/home/abui.../stplqt2.f(3)

🌸 /home/abui.../stplqt2.f(3) — Library Functions Manual 💅

okay bestie, so this is a man page out of LAPACK's Library Functions Manual, and it's literally all about one lil Fortran subroutine. she's niche, she's math, she ate. let's get into it ✨

---

🌈 NAME 🌈

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stplqt2.f

yes that's the whole name, no cap — the file path is the name. she's giving "full government name because my mom is calling" energy 🫶

---

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine STPLQT2 (m, n, l, a, lda, b, ldb, t, ldt, info)

so like, STPLQT2 computes a LQ factorization of a real or complex triangular-pentagonal matrix — which is literally just a triangular block + a pentagonal block hanging out together — using the compact WY representation for Q. iconic behavior honestly 💖

---

🦋 Function/Subroutine Documentation 🦋

subroutine STPLQT2 (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldt, * ) t, integer ldt, integer info)

STPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix — that's a matrix made of a triangular block plus a pentagonal block — and it does it with the compact WY representation for Q. slay 💅

✨ Purpose ✨

fr fr, here's the deal straight from the source:

!>
!> STPLQT2 computes a LQ a factorization of a real
!> matrix C, which is composed of a triangular block A and pentagonal block B,
!> using the compact WY representation for Q.
!>

🌸 Parameters 🌸

• M — M is INTEGER. the total number of rows of the matrix B, bestie. M >= 0.

!>          M is INTEGER
!>          The total number of rows of the matrix B.
!>          M >= 0.
!>

• N — N is INTEGER. the number of columns of the matrix B, and also the order of the triangular matrix A. N >= 0.

!>          N is INTEGER
!>          The number of columns of the matrix B, and the order of
!>          the triangular matrix A.
!>          N >= 0.
!>

• L — L is INTEGER. the number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. peep Further Details if you wanna know why 👀

!>          L is INTEGER
!>          The number of rows of the lower trapezoidal part of B.
!>          MIN(M,N) >= L >= 0.  See Further Details.
!>

• A — A is REAL array, dimension (LDA,M). on entry it's the lower triangular M-by-M matrix A. on exit, everything on and below the diagonal holds the lower triangular matrix L. glow-up moment ✨

!>          A is REAL array, dimension (LDA,M)
!>          On entry, the lower triangular M-by-M matrix A.
!>          On exit, the elements on and below the diagonal of the array
!>          contain the lower triangular matrix L.
!>

• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M).

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>

• B — B is REAL array, dimension (LDB,N). on entry it's the pentagonal M-by-N matrix B — the first N-L columns are rectangular and the last L columns are lower trapezoidal. on exit, B holds the pentagonal matrix V. again, Further Details is right there 🧚

!>          B is REAL array, dimension (LDB,N)
!>          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
!>          are rectangular, and the last L columns are lower trapezoidal.
!>          On exit, B contains the pentagonal matrix V.  See Further Details.
!>

• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,M).

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,M).
!>

• T — T is REAL array, dimension (LDT,M). the N-by-N upper triangular factor T of the block reflector. Further Details, bestie, go look 👑

!>          T is REAL array, dimension (LDT,M)
!>          The N-by-N upper triangular factor T of the block reflector.
!>          See Further Details.
!>

• LDT — LDT is INTEGER. the leading dimension of the array T. LDT >= max(1,M).

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= max(1,M)
!>

• INFO — INFO is INTEGER. = 0: successful exit, we love to see it 🎉. < 0: if INFO = -i, the i-th argument had an illegal value, not cute 💀

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

🫶 Author 🫶

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

the whole squad really showed up for this one 💜

🔥 Further Details 🔥

okay this is the part where she gets detailed, strap in:

!>
!>  The input matrix C is a M-by-(M+N) matrix
!>
!>               C = [ A ][ B ]
!>
!>
!>  where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
!>  matrix consisting of a M-by-(N-L) rectangular matrix B1 left of a M-by-L
!>  upper trapezoidal matrix B2:
!>
!>               B = [ B1 ][ B2 ]
!>                   [ B1 ]  <-     M-by-(N-L) rectangular
!>                   [ B2 ]  <-     M-by-L lower trapezoidal.
!>
!>  The lower trapezoidal matrix B2 consists of the first L columns of a
!>  N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
!>  B is rectangular M-by-N; if M=L=N, B is lower triangular.
!>
!>  The matrix W stores the elementary reflectors H(i) in the i-th row
!>  above the diagonal (of A) in the M-by-(M+N) input matrix C
!>
!>               C = [ A ][ B ]
!>                   [ A ]  <- lower triangular M-by-M
!>                   [ B ]  <- M-by-N pentagonal
!>
!>  so that W can be represented as
!>
!>               W = [ I ][ V ]
!>                   [ I ]  <- identity, M-by-M
!>                   [ V ]  <- M-by-N, same form as B.
!>
!>  Thus, all of information needed for W is contained on exit in B, which
!>  we call V above.  Note that V has the same form as B; that is,
!>
!>               W = [ V1 ][ V2 ]
!>                   [ V1 ] <-     M-by-(N-L) rectangular
!>                   [ V2 ] <-     M-by-L lower trapezoidal.
!>
!>  The rows of V represent the vectors which define the H(i)'s.
!>  The (M+N)-by-(M+N) block reflector H is then given by
!>
!>               H = I - W**T * T * W
!>
!>  where W^H is the conjugate transpose of W and T is the upper triangular
!>  factor of the block reflector.
!>

like, the whole V/W/H pipeline is genuinely elegant once you see it — she's doing main character math 💫

Definition at line 176 of file stplqt2.f.

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (a robot wrote this one, no thoughts head empty 🤖✨)

---

and that's the whole page bestie!! 🎀 sign-off time: this was <rainbow>LAPACK — Version 3.12.0 — /home/abui.../stplqt2.f(3)</rainbow> 💖 go forth and factorize responsibly 🦋