SRC/DEPRECATED/ztzrqf.f(3)

okay bestie, this is the Library Functions Manual page for SRC/DEPRECATED/ztzrqf.f(3) — and yes, it’s giving deprecated LAPACK energy. 💅

🌸 NAME

SRC/DEPRECATED/ztzrqf.f — literally the file this page is about.

✨ SYNOPSIS

🎀 Functions/Subroutines

• subroutine ztzrqf (m, n, a, lda, tau, info) — ZTZRQF

💖 Function/Subroutine Documentation

subroutine ztzrqf (integer m, integer n, complex*16, dimension( lda, * ) a,
     integer lda, complex*16, dimension( * ) tau, integer info)

ZTZRQF

🎀 Purpose

🚨 Deprecated alert, bestie: this routine is deprecated and has been replaced by routine ZTZRZF.

ZTZRQF reduces the M-by-N (M<=N) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.

The upper trapezoidal matrix A is factored as

A = ( R  0 ) * Z,

where Z is an N-by-N unitary 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 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 M+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.
• 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 ), whose conjugate transpose 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 ( 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 ztzrqf.f.

🌈 Author

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cute footer sign-off, bestie: LAPACK Version 3.12.0, source path SRC/DEPRECATED/ztzrqf.f(3) — that’s the whole vibe check, periodt. 💖✨