SRC/zgerqf.f(3)

🌸 NAME 🌸

SRC/zgerqf.f — okay bestie, this is the manual page for that file, and the manual-name energy is SRC/zgerqf.f(3) from the Library Functions Manual 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zgerqf (m, n, a, lda, tau, work, lwork, info)
           ZGERQF

💖 Function/Subroutine Documentation 💖

subroutine zgerqf (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )
    work, integer lwork, integer info)

🌟 ZGERQF 🌟

✨ Purpose ✨

The way that ZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * Q. That's the whole mission, no cap.

🦋 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*16 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 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*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors (see Further Details).
• WORK — WORK is COMPLEX*16 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 >= M, otherwise. For optimum performance LWORK >= M*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 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 138 of file zgerqf.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

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