SRC/DEPRECATED/dtzrqf.f(3)

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version 3.12.1 · 3 versions
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🌸 NAME 🌸

okay so bestie, welcome to SRC/DEPRECATED/dtzrqf.f(3) — a Library Functions Manual page, and the main character here is the deprecated DTZRQF routine 💅 no cap.

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine dtzrqf (m, n, a, lda, tau, info) — the call, and the routine's whole name is DTZRQF 🌈

🫶 Function/Subroutine Documentation 🫶

subroutine dtzrqf (integer m, integer n, double precision, dimension( lda, *
       ) a, integer lda, double precision, dimension( * ) tau, integer info)

This is DTZRQF 🎀.

🎯 Purpose 🎯

Heads up, bestie: this routine is deprecated and has been replaced by routine DTZRZF. So maybe don't make it your main character unless you have to 😭.

DTZRQF 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. Slay, linear algebra 💖.

🧚 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.

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.

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.

🔍 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 ( n - m ) element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of X.

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

Z is given by

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

📍 Definition at line 📍

Definition at line 137 of file dtzrqf.f.

🌟 Author 🌟

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