SRC/cgeqrt.f(3)

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NAME ✨

SRC/cgeqrt.f

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SYNOPSIS 🎀

Functions/Subroutines 💅

subroutine cgeqrt (m, n, nb, a, lda, t, ldt, work, info)
    CGEQRT

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💖 Function/Subroutine Documentation 💖

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

Purpose ✨

Okay so CGEQRT computes a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q. That’s the main character move, no cap. 💅

Parameters 🎀

• M — M is INTEGER. It’s the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. It’s 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 array, dimension (LDA,N). On entry, it’s 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 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 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 cgeqrt.f.

Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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