SRC/zgeqrt2.f(3)

okay so welcome to the SRC/zgeqrt2.f(3) page from the Library Functions Manual — this is your group-chat rundown, bestie, and yes it's giving very technical but we're gonna make it make sense. 💅✨

🌸 NAME 🌸

SRC/zgeqrt2.f — literally the page name, no cap. 🎀

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

• subroutine zgeqrt2 (m, n, a, lda, t, ldt, info) — ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

🌈 Function/Subroutine Documentation 🌈

here's the full signature, bestie, exactly as written:

subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer
    info)

ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q. 💖

🎯 Purpose 🎯

ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A, using the compact WY representation of Q. periodt. ✨

🧸 Parameters 🧸

• M — M is INTEGER. The number of rows of the matrix A. Constraint: M >= N.
• N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0.
• A — A is COMPLEX*16 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. Constraint: LDA >= max(1,M).
• T — T is COMPLEX*16 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. Constraint: LDT >= max(1,N).
• INFO — INFO is INTEGER. Exit status tea:
  • = 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. 💜

Definition at line 126 of file zgeqrt2.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, page SRC/zgeqrt2.f(3), and yes: generated automatically by Doxygen for LAPACK from the source code. bye! 💖✨🦋