SRC/zunm2r.f(3)

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🌸 NAME 🌸

SRC/zunm2r.f

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zunm2r (side, trans, m, n, k, a, lda, tau, c, ldc, work, info) — ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

💖 Function/Subroutine Documentation 💖

🦋 subroutine zunm2r (...)

subroutine zunm2r (character side, character trans, integer m, integer n,
    integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc,
    complex*16, dimension( * ) work, integer info)

ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

🌈 Purpose 🌈

okay so here’s the whole point, no cap:

ZUNM2R overwrites the general complex m-by-n matrix C with

      Q * C  if SIDE = 'L' and TRANS = 'N', or

      Q**H* C  if SIDE = 'L' and TRANS = 'C', or

      C * Q  if SIDE = 'R' and TRANS = 'N', or

      C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by ZGEQRF. 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 Q**H from the Left. = 'R': apply Q or Q**H from the Right.
• TRANS — TRANS is CHARACTER*1. = 'N': apply Q (No transpose). = 'C': apply Q**H (Conjugate transpose).
• 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.
• A — A is COMPLEX*16 array, dimension (LDA,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns of its array argument A. A is modified by the routine but restored on exit.
• LDA — LDA is INTEGER. The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
• TAU — TAU is COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQRF.
• C — C is COMPLEX*16 array, dimension (LDC,N). On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L', (M) 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 157 of file zunm2r.f. 📌

Definition at line 157 of file zunm2r.f.

🌟 Author 🌟

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