ap, real, dimension( * ) bp, integer info)
    SSPGST

💜 Purpose

!> !> SSPGST reduces a real symmetric-definite generalized eigenproblem !> to standard form, using packed storage. !> !> If ITYPE = 1, the problem is A*x = lambda*B*x, !> and A is overwritten by inv(UT)*A*inv(U) or inv(L)*A*inv(LT) !> !> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or !> B*A*x = lambda*x, and A is overwritten by U*A*UT or LT*A*L. !> !> B must have been previously factorized as UT*U or L*LT by SPPTRF. !>

so like, tl;dr: bestie takes a generalized eigenproblem and reduces it to standard form, using packed storage the whole time. and listen 👀 — B has to have already been factorized as U**T*U or L*L**T by SPPTRF before you come here. no prep, no vibes, no entry. 🙈

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✨ Parameters

• ITYPE

!> ITYPE is INTEGER !> = 1: compute inv(UT)*A*inv(U) or inv(L)*A*inv(LT); !> = 2 or 3: compute U*A*UT or LT*A*L. !>

(so it's giving very much "which one of the three modes are we in" energy 🔥)

• UPLO

!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored and B is factored as !> UT*U; !> = 'L': Lower triangle of A is stored and B is factored as !> L*LT. !>

like, 'U' for upper triangle, 'L' for lower — pick your side, there is no third option ngl 💅

• N

!> N is INTEGER !> The order of the matrices A and B. N >= 0. !>

the order of A and B, and it's gotta be N >= 0 fr fr

• AP

!> AP is REAL array, dimension (N*(N+1)/2) !> On entry, the upper or lower triangle of the symmetric 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. !> !> On exit, if INFO = 0, the transformed matrix, stored in the !> same format as A. !>

so AP is a REAL array of dimension (N*(N+1)/2) and it's packed columnwise, meaning the offset math is literally the main character here 👑 — memorize those two index formulas or perish bestie:

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.

and on exit, if INFO = 0, you get the transformed matrix back 🦋 — same format as A, no glow-up in the structure, only in the values ✨

• BP

!> BP is REAL array, dimension (N*(N+1)/2) !> The triangular factor from the Cholesky factorization of B, !> stored in the same format as A, as returned by SPPTRF. !>

REAL array, dimension (N*(N+1)/2), and it's the triangular factor from the Cholesky factorization of B — stored in the same format as A, exactly as SPPTRF returned it 🫶

• INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

INFO = 0? slay, successful exit 💖 INFO < 0? if INFO = -i, then the i-th argument had an illegal value 😭 someone did NOT read the docs

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👑 Author

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

(that's the whole squad, four institutions, no cap 🎓)

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⭐ Definition

Definition at line 112 of file sspgst.f.

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🧚 Author (the meta one, yes really)

Generated automatically by Doxygen for LAPACK from the source code. (so nobody hand-wrote this page, a robot did it, and honestly? it ate 🤖💅)

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and that's the whole page bestie — no options skipped, no numbers dropped, everything's here 💜

That was all brought to you by LAPACK, Version 3.12.0 — and the date slot on this footer is genuinely empty, so like, no date, just vibes and the filename /home/abui...RC/sspgst.f(3) 🎀✨ bye pookie, go invert something 🦋