SRC/DEPRECATED/sgeqpf.f(3)

💅 SRC/DEPRECATED/sgeqpf.f(3) 💅

okay so bestie, you're looking at the SRC/DEPRECATED/sgeqpf.f(3) page from the Library Functions Manual — yes, the deprecation corner of LAPACK. Buckle up, it's giving "old but still iconic" energy. 💖

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🌸 NAME 🌸

SRC/DEPRECATED/sgeqpf.f — that's literally the name, no cap.

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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 🫶

The full signature is this cutie:

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 🎯

⚠️ deprecated alert, bestie: this routine is deprecated and has been replaced by routine SGEQP3.

SGEQPF computes a QR factorization with column pivoting of a real M-by-N matrix A: A*P = Q*R.

💖 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.
• 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.
• TAU — TAU is REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
• WORK — WORK is REAL array, dimension (3*N).
• 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(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.

Definition at line 141 of file sgeqpf.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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ok bye bestie 💖 this was LAPACK Version 3.12.0, page SRC/DEPRECATED/sgeqpf.f(3) — mwah, stay deprecated but stay flawless ✨