SRC/cgeqrt3.f(3)

✨ SRC/cgeqrt3.f(3) ✨

okay so bestie, this page lives in the Library Functions Manual and it is all about one recursive LAPACK baddie. Buckle up, it is giving QR factorization with main character energy. 💖✨

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✨ NAME ✨

SRC/cgeqrt3.f — that is it, that is the name. Minimalist icon behavior. 💅

🌸 SYNOPSIS 🌸

🧩 Functions/Subroutines

• recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info) — CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

💖 Function/Subroutine Documentation 💖

recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

🎯 Purpose

CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. No cap, it is recursive. 🔁

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

🎀 Parameters 🎀

• M — M is INTEGER. The number of rows of the matrix A. M >= N.
• 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 complex M-by-N matrix A. On exit, the elements on and above the diagonal contain the N-by-N upper triangular matrix R; the elements below the diagonal are the columns of V. See below for further details. 👀
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is COMPLEX array, dimension (LDT,N). The N-by-N upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T; the elements below the diagonal are not used. See below for further details. ✨
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= max(1,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 V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is

               V = (  1       )
                   ( v1  1    )
                   ( v1 v2  1 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by

H = I - V * T * V**H

where V**H is the conjugate transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 131 of file cgeqrt3.f.

🖋️ Author

Generated automatically by Doxygen for LAPACK from the source code.

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