SRC/cgeqp3.f(3)

SRC/cgeqp3.f(3) 💅

okay so we're in the LAPACK Library Functions Manual, and this is the page for CGEQP3. She's that subroutine: QR factorization with column pivoting, A*P = Q*R, Level 3 BLAS energy. iconic behavior, no cap.

✨ NAME ✨

SRC/cgeqp3.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

       subroutine cgeqp3 (m, n, a, lda, jpvt, tau, work, lwork, rwork, info)
           CGEQP3

🧚 Function/Subroutine Documentation 🧚

Meet the full signature, bestie — every type and dimension is right here:

   subroutine cgeqp3 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau,
       complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork,
       integer info)
       CGEQP3

Purpose: 💅

CGEQP3 computes a QR factorization with column pivoting of a matrix A:

A*P = Q*R

using Level 3 BLAS. periodt.

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 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 trapezoidal 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. 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 COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors.
• WORK — WORK is COMPLEX 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 >= N+1. For optimal performance LWORK >= ( 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.
• 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(k), where k = min(m,n).

Each H(i) has the form:

H(i) = I - tau * v * v**H

where tau is a complex 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).

Contributors: 🌈

• G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
• X. Sun, Computer Science Dept., Duke University, USA

Definition at line 157 of file cgeqp3.f.

Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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okay bye bestie 💖 this page is from LAPACK Version 3.12.0 and the footer is giving SRC/cgeqp3.f(3). slay and stay pivoted.