/home/abui.../sorbdb2.f(3)

💅 NAME

okay so this is the manpage for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sorbdb2.f — yes that's the whole entire path, she's long but she's worth it 🫶 (it's a LAPACK Library Functions Manual page, iykyk)

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✨ SYNOPSIS

🎀 Functions/Subroutines

subroutine SORBDB2 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1,
    taup2, tauq1, work, lwork, info)

SORBDB2. that's her. that's the girl 💅

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🦋 Function/Subroutine Documentation

subroutine SORBDB2 (integer m, integer p, integer q, real,
    dimension(ldx11,*) x11, integer ldx11, real, dimension(ldx21,*) x21,
    integer ldx21, real, dimension(*) theta, real, dimension(*) phi, real,
    dimension(*) taup1, real, dimension(*) taup2, real, dimension(*) tauq1,
    real, dimension(*) work, integer lwork, integer info)

SORBDB2 (again, bestie, same subroutine — just the full signature this time 💖)

🔥 Purpose

no cap, here's what she actually does:

!>
!> SORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
!> matrix X with orthonormal columns:
!>
!>                            [ B11 ]
!>      [ X11 ]   [ P1 |    ] [  0  ]
!>      [-----] = [---------] [-----] Q1**T .
!>      [ X21 ]   [    | P2 ] [ B21 ]
!>                            [  0  ]
!>
!> X11 is P-by-Q, and X21 is (M-P)-by-Q. P must be no larger than M-P,
!> Q, or M-Q. Routines SORBDB1, SORBDB3, and SORBDB4 handle cases in
!> which P is not the minimum dimension.
!>
!> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
!> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
!> Householder vectors.
!>
!> B11 and B12 are P-by-P bidiagonal matrices represented implicitly by
!> angles THETA, PHI.
!>
!>

ok so the vibe: X11 is P-by-Q and X21 is (M-P)-by-Q, and P has to be no larger than M-P, Q, or M-Q — that's the whole assignment, bestie. P1, P2, Q1 are P-by-P, (M-P)-by-(M-P), and (M-Q)-by-(M-Q) respectively, and they don't even get their own storage, they're represented implicitly by Householder vectors. main character energy, honestly 👑

🫶 also note: B11 and B12 are P-by-P bidiagonal matrices represented implicitly by angles THETA, PHI — yes the routine itself says B12 there, I'm not touching it, that's what it says.

🌸 Parameters

🍓 M

M is INTEGER the number of rows of X11 plus the number of rows in X21. that's it, that's the math 💜

🍓 P

P is INTEGER the number of rows in X11. constraint era: 0 <= P <= min(M-P,Q,M-Q).

🍓 Q

Q is INTEGER the number of columns in X11 and X21. constraint: 0 <= Q <= M.

🍓 X11

X11 is REAL array, dimension (LDX11,Q) on entry, the top block of the matrix X to be reduced. on exit, the columns of tril(X11) specify reflectors for P1 and the rows of triu(X11,1) specify reflectors for Q1. she goes in one thing and comes out a whole different vibe ✨

🍓 LDX11

LDX11 is INTEGER the leading dimension of X11. requirement: LDX11 >= P.

🍓 X21

X21 is REAL array, dimension (LDX21,Q) on entry, the bottom block of the matrix X to be reduced. on exit, the columns of tril(X21) specify reflectors for P2.

🍓 LDX21

LDX21 is INTEGER the leading dimension of X21. requirement: LDX21 >= M-P.

🍓 THETA

THETA is REAL array, dimension (Q) the entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. see Further Details 👀

🍓 PHI

PHI is REAL array, dimension (Q-1) the entries of the bidiagonal blocks B11, B21 are defined by THETA and PHI. see Further Details 👀 (and yes, it's Q-1, not Q, do not come for me)

🍓 TAUP1

TAUP1 is REAL array, dimension (P-1) the scalar factors of the elementary reflectors that define P1.

🍓 TAUP2

TAUP2 is REAL array, dimension (Q) the scalar factors of the elementary reflectors that define P2.

🍓 TAUQ1

TAUQ1 is REAL array, dimension (Q) the scalar factors of the elementary reflectors that define Q1.

🍓 WORK

WORK is REAL array, dimension (LWORK) the workspace, bestie. she works 💅

🍓 LWORK

LWORK is INTEGER the dimension of the array WORK. requirement: LWORK >= M-Q.

and here's the iconic part: if LWORK = -1, then a workspace query is assumed. the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. so like, -1 is not a mistake, it's a whole mood 🧚

🍓 INFO

INFO is INTEGER

• = 0: successful exit. slay 🎉
• < 0: if INFO = -i, the i-th argument had an illegal value. not slay 😭

👑 Author

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

🦋 Further Details

!>
!>  The upper-bidiagonal blocks B11, B21 are represented implicitly by
!>  angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
!>  in each bidiagonal band is a product of a sine or cosine of a THETA
!>  with a sine or cosine of a PHI. See [1] or SORCSD for details.
!>
!>  P1, P2, and Q1 are represented as products of elementary reflectors.
!>  See SORCSD2BY1 for details on generating P1, P2, and Q1 using SORGQR
!>  and SORGLQ.
!>

so every single entry in each bidiagonal band is a product of a sine or cosine of a THETA with a sine or cosine of a PHI — trig girlies stay winning 🌈 and P1, P2, Q1 are products of elementary reflectors, so if you wanna generate them peep SORCSD2BY1 for the SORGQR and SORGLQ tea 🎀

⭐ References:

[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

💀 Definition at line 199 of file sorbdb2.f.

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🌸 Author

Generated automatically by Doxygen for LAPACK from the source code. (she wasn't hand-written, she was generated, and honestly? iconic 💅)

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k bye bestie, go bidiagonalize something 🦋✨ — LAPACK, Version 3.12.0, /home/abui.../sorbdb2.f(3)