SRC/cgeqrf.f(3)

✨ NAME ✨

okay bestie, this is the SRC/cgeqrf.f(3) page from the Library Functions Manual, and it’s all about one iconic subroutine: cgeqrf. QR factorization but make it complex, periodt. 💅

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

• subroutine cgeqrf (m, n, a, lda, tau, work, lwork, info) — the whole call, exactly like that, no cap.
• CGEQRF — the label chilling with it.

💅 Function/Subroutine Documentation 💅

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

Also labeled CGEQRF. main character subroutine energy. 💖

🎯 Purpose 🎯

CGEQRF 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 min(m,n) 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 (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 >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. For optimum performance LWORK >= N*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 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 145 of file cgeqrf.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie — footer vibes are LAPACK, Version 3.12.0, and SRC/cgeqrf.f(3). No extra date line, just QR-flavored main character energy. 💖✨🎀