SRC/ctpmqrt.f(3)

💖 SRC/ctpmqrt.f 💖

okay so this is the SRC/ctpmqrt.f(3) page from the Library Functions Manual, and we are diving in, bestie 🫶✨

🌸 NAME 🌸

SRC/ctpmqrt.f — that's literally the NAME section, and yes it's just the file path. iconic minimalism 💅

✨ SYNOPSIS ✨

Functions/Subroutines

here's the function reveal:

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

CTPMQRT is the main-character routine name 👑

💅 Function/Subroutine Documentation 💅

🫶 subroutine ctpmqrt

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

CTPMQRT again, because the page said it twice and we respect the repetition 🎀

🎯 Purpose

ok so CTPMQRT applies a complex orthogonal matrix Q obtained from a complex block reflector H to a general complex matrix C, which consists of two blocks A and B. that's the whole vibe ✨

🎀 Parameters

• SIDE — CHARACTER*1. = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. 💅
• TRANS — CHARACTER*1. = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. 🔥
• M — INTEGER. The number of rows of the matrix B. M >= 0.
• N — INTEGER. The number of columns of the matrix B. N >= 0.
• K — INTEGER. The number of elementary reflectors whose product defines the matrix Q.
• L — INTEGER. The order of the trapezoidal part of V. K >= L >= 0. See Further Details.
• 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 CTPQRT.
• V — 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 CTPQRT in B. See Further Details.
• LDV — INTEGER. The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N).
• T — COMPLEX array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix.
• LDT — INTEGER. The leading dimension of the array T. LDT >= NB.
• A — COMPLEX 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**H*C or C*Q or C*Q**H. See Further Details.
• LDA — INTEGER. The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M). (not me side-eyeing the page saying LDC here — I'm just relaying the tea 💀)
• B — COMPLEX 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**H*C or C*Q or C*Q**H. See Further Details.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• WORK — COMPLEX 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.

🌈 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 complex 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='C' and SIDE='L', C is on exit replaced with Q**H * C.
• If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
• If TRANS='C' and SIDE='R', C is on exit replaced with C * Q**H.

Definition at line 214 of file ctpmqrt.f.

💜 Author 💜

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LAPACK Version 3.12.0, source SRC/ctpmqrt.f(3) — that's the whole page, bestie, bye! 💋✨