SGEQP3(3)

🦋 NAME 🦋

okay so bestie, this is the man page for sgeqp3.f(3) from the Library Functions Manual — and the NAME section is literally just this file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgeqp3.f

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🌈 SYNOPSIS 🌈

Functions/Subroutines

subroutine SGEQP3 (m, n, a, lda, jpvt, tau, work, lwork, info)

SGEQP3

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💖 Function/Subroutine Documentation 💖

subroutine SGEQP3 (integer m, integer n, real, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau,
    real, dimension( * ) work, integer lwork, integer info)

SGEQP3

🎯 Purpose 🎯

okay so the whole point: SGEQP3 computes a QR factorization with column pivoting of a matrix A:

A*P = Q*R

and it does this using Level 3 BLAS. slay. ✨

🧮 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 trapezoidal 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. 🦋
• 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(J).ne.0, the J-th column of A is permuted to the front of A*P (a leading column); if JPVT(J)=0, the J-th column of A is a free column. On exit, if JPVT(J)=K, then the J-th column of A*P was the the K-th column of A. 🫶
• TAU — TAU is REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors. ⭐
• WORK — WORK is REAL 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 >= 3*N+1. For optimal performance LWORK >= 2*N+( N+1 )*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 — 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.

🧚 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/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), and tau in TAU(i). 🌸

🌟 Contributors 🌟

• G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
• X. Sun, Computer Science Dept., Duke University, USA

Definition at line 150 of file sgeqp3.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶 — cute little footer sign-off: source/version is LAPACK Version 3.12.0, page path is /home/abui...RC/sgeqp3.f(3), and it was auto-generated by Doxygen for LAPACK from the source code. periodt. 💖✨