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

📦 version 3.12.0, in opensuse-leap 16.0

Okay bestie, this is the Library Functions Manual page for /home/abui...D/dgeqpf.f(3). Buckle up, because this routine is a LAPACK legacy girlie with receipts. 💅

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

DGEQPF

🦋 Function/Subroutine Documentation 🦋

subroutine DGEQPF (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQPF

💅 Purpose 💅

Okay so here’s the tea, bestie: this routine is deprecated and has been replaced by routine DGEQP3. 🚨

DGEQPF 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
  • WORK — WORK is DOUBLE PRECISION 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 dgeqpf.f. 📍

👑 Author 👑

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💖 That’s the whole page, bestie! Source/version vibes: LAPACK Version 3.12.0; file: /home/abui...D/dgeqpf.f(3). The footer has no date, so I’m not inventing one — periodt. 🫶

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