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

💖 NAME 💖

Okay so this is the ztzrqf.f(3) page from the Library Functions Manual, and the official NAME line points at this exact path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/DEPRECATED/ztzrqf.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

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🦋 Function/Subroutine Documentation 🦋

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

ZTZRQF

💡 Purpose 💡

Bestie, major heads-up: this routine is deprecated and has been replaced by routine ZTZRZF. Not me delivering bad news, just keeping it real. 💅

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 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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🎀 Sign-off time: this came from LAPACK, Version 3.12.0, with the footer path /home/abui...D/ztzrqf.f(3). The original footer didn’t show a separate date, so I’m not gonna make one up — periodt. 💅✨