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

💅 NAME

okay bestie, the header says /home/abui.../ztpmqrt.f(3) and the manual name is Library Functions Manual — cute. The actual NAME situation is this file:

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

✨ SYNOPSIS

Functions/Subroutines

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

🫶 Function/Subroutine Documentation

subroutine ZTPMQRT (character side, character trans, integer m, integer n,
    integer k, integer l, integer nb, complex*16, dimension( ldv, * ) v,
    integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( * ) work, integer info)
    ZTPMQRT

🎯 Purpose

ZTPMQRT 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.

🌸 Parameters

• SIDE — SIDE is CHARACTER*1.
  • = 'L': apply Q or Q**H from the Left;
  • = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1.
  • = 'N': No transpose, apply Q;
  • = 'C': Conjugate transpose, apply Q**H.
• 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.
• NB — NB is 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 — V is COMPLEX*16 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. The leading dimension of the array V. If SIDE = 'L', LDV >= max(1,M); if SIDE = 'R', LDV >= max(1,N).
• T — T is COMPLEX*16 array, dimension (LDT,K). The upper triangular factors of the block reflectors as returned by CTPQRT, stored as a NB-by-K matrix.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= NB.
• A — A is COMPLEX*16 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 — LDA is INTEGER. The leading dimension of the array A. If SIDE = 'L', LDC >= max(1,K); If SIDE = 'R', LDC >= max(1,M).
• B — B is COMPLEX*16 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 — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,M).
• WORK — WORK is COMPLEX*16 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 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 ztpmqrt.f.

🪄 Author

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie 💖 source/version: LAPACK, Version 3.12.0; page: /home/abui.../ztpmqrt.f(3) — mwah, slay, bye 💅✨