SRC/zlatrz.f(3)

Hey bestie! You're looking at SRC/zlatrz.f(3) from the Library Functions Manual — yes, the LAPACK girlies are back and this one is all about zlatrz. 💅

🌸 NAME 🌸

SRC/zlatrz.f — the source file that's serving the zlatrz moment.

✨ SYNOPSIS ✨

💕 Functions/Subroutines 💕

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

💅 Function/Subroutine Documentation 💅

Okay so here's the full signature, no cap:

subroutine zlatrz (integer m, integer n, integer l, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16,
       dimension( * ) work)

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

🎯 Purpose

ZLATRZ 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. That's the whole serve, bestie. ✨

🧾 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*16 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*16 array, dimension (M). The scalar factors of the elementary reflectors.
• WORK — WORK is COMPLEX*16 array, dimension (M).

🌟 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 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 zlatrz.f. 📍

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

xoxo, your Unix bestie 💖 — LAPACK Version 3.12.0, source SRC/zlatrz.f(3). The footer didn't give me a date, so I'm not inventing one, periodt. 🎀