/home/abui...D/cgeqpf.f(3)

💖 cgeqpf.f(3) — Library Functions Manual 💖

okay so bestie, this is the <pink>Library Functions Manual</pink> page for cgeqpf.f(3). Buckle up, because this one is a deprecated LAPACK baddie with receipts. 💅

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✨ NAME ✨

The name/path is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/DEPRECATED/cgeqpf.f

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🦋 SYNOPSIS 🦋

🌸 Functions/Subroutines 🌸

       subroutine CGEQPF (m, n, a, lda, jpvt, tau, work, rwork, info)

CGEQPF — that's the main character, no cap.

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💅 Function/Subroutine Documentation 💅

   subroutine CGEQPF (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau,
       complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGEQPF again, bestie — yes, the icon is showing up twice. 🫶

✨ Purpose ✨

🚨 This routine is deprecated and has been replaced by routine CGEQP3. Like, for real, don’t build your whole personality on CGEQPF unless you have to.

CGEQPF computes a QR factorization with column pivoting of a complex M-by-N matrix A: A*P = Q*R. Slay. 💖

🎀 Parameters 🎀

• M — M is INTEGER; it’s the number of rows of matrix A. M >= 0.
• N — N is INTEGER; it’s the number of columns of matrix A. N >= 0.
• A — A is COMPLEX array, dimension (LDA,N). On entry, this is the M-by-N matrix A. On exit, the upper triangle of the array contains the min(M,N)-by-N upper triangular matrix R; the elements below the diagonal, together with the array TAU, represent the unitary matrix Q as a product of min(m,n) elementary reflectors. That’s a whole glow-up, honestly. 😭
• LDA — LDA is INTEGER; it’s the leading dimension of the array A. LDA >= max(1,M). Respect the leading dimension, bestie.
• JPVT — JPVT is INTEGER array, dimension (N). On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to the front of A*P (a leading column); if JPVT(i) = 0, the i-th column of A is a free column. On exit, if JPVT(i) = k, then the i-th column of A*P was the k-th column of A. So it’s giving “receipts of where everything went.” 💀
• TAU — TAU is COMPLEX array, dimension (min(M,N)); these are the scalar factors of the elementary reflectors. Iconic little scalars.
• WORK — WORK is COMPLEX array, dimension (N). Werk, work, same vibes. 💅
• RWORK — RWORK is REAL array, dimension (2*N). Not to be confused with WORK; they are different queens.
• INFO — INFO is INTEGER: = 0 means successful exit; < 0 means if INFO = -i, the i-th argument had an illegal value. So if INFO is negative, something got read for filth at argument -i. 🙈

👑 Author 👑

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

⭐ Further Details ⭐

The matrix Q is represented as a product of elementary reflectors:

Q = H(1) H(2) . . . H(n)

Each H(i) has the form:

H = I - tau * v * v**H

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i). Literally the blueprint, no cap. 🦋

The matrix P is represented in jpvt as follows: if

jpvt(j) = i

then the jth column of P is the ith canonical unit vector. The way that indexing lines up is highkey a vibe. ✨

Partial column norm updating strategy modified by Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. -- April 2011 -- For more details see LAPACK Working Note 176. Respect the lore. 📚

Definition at line 147 of file cgeqpf.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 — footer path says /home/abui...D/cgeqpf.f(3), and that’s the whole sign-off, bestie. Mwah. 💋✨