CUNMR3(3)

✨ CUNMR3(3) ✨

okay bestie, welcome to the Library Functions Manual entry for CUNMR3(3) — and no cap, this one is a Fortran subroutine that multiplies a general matrix by the unitary matrix from an RZ factorization determined by ctzrzf (unblocked algorithm). Let’s get into it 💅

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💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cunmr3.f

🌈 SYNOPSIS 🌈

💫 Functions/Subroutines 💫

   subroutine CUNMR3 (side, trans, m, n, k, l, a, lda, tau, c, ldc, work,
           info)
           CUNMR3 multiplies a general matrix by the unitary matrix from a RZ
           factorization determined by ctzrzf (unblocked algorithm).

🦋 Function/Subroutine Documentation 🦋

   subroutine CUNMR3 (character side, character trans, integer m, integer n,
       integer k, integer l, complex, dimension( lda, * ) a, integer lda,
       complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer
       ldc, complex, dimension( * ) work, integer info)

CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

✨ Purpose: ✨

Okay so here’s the assignment, bestie: CUNMR3 overwrites the general complex m by n matrix C with one of these four flavors:

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 CTZRZF. 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; it’s the number of rows of the matrix C. M >= 0.
• N — N is INTEGER; it’s the number of columns of the matrix C. N >= 0.
• K — K is INTEGER; it’s the number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
• L — L is INTEGER; it’s the number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
• A — A is COMPLEX array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
• LDA — LDA is INTEGER; it’s the leading dimension of the array A. LDA >= max(1,K).
• TAU — TAU is COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CTZRZF.
• C — C is COMPLEX 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; it’s the leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX 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.

🎀 Contributors: 🎀

• A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

🧚 Further Details: 🧚

bestie, the Further Details section is serving minimalism. This is literally all it has:

!>

Definition at line 176 of file cunmr3.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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