SRC/cungrq.f(3)

💖 SRC/cungrq.f(3) 💖

okay bestie, this one's from the Library Functions Manual, and it's giving “complex matrix glow-up” energy. It's all about SRC/cungrq.f and the subroutine CUNGRQ. 🦋

✨ NAME ✨

SRC/cungrq.f — home of CUNGRQ, the routine that builds an M-by-N complex matrix Q with orthonormal rows from the reflectors returned by CGERQF. 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine cungrq (m, n, k, a, lda, tau, work, lwork, info) — CUNGRQ

🦋 Function/Subroutine Documentation 🦋

🎀 subroutine cungrq 🎀

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

CUNGRQ

🎯 Purpose

Bestie, CUNGRQ generates an M-by-N complex matrix Q with orthonormal rows. It's defined as the last M rows of a product of K elementary reflectors of order N, like this:

Q  =  H(1)**H H(2)**H . . . H(k)**H

...and it's exactly what CGERQF hands back. ✨

🌈 Parameters

• M — INTEGER. The number of rows of the matrix Q. M >= 0.
• N — INTEGER. The number of columns of the matrix Q. N >= M.
• K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
• A — COMPLEX array, dimension (LDA,N). On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGERQF in the last k rows of its array argument A. On exit, the M-by-N matrix Q.
• LDA — INTEGER. The first dimension of the array A. LDA >= max(1,M).
• TAU — COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGERQF.
• WORK — COMPLEX array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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 — INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument has an illegal value

👑 Author

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

🧚 Definition

Definition at line 127 of file cungrq.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie! LAPACK Version 3.12.0, source SRC/cungrq.f(3), and yes, she ate. 💖✨