SRC/clatrz.f(3)

💖 SRC/clatrz.f(3) 💖

Hii bestie! Welcome to the Library Functions Manual page for SRC/clatrz.f(3) — title and manual name folded in right here, all cozy. 🧚✨

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🌸 NAME 🌸

SRC/clatrz.f — that's the file, and that's the whole NAME section. No cap, it's literally just the file. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine clatrz (m, n, l, a, lda, tau, work) — CLATRZ factors an upper trapezoidal matrix by means of unitary transformations. 🫶

📚 Function/Subroutine Documentation 📚

Signature time, and we're keeping it exactly as written because code is sacred:

subroutine clatrz (integer m, integer n, integer l, complex, dimension( lda,
       * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * )
       work)

CLATRZ factors an upper trapezoidal matrix by means of unitary transformations. Periodt. 💖

🎯 Purpose

Okay so the glow-up here is that CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix

[ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z

by means of unitary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices. ✨

🌈 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 >= 0. 📐
• L — L is INTEGER. The number of columns of the matrix A containing the meaningful part of the Householder vectors. N-M >= L >= 0. 🧠
• 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 N-L+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. 💅
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). 📏
• TAU — TAU is COMPLEX array, dimension (M). The scalar factors of the elementary reflectors. ✨
• WORK — WORK is COMPLEX array, dimension (M). 🛠️

👑 Author

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

🌟 Contributors:

Big shoutout to A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA — that's the contributor list, and we're obsessed. 🫶

🔥 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 )**H,   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. 💖

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 clatrz.f.

Definition at line 139 of file clatrz.f. — noted, bestie, not changing a single character. 📌

🧾 Author

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

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That's the whole page, bestie — muah 💋. Signing off from LAPACK Version 3.12.0 and SRC/clatrz.f(3); the footer didn't show a date, so no fake date here, just the source/version vibes. 🎀🦋💜