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

okay bestie, this page is from the Library Functions Manual — page /home/abui...D/stzrqf.f(3) — and it's giving deprecated LAPACK math but make it cute. 💅✨

🎀 NAME 🎀

the full file name is:

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

(the original page line-wraps it after lapack-, bestie 🫶)

✨ SYNOPSIS ✨

Functions/Subroutines — yes, that's the section vibe:

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

💖 Function/Subroutine Documentation 💖

the detailed signature is literally:

subroutine STZRQF (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, integer info)

🎯 Purpose 🎯

okay so important tea: this routine is deprecated and has been replaced by routine STZRZF. no cap, that's the headline. ☕💅

STZRQF 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. periodt. 👑✨

🫶 Parameters 🫶

• M — M is INTEGER; it's the number of rows of the matrix A. M >= 0.
• N — N is INTEGER; it's the number of columns of the matrix A. N >= M.
• A — A is REAL 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. slay. 💖
• LDA — LDA is INTEGER; it's the leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is REAL array, dimension (M); these are 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 stzrqf.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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