SRC/cupmtr.f(3)

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SRC/cupmtr.f — Library Functions Manual ✨

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💖 NAME 💖

SRC/cupmtr.f

That’s the name, and this whole page is its lore. 🫶

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine cupmtr (...) — the main-character subroutine, CUPMTR, is right here:
subroutine cupmtr (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)

CUPMTR — iconic. No cap. 👑

👑 Function/Subroutine Documentation 👑

subroutine cupmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUPMTR

Literally the whole signature, preserved exactly, because we do not play fast and loose with argument lists. 🎀

🎯 Purpose 🎯

CUPMTR 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'. Q is defined as the product of nq-1 elementary reflectors, as returned by CHPTRD using packed storage:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

That’s the whole vibe: Q goes left or right, normal or conjugate-transpose, and C gets overwritten. Slay. 🔥

🧸 Parameters 🧸

  • SIDE — SIDE is CHARACTER*1; = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right.
  • UPLO — UPLO is CHARACTER*1; = 'U': Upper triangular packed storage used in previous call to CHPTRD; = 'L': Lower triangular packed storage used in previous call to CHPTRD.
  • 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 C. M >= 0.
  • N — N is INTEGER; The number of columns of the matrix C. N >= 0.
  • AP — AP is COMPLEX array, dimension (M*(M+1)/2) if SIDE = 'L', (N*(N+1)/2) if SIDE = 'R'. The vectors which define the elementary reflectors, as returned by CHPTRD. AP is modified by the routine but restored on exit.
  • TAU — TAU is COMPLEX array, dimension (M-1) if SIDE = 'L' or (N-1) if SIDE = 'R'. TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CHPTRD.
  • 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; 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.

Definition at line 148 of file cupmtr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. That’s the official tea. 🫶

Signed off by the footer, bestie: LAPACK Version 3.12.0, page SRC/cupmtr.f(3). The footer didn’t hand us a date, so I’m not inventing one — no cap. 💅✨

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