STZRZF(3)

💅 STZRZF(3) — Library Functions Manual 🦋

okay bestie, we’re in the Library Functions Manual and this is the page for STZRZF(3). It’s giving very specific LAPACK energy, and honestly? Iconic.

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🌸 NAME

This page is filed under /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/stzrzf.f — that’s the NAME entry, bestie. No cap.

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✨ SYNOPSIS

🧩 Functions/Subroutines

subroutine STZRZF (m, n, a, lda, tau, work, lwork, info)
    STZRZF

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🧚 Function/Subroutine Documentation

subroutine STZRZF (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer lwork, integer info)
       STZRZF

🎯 Purpose

STZRZF reduces the M-by-N (M<=N) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations. Slay.

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. Literally the whole plot.

🫶 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’s doing a lot of work, honestly.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is REAL array, dimension (M). The scalar factors of the elementary reflectors.
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• INFO — INFO is INTEGER. = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

bestie, LWORK = -1 is the “just tell me the size, don’t actually run it” mode. Very main character. 💅

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

🫶 Contributors

• A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

🔥 Further Details

The N-by-N matrix Z can be computed by

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

where each N-by-N Z(k) is given by

Z(k) = I - tau(k)*v(k)*v(k)**T

with v(k) being the kth row vector of the M-by-N matrix

V = ( I   A(:,M+1:N) )

I is the M-by-M identity matrix, A(:,M+1:N) is the output stored in A on exit from STZRZF, and tau(k) is the kth element of the array TAU. That’s the whole lore drop.

📌 Definition at line 150 of file stzrzf.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the wrap, bestie! The footer gives us LAPACK Version 3.12.0 and points back to /home/abui...RC/stzrzf.f(3) — no separate date on this one, just version and path. 💖✨