SRC/zgeqrt.f(3)

🌸 NAME 🌸

okay so this page is SRC/zgeqrt.f, straight out of the Library Functions Manual, and it's literally the glow-up manual for ZGEQRT, bestie. No cap.

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info) — this is the ZGEQRT one, periodt.

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💅 Function/Subroutine Documentation 💅

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

This is ZGEQRT, and the signature ate, fr fr:

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

🎀 Purpose 🎀

ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q. That's the whole vibe. ✨

🌈 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.
• NB — NB is INTEGER. The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.
• A — A is COMPLEX*16 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 are the columns of V.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• T — T is COMPLEX*16 array, dimension (LDT,MIN(M,N)). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= NB.
• WORK — WORK is COMPLEX*16 array, dimension (NB*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.

Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-K matrix T as:

T = (T1 T2 ... TB).

Definition at line 140 of file zgeqrt.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 · SRC/zgeqrt.f(3) — footer handled, bestie, now go slay some QR factorization 💖✨