CTZRZF(3)

💅 CTZRZF(3) — like, the LAPACK one, bestie

okay so real talk: this page lives in the Library Functions Manual section of your man pages, and it's about a Fortran subroutine that is honestly kind of iconic once you get what it's doing. the file it came from is literally:

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

no cap, that's the NAME section. it's giving "the path is the name" energy and we respect it. 💖

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CTZRZF (m, n, a, lda, tau, work, lwork, info)

CTZRZF

🦋 Function/Subroutine Documentation 🦋

subroutine CTZRZF (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer lwork, integer info)

CTZRZF

🎀 Purpose 🎀

okay so here's the whole vibe, bestie:

CTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. slay. ✨

the upper trapezoidal matrix A is factored as

A = ( R  0 ) * Z,

where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix. literally that's it, that's the whole plot. 💅

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🌸 Parameters 🌸

• M — M is INTEGER. the number of rows of the matrix A. M >= 0. no negativity allowed, we're manifesting positivity only. 🫶
• N — N is INTEGER. the number of columns of the matrix A. N >= M. yeah, it's gotta be at least as wide as it is tall. iykyk.
• A — A is COMPLEX array, dimension (LDA,N). on entry, the leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. on exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors. so A is doing double duty, main character energy tbh. 👑
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M). don't skimp on this one, the vibe check is strict.
• TAU — TAU is COMPLEX array, dimension (M). the scalar factors of the elementary reflectors. little guys, huge responsibility. 🎀
• WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. it's a workspace, it works. 😭
• LWORK — LWORK is INTEGER. the dimension of the array WORK. LWORK >= max(1,M). for optimum performance LWORK >= M*NB, where NB is the optimal blocksize.

bestie listen: 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 isn't "bad", it's "asking politely". 🧚

• INFO — INFO is INTEGER.
  • = 0: successful exit 🌈
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

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⭐ Author ⭐

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

💜 Contributors: 💜

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

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🔥 Further Details: 🔥

okay this is the part where it gets cute, so pay attention bestie:

the N-by-N matrix Z can be computed by

Z =  Z(1)*Z(2)* ... *Z(M)

where each N-by-N Z(k) is given by

Z(k) = I - tau(k)*v(k)*v(k)**H

with v(k) is the kth row vector of the M-by-N matrix

V = ( I   A(:,M+1:N) )

I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from CTZRZF, and tau(k) is the kth element of the array TAU.

see? it all connects. obsessed. 🦋

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Definition at line 150 of file ctzrzf.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — no notes, ate and left no crumbs 💅✨ so like, this was LAPACK, Version 3.12.0, straight out of /home/abui...RC/ctzrzf.f(3) — catch you in the next man page, mwah 🎀💖🫶