/home/abui...D/dtzrqf.f(3)

okay bestie, welcome to the manual page for /home/abui...D/dtzrqf.f(3) — it lives under Library Functions Manual, and it's all about the LAPACK routine DTZRQF. Yes, that path is literally the name, we don't argue with the filesystem. 💅

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/DEPRECATED/dtzrqf.f — that's the whole name line, bestie. It's the source file for the deprecated DTZRQF routine. 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DTZRQF (m, n, a, lda, tau, info)

DTZRQF — say it with me, it's giving linear algebra main character energy. 🦋

🧚 Function/Subroutine Documentation 🧚

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

DTZRQF again, because the signature said so and we respect the signature. 💖

Purpose

⚠️ warning, babe: this routine is deprecated and has been replaced by routine DTZRZF.

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. ✨

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 137 of file dtzrqf.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🧚

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and that's the whole page, bestie! footer vibes: LAPACK · Version 3.12.0 · /home/abui...D/dtzrqf.f(3). That's the source/version/path situation right there — no invented date from me, periodt. bye diva! 💖✨