SRC/DEPRECATED/cgeqpf.f(3)

🎀 SRC/DEPRECATED/cgeqpf.f(3) 🎀

okay bestie, this page is from the Library Functions Manual, and it’s all about SRC/DEPRECATED/cgeqpf.f — yes, the path is the title, we don’t make the rules. 💅

✨ NAME ✨

SRC/DEPRECATED/cgeqpf.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine cgeqpf (m, n, a, lda, jpvt, tau, work, rwork, info)
    CGEQPF

🦋 Function/Subroutine Documentation 🦋

subroutine cgeqpf (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau,
    complex, dimension( * ) work, real, dimension( * ) rwork, integer info)
    CGEQPF

Purpose

This routine is deprecated and has been replaced by routine CGEQP3. 🫶

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

Parameters

• M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= 0. 🌈
• N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0. 🦋
• A — A is COMPLEX 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 unitary 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 COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors. ⭐
• WORK — WORK is COMPLEX array, dimension (N). 💜
• RWORK — RWORK is REAL array, dimension (2*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**H

where tau is a complex scalar, and v is a 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). 🧚

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 147 of file cgeqpf.f. 🫶

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie — mwah 💋. This one is LAPACK Version 3.12.0, from SRC/DEPRECATED/cgeqpf.f(3). 🎀