/home/abui.../ztplqt2.f(3)

💅 ztplqt2.f — Library Functions Manual 💅

okay so this is the ztplqt2.f(3) page from the Library Functions Manual. It's LAPACK, it's Fortran, it's giving linear algebra main character energy. The header path is /home/abui.../ztplqt2.f(3) and the NAME section points at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztplqt2.f. Slay. 💅

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ztplqt2.f

That's the literal name/path, no notes, just the file. 🎀

✨ SYNOPSIS ✨

✨ Functions/Subroutines ✨

• subroutine ZTPLQT2 (m, n, l, a, lda, b, ldb, t, ldt, info) — the icon itself. The synopsis says exactly:

ZTPLQT2 computes a LQ factorization of a real or complex triangular-
pentagonal"matrix,whichiscomposedofatriangularblockandapentagonalblock,usingthecompactWYrepresentationforQ.

🫶 Function/Subroutine Documentation 🫶

Here's the full signature with all the types, dimensions, and vibes intact:

subroutine ZTPLQT2 (integer m, integer n, integer l, complex*16, dimension(
     lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,
     complex*16, dimension( ldt, * ) t, integer ldt, integer info)

And the main character sentence is literally: ZTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q. 💅

🎯 Purpose 🎯

The exact purpose blurb is: ZTPLQT2 computes a LQ a factorization of a complex matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q. ✨ (Yes, it says "LQ a factorization" — that's the source, bestie.)

🌸 Parameters 🌸

• M — M is INTEGER. The total number of rows of the matrix B. Constraint: M >= 0. 💖
• N — N is INTEGER. The number of columns of the matrix B, and the order of the triangular matrix A. Constraint: N >= 0. ✨
• L — L is INTEGER. The number of rows of the lower trapezoidal part of B. Constraint: MIN(M,N) >= L >= 0. See Further Details. 🎀
• A — A is COMPLEX*16 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. Constraint: LDA >= max(1,M). 🌸
• B — B is COMPLEX*16 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. Constraint: LDB >= max(1,M). 🫶
• T — T is COMPLEX*16 array, dimension (LDT,M). The N-by-N upper triangular factor T of the block reflector. See Further Details. 😭 (yes, N-by-N and (LDT,M) live together in the source, no cap)
• LDT — LDT is INTEGER. The leading dimension of the array T. Constraint: LDT >= max(1,M). 🔥
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. 👑

👑 Author 👑

These absolute legends:

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

🧚 Further Details 🧚

Okay bestie, matrix lore time. The input matrix C is an M-by-(M+N) matrix:

C = [ A ][ B ]

where A is an lower triangular M-by-M matrix, and B is an M-by-N pentagonal matrix consisting of an M-by-(N-L) rectangular matrix B1 left of an 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 an 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. (The source says W**T in the equation and W^H in the next line — iconic inconsistency, keep both. 💀)

Definition at line 176 of file ztplqt2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie. The footer says LAPACK Version 3.12.0 and points to /home/abui.../ztplqt2.f(3) — plus the usual Doxygen auto-gen date-ish footer energy. No actual date is spelled out, just the version and path, periodt. 💅✨🫶