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

okay so this is stpmqrt.f(3) from the Library Functions Manual — the header is literally /home/abui.../stpmqrt.f(3), and we’re folding all that main-character energy right in here 💅✨

💖 NAME

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

That’s the name line, bestie — it’s giving “source file is the moment” and we’re respecting it 🫶

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine STPMQRT (side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda,
           b, ldb, work, info)
           STPMQRT

🎀 Function/Subroutine Documentation

subroutine STPMQRT (character side, character trans, integer m, integer n,
    integer k, integer l, integer nb, real, dimension( ldv, * ) v, integer
    ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( lda, * )
    a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
    dimension( * ) work, integer info)
    STPMQRT

🦋 Purpose

STPMQRT 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. no cap, that’s the whole purpose and it ate 💖

🫶 Parameters

SIDE

SIDE is CHARACTER*1 and it picks the side, bestie:

• = '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. It’s the number of rows of the matrix B. M >= 0.

N

N is INTEGER. It’s the number of columns of the matrix B. N >= 0.

K

K is INTEGER. It’s the number of elementary reflectors whose product defines the matrix Q.

L

L is INTEGER. It’s the order of the trapezoidal part of V. K >= L >= 0. See Further Details.

NB

NB is INTEGER. It’s 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 CTPQRT.

V

V is REAL 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 CTPQRT in B. See Further Details.

LDV

LDV is INTEGER. It’s the leading dimension of the array V.

• If SIDE = 'L', LDV >= max(1,M);
• if SIDE = 'R', LDV >= max(1,N).

T

T is REAL array, dimension (LDT,K). These are the upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix.

LDT

LDT is INTEGER. It’s the leading dimension of the array T. LDT >= NB.

A

A is REAL 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. It’s the leading dimension of the array A.

• If SIDE = 'L', LDC >= max(1,K);
• If SIDE = 'R', LDC >= max(1,M).

yes, it says LDC there — I’m not fixing it, I’m just reporting live from the source 💅

B

B is REAL 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. It’s the leading dimension of the array B. LDB >= max(1,M).

WORK

WORK is REAL array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB 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 upper trapezoidal, consisting of the first L rows of a K-by-K upper triangular matrix. If L=K, V2 is upper 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 M-by-K.
                    [B]

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

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

Definition at line 214 of file stpmqrt.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

---

and that’s the cute little sign-off, bestie: footer says LAPACK Version 3.12.0 and the path /home/abui.../stpmqrt.f(3) — iconic source-code fairy dust, no notes 🌟💜