SRC/DEPRECATED/stzrqf.f(3)

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version 3.12.1 · 3 versions
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✨ SRC/DEPRECATED/stzrqf.f ✨

okay so bestie, this is a page straight out of the Library Functions Manual and it's giving "vintage LAPACK, but make it deprecated" 🫶 buckle up, we're doing linear algebra.

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine stzrqf (m, n, a, lda, tau, info) — STZRQF

💜 Function/Subroutine Documentation 💜

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

STZRQF 👑

✨ Purpose ✨

!> This routine is deprecated and has been replaced by routine STZRZF.

ok so real talk first: this one is deprecated, no cap 😭 it's been replaced by STZRZF. She's iconic but she's retired. Use the new one, iykyk.

STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. literally her whole job 💅

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. slay.

🎀 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 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. she goes in one girl and comes out another 😌
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). respect the leading dimension or else 🫠
  • TAU — TAU is REAL array, dimension (M). The scalar factors of the elementary reflectors. tiny but mighty 🍓
  • INFO — INFO is INTEGER. Here's the vibe check:
    • = 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.

(the academic royal family, fr fr 🏰)

🔥 Further Details 🔥

so the math lore here is chef's kiss — 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. (yes bestie, X — that's what the page says, I don't make the rules 🙈)

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. everything's accounted for, nothing's lost, we love a clean handoff 💖

Z is given by

     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

periodt. 🌈

Definition at line 137 of file stzrqf.f.

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page bestie, go forth and factor your trapezoidal matrices (but like, with STZRZF now, remember? 😭💅). this lil transmission came to you courtesy of LAPACK, Version 3.12.0, and the file is SRC/DEPRECATED/stzrqf.f(3) — mwah, stan the deprecated icons 🎀🦋💜

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