DGEQP3(3)

DGEQP3(3) — Library Functions Manual ✨🦋

okay bestie, buckle up: this is the manual page for DGEQP3, and she is literally the QR-with-column-pivoting moment of your linear algebra dreams. The manual name is right there: Library Functions Manual. Now let's get into the lore 💅.

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgeqp3.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine DGEQP3 (m, n, a, lda, jpvt, tau, work, lwork, info)
    DGEQP3

DGEQP3 is the function/subroutine in question, and yes, she is iconic 👑.

🌸 Function/Subroutine Documentation 🌸

subroutine DGEQP3 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)
    DGEQP3

okay so here's the full signature, exactly as printed — do not come for me about the line wrap, she is serving definition realness 💅.

💡 Purpose 💡

the whole reason she exists:

!>
!> DGEQP3 computes a QR factorization with column pivoting of a
!> matrix A:  A*P = Q*R  using Level 3 BLAS.
!>

periodt. She computes a QR factorization with column pivoting of a matrix A, specifically A*P = Q*R, using Level 3 BLAS 🔥.

🧚 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 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 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 (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 reflector representation, in all her glory:

!>
!>  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).
!>

yup, that's the exact reflector tea ☕.

🌈 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 dgeqp3.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this footer is giving LAPACK Version 3.12.0, source /home/abui...RC/dgeqp3.f(3). No date on this footer, bestie, just version and source — periodt 🫶.