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

🎀 NAME 🎀

ok so bestie, this page is literally about the file:

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

yes that's the whole name. it's giving "my professor's file path energy" 💀 and yes, the DEPRECATED folder is right there in the path, we'll get to that 🙈

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine SGEQPF (m, n, a, lda, jpvt, tau, work, info) — SGEQPF

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💅 Function/Subroutine Documentation 💅

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

SGEQPF

🌸 Purpose 🌸

This routine is deprecated and has been replaced by routine SGEQP3.

like, it still works, but it's the vintage one okay 😭 the glow-up already happened, it's called SGEQP3, and this one is the "before" photo.

SGEQPF computes a QR factorization with column pivoting of a real M-by-N matrix A:

A*P = Q*R

periodt. iconic math behavior 💖

🦋 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 >= 0

A

A is REAL array, dimension (LDA,N)
On entry, 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 orthogonal matrix Q as a product of
min(m,n) elementary reflectors.

so like, it goes in as A and comes out as R + the little hidden ingredients for Q. it's giving before-and-after makeover ✨👑

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

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.

okay so this array is lowkey the main character 🫶 on the way in it's telling you which columns get to skip the line, and on the way out it's the receipt of who came from where. JPVT(i) .ne. 0? leading column, front of the queue. JPVT(i) = 0? free column, living its best free life. then after, JPVT(i) = k means the i-th column of A*P used to be the k-th column of A. iykyk 💫

TAU

TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK

WORK is REAL array, dimension (3*N)

scratch space bestie, 3*N of it, not a single element less 🍓

INFO

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

0 = slay, we're done. < 0 = not me getting -i because the i-th argument was illegal 😭

👑 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**T

where tau is a real scalar, and v is a real 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).

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.

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.

like okayyy the Zagreb girlies really came through with the partial column norm updating strategy update in April 2011 💅 we stan a documented glow-up 🌈

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Definition at line 141 of file sgeqpf.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. no cap, the robots wrote this one 🤖✨

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and that's the whole page bestie!! 🎀💖

LAPACK — Version 3.12.0 — /home/abui...D/sgeqpf.f(3)

mwah, go factor some matrices, ily 🫶🦋