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

🦋 NAME 🦋

okay bestie, this page is literally /home/abui...D/ctzrqf.f(3) from the <purple>Library Functions Manual</purple> — manual name folded in right here, slay. The file being documented is:

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

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✨ SYNOPSIS ✨

Functions/Subroutines:

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

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💻 Function/Subroutine Documentation 💻

the signature is giving main-character energy, and it is exactly:

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

🎀 Purpose 🎀

🚨 deprecated alert: this routine is deprecated and has been replaced by routine CTZRZF.

CTZRQF 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 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 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 ctzrqf.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie 💖 — it’s from LAPACK, Version 3.12.0, with footer path /home/abui...D/ctzrqf.f(3). mwah 🫶✨