SRC/DEPRECATED/dgeqpf.f(3)

💅 SRC/DEPRECATED/dgeqpf.f(3) 💅

okay bestie, this page is from the Library Functions Manual and it’s all about SRC/DEPRECATED/dgeqpf.f — the DGEQPF subroutine, which is deprecated but still iconic in a “please use the new one” way. Let’s go. 💖

🏷️ NAME 🏷️

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 🎯

🚨 Deprecated alert, no cap: This routine is deprecated and has been replaced by routine DGEQP3.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. It’s the number of rows of the matrix A. Constraint: M >= 0. slay.
• N — N is INTEGER. It’s the number of columns of the matrix A. Constraint: N >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N).
  • On entry, it’s 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. Constraint: 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 🤖

Generated automatically by Doxygen for LAPACK from the source code.

---

💖 that’s the whole page, bestie 💖 Footer tea: LAPACK Version 3.12.0, source SRC/DEPRECATED/dgeqpf.f(3). There’s no date printed on this one, so I’m not inventing one — mwah 💋