SRC/ctzrzf.f(3)

💅 SRC/ctzrzf.f(3) — Library Functions Manual 💅

okay bestie, welcome to the SRC/ctzrzf.f glow-up ✨ this is the Library Functions Manual page for a LAPACK subroutine, and it’s giving “complex upper trapezoidal matrix gets a unitary transformation makeover” energy. Let’s get into it fr fr.

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🌸 NAME 🌸

SRC/ctzrzf.f — that’s the page name, bestie. This is the manual entry for the ctzrzf subroutine and its function/subroutine docs. 💖

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine ctzrzf (m, n, a, lda, tau, work, lwork, info) — the CTZRZF routine itself, iconic behavior only 👑

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

CTZRZF — yes, that’s the label, periodt 💅

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💖 Function/Subroutine Documentation 💖

🧚 subroutine ctzrzf 🧚

subroutine ctzrzf (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer lwork, integer info)

CTZRZF — the function name, main character energy fr fr.

🌟 Purpose 🌟

So what does it do? The !> vibes say:

CTZRZF 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.

periodt 💅

🍓 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.
• WORK — WORK is COMPLEX 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.

🌈 Author 🌈

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

These are the author credits, not me, bestie 😌

🫶 Contributors 🫶

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

ty for the contributions, icon 💜

🦋 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)**H

with v(k) is 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 CTZRZF, and tau(k) is the kth element of the array TAU.

That’s the factorization lore, and it ate 🔥

Definition at line 150 of file ctzrzf.f. — noted, bestie 🎯

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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okay that’s the whole page, bestie: source/version is LAPACK Version 3.12.0, page tag is SRC/ctzrzf.f(3), and the footer doesn’t print a separate date line — mwah 💋🎀