SLATRZ(3)

💖 SLATRZ(3) 💖

okay bestie, quick vibe check: this is the SLATRZ(3) page from the LAPACK Library Functions Manual, and it lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slatrz.f. she’s giving “deep linear algebra, but make it cute” 💅

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✨ SYNOPSIS ✨

Functions/Subroutines:

• subroutine SLATRZ (m, n, l, a, lda, tau, work) — SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.

🫶 Function/Subroutine Documentation 🫶

subroutine SLATRZ (integer m, integer n, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work)

SLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations. yes, that’s the whole main-character job description, and she ate 🔥

Purpose

SLATRZ factors the M-by-(M+L) real upper trapezoidal matrix

[ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ]

as ( R 0 ) * Z, by means of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal matrix, and R and A1 are M-by-M upper triangular matrices.

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🌸 Parameters 🌸

• M — M is INTEGER. the number of rows of the matrix A. M >= 0. no negative row energy allowed, bestie 🙈
• N — N is INTEGER. the number of columns of the matrix A. N >= 0. periodt.
• L — L is INTEGER. the number of columns of the matrix A containing the meaningful part of the Householder vectors. constraint check: N-M >= L >= 0.
• A — A is REAL 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 N-L+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. she’s doing a little before-and-after reveal, iconic behavior 💖
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is REAL array, dimension (M). the scalar factors of the elementary reflectors. little scalar icons, lowkey carrying the whole transformation 🎀
• WORK — WORK is REAL array, dimension (M). the workspace bestie, respect her.

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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 💜

the factorization is obtained by Householder’s method. the kth transformation matrix, Z( k ), which is used to introduce zeros into the ( m - k + 1 )th row of A, is given in the form

Z( k ) = ( I     0   ),
         ( 0  T( k ) )

where

T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
                                             (   0    )
                                             ( z( k ) )

tau is a scalar and z( k ) is an l element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of A2. not me getting emotional over annihilation, but okay 😭

the scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A2, such that the elements of z( k ) are in a( k, l + 1 ), ..., a( k, n ). the elements of R are returned in the upper triangular part of A1.

Z is given by

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

Definition at line 139 of file slatrz.f.

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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ok that’s the whole lore dump 💀 every flag, constraint, formula, and little Fortran detail is here. no cap.

and for the cute sign-off: this is LAPACK Version 3.12.0, from the path /home/abui...RC/slatrz.f(3) — slay, stay orthogonal, and hydrate before you factorize 🫶✨💅