SRC/dtzrzf.f(3)

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version 3.12.1 · 7 versions
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💖 NAME 💖

Okay so welcome to SRC/dtzrzf.f(3), bestie — it's a Library Functions Manual page, and the whole vibe is SRC/dtzrzf.f. The main character? DTZRZF. Periodt. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

DTZRZF — the subroutine name, living its best life. 🦋

🌸 Function/Subroutine Documentation 🌸

subroutine dtzrzf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DTZRZF — that's the routine, no cap. 🔥

💅 Purpose 💅

Okay so DTZRZF 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. Obsessed with the structure, honestly. ✨

🍓 Parameters 🍓

  • M — it's giving M is INTEGER; the number of rows of the matrix A. M >= 0.
  • N — the column count, icon behavior N is INTEGER; the number of columns of the matrix A. N >= M.
  • A — A is DOUBLE PRECISION 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. Main character array fr fr. 💖
  • LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
  • TAU — TAU is DOUBLE PRECISION array, dimension (M); the scalar factors of the elementary reflectors. Little scalars, big plot. 🎀
  • WORK — WORK is DOUBLE PRECISION 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. Workspace query realness. 🫶
  • INFO — INFO is INTEGER; = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Illegal value? Not the vibe. 💀

👑 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

where 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 DTZRZF, and tau(k) is the kth element of the array TAU. This math is lowkey iconic. 🌈

Definition at line 150 of file dtzrzf.f.

💀 Author 💀

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Okay bestie, that's the whole page — footer sign-off: LAPACK Version 3.12.0, SRC/dtzrzf.f(3), and the manual-page source/version energy is immaculate. 💖✨

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