SRC/dgemqrt.f(3)

✨ NAME ✨

SRC/dgemqrt.f — yes bestie, that's the file, and it's from the Library Functions Manual. We are in serious linear algebra territory, but make it cute. 💖

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🌈 SYNOPSIS 🌈

Functions/Subroutines

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

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💅 Function/Subroutine Documentation 💅

   subroutine dgemqrt (character side, character trans, integer m, integer n,
       integer k, integer nb, double precision, dimension( ldv, * ) v, integer
       ldv, double precision, dimension( ldt, * ) t, integer ldt, double
       precision, dimension( ldc, * ) c, integer ldc, double precision,
       dimension( * ) work, integer info)
       DGEMQRT

🌟 Purpose 🌟

okay so DGEMQRT overwrites the general real M-by-N matrix C with:

                 SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q C            C Q
TRANS = 'T':   Q**T C            C Q**T

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

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

It's generated using the compact WY representation as returned by DGEQRT. No cap, that compact WY representation is iconic. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. 🦋

🎀 Parameters 🎀

• SIDE — CHARACTER*1. = 'L': apply Q or QT from the Left; = 'R': apply Q or QT from the Right. Left vs right, bestie, choose your fighter.
• TRANS — CHARACTER*1. = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T.
• M — INTEGER. The number of rows of the matrix C. M >= 0.
• N — INTEGER. The number of columns of the matrix C. N >= 0.
• K — 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 — INTEGER. The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in DGEQRT.
• V — DOUBLE PRECISION 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 DGEQRT in the first K columns of its array argument A.
• LDV — INTEGER. The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). Yep, the source says LDA right there in the LDV entry, and I am copying it faithfully.
• T — DOUBLE PRECISION array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by DGEQRT, stored as a NB-by-N matrix.
• LDT — INTEGER. The leading dimension of the array T. LDT >= NB.
• C — DOUBLE PRECISION array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
• LDC — INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — DOUBLE PRECISION array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'.
• INFO — 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.

Definition at line 166 of file dgemqrt.f.

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🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code.

That's the whole page, bestie: LAPACK, Version 3.12.0, source SRC/dgemqrt.f(3). The footer doesn't show a date, just that version + source flex. Mwah 💋✨