SRC/cgeqr2.f(3)

🎀 SRC/cgeqr2.f(3) 🎀

okay bestie, welcome to the Library Functions Manual — this page is literally all about SRC/cgeqr2.f, and it’s giving “tiny but mighty LAPACK routine” energy. 💅

💖 NAME 💖

SRC/cgeqr2.f — the file this page is about, no cap.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine cgeqr2 (m, n, a, lda, tau, work, info) — CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

🌸 Function/Subroutine Documentation 🌸

subroutine cgeqr2 (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,
    integer info)

CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

🔥 Purpose 🔥

CGEQR2 computes a QR factorization of a complex m-by-n matrix A:

   A = Q * ( R ),
            ( 0 )

where:

• Q is a m-by-m orthogonal matrix;
• R is an upper-triangular n-by-n matrix;
• 0 is a (m-n)-by-n zero matrix, if m > n.

💜 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 elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, 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 (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 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).

Definition at line 129 of file cgeqr2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💅 okay that’s the whole page, bestie — LAPACK Version 3.12.0, source/page SRC/cgeqr2.f(3). mwah 💖