DTZRZF(3)

💜 NAME

ok so bestie, this page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtzrzf.f — that's the source file, and the man page itself came from /home/abui...RC/dtzrzf.f(3). no cap, that's the whole name section 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines 🌸

• subroutine DTZRZF (m, n, a, lda, tau, work, lwork, info) — DTZRZF. that's her. that's the girl 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine DTZRZF (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DTZRZF 👑 (yes, the same name again — she's consistent)

🎀 Purpose 🎀

ok so here's the vibe, straight from the source, bestie:

!>
!> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
!> to upper triangular form by means of orthogonal transformations.
!>
!> The upper trapezoidal matrix A is factored as
!>
!>    A = ( R  0 ) * Z,
!>
!> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
!> triangular matrix.
!>

so basically: she takes your real upper trapezoidal matrix A (that's M-by-N, and M is <= N, iykyk) and reduces it to upper triangular form using orthogonal transformations. the factorization goes A = ( R 0 ) * Z where Z is N-by-N orthogonal and R is M-by-M upper triangular. iconic behavior honestly ✨

💖 Parameters 💖

• M — M is INTEGER. the number of rows of the matrix A. M >= 0. 🍓
• N — N is INTEGER. the number of columns of the matrix A. N >= M. 🍓
• A — A is DOUBLE PRECISION 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 orthogonal matrix Z as a product of M elementary reflectors. so she goes in as your matrix and comes out serving two looks at once 💅

• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M). 🫶
• TAU — TAU is DOUBLE PRECISION array, dimension (M). the scalar factors of the elementary reflectors. 🧚
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. ✨
• 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.

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 -1 means "don't actually do it, just tell me how much room I need" — queen of planning ahead ngl 🌈

• INFO — 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.

🌟 Contributors: 🌟

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

🔥 Further Details: 🔥

!>
!>  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)**T
!>
!>  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 DTZRZF,
!>  and tau(k) is the kth element of the array TAU.
!>
!>

so if you ever need to actually build Z yourself, that's the recipe — Z = Z(1)*Z(2)* ... *Z(M), each Z(k) = I - tau(k)*v(k)*v(k)**T, and v(k) is the kth row vector of 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 DTZRZF, and tau(k) is the kth element of the array TAU. main character math fr fr 🦋

Definition at line 150 of file dtzrzf.f. 📍

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. not a human wrote this part, and we respect the robot's hustle 🤖💖

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ok that's the whole page bestie, go forth and reduce some trapezoidal matrices 💅✨

LAPACK — Version 3.12.0, page from /home/abui...RC/dtzrzf.f(3) — mwah, that's the sign-off, ily, go read the source 🎀🫶