SRC/zunm22.f(3)

🦋 SRC/zunm22.f — Library Functions Manual 🦋

✨ NAME ✨

SRC/zunm22.f

okay bestie, this is the page for the LAPACK routine zunm22, and it is lowkey iconic: it multiplies a general matrix by a banded unitary matrix. 💅

🌈 SYNOPSIS 🌈

🎀 Functions/Subroutines 🎀

• subroutine zunm22 — the actual glow-up:

subroutine zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work,
    lwork, info)

ZUNM22 multiplies a general matrix by a banded unitary matrix. ✨

💅 Function/Subroutine Documentation 💅

subroutine zunm22 (character side, character trans, integer m, integer n,
    integer n1, integer n2, complex*16, dimension( ldq, * ) q, integer ldq,
    complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( *
    ) work, integer lwork, integer info)

ZUNM22 multiplies a general matrix by a banded unitary matrix. 🫶

🎯 Purpose 🎯

Bestie, here's the whole point: ZUNM22 overwrites the general complex M-by-N matrix C with

                  SIDE = 'L'     SIDE = 'R'
  TRANS = 'N':      Q * C          C * Q
  TRANS = 'C':      Q**H * C       C * Q**H

where Q is a complex unitary matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'.

The unitary matrix Q processes a 2-by-2 block structure

         [  Q11  Q12  ]
     Q = [            ]
         [  Q21  Q22  ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix. 💜

🌸 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.
• N1 — N1 is INTEGER; the dimension of Q12. N1 >= 0.
• N2 — N2 is INTEGER; the dimension of Q21. N2 >= 0.
• The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'. 🫡
• Q — Q is COMPLEX*16 array, dimension (LDQ,M) if SIDE = 'L'; (LDQ,N) if SIDE = 'R'.
• LDQ — LDQ is INTEGER; the leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.
• 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 (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER; the dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= M*N.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• 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 160 of file zunm22.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. ✨

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💖 Cute sign-off: this page is rockin' LAPACK Version 3.12.0, with source/page SRC/zunm22.f(3) — that's the footer energy, bestie, and we are out! 🫶💅