SRC/sgeqrf.f(3)

💖 SRC/sgeqrf.f 💖

okay so this is a page from the LAPACK manual (Library Functions Manual, bestie, we're in the big leagues now) and it's all about SGEQRF. yes that's a real name, no I will not be pronouncing it out loud. let's get into it ✨

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

• subroutine sgeqrf (m, n, a, lda, tau, work, lwork, info) — SGEQRF

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🦋 Function/Subroutine Documentation 🦋

subroutine sgeqrf (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, real, dimension( * ) tau, real, dimension( * ) work,
    integer lwork, integer info)

SGEQRF (yes, again, that's the whole subtitle, she's mysterious)

🌸 Purpose 🌸

SGEQRF computes a QR factorization of a real M-by-N matrix A:

A = Q * ( R ),
         ( 0 )

where:

• Q is a M-by-M orthogonal matrix;
• R is an upper-triangular N-by-N matrix;
• 0 is a (M-N)-by-N zero matrix, if M > N.

like literally she's taking your matrix and breaking it down into its most iconic form. main character decomposition energy, no cap 💅

🎀 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 elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).

so she comes in as your cute little A and leaves as R up top and Q-stuff down below. glow-up fr 🦋

• LDA

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

• TAU

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

• WORK

WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

she's the workspace, she's doing the behind-the-scenes labor, and she'll tell you exactly how much room she wanted. queen behavior 👑

• LWORK

LWORK is INTEGER The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. For optimum performance LWORK >= N*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.

bestie LWORK = -1 is the "don't actually do it, just tell me how much space I need" mode. iconic honestly. 💅

• 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.

four whole institutions collaborated on this. the group project that actually got finished 😭🫶

🧚 Further Details 🧚

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), where k = min(m,n).

Each H(i) has the form

H(i) = 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), and tau in TAU(i).

so Q isn't stored as a big ol' matrix, she's stored as a stack of these little reflector guys. efficient queen. 🔥

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Definition at line 145 of file sgeqrf.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a robot doing her best 🎀)

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okay that's the whole page bestie, go forth and factorize responsibly 🌈💖

LAPACK — Version 3.12.0 — SRC/sgeqrf.f(3) ✨ mwah, see u in the next manpage 🫶💅