SOPGTR(3)

💅 SOPGTR(3) — bestie's guide to the packed-reflector glow-up 💅

okay so first things first, the manual name is SOPGTR and it lives in section 3, and the whole page is literally just vibing out of this one file:

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

that's the path, no cap, that's the NAME section, we move ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine SOPGTR (uplo, n, ap, tau, q, ldq, work, info) — that's the whole squad, right there 🫶

SOPGTR

(yeah that's the entire description in the synopsis, she's mysterious like that 💅)

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🦋 Function/Subroutine Documentation 🦋

subroutine SOPGTR (character uplo, integer n, real, dimension( * ) ap, real,
     dimension( * ) tau, real, dimension( ldq, * ) q, integer ldq, real,
     dimension( * ) work, integer info)

SOPGTR

🎀 Purpose 🎀

!> !> SOPGTR generates a real orthogonal matrix Q which is defined as the !> product of n-1 elementary reflectors H(i) of order n, as returned by !> SSPTRD using packed storage: !> !> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), !> !> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). !>

so literally what this icon does is build you a real orthogonal matrix Q — and Q is defined as the product of n-1 elementary reflectors H(i) of order n, exactly as they came back from SSPTRD, using packed storage. it's giving assembly line but make it linear algebra 💖 the order of the product depends on UPLO:

• if UPLO = 'U', then Q = H(n-1) . . . H(2) H(1)
• if UPLO = 'L', then Q = H(1) H(2) . . . H(n-1)

periodt. that's it, that's the whole job 🔥

🌈 Parameters 🌈

• UPLO

!> UPLO is CHARACTER*1 !> = 'U': Upper triangular packed storage used in previous !> call to SSPTRD; !> = 'L': Lower triangular packed storage used in previous !> call to SSPTRD. !>

so UPLO is a CHARACTER*1 and it's basically the receipts from your last SSPTRD call 👑 = 'U' means upper triangular packed storage was used in the previous call to SSPTRD, and = 'L' means lower triangular packed storage was used in the previous call to SSPTRD. pick the one that matches what you actually did, bestie, don't lie to the compiler 🙈

• N

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

N is INTEGER, it's the order of the matrix Q, and it has to be N >= 0. that's the vibe check ✅

• AP

!> AP is REAL array, dimension (N*(N+1)/2) !> The vectors which define the elementary reflectors, as !> returned by SSPTRD. !>

AP is a REAL array, dimension (N*(N+1)/2) — ok that dimension is iconic honestly — and it holds the vectors which define the elementary reflectors, as returned by SSPTRD. it's the packed one, she's compact, she's efficient 💅

• TAU

!> TAU is REAL array, dimension (N-1) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SSPTRD. !>

TAU is a REAL array, dimension (N-1), and TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD. note the "must" — this is not a suggestion, this is the law 🫡

• Q

!> Q is REAL array, dimension (LDQ,N) !> The N-by-N orthogonal matrix Q. !>

Q is a REAL array, dimension (LDQ,N), and it's the N-by-N orthogonal matrix Q. she's the main character of this whole function, honestly 🌟

• LDQ

!> LDQ is INTEGER !> The leading dimension of the array Q. LDQ >= max(1,N). !>

LDQ is INTEGER, it's the leading dimension of the array Q, and it's gotta satisfy LDQ >= max(1,N). no shortcuts, the leading dimension is not here to be flexible 💀

• WORK

!> WORK is REAL array, dimension (N-1) !>

WORK is a REAL array, dimension (N-1). she's the workspace, she does the invisible labour, respect her 🫶

• INFO

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

INFO is INTEGER and it's your little status report 🎀 = 0 means successful exit — slay, we love a clean run — and < 0 means if INFO = -i, the i-th argument had an illegal value. read that number, it's literally telling you which argument to go apologise to 😭

👑 Author 👑

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

the whole academic friend group came together for this one, we stan a collaborative effort 💜

⭐ Definition at line 113 of file sopgtr.f. ⭐

yes bestie, line 113, write it down, cite your sources 📝

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

so nobody hand-wrote this page, Doxygen did it for LAPACK automatically from the source code. the robots are doing the documentation now and honestly? they ate 🤖✨

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and that's the whole page!! no notes, only reflectors 🦋

💖 this has been sopgtr.f(3) from LAPACK, Version 3.12.0, served fresh from /home/abui...RC/sopgtr.f(3) — mwah, go build your orthogonal matrix, bestie 💅🎀🌸