CGERQ2(3)

🌸 NAME

Okay bestie, welcome to the CGERQ2(3) page — yes, the Library Functions Manual cutie — and the NAME line is literally this source-file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgerq2.f

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💖 SYNOPSIS

📚 Functions/Subroutines

• subroutine CGERQ2 (m, n, a, lda, tau, work, info) — CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

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🦋 Function/Subroutine Documentation

subroutine CGERQ2 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer info)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

🎯 Purpose

The tea is: CGERQ2 computes an RQ factorization of a complex m by n matrix A:

A = R * Q.

🧸 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, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; the remaining elements, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• TAU — TAU is COMPLEX array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX array, dimension (M).
• 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 H(2)**H . . . H(k)**H, 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 complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

📌 Definition at line 122 of file cgerq2.f.

👑 Author

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