SRC/sgemlqt.f(3)

💅 SRC/sgemlqt.f(3) — Library Functions Manual 💅

🎀 NAME 🎀

SRC/sgemlqt.f — bestie, that's the file this page is about. The routine inside is sgemlqt, and it's giving compact-WY reflector realness.

✨ SYNOPSIS ✨

Functions/Subroutines

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

SGEMLQT

💖 Function/Subroutine Documentation 💖

subroutine sgemlqt (character side, character trans, integer m, integer n,
     integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real,
     dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer
     ldc, real, dimension( * ) work, integer info)

SGEMLQT

🌸 Purpose

okay so SGEMLQT 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

generated using the compact WY representation as returned by SGELQT. 👑

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

🦋 Parameters

• SIDE — SIDE is CHARACTER*1; = 'L': apply Q or QT from the Left; = 'R': apply Q or QT from the Right.
• TRANS — TRANS is CHARACTER*1; = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T.
• M — M is INTEGER; the number of rows of the matrix C. M >= 0.
• N — N is INTEGER; the number of columns of the matrix C. N >= 0.
• 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.
• MB — MB is INTEGER; the block size used for the storage of T. K >= MB >= 1. This must be the same value of MB used to generate T in SGELQT.
• V — V is REAL array, dimension (LDV,M) if SIDE = 'L', (LDV,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQT in the first K rows of its array argument A.
• LDV — LDV is INTEGER; the leading dimension of the array V. LDV >= max(1,K).
• T — T is REAL array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by SGELQT, stored as a MB-by-K matrix.
• LDT — LDT is INTEGER; the leading dimension of the array T. LDT >= MB.
• C — C is REAL 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 — LDC is INTEGER; the leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is REAL array. The dimension of WORK is N*MB if SIDE = 'L', or M*MB if SIDE = 'R'.
• 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.

Definition at line 151 of file sgemlqt.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page 💖 — it's from LAPACK Version 3.12.0, source SRC/sgemlqt.f(3), and the footer doesn't print a separate date, so no secret date lore here. slay and bye! 🦋✨