SRC/cgemqrt.f(3)

✨ SRC/cgemqrt.f — CGEMQRT ✨

okay bestie, buckle up 💅 this is a LAPACK Library Functions Manual situation, and the function is literally called cgemqrt. it's giving "math girlie does linear algebra" and honestly? we're obsessed. let's get into it 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine cgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)

CGEMQRT — she's the main character of this whole page, no cap 🔥

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💖 Function/Subroutine Documentation 💖

subroutine cgemqrt (character side, character trans, integer m, integer n,
    integer k, integer nb, complex, dimension( ldv, * ) v, integer ldv,
    complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, *
    ) c, integer ldc, complex, dimension( * ) work, integer info)

CGEMQRT 👑

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🎀 Purpose 🎀

CGEMQRT overwrites the general complex M-by-N matrix C with

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'C':    Q**H C            C Q**H

where Q is a complex orthogonal matrix defined as the product of K elementary reflectors:

      Q = H(1) H(2) . . . H(K) = I - V T V**H

generated using the compact WY representation as returned by CGEQRT.

Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

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🌈 Parameters 🌈

• SIDE — SIDE is CHARACTER*1 🌸
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1 ✨
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• M — M is INTEGER, and it's literally the number of rows of the matrix C. M >= 0. periodt 💅
• N — N is INTEGER, the number of columns of the matrix C. N >= 0. slay.
• K — K is INTEGER, the number of elementary reflectors whose product defines the matrix Q. 🦋
  • If SIDE = 'L', M >= K >= 0;
  • if SIDE = 'R', N >= K >= 0.
• NB — NB is INTEGER, the block size used for the storage of T. K >= NB >= 1. no cap, this must be the same value of NB used to generate T in CGEQRT. don't fumble that bestie 😭
• V — V is COMPLEX array, dimension (LDV,K) 🌟 The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRT in the first K columns of its array argument A.
• LDV — LDV is INTEGER, the leading dimension of the array V. 💜
  • If SIDE = 'L', LDA >= max(1,M);
  • if SIDE = 'R', LDA >= max(1,N).
• T — T is COMPLEX array, dimension (LDT,K) 🎀 The upper triangular factors of the block reflectors as returned by CGEQRT, stored as a NB-by-N matrix.
• LDT — LDT is INTEGER, the leading dimension of the array T. LDT >= NB. 🧚
• C — C is COMPLEX array, dimension (LDC,N) 💖
  • On entry, the M-by-N matrix C.
  • On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q.
• LDC — LDC is INTEGER, the leading dimension of the array C. LDC >= max(1,M). ⭐
• WORK — WORK is COMPLEX array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. get you a work array that can do both 🫶
• INFO — INFO is INTEGER 🔥
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

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🦋 Definition 🦋

Definition at line 166 of file cgemqrt.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page bestie, you ate that 🍓💅

and btw this iconic little document is from LAPACK, Version 3.12.0 — like, the source code era, fr fr. love that for us 🌈👑💖