/home/abui.../dtpmlqt.f(3)

💅 dtpmlqt.f(3) — Library Functions Manual 💅

okay bestie, welcome to dtpmlqt.f(3) from the Library Functions Manual — yes, the manual name is literally folded right up here so we don't have to copy that whole header line, slay. This page is giving big <purple>Fortran subroutine documentation</purple> energy, and we're gonna keep every tiny detail exactly where it belongs. periodt. 💖

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtpmlqt.f

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🌸 SYNOPSIS 🌸

   Functions/Subroutines
       subroutine DTPMLQT (side, trans, m, n, k, l, mb, v, ldv, t, ldt, a, lda,
           b, ldb, work, info)
           DTPMLQT

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🎀 Function/Subroutine Documentation 🎀

   subroutine DTPMLQT (character side, character trans, integer m, integer n,
       integer k, integer l, integer mb, double precision, dimension( ldv, * )
       v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt,
       double precision, dimension( lda, * ) a, integer lda, double precision,
       dimension( ldb, * ) b, integer ldb, double precision, dimension( * )
       work, integer info)
       DTPMLQT

👑 Purpose

okay so the source says DTPMQRT right there — not DTPMLQT — and we are not fixing it, bestie, because the whole point is keeping the facts exactly as written:

DTPMQRT applies a real orthogonal matrix Q obtained from a real block reflector H to a general real matrix C, which consists of two blocks A and B. that's the whole plot. 🫶

💅 Parameters

• SIDE — SIDE is CHARACTER*1; = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
• TRANS — TRANS is CHARACTER*1; = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
• M — M is INTEGER; the number of rows of the matrix B. M >= 0.
• N — N is INTEGER; the number of columns of the matrix B. N >= 0.
• K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q.
• L — L is INTEGER; the order of the trapezoidal part of V. K >= L >= 0. See Further Details.
• 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 DTPLQT.
• V — V is DOUBLE PRECISION array, dimension (LDV,K); the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DTPLQT in B. See Further Details.
• LDV — LDV is INTEGER; the leading dimension of the array V. LDV >= K.
• T — T is DOUBLE PRECISION array, dimension (LDT,K); the upper triangular factors of the block reflectors as returned by DTPLQT, stored as a MB-by-K matrix.
• LDT — LDT is INTEGER; the leading dimension of the array T. LDT >= MB.
• A — A is DOUBLE PRECISION array, dimension (LDA,N) if SIDE = 'L' or (LDA,K) if SIDE = 'R'. On entry, the K-by-N or M-by-K matrix A. On exit, A is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
• LDA — LDA is INTEGER; the leading dimension of the array A. If SIDE = 'L', LDA >= max(1,K); If SIDE = 'R', LDA >= max(1,M).
• B — B is DOUBLE PRECISION array, dimension (LDB,N). On entry, the M-by-N matrix B. On exit, B is overwritten by the corresponding block of Q*C or Q**T*C or C*Q or C*Q**T. See Further Details.
• LDB — LDB is INTEGER; the leading dimension of the array B. LDB >= max(1,M).
• WORK — WORK is DOUBLE PRECISION 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.

🦋 Further Details

The columns of the pentagonal matrix V contain the elementary reflectors H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a trapezoidal block V2:

        V = [V1] [V2].

The size of the trapezoidal block V2 is determined by the parameter L, where 0 <= L <= K; V2 is lower trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is lower triangular; if L=0, there is no trapezoidal block, hence V = V1 is rectangular.

If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is K-by-M.
                    [B]

If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is K-by-N.

The real orthogonal matrix Q is formed from V and T.

• If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
• If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
• If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
• If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.

Definition at line 212 of file dtpmlqt.f.

💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖✨ and that's the whole page, bestie! Source/version/file vibe check: LAPACK, Version 3.12.0, from /home/abui.../dtpmlqt.f(3). no cap, we kept every detail. byeee 🫶💅